# Eco. 361——–24-3-2021 (Online Discussion Quiz 1 —Lewis-Fei-Ranis Model of Economic Growth and Haris-Todaro Model of Migration)

Briefly discuss each of the following models and how they apply to the Nigerian Economy

1. Lewis-Fei-Ranis Model of Economic Growth
2. Haris-Todaro Model of Migration

Name:

Reg No:

l

### Eco. 101 Online Quiz/Discussion (Understanding Normative&Positive Economics and Ceteris Paribus)

1. Okonkwo Chidinma Alisa says:

Okonkwo Chidinma Alisa
2017/243086
decenteconomistalisa@gmail.com
chidimmalisa.blogspot.com

AN ESSAY ON THE HARRIS – TODARO MODEL OF MIGRATION

INTRODUCTION
It has been observed that for an economy to grow and advance, it must shift her labour force (most of it or some of it) from the traditional or subsistence part of the economy to the modern or commercial part of the economy. That is, labour has to be moved from the sector of the economy where production is low to the sector where production is high in order to increase production and then create more goods and services which would ensure increased economic growth. Development Economics has also however given more credit to the dualistic models than the single models. The dualistic growth models usually consisted of a rural-traditional or agricultural sector alongside with an urban-modern or manufacturing sector. The famous single-sector model is the growth theory of Harrod-Domar (Harrod 1939 and 1948, Domar 1946) brought up by two economists Sir Roy Harrod of England and Professor Evesey Domar of the United States. They were of the view that a country’s level of output was being influenced or determined directly by the net-savings ratio (s) and inversely by the capital-output ratio (c). That is, ∆Y/Y = s/c. This growth model was however criticized in the issue that it only focused on the capital-output ratio which is how many units of capital could be used to produce a unit of output. It did not take into consideration those poor countries with low capital formation as their growth was actually limited to the amount or level of capital that country had or could raise. These growth models were known as or referred to as “orthodox” by Corden and Findley (1971).
Asides this model, there is also the most influential dualistic framework which is that of Lewis (1954). The idea of surplus labour, subsistence wages in the development of a dualistic economy in Lewis (1954) was later diagrammatically formalized by Ranis and Fei (1961). These two also showed how agricultural surplus could lead to the growth of industries. The common characteristics of the dualistic theories brought up as well as other alike models include the following:
No unemployment in the modern sector.
The sectoral wage differential is assumed fixed or proportional to the wage level in the urban sector.
The new or modern thinking were later brought up of the notable was the one propounded by Michael Todaro (1969) and John Harris (Harris and Todaro 1970). The Harris-Todaro Model is an equilibrium version of the Todaro Migration Model which forecasts and explains the rural-urban migration as an economically rational process despite the high urban unemployment. The migrants calculate the value of the urban expected income or its equivalent and move of it is more than the average rural income. The importance of this was as a result of the Keynesian Revolution is that “equilibrium could occur or come about even when there is a chronic level of unemployment in the urban sector”. This implies that the economy would still or could still be in balance even with the existence of a severe urban unemployment. It has also been deduced that the most important factor why urban population was more than of the rural sector was due to the fact that labour from the rural sector moved to the urban sector in search of “greener pastures”.
In the situation of a dualistic model, the rural sector is letting go of much labour too quickly while the urban sector is hiring or accepting labour too slowly as it is assumed that the urban sector is capital-intensive (Lewis 1965). The manifestations of the employment problem in the urban areas as much labour get unemployed is the outcome of the poverty and underemployment in the Third World Countries (Lubell 1988). It has also been recognized that labour migration was due to the fact that the rural-urban wages were different compared to each other. The contribution of Todaro is the introduction of the possibility of employment as a factor in the decision-making process of a potential migrant. He devised what he called a two-stage process in the less-developed countries.
The first stage is characterized by where the labour migrant decides to move from the rural sector for a period of time (that is, from the traditional informal sector). The second stage is then reached when that labour migrant has gotten a more permanent job in the modern or urban sector. So the two-stage process is simply involving first, when the labour migrant resolves to leave his place in the rural sector for a certain time period and second, the labour migrant finds a more permanent job in the urban sector. However, Todaro and some others did not take into consideration the informal urban sector explicitly as its employees were usually underemployed as they were not distinguished from the unemployed as they made no income of their own but relied on their relatives as explained of the informal sector by Lewis (1954).
According to Todaro, the probability or tendency of getting a job depends on the size of the urban population that is employed, number of newly created jobs in the urban sector, as well as the length or duration a labour migrant has been in that sector. Consequently it implied that according to Todaro, the longer a labour migrant has been in the manufacturing sector, the more likely he or she is to get a job there. An extension of this was done by Harris and Todaro (1970), where they explained that the urban wage is equal or equivalent to the expected value of the urban wage and this formed the notable Harris-Todaro Equation which is of the form:
Wa = βWm where,
Wa = Flexible wage in the agricultural sector is equal to the value of the marginal product in that sector, β = Probability of employment (dependent on the three (3) factors listed earlier), and Wm = Wage in the manufacturing sector which is assumed fixed or constant institutionally either because of the involvement of the union’s activities or a friendly government towards the workers in the modern sector. This is unlike in the orthodox models where the wage difference in the rural-urban sectors is not fixed or constant.

THE BASIC MODEL
The Harris-Todaro Model would be referred to as the H – T Model from henceforth, assume that migration from the rural to the urban areas depends primarily on the difference in wages between the rural and urban labour markets (which is the wage differential). That is the expected urban wage is the actual urban wage multiplied by the probability of getting a job, or Weu = PWu where,
Weu = Expected Urban Wage and P = Probability of getting a job where P is expressed as: P = where,

Eu = Urban Employment, Uu = Urban Unemployment and L = Total Labour Force. Another assumption of the Harris-Todaro is that all the members of the urban labour force have equal chances of obtaining or getting the jobs available for them. So Weu = Urban Wage multiplied by the Urban Employment Rate.

POLICY IMPLICATIONS OF THE H – T MODEL
The H – T Model has some impressing implications from the policy point of view. Let’s take for an instance, if the government of a country is concerned with fostering industrial development in an urban area, employment would increase and this would lead to an increase in productive of getting urban employment in the minds of the rural inhabitants. Migration to the urban area would then increase and the outcome would be that the unemployment rate in the urban areas would rise more than how it was before the development industrially occurred. Due to this, labour migrants would prefer to accept the wage in the urban informal sector than going back to wait for long for jobs that would not come in time as urban employment is now in equilibrium. However, the effect of this is that the earnings in the urban modern industrial sectors would be more or higher than those in the rural traditional sectors. The long-term solution to this issue would be to fix a wage policy for the two sectors that would reduce the real income differences between the two sectors.

THE ASSUMPTIONS OF THE MODEL
In analyzing the H – T Model, there are some assumptions alongside those listed before which include:
There is fixed amounts of labour (L) and capital (K) factor inputs.
Capital is fully employed but labour unemployment exists in the urban sector due to the fixed urban wage, W is higher than the flexible rural wage, w.
The economy is small and imports the urban output, X and exports the agricultural output, Y which is used as a numeraire.

MATHEMATICAL EXPRESSION OF THE MODEL
Let Lj and Kj represent the labour and capital factor inputs employed in the sectors respectively, we then have the output of the urban manufacturing sector to be of the form: X = F (Lx, Kx) and the output of the rural agricultural sector to be of the form: Y = G (Ly, Ky).
Due to the wage inflexibility in the manufacturing sector, some form of unemployment would exist in the urban sector. The profit of the urban sector would therefore equal: Πx = PF – WLX – rKx, where P = Producer’s price of the urban output and W = Fixed value of urban wage. The profit of the rural sector would be of the form: Πy = G – wLY – rKY, where w = Flexible value of rural wage and the price of the numeraire Y is unity or equal to one (1). The first-order conditions for the optimal labour employment are: PFL – W = 0; GL – w = 0. These give the conditional labour demand functions: Lx = Lx (Kx, P, W) and LY = LY (KY, P, w).
The rural wage w = the expected urban wage. Therefore, the relationship between the two wages in the two sectors is explained by the H – T conditions which are:
w = βW = where β = which is the probability of getting

employed and λ = Lu/Lx = Relative Unemployment in the urban sector.

COMPARISON WITH THE REAL WORLD
The successful East Asian Countries of Taiwan, Korea, and Singapore, as well as the not-so successful countries like Brazil, Chile, and several others, is usually the example that is given to explain the comparison of this model with the real world. It is argued (Balassa 1989) that the import-substitution policies in many less-developed countries are based against the primary agricultural sector which is the exporting sector while the export-oriented polices provide similar incentives to the two sectors. Countries that adopt inward-looking strategies, the limitation of the domestic markets and the lack of competition leads to the allocative and technological inefficiency. As in contrast with the onward-looking countries which are able to mobilize domestic resources effectively in the production if goods that are in competition in the wide markets worldwide which would result in technology. It is now in our own opinion that majority of the less-developed countries have approached what is said to be the take-off stage as described by Lewis (1954) and Fei and Ranis (1961) characterized by the rapidly growing economies, transfer of labour from the traditional sector, and the persistent or continuous problems of the high urban unemployment and underemployment rates.

2. Okonkwo Chidinma Alisa says:

LEWIS-FEI-RANIS MODEL OF SURPLUS LABOUR

This growth model further explains that the traditional sector comprises of the agricultural sector which is existent, and the modern sector comprises of the fast-growing but small industrial or manufacturing sector. It is also said that the two sectors (traditional and modern) both exist in the dual economy which lays the basis for the problem of development. How these two sectors would interact in order to yield economic development is the major issue here. This therefore forms the foundation for development too be that economic development can only occur or happen or evolve if and only if the resources in the traditional agricultural sector can be shifted to the modern industrial sector such that the industrial sector is advanced or increased or even taken to another level (higher) in the economy. This then can only be achieved when the labour factor resource is transferred from the traditional agricultural sector to the modern industrial sector. However, this does not imply that the traditional agricultural sector should be neglected because it is this sector that supplies the raw materials needed by the modern industrial sector as well as food.
ARGUMENTS OF THE FEI – RANIS GROWTH MODEL
Like in the Harrod – Domar Growth Model, we have that savings and investment are the key instruments that are used to drive economic development when it comes to the less-developed countries. Lewis argued that, economic growth in a less-developed or under-developed economy could only be achieved by capital accumulation in the modern industrial sector, which is done by taking or shifting excess or surplus labour from the traditional agricultural sector to the modern industrial sector. So, Lewis advocated that an economy like that transits or moves from the first stage (excess labour) to the second stage (scarce labour) of economic development.
Later on, Fei and Ranis formalized the three stages of dualistic economic development by dividing the first two stages of Lewis Model into the first two stages of the Fei – Ranis Growth Model and the second stage of Lewis Model forming the third stage of the Fei – Ranis Growth Model.

3. Esokawu Jonathan Chukwudi says:

Good morning Mr. President and the honourable members of this parliament. To begin with the Surplus Labour theory was proposed by Arthur Lewis and was later modified by Fei and Ranis. The model describes a dual system of economy in which the Agricultural sector was seen as dominant in any developing nation and the Industrial sector was taken to be dominant in the developed nation. Lewis and Fei – Ranis model assumed that the agricultural sector has a surplus unproductive labour, and that this surplus labour is absorbed by the industrial sector due to it better wage rate. This added labour continually expands the industrial sector until all the surplus labour is absorbed. Thus, the industrial sector becomes the dominant sector and the nation according to there model is assumed to be developed.

4. ONUOHA JONAH IHEUKWUMERE. Reg Number:2017/249413 Department ( ECONOMICS/POLITICAL SCIENCE) says:

The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model.[1] It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature.[2] According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector.[3] Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Surplus value, Marxian economic concept that professed to explain the instability of the capitalist system. Adhering to David Ricardo’s labour theory of value, Karl Marx held that human labour was the source of economic value. The capitalist pays his workers less than the value their labour has added to the goods, usually only enough to maintain the worker at a subsistence level. Of the total worth of the worker’s labour, however, this compensation, in Marxian theory, accounts for only a mere portion, equivalent to the worker’s means of subsistence. The remainder is “surplus labour,” and the value it produces is “surplus value.” To make a profit, Marx argued, the capitalist appropriates this surplus value, thereby exploiting the labour.II. THE HARRIS-TODARO MODEL

A. Assumptions

Harris and Todaro [1] studied the migration of workers in a two-sector economic system, namely, rural sector and urban sector. The difference between these sectors are the type of goods produced, the technology of production and the process of wage determination. The rural sector is specialized in the production of agricultural goods. The productive process of this sector can be described by a Cobb-Douglas production function:

where Ya is the production level of the agricultural good, Na is the amount of workers used in the agricultural production, Aa > 0 and 0 < f 0 and 0 < a 0 and g > 0 are a parametric constants. g is the elasticity of p with respect to the ratio Ym/Ya.

The overall population of workers in the economy is N, which is kept constant during the whole period of analysis. By assumption there are only two sectors and rural prices are wholly flexible, which implies that there is full employment in the rural area, i.e., all workers living at the rural sector are employed at any period. Then at any period the following equality is verified:

B. Temporary Equilibrium

Given a parametric constant vector (Aa,Am,f,a,r,g), an initial urban population Nu, and a minimum wage wm one can calculate the temporary equilibrium of the economic system by using eqs. (1 – 6).

From eq. (4) one can find the employment level at the manufacturing sector

Replacing eq. (7) in eq. (2) we get the production level of the manufacturing sector

From eq. (6) one can obtain the relation

which is used with eq. (1) to obtain the agricultural production

By using eqs. (5), (8) and (10) the terms of trade are determined

Finally, by using eqs. (3), (9) and (11), the rural wage in units of manufacturated good is obtained

In sum, the vector (Nm,Ym,Na,Ya,p,wa) configures a temporary equilibrium that might be altered whether occurs a migration of workers, induced by the differential of sectorial wages, which changes the sectorial distribution of overall population.

C. The Long Run Equilibrium

Harris and Todaro, in determining the long run equilibrium, i.e., the absence of a net rural-urban migratory flow, argue that the rural workers, in their decision on migrating to the urban area, estimate the expected urban wage, , defined as:

The ratio Nm/Nu, which is the employment rate, is an estimative of the probability that a worker living at urban sector gets a job in this sector.

As mentioned before, the key assumption of the model of Harris and Todaro is that there will be a migratory flow from the rural to the urban sector while the expected urban wage is higher than the rural wage. Thus, the long run equilibrium is attained when the urban worker population reaches a level such that the expected urban wage equates the rural wage:

This equality is known in the economic literature as the Harris-Todaro condition. Harris and Todaro argue that the differential of expected wages in eq. (14) can be a constant value d ¹ 0. When this differential reaches d, the net migration ceases. This generalized Harris-Todaro condition can be expressed as follows:

The level of the urban population that satisfies the eq. (15), i.e., the equilibrium urban share = /N, is determined from the solution of the equation resulting from substitution of equations (12), (13) in eq. (15):

The solution of eq. (16) is parametrized by the vector (Aa,Am,r,g,a,f,wm).

Harris and Todaro [1], in order to evaluate the stability of the long run equilibrium, postulate a mechanism of adjustment that is based on the following function of sign preservation:

The differential equation that governs the state transition in the model of Harris and Todaro is obtained by replacing equations (12), (13) in eq. (17). Based on this postulated adjustment process, Harris and Todaro [1] show that the long run equilibrium is globally asymptotically stable. This means that the economy would tend to long run equilibrium with unemployment in the urban sector generated by the presence of a relatively high minimum wage for all possible initial conditions. From now on we will refer to the long run equilibrium simply as equilibrium.

Based on the numerical solutions of eq. (16) one can evaluate the impact that the variation of the minimum wage and the elasticity of the terms of trade on the equilibrium. In Fig. 1 we see that under the hypothesis of a Cobb-Douglas technology, the equilibrium urban share, , does not depend on the minimum wage wm. However, changes in the value of wm reduces the labor demand on the manufacturing sector what results in higher unemployment rates in the equilibrium.

In turn, as seen in Fig. 2, changes in the elasticity of the terms of trade alter slightly the equilibrium urban share and unemployment rate. A net migration toward urban sector shift the terms of trade to higher values. The greater g the greater this shift, what cause an increase in the rural wage in units of manufacturing good, becoming the urban sector less attractive.

III. HARRIS-TODARO AGENT-BASED MODEL

In this section we describe the implementation of the computational model we proposed, as well as the aggregate patterns obtained numerically and the comparison with the respective analytical results.

A. Computational Implementation

Initially, workers are randomly placed in a square lattice with linear dimension L = 500. The reference values of the parameters used for these simulations are the same done to evaluate the equilibrium of the Harris-Todaro model, namely, Aa = 1.0, Am = 1.0, f = 0.3, a = 0.7, r = 1.0 and g = 1.0. The value of the minimum wage used is wm = 0.8 and the initial urban fraction of the total population is nu = 0.2, where nu = Nu/N is the normalized urban population also called urban share. The initial value nu = 0.2 is in agreement with historical data of developing economies. Given these parameters, one can calculate the vector which characterizes temporary equilibrium of the system by using eqs. (7 – 12).

By using eq. (7), the employment level of the urban sector, Nm, is obtained. If nu Nm/N there will be a fraction of Nm/Nu workers employed, which earn the minimum wage, wi = wm, and (1-Nm/Nu) workers unemployed, which earn a wage wi = 0.

Each worker can be selected to review his sectorial location with probability a, called activity [11]. Therefore, in each time step only a fraction of workers becomes potential migrants, going through the sectorial location reviewing process. Potential migrants will determine their satisfaction level of being in the current sector by comparing their earnings, wi, among nearest neighbors.

The potential migrant starts the comparison process with a initial satisfaction level si = 0. When wi > wneighbor the satisfaction level si is added in one unit; if wi < wneighbor, si is diminished in one unit; if wi = wneighbor, si does not change. After the worker has passed through the reviewing process his/her satisfaction level is checked. The migration will occur only if si < 0, what means that the worker's i earnings is less than the most of his/her nearest neighbors.

After all the potential migrants complete the reviewing process and have decided migrate or not, a new configuration of the system is set. Therefore, once again a new temporary equilibrium of the system is calculated by using eqs. (8 – 12). The whole procedure is repeated until a pre-set number of steps is reached. It is important to emphasize that Nm is kept constant throughout the simulation. Its given by eq. (7) which depends on the technological parameters, a,Am, and the minimum wage, wm, which are constants too.

B. Analysis of the Emergent Properties

In this section we develop the analysis of the long run aggregate regularities of Harris-Todaro agent-based computational model. These long run properties will be compared between the solution of the analytical model and simulations we ran.

Figures 3, 4 and 5 show the basic characteristics of the transitional dynamics and long run equilibrium generated by simulations. When the economic system has a low initial urban share, nu = 0:2 or nu = 0:3, there is a net migration toward urban sector. This migration takes the urban sector from a full employment situation to an unemployment one. The positive differential of expected wages that pulls workers to the urban sector diminishes. However, if the economic system initiates with a high urban share, nu = 0:8, or nu = 0:9 there is net flow of migration toward rural sector in such a way that the unemployment rate of the urban sector decreases.
As is well known, the rebirth of the sub-discipline of development economics coincided
more or less with the early post-World War II era. It is also relevant to recall that this revival of development theory and policy heavily emphasized the breaking of colonial ties which were associated, somewhat erroneously, with the workings of the market and, consequently, placed major emphasis on the role of the state in the newly independent countries of the Third World. Unfortunately, the tool kit available to development economists of the day was also fairly limited. On the one hand, there was the Harrod-Domar (Harrod 1939, Domar 1957) model, focusing basically on the steady state properties of the developed economy, with little possibility for alternative technology choice and even less for the role of prices, relying heavily instead on savings-pushed growth competing with population growth. Full employment, market clearance, and perfect competition were assumed. On the other hand, there was the Keynesian (1936) model, focusing on advanced economy cyclical issues. Although, as Albert Hirschman (1982) has pointed out, Keynes deviated from the neoclassical mono-economics, full employment orthodoxy of the day, he focused on the temporary unemployment of both capital and labor in the advanced economy, not the secular underemployment of labor in the developing world. Clearly, savings-oriented one-sector models were all the vogue, incorporated in both approaches,

5. ONUOHA JONAH IHEUKWUMERE. Reg Number:2017/249413 Department: Combined social science ( ECONOMICS/POLITICAL SCIENCE) says:

The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model.[1] It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature.[2] According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector.[3] Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Surplus value, Marxian economic concept that professed to explain the instability of the capitalist system. Adhering to David Ricardo’s labour theory of value, Karl Marx held that human labour was the source of economic value. The capitalist pays his workers less than the value their labour has added to the goods, usually only enough to maintain the worker at a subsistence level. Of the total worth of the worker’s labour, however, this compensation, in Marxian theory, accounts for only a mere portion, equivalent to the worker’s means of subsistence. The remainder is “surplus labour,” and the value it produces is “surplus value.” To make a profit, Marx argued, the capitalist appropriates this surplus value, thereby exploiting the labour.II. THE HARRIS-TODARO MODEL

A. Assumptions

Harris and Todaro [1] studied the migration of workers in a two-sector economic system, namely, rural sector and urban sector. The difference between these sectors are the type of goods produced, the technology of production and the process of wage determination. The rural sector is specialized in the production of agricultural goods. The productive process of this sector can be described by a Cobb-Douglas production function:

where Ya is the production level of the agricultural good, Na is the amount of workers used in the agricultural production, Aa > 0 and 0 < f 0 and 0 < a 0 and g > 0 are a parametric constants. g is the elasticity of p with respect to the ratio Ym/Ya.

The overall population of workers in the economy is N, which is kept constant during the whole period of analysis. By assumption there are only two sectors and rural prices are wholly flexible, which implies that there is full employment in the rural area, i.e., all workers living at the rural sector are employed at any period. Then at any period the following equality is verified:

B. Temporary Equilibrium

Given a parametric constant vector (Aa,Am,f,a,r,g), an initial urban population Nu, and a minimum wage wm one can calculate the temporary equilibrium of the economic system by using eqs. (1 – 6).

From eq. (4) one can find the employment level at the manufacturing sector

Replacing eq. (7) in eq. (2) we get the production level of the manufacturing sector

From eq. (6) one can obtain the relation

which is used with eq. (1) to obtain the agricultural production

By using eqs. (5), (8) and (10) the terms of trade are determined

Finally, by using eqs. (3), (9) and (11), the rural wage in units of manufacturated good is obtained

In sum, the vector (Nm,Ym,Na,Ya,p,wa) configures a temporary equilibrium that might be altered whether occurs a migration of workers, induced by the differential of sectorial wages, which changes the sectorial distribution of overall population.

C. The Long Run Equilibrium

Harris and Todaro, in determining the long run equilibrium, i.e., the absence of a net rural-urban migratory flow, argue that the rural workers, in their decision on migrating to the urban area, estimate the expected urban wage, , defined as:

The ratio Nm/Nu, which is the employment rate, is an estimative of the probability that a worker living at urban sector gets a job in this sector.

As mentioned before, the key assumption of the model of Harris and Todaro is that there will be a migratory flow from the rural to the urban sector while the expected urban wage is higher than the rural wage. Thus, the long run equilibrium is attained when the urban worker population reaches a level such that the expected urban wage equates the rural wage:

This equality is known in the economic literature as the Harris-Todaro condition. Harris and Todaro argue that the differential of expected wages in eq. (14) can be a constant value d ¹ 0. When this differential reaches d, the net migration ceases. This generalized Harris-Todaro condition can be expressed as follows:

The level of the urban population that satisfies the eq. (15), i.e., the equilibrium urban share = /N, is determined from the solution of the equation resulting from substitution of equations (12), (13) in eq. (15):

The solution of eq. (16) is parametrized by the vector (Aa,Am,r,g,a,f,wm).

Harris and Todaro [1], in order to evaluate the stability of the long run equilibrium, postulate a mechanism of adjustment that is based on the following function of sign preservation:

The differential equation that governs the state transition in the model of Harris and Todaro is obtained by replacing equations (12), (13) in eq. (17). Based on this postulated adjustment process, Harris and Todaro [1] show that the long run equilibrium is globally asymptotically stable. This means that the economy would tend to long run equilibrium with unemployment in the urban sector generated by the presence of a relatively high minimum wage for all possible initial conditions. From now on we will refer to the long run equilibrium simply as equilibrium.

Based on the numerical solutions of eq. (16) one can evaluate the impact that the variation of the minimum wage and the elasticity of the terms of trade on the equilibrium. In Fig. 1 we see that under the hypothesis of a Cobb-Douglas technology, the equilibrium urban share, , does not depend on the minimum wage wm. However, changes in the value of wm reduces the labor demand on the manufacturing sector what results in higher unemployment rates in the equilibrium.

In turn, as seen in Fig. 2, changes in the elasticity of the terms of trade alter slightly the equilibrium urban share and unemployment rate. A net migration toward urban sector shift the terms of trade to higher values. The greater g the greater this shift, what cause an increase in the rural wage in units of manufacturing good, becoming the urban sector less attractive.

III. HARRIS-TODARO AGENT-BASED MODEL

In this section we describe the implementation of the computational model we proposed, as well as the aggregate patterns obtained numerically and the comparison with the respective analytical results.

A. Computational Implementation

Initially, workers are randomly placed in a square lattice with linear dimension L = 500. The reference values of the parameters used for these simulations are the same done to evaluate the equilibrium of the Harris-Todaro model, namely, Aa = 1.0, Am = 1.0, f = 0.3, a = 0.7, r = 1.0 and g = 1.0. The value of the minimum wage used is wm = 0.8 and the initial urban fraction of the total population is nu = 0.2, where nu = Nu/N is the normalized urban population also called urban share. The initial value nu = 0.2 is in agreement with historical data of developing economies. Given these parameters, one can calculate the vector which characterizes temporary equilibrium of the system by using eqs. (7 – 12).

By using eq. (7), the employment level of the urban sector, Nm, is obtained. If nu Nm/N there will be a fraction of Nm/Nu workers employed, which earn the minimum wage, wi = wm, and (1-Nm/Nu) workers unemployed, which earn a wage wi = 0.

Each worker can be selected to review his sectorial location with probability a, called activity [11]. Therefore, in each time step only a fraction of workers becomes potential migrants, going through the sectorial location reviewing process. Potential migrants will determine their satisfaction level of being in the current sector by comparing their earnings, wi, among nearest neighbors.

The potential migrant starts the comparison process with a initial satisfaction level si = 0. When wi > wneighbor the satisfaction level si is added in one unit; if wi < wneighbor, si is diminished in one unit; if wi = wneighbor, si does not change. After the worker has passed through the reviewing process his/her satisfaction level is checked. The migration will occur only if si < 0, what means that the worker's i earnings is less than the most of his/her nearest neighbors.

After all the potential migrants complete the reviewing process and have decided migrate or not, a new configuration of the system is set. Therefore, once again a new temporary equilibrium of the system is calculated by using eqs. (8 – 12). The whole procedure is repeated until a pre-set number of steps is reached. It is important to emphasize that Nm is kept constant throughout the simulation. Its given by eq. (7) which depends on the technological parameters, a,Am, and the minimum wage, wm, which are constants too.

B. Analysis of the Emergent Properties

In this section we develop the analysis of the long run aggregate regularities of Harris-Todaro agent-based computational model. These long run properties will be compared between the solution of the analytical model and simulations we ran.

Figures 3, 4 and 5 show the basic characteristics of the transitional dynamics and long run equilibrium generated by simulations. When the economic system has a low initial urban share, nu = 0:2 or nu = 0:3, there is a net migration toward urban sector. This migration takes the urban sector from a full employment situation to an unemployment one. The positive differential of expected wages that pulls workers to the urban sector diminishes. However, if the economic system initiates with a high urban share, nu = 0:8, or nu = 0:9 there is net flow of migration toward rural sector in such a way that the unemployment rate of the urban sector decreases.
As is well known, the rebirth of the sub-discipline of development economics coincided
more or less with the early post-World War II era. It is also relevant to recall that this revival of development theory and policy heavily emphasized the breaking of colonial ties which were associated, somewhat erroneously, with the workings of the market and, consequently, placed major emphasis on the role of the state in the newly independent countries of the Third World. Unfortunately, the tool kit available to development economists of the day was also fairly limited. On the one hand, there was the Harrod-Domar (Harrod 1939, Domar 1957) model, focusing basically on the steady state properties of the developed economy, with little possibility for alternative technology choice and even less for the role of prices, relying heavily instead on savings-pushed growth competing with population growth. Full employment, market clearance, and perfect competition were assumed. On the other hand, there was the Keynesian (1936) model, focusing on advanced economy cyclical issues. Although, as Albert Hirschman (1982) has pointed out, Keynes deviated from the neoclassical mono-economics, full employment orthodoxy of the day, he focused on the temporary unemployment of both capital and labor in the advanced economy, not the secular underemployment of labor in the developing world. Clearly, savings-oriented one-sector models were all the vogue, incorporated in both approaches,

6. Utoh Joshua says:

University of nigeria nsukka
Faculty of Education
Department of library and information science (lis)

An assignment to be submitted in partial fulfilment of the requirement of the course
Development economics (Eco 361)

Topic
Discuss Lewis Fei Ranis model (surplus labor theory)

Name
Utoh Joshua odinaka
Reg no: 2017/243123

Date
March, 2021
Discuss Lewis Fei Ranis model (surplus labor theory)

Lewis Fei Ranis model (surplus labor theory)
Introduction
Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model.
It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.

Basics of the model
Depiction of Phase1, Phase2 and Phase3 of the dual economy model using average output.
One of the biggest drawbacks of the Lewis model was the undermining of the role of agriculture in boosting the growth of the industrial sector. In addition to that, he did not acknowledge that the increase in productivity of labor should take place prior to the labor shift between the two sectors. However, these two ideas were taken into account in the Fei–Ranis dual economy model of three growth stages. They further argue that the model lacks in the proper application of concentrated analysis to the change that takes place with agricultural development In Phase 1 of the Fei–Ranis model, the elasticity of the agricultural labor work-force is infinite and as a result, suffers from disguised unemployment. Also, the marginal product of labor is zero. This phase is similar to the Lewis model. In Phase 2 of the model, the agricultural sector sees a rise in productivity and this leads to increased industrial growth such that a base for the next phase is prepared. In Phase 2, agricultural surplus may exist as the increasing average product (AP), higher than the marginal product (MP) and not equal to the subsistence level of wages.
According to Fei and Ranis, AD amount of labor (see figure) can be shifted from the agricultural sector without any fall in output. Hence, it represents surplus labor. After AD, MP begins to rise, and industrial labor rises from zero to a value equal to AD. AP of agricultural labor is shown by BYZ and we see that this curve falls downward after AD. This fall in AP can be attributed to the fact that as agricultural laborers shift to the industrial sector, the real wage of industrial laborers decreases due to shortage of food supply, since less laborers are now working in the food sector. The decrease in the real wage level decreases the level of profits, and the size of surplus that could have been re-invested for more industrialization. However, as long as surplus exists, growth rate can still be increased without a fall in the rate of industrialization. This re-investment of surplus can be graphically visualized as the shifting of MP curve outwards. In Phase2 the level of disguised unemployment is given by AK. [4] This allows the agricultural sector to give up a part of its labor-force until
Phase 3 begins from the point of commercialization which is at K in the Figure. This is the point where the economy becomes completely commercialized in the absence of disguised unemployment. The supply curve of labor in Phase 3 is steeper and both the sectors start bidding equally for labor.
The amount of labor that is shifted and the time that this shifting takes depends upon:
1. The growth of surplus generated within the agricultural sector, and the growth of industrial capital stock dependent on the growth of industrial profits;
2. The nature of the industry’s technical progress and its associated bias;
3. Growth rate of population.
So, the three fundamental ideas used in this model are:
1. Agricultural growth and industrial growth are both equally important;
2. Agricultural growth and industrial growth are balanced;
3. Only if the rate at which labor is shifted from the agricultural to the industrial sector is greater than the rate of growth of population will the economy be able to lift itself up from the Malthusian population trap .
This shifting of labor can take place by the landlords’ investment activities and by the government’s fiscal measures. However, the cost of shifting labor in terms of both private and social cost may be high, for example transportation cost or the cost of carrying out construction of buildings. In addition to that, per capita agricultural consumption can increase, or there can exist a wide gap between the wages of the urban and the rural people. These three occurrences- high cost, high consumption and high gap in wages, are called as leakages , and leakages prevent the creation of agricultural surplus. In fact, surplus generation might be prevented due to a backward-sloping supply curve of labor as well, which happens when high income-levels are not consumed. This would mean that the productivity of laborers with rise in income will not rise. However, the case of backward-sloping curves is mostly unpractical.

Comparison with other models
According to Ranis-Fei’s point, it shows the Lewis turning point i.e. the point after which the supply curve of labour in the industrial sector will turn upwards. However Lewis himself did not consider this point as the upward turning point.
For him all labour in the agriculture sector whose marginal productivity was either zero or was less than the institutional wage was available to the industrial sector at the institutional wage (or at a rate a little above it,) Fie never pointed out that as soon as the zero value labour was transferred to the industrial sector (i.e. up to the end of phase I in the present model) the supply curve for labour will start turning upwards. For him some other labour too (whose marginal productivity was less than the institutional wage, was also available at a constant wage rate.
The reason for this difference in the views of the authors of two models is that unlike Ranis and Fei, Lewis did not take into account the effect of changing terms on trade on the supply price of labour in the industrial sector. He totally ignored it.
Fei assumed as if the wages to the transferred labour will be paid in agricultural products and as the institutional wages fixed in terms of agricultural produce, the labour transferred to the industrial sector will continue to be available at the constant wage rate i.e. that institutional wage.
Ranis and Fei, on the other hand assumed that the labour in the industrial sector will be paid, in terms of the industrial products and they had to bring the hanging terms of trade into the picture. the turning point will appear at the end of the phase II. If i.e. upto the point where labour in the agricultural sector is paid institutional wages.
Assumptions of the Lewis Model:
(A) Surplus Labour in the Subsistence Sectors:
The basic assumption of the model is that there exists surplus labour in the subsistence sectors. It includes labour whose marginal productivity is zero as well as that whose marginal productivity is positive but is less than the institutional wage. This labour comprises farmers, agricultural labourers, petty traders domestic servants and women.
The surplus labour in the agriculture sector acts as a source of unlimited supply of labour for the manufacturing sector. By unlimited supply of labour. Lewis means that the supply of labour is perfectly elastic at a particular wages. This particular wage is somewhat higher than the institutional wage which each worker in the agricultural sector gets.
Lewis calls it as institutional wage because every worker gets this wage because of some institutional arrangements. This wages is equal to an average share of each worker in the total output in the subsistence sector. If market forces were allowed to operate in the subsistence sector labourers with zero margin productivity or those with a very low marginal productivity would not have received this wage.

(B) Importance of Saving:
Another important assumption that Lewis makes is about the savings generated in the capitalist sector and in the subsistence sector. The capitalist sector invests all its savings for its further expansion. Those in the subsistence sector, on the other hand squander away their savings, if any in purchase of jewellery & for construction of temples etc. The propensity to save of the people in subsistence sector is also lower when compared with that of those in the capitalist sector. Lewis in fact so much fascinated by the higher propensity to save of the capitalist sector that he even advocates a transfer of income from the subsistence sector to the capitalist sector. He feels that steps have to be taken to raise the rate of savings from 10% to 15% if the development of the economy has to be smooth.

Impact of the Open Economy:
The open economy can encourage the immigration of labour. If this happens, it will help in the expansion of the capitalist sector. But immigration may not be so easy. If in that case the pace of expansion of the capitalist sector slows down, capital may move out of the country as the economy is an open one. This may in turn lead to balance of payments problems and the problem of stability of rate of exchange.
Some of the objections against Lewis’s model are as follows:
(1) The assumption that disguised unemployment exists in the agriculture sector has not been accepted by many economists. Schultz, Viner, Heberler and Hopper are a few of such economists. According to them, the production in the subsistence sector will be affected when labour is withdrawn from it.
(2) Lewis ignored the cost involved in training the unskilled worker transferred from the subsistence sector. Even if it is obtained at a constant wage rate, so for as its transfer from the subsistence sector is concerned, the supply curve may slope upwards so far as the capitalist, sector is concerned if the cost of training rises as more and more labour is transferred.
(3) When labour is transferred from the subsistence sector share of agricultural output falling to each one left in the agricultural sector will go a rising. This means the institutional wage will go on rising with every transfer and so will be the wages paid in the capitalist sector.
(4) The model assumes that, besides labour, there is unlimited supply of entrepreneurs in the capitalist sector. This is not true in the case of many of the underdeveloped countries.
(5) It is wrong to assume that a capitalist will always re-invest their profits. They to can indulge in un-productive pursuits. They can use their profits for speculative purposes.

Conclusion
In conclusion to the Lewis Ranis-Fei’s model (surplus labour theory), taking it to the real life situation, Stagnation has not been taken into consideration, and no distinction is made between labor through family and labor through wages. There is also no explanation of the process of self-sustained growth, or of the investment function. There is complete negligence of terms of trade between agriculture and industry, foreign exchange, money and price.

7. INTRODUCTION
Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.
Basic of the model

Depiction of Phase1, Phase2 and Phase3 of the dual economy model using average output.
One of the biggest setbacks of the Lewis model was the undermining of the role of agriculture in boosting the growth of the industrial sector. In addition to that, he did not acknowledge that the increase in productivity of labor should take place prior to the labor shift between the two sectors. However, these two ideas were taken into account in the Fei–Ranis dual economy model of three growth stages. They further argue that the model lacks in the proper application of concentrated analysis to the change that takes place with agricultural development. In Phase 1 of the Fei–Ranis model, the elasticity of the agricultural labor work-force is infinite and as a result, suffers from disguised unemployment. Also, the marginal product of labor is zero. This phase is similar to the Lewis model. In Phase 2 of the model, the agricultural sector sees a rise in productivity and this leads to increased industrial growth such that a base for the next phase is prepared. In Phase 2, agricultural surplus may exist as the increasing average product (AP), higher than the marginal product (MP) and not equal to the subsistence level of wages.
Using the figure above:
Phase 1: AL (from figure) = MP = 0 and AB (from figure) = AP
According to Fei and Ranis, AD amount of labor (see figure) can be shifted from the agricultural sector without any fall in output. Hence, it represents surplus labor.
Phase 2: AP MP
After AD, MP begins to rise, and industrial labor rises from zero to a value equal to AD. AP of agricultural labor is shown by BYZ and we see that this curve falls downward after AD. This fall in AP can be attributed to the fact that as agricultural laborers shift to the industrial sector, the real wage of industrial laborers decreases due to shortage of food supply, since less laborers are now working in the food sector. The decrease in the real wage level decreases the level of profits, and the size of surplus that could have been re-invested for more industrialization. However, as long as surplus exists, growth rate can still be increased without a fall in the rate of industrialization. This re-investment of surplus can be graphically visualized as the shifting of MP curve outwards. In Phase2 the level of disguised unemployment is given by AK. This allows the agricultural sector to give up a part of its labor-force until
MP = Real wages = AB = Constant institutional wages (CIW)
Phase 3 begins from the point of commercialization which is at K in the Figure. This is the point where the economy becomes completely commercialized in the absence of disguised unemployment. The supply curve of labor in Phase 3 is steeper and both the sectors start bidding equally for labor.

Phase 3: MP CIW
The amount of labor that is shifted and the time that this shifting takes depends upon:
1. The growth of surplus generated within the agricultural sector, and the growth of industrial capital stock dependent on the growth of industrial profits
2. The nature of the industry’s technical progress and its associated bias
3. Growth rate of population.
So, the three fundamental ideas used in this model are:
1. Agricultural growth and industrial growth are both equally important
2. Agricultural growth and industrial growth are balanced;
3. Only if the rate at which labor is shifted from the agricultural to the industrial sector is greater than the rate of growth of population will the economy be able to lift itself up from the Malthusian population trap.
However, this shifting of labor can take place by the landlords’ investment activities and by the government’s fiscal measures. However, the cost of shifting labor in terms of both private and social cost may be high, for example transportation cost or the cost of carrying out construction of buildings. In addition to that, per capita agricultural consumption can increase, or there can exist a wide gap between the wages of the urban and the rural people. These three occurrences- high cost, high consumption and high gap in wages, are called as leakages, and leakages prevent the creation of agricultural surplus. In fact, surplus generation might be prevented due to a backward-sloping supply curve of labor as well, which happens when high income-levels are not consumed. This would mean that the productivity of laborers with rise in income will not rise. However, the case of backward-sloping curves is mostly unpractical.

ASSUMPTIONS OF THE LEWIS MODEL
(A). Surplus Labour in the Subsistence Sectors:
The basic assumption of the model is that there exists surplus labour in the subsistence sectors. It includes labour whose marginal productivity is zero as well as that whose marginal productivity is positive but is less than the institutional wage. This labour comprises farmers, agricultural laborers, petty traders’ domestic servants and women.
The surplus labour in the agriculture sector acts as a source of unlimited supply of labour for the manufacturing sector. By unlimited supply of labour. Lewis means that the supply of labour is perfectly elastic at a particular wage. This particular wage is somewhat higher than the institutional wage which each worker in the agricultural sector gets.
Lewis calls it as institutional wage because every worker gets this wage because of some institutional arrangements. This wages is equal to an average share of each worker in the total output in the subsistence sector. If market forces were allowed to operate in the subsistence sector labourers with zero margin productivity or those with a very low marginal productivity would not have received this wage.
(B). Importance of Saving:
Another important assumption that Lewis makes is about the savings generated in the capitalist sector and in the subsistence sector. The capitalist sector invests its entire savings for its further expansion.
Those in the subsistence sector, on the other hand squander away their savings, if any in purchase of jewellery and for construction of temples etc. The propensity to save of the people in subsistence sector is also lower when compared with that of those in the capitalist sector.
Lewis in fact so much fascinated by the higher propensity to save of the capitalist sector that he even advocates a transfer of income from the subsistence sector to the capitalist sector. He feels that steps have to be taken to raise the rate of savings from 10% to 15% if the development of the economy has to be smooth.
CRITICISM OF THE MODEL
1. The assumption that disguised unemployment exists in the agriculture sector has not been accepted by many economists. Schultz, Viner, Heberler and Hopper are few of such economists. According to them, the production in the subsistence sector will be affected when labour is withdrawn from it.
2. Lewis ignored the cost involved in training the unskilled worker transferred from the subsistence sector. Even if it is obtained at a constant wage rate, so for as its transfer from the subsistence sector is concerned, the supply curve may slope upwards so far as the capitalist, sector is concerned if the cost of training rises as more and more labour is transferred.
3. When labour is transferred from the subsistence sector share of agricultural output falling to each one left in the agricultural sector will go a rising. This means the institutional wage will go on rising with every transfer and so will be the wages paid in the capitalist sector.
4. The model assumes that, besides labour, there is unlimited supply of entrepreneurs in the capitalist sector. This is not true in the case of many of the underdeveloped countries.
5. It is wrong to assume that a capitalist will always re-invest their profits. They too can indulge in un-productive pursuits. They can use their profits for speculative purposes.
6. It is also wrong to assume that landlords always squander away their savings. The role of landlords of Japan in industrialization of the country is well known.
7. The model assumes that there already exists a market for the industrial products in the country. This is wrong. People of an underdeveloped country may not be able to purchase the products perturbed by the expanding capitalist sector. Foreign markets, too, may not be available to the capitalist sector in the beginning.
8. Inflation is not liquidating, as has been assumed by Lewis, Experience of various, countries shows that if once prices start rising, it becomes difficult to control them.
9. It is not easy to transfer labour from the subsistence Sector to the capitalist sector by offering them an incentive of a little higher wage. Mobility of labour is very low. Many factors like family affection, difference in language, caste, religion etc. affect it adversely.
10. Every underdeveloped country does not have surplus labour in the subsistence sector. As such, the model does not apply to countries which are sparsely populated.
The only positive point in the model is its ‘general’ emphasis on the role of saving in economic development and on the potential that overpopulated countries have in developing themselves with the help of surplus labour.
CONCLUSION
This model divides the economy in an underdeveloped country in two sectors which are the Subsistence sector and the capitalist sector. Subsistence sector is identified with the agricultural sector of the economy while the capitalist sector implies mainly the manufacturing sector of the economy. Capitalist sector also includes plantations and mining where hired labour is employed for purposes of production. The capitalist sector can either be private or public in nature. Subsistence sector, that the agricultural sector is considered to be labour intensive. It does not use reproducible capital. It uses poor techniques of production and has very low productivity. Therefore, when the subsistence (rural area) sector produces, its sent it surplus to the capitalist sector (urban area) for further production. This can provide employment in both sectors when more workers are employed in the subsistence sector so as to produce more agricultural surplus which will also lead to increase in labour in the capitalist sector. In my opinion this can work in real life if there is a limited number of labour that migrate from the rural area to the urban area.

8. Joy Asika says:

Name : ASIKA JOY OGECHUKWU
DEPT: ECONOMICS
REG NO: 2017/242025

LEWIS-FEI-RANIS MODEL (SURPLUS LABOUR THEORY)
The Fei–Ranis model of economic growth is a dualism model that has been developed by John C.H. Fei and Gustav Rani’s and can be understood as an extension of the lewis model. He takes into account the economic situation of underdeveloped and underemployment of resources,unlike many other growth models that consider underdeveloped countries to be homogenous in nature. There exist surplus labour(marginal productivity is zero) in the subsistence sector and this labour is made available for the industrial and urban sector but at a constant wage determine by minimum level of existence in traditional family farming because of disguised unemployment in agriculture. At some later point,if the surplus labour is been exhausted then only a rising wage rate will draw more labour out of agriculture.
ASSUMPTION (ARGUMENTS)
An economy starts with 2 sectors:A rural agricultural sector and urban industrial sector.
Agriculture generally under-employs workers and marginal productivity of labour is virtually zero.
Transferring workers out of agriculture doesn’t reduce productivity in the whole economy.
Labour is then released for work in the more productive urban sector.
Industrialization is now possible,given the increase in supply of workers who have moved from the land.
Industrial firms starts to make profit which can be re-invested into more industrialization and capital starts to accumulate.
As soon as capital accumulate further economy development can sustain itself.
CRITICISM
No distinction is made between labor through family and labor through wages.
There is uneven distribution of income due the migration among two sectors.
There is complete negligence of terms of trade between agriculture and industry,foreign exchange,money and price and assume a close model, which is very unrealistic.

TODARO’S HARRIS MODEL OF MIGRATION
Also knows as the structural change model. It focuses on mechanism by which underdeveloped economy transform their domestic economic structure from heavy emphasis on traditional subsistence agriculture to a more modern, urbanized and industrial diverse manufacturing and service economy. It also apply tool of neo classical prices and resource allocation theory and modern econometrics to describe how transformation processes take place.
By structural transformation that is a way that the contribution to national income by the manufacturing sector surpasses the contribution by agricultural sector.

9. Name : ASIKA JOY OGECHUKWU
REG NO: 2017/242025 ECONOMICS DEPT
Website: http://www.joybloggers.com

1. LEWIS-FEI-RANIS MODEL (SURPLUS LABOUR THEORY)
The Fei–Ranis model of economic growth is a dualism model that has been developed by John C.H. Fei and Gustav Rani’s and can be understood as an extension of the lewis model. He takes into account the economic situation of underdeveloped and underemployment of resources,unlike many other growth models that consider underdeveloped countries to be homogenous in nature. There exist surplus labour(marginal productivity is zero) in the subsistence sector and this labour is made available for the industrial and urban sector but at a constant wage determine by minimum level of existence in traditional family farming because of disguised unemployment in agriculture. At some later point,if the surplus labour is been exhausted then only a rising wage rate will draw more labour out of agriculture.

ASSUMPTION (ARGUMENTS)
An economy starts with 2 sectors:A rural agricultural sector and urban industrial sector.
Agriculture generally under-employs workers and marginal productivity of labour is virtually zero.
Transferring workers out of agriculture doesn’t reduce productivity in the whole economy.
Labour is then released for work in the more productive urban sector.
Industrialization is now possible,given the increase in supply of workers who have moved from the land.
Industrial firms starts to make profit which can be re-invested into more industrialization and capital starts to accumulate.
As soon as capital accumulate further economy development can sustain itself.

CRITICISM
No distinction is made between labor through family and labor through wages.
There is uneven distribution of income due the migration among two sectors.
There is complete negligence of terms of trade between agriculture and industry,foreign exchange,money and price and assume a close model, which is very unrealistic.

2. HARRIS -TODARO MODEL OF MIGRATION
Known as the structural change model. It focuses on mechanism by which underdeveloped economy transform their domestic economic structure from heavy emphasis on traditional subsistence agriculture to a more modern urbanized and industrial diverse manufacturing service economy. It also apply tool of neo classical prices and resource allocation theory and modern econometrics to describe how transformation processes take place. By structural transformation that is a way that the contribution to national income by the manufacturing sector surpasses the contribution by agricultural sector.
The new or modern thinking were later brought up of the notable was the one propounded by Michael Todaro (1969) and John Harris (Harris and Todaro 1970). The Harris-Todaro Model is an equilibrium version of the Todaro Migration Model which forecasts and explains the rural-urban migration as an economically rational process despite the high urban unemployment. The migrants calculate the value of the urban expected income or its equivalent and move of it is more than the average rural income. The importance of this was as a result of the Keynesian Revolution is that “equilibrium could occur or come about even when there is a chronic level of unemployment in the urban sector”. This implies that the economy would still or could still be in balance even with the existence of a severe urban unemployment. It has also been deduced that the most important factor why urban population was more than of the rural sector was due to the fact that labour from the rural sector moved to the urban sector in search of “greener pastures”.
In the situation of a dualistic model, the rural sector is letting go of much labour too quickly while the urban sector is hiring or accepting labour too slowly as it is assumed that the urban sector is capital-intensive (Lewis 1965). The manifestations of the employment problem in the urban areas as much labour get unemployed is the outcome of the poverty and underemployment in the Third World Countries (Lubell 1988). It has also been recognized that labour migration was due to the fact that the rural-urban wages were different compared to each other. The contribution of Todaro is the introduction of the possibility of employment as a factor in the decision-making process of a potential migrant. He devised what he called a two-stage process in the less-developed countries.
The first stage is characterized by where the labour migrant decides to move from the rural sector for a period of time (that is, from the traditional informal sector). The second stage is then reached when that labour migrant has gotten a more permanent job in the modern or urban sector. So the two-stage process is simply involving first, when the labour migrant resolves to leave his place in the rural sector for a certain time period and second, the labour migrant finds a more permanent job in the urban sector. However, Todaro and some others did not take into consideration the informal urban sector explicitly as its employees were usually underemployed as they were not distinguished from the unemployed as they made no income of their own but relied on their relatives as explained of the informal sector by Lewis (1954).
According to Todaro, the probability or tendency of getting a job depends on the size of the urban population that is employed, number of newly created jobs in the urban sector, as well as the length or duration a labour migrant has been in that sector. Consequently it implied that according to Todaro, the longer a labour migrant has been in the manufacturing sector, the more likely he or she is to get a job there. An extension of this was done by Harris and Todaro (1970), where they explained that the urban wage is equal or equivalent to the expected value of the urban wage and this formed the notable Harris-Todaro Equation which is of the form:
Wa = βWm where,
Wa = Flexible wage in the agricultural sector is equal to the value of the marginal product in that sector, β = Probability of employment (dependent on the three (3) factors listed earlier), and Wm = Wage in the manufacturing sector which is assumed fixed or constant institutionally either because of the involvement of the union’s activities or a friendly government towards the workers in the modern sector. This is unlike in the orthodox models where the wage difference in the rural-urban sectors is not fixed or constant.

THE BASIC MODEL
The Harris-Todaro Model would be referred to as the H – T Model from henceforth, assume that migration from the rural to the urban areas depends primarily on the difference in wages between the rural and urban labour markets (which is the wage differential). That is the expected urban wage is the actual urban wage multiplied by the probability of getting a job, or Weu = PWu where,
Weu = Expected Urban Wage and P = Probability of getting a job where P is expressed as: P = where,

Eu = Urban Employment, Uu = Urban Unemployment and L = Total Labour Force. Another assumption of the Harris-Todaro is that all the members of the urban labour force have equal chances of obtaining or getting the jobs available for them. So Weu = Urban Wage multiplied by the Urban Employment Rate.

POLICY IMPLICATIONS OF THE H – T MODEL
The H – T Model has some impressing implications from the policy point of view. Let’s take for an instance, if the government of a country is concerned with fostering industrial development in an urban area, employment would increase and this would lead to an increase in productive of getting urban employment in the minds of the rural inhabitants. Migration to the urban area would then increase and the outcome would be that the unemployment rate in the urban areas would rise more than how it was before the development industrially occurred. Due to this, labour migrants would prefer to accept the wage in the urban informal sector than going back to wait for long for jobs that would not come in time as urban employment is now in equilibrium. However, the effect of this is that the earnings in the urban modern industrial sectors would be more or higher than those in the rural traditional sectors. The long-term solution to this issue would be to fix a wage policy for the two sectors that would reduce the real income differences between the two sectors.

THE ASSUMPTIONS OF THE MODEL
In analyzing the H – T Model, there are some assumptions alongside those listed before which include:
There is fixed amounts of labour (L) and capital (K) factor inputs.
Capital is fully employed but labour unemployment exists in the urban sector due to the fixed urban wage, W is higher than the flexible rural wage, w.
The economy is small and imports the urban output, X and exports the agricultural output, Y which is used as a numeraire.

10. Ndem Nneka Grace says:

Ndem Nneka grace
2017/249529
Nnekagrace74@gmail.com
Nnekagrace.Blogspot.com

Lewis-Fei-Ranis Model of Economic Growth

One of the best known early theoretical models of development that focused on the structural transformation of a primarily subsistence economy was that formulated by Nobel Laureate W. Arthur Lewis in the mid-1950s, and later modified, formalized, and extended by John Fei and Gustav Ranis. The Lewis two-sector model became the general theory of the 1960s and early 1970s, and it is sometimes still applied, particularly to study the recent growth experience in China and labor markets in other developing countries.
The Fei-Ranis model is an improvement over the lewis model. John Fei and Gustav Ranis analyze the transition process through which an underdeveloped economy hopes to move from a condition of stagnation to one of self-sustained growth.
The theory relates to underdeveloped labor surplus and resources; poor economy in which the vast majority of the population is engaged in agriculture amidst widespread unemployment and high rates of population growth.

ASSUMPTIONS OF THE MODEL

1. There is a dual economy divided into a traditional and stagnant agricultural sector and an active industrial sector.
2. The output of the agricultural sector is a function of land and labor alone.
3. There is no accumulation of capital in agriculture except in the form of land reclamation.
4. Land is fixed in supply.
5. Population growth is taken as an exogenous phenomenon.
The real wage in the industrial sector remains fixed and is equal to the initial level of real income in the agricultural sector. It is called an institutional wage.
6. Workers in either sector consume only agricultural products.
Given these assumptions, Fei and Ranis analyze the development of a labor surplus economy into three phases;
In the first phase, the disguised unemployed workers who are not adding to agricultural output are transferred to the industrial sector at a constant institutional wage.
In the second phase, agricultural workers add to agricultural output but produce less than the institutional wage they get. Such workers are shifted to the industrial sector. If the migration of the workers to the industrial sector continues, a point is eventually reached when farmworkers produce output equal to the institutional wage.
In the third phase, which makes the end of the take-of and the beginning of the self-sustained growth when farmworkers produce more than the institutional wage they get. In this phase, the surplus labor is exhausted and the agricultural sector becomes commercialized.

CRITICISMS OF FEI-RANIS MODEL
1. Commercialization of agriculture leads to inflation. According to the model, when the agricultural sector enters the third phase, it becomes commercialized, but the economy is not likely to move smoothly into a self-sustained growth because inflationary pressure will start.
2. Supply of land is not fixed. Fei-Ranis begins with the assumption that the supply of land is fixed during the development process. In the long run, the amount of land is not fixed, as the statistics of crop average in many Asian countries reveal.
3. Institutional wage not constant in the agricultural sector. The model assumes that the institutional wage remains constant in the first two phases even when agricultural productivity increases. This is unrealistic because with a general rise in agricultural productivity farm wages also tend to rise.
CONCLUSION
However, these limitations do not undermine the importance of the Fei-Ranis model for the economic development of labor surplus countries. It systematically analyses the development process from the take-off to self-sustained growth through the interaction of the agricultural and industrial sectors of an underdeveloped economy.

THE HARRIS-TODARO MODEL OF MIGRATION
The Harris-Todaro model is based on the experiences of tropical African facing the problems of rural-urban migration and urban unemployment. The labor migration is due to rural-urban differences in average expected wages. The minimal urban wage is substantially higher than the rural wages. If more employment opportunities are created in the urban sector at the minimum wage, the expected wage shall tend to rise and rural-urban migration shall be induced leading to growing levels of urban unemployment. To remove urban unemployment, Harris and Todaro suggests a subsized minimal wage through a lump sum tax.

ASSUMPTIONS OF THE HARRIS-TODAROS MODEL
1. There are two sectors in the economy: the rural or agricultural sector (A) and the urban or manufacturing sector (M).
2. The model operates in the short run.
3. Capital is available in fixed quantities in the two sectors.
4. The number of urban/manufacturing jobs available is exogenously fixed.
5. Rural-urban migration continues so long as the expected urban real income is more than the real agricultural income.
6. The rural wage equals the rural marginal product of labor and the urban wage is exogenously determined.
7. There is perfect competition among producers in both sectors.

MATHEMATICAL EXPRESSION OF THE HARRIS-TODARO MODEL
Output in the rural sector is suppose to be a function of labour so that the production function for agricultural good is;
Xa = f (Na, L-bar, K-bar) f’>0; f”0; f ” 0.
P is the price of agricultural good in terms of the price of manufactured good which is a function (p) of the relative output of agricultural and manufactured goods.
The agricultural wage equals the value of marginal product (MP) of labor expressed in terms of the manufactured good,
Wa = f’a (Na) = p(f’m).
In the urban sector the producers are wage- takers and they aim at profit maximization which means that the urban market wage is;
Wa = f’m (Nm).
The urban expected wage which leads to the migration of workers from the rural to the urban sector is given as;
Wu = W-bar m x Nm/Nu, Nm/Nu ≤ 1.
Where the expected real wage (Wu) in the urban sector is equal to the urban real minimum wage (Wm) adjusted for the proportion of the total urban labor force (Nu) actually employed.

POLICY IMPLICATIONS OF THE H-T MODEL
Harris-Todaro have drawn a few important policy implications of their model. According to them, the payment of minimum wage to the additional industrial worker will induce more rural-urban migration. To solve this problem of an institutional determined wage that is higher than the equilibrium level, labor should be employed according to a shadow wage and /or at a payroll subsidy wage. Since the opportunity cost (I.e shadow wage) of an agricultural worker is lower than the marginal product of an industrial worker, the implementation of shadow wage criterion will have important effects on the level of agricultural output and on urban unemployment.

CRITICISM OF THE HARRIS-TODARO MODEL
1. The Harris-Todaro model does not specify alternate policy prescriptions such as giving a wage subsidy to the urban sector and at the same time restricting the migration of those rural workers who are not able to find jobs in the urban sector.
2. Harris-Todaro suggest non-distortionary lump sum tax to finance subsidy, but a lump sum tax is seldom non-distortionary.
3. This model does not consider or incorporate the cost of rural-urban migration or the relatively higher costs of urban living which the migrants have to incur in the urban sector.
4. The model does not take into consideration the generation of savings as a source of financing subsidy. Though savings are low in LDCs, yet they are an important source of non-distortionary finance to subsidise wages.
CONCLUSION
Despite these criticisms, the Harris-Todaro model is more realistic than the other dual economy models because it tries to tackle the problem of rural-urban migration that actually exists in LDCs. For instance the Lewis model assumes that there is no unemployment in the urban sector and when rural-urban migration takes place, the number of new jobs created in the urban sector exactly equals the number of migrants. This is unrealistic.

11. Name: chukwu mmesoma faith
Reg no: 2017/243807
Department: education and economics

Lewis-Fei-Ranis surplus labour theory
Lewis (1954) proposed a seminal theory of dualistic economic development for over-populated and under-developed economies with vast amounts of surplus agricultural labour for which he was later to be awarded the 1979 Nobel Prize in Economics. Economic growth in such an economy can be achieved by rapid capital accumulation in the non-agricultural (industrial and service) sector, facilitated by drawing surplus labour in the agricultural sector.
Throughout the paper we refer to the two sectors as agricultural and non-agricultural. Various authors have used different terms interchangeably for these two sectors. Lewis (1954) originally named the two sectors as the subsistence and the capitalistic sectors and later on in Lewis (1979) referred to them as the traditional and modern sectors.
In the Lewis theory, an economy transits from the first, labour-surplus “stage” to the second, labour-scarce “stage” of development.
Later, Ranis and Fei (1961) formalized the Lewis theory and defined three “phases” of dualistic economic development by sub-dividing the first stage in the Lewis model into two phases. Thus, the second labour-scarce stage of the Lewis model corresponds to phase three of the Ranis-Fei model. These three phases, illustrated in the diagram below, which are distinguished by the marginal productivity of agricultural labour. The entry into each phase is marked three turning points:
• The breakout point leads to phase one growth with redundant agricultural labour.
• The shortage point leads to phase two growth with disguised agricultural
unemployment.
• The commercialisation point leads to phase three of self-sustaining economic
growth with the commercialisation of the agricultural sector.

ASSUMPTIONS OF THE MODEL
1) Dual economy 1 active industrial sector, 2 traditional agriculture sector which is stagnant
2) Supply of land is fixed
3) Population growth is an exogenous phenomenon
5) No accumulation of capital in agricultural sector except land reclamation
6) The output in agricultural sector is function of land and labour only
7) Industrial sector is function of capital and labour alone
8) Land has no role as a factor of production
MP of labour becomes zero at some point. if the population is excess the quantity where MPL becomes zero, then labour can be transferred to industrial sector without any loss of agricultural production.
On the basis of the above sited assumptions, the development of labour surplus can be divided into the following phases;
In the first phase, they are disguised unemployed worker who are not contributing to agricultural production and can be easily shifted to industrial sector at a constant institutional wage rate.
In the second phase, they are agricultural worker who are adding to agricultural output but produce less than the institutional wages they get. This type of workers can also be transferred to industrial sector.
In the third phase, this is the stage of self-sustained growth, starting from where workers are adding to agricultural output and producing more than the institutional wages they get.

USING CHINA AS REAL LIFE EXAMPLE
China’s 1.3 billion inhabitants account for a fifth of the world’s population. Over 50 percent of the Chinese population is engaged in the rural agricultural sector. China’s agricultural labour productivity is very low due to the presence of surplus labour relative to other scarce resources. The agricultural wage rate is lower than the non-agricultural one. The 1978 Economic Reform propelled the Chinese economy into a path of rapid economic growth, at the rate of approximately eight percent per annum.
In systematically assessing the Lewis (1954) theory and its formalization by Ranis and Fei (1961) for China. We address the three core questions:
(1) Is the main source of economic growth non-agricultural capital accumulation?
(2) What is the net effect of agricultural to non-agricultural labour reallocation?
(3) What phase of economic development is the Chinese economy in? In other words, has China passed the commercialization point signified by the exhaustion of surplus labour, as discussed by Cai (2007) and Knight (2007)?
To answer these questions, we estimate Cobb-Douglas production functions for China’s agricultural and non-agricultural sectors, using time-series national-level data over 1965-2002. Our results show that China’s overall economic growth is driven by the rapid development of the non-agricultural sector, which results from the fast accumulation of non-agricultural capital. As capital accumulates, employment expands and contributes almost as much as capital to economic growth in the non-agricultural sector. This confirms the answer to our first question that capital accumulation is the main source of economic growth in the non-agricultural sector.
Secondly, we evaluate the effect of labour reallocation away from agriculture to non-agriculture by comparing the labour productivities of the two sectors. In addition, we repeat the exercise by applying the Labour Reallocation Effects (LRE) equation specified by the World Bank (1996). Both approaches suggest that labour reallocation has a positive impact on China’s economic growth, accounting for 1 to 2 percent per annum of GDP growth. We find the effect of labour reallocation has declined since the mid-1990s because of less absorption of the surplus rural labour in the non-agricultural sector, particularly in industry. Our result coincides with the findings of Kuijs and Wang (2005), Woo (1998), and World Bank (1996).
Thirdly, we identify the phase of China’s economic development by examining the evolution of labour productivities over time as indicated in the Lewis-Ranis-Fei model. We find that the Chinese economy has fully absorbed the redundant agricultural labour, as shown by the rising marginal productivity of labour since the 1978 Economic Reform, but has not yet completely reallocated the disguised unemployment, as shown by the marginal labour productivity being still lower than the institutional wage defined by the initial low average productivity of labour. All this indicates that, following the 1978 Economic Reform, China entered phase two of economic development defined in the Lewis-Ranis-Fei model. However, it has not reached phase three marked by the exhaustion of the disguised agricultural unemployment. Furthermore, we find that the gap of labour productivities between the two sectors is widening, which is at odds with the theoretical expectation. This reflects the effects of market imperfections and government intervention. A “critical minimum effort” is required for China to release the remaining disguised agricultural unemployment and enter phase three of economic development.

CRITICISMS OF THE MODEL
1) Capital accumulation: this model assumes that the rate of the labour transfer, employment creation and output expansion depends on the rate of capital accumulated in the modern sector.
2) Surplus labour: this model assumes that there is a surplus labour in the rural economy and full employment in the urban sector
3) Competitive labour market in the morden sector: this model implies that the supply of labour is perfectly elastic.

12. Anyabuike Victor ifeanyi (2017/243144)economics education says:

The Harris–Todaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and welfare economics to explain some of the issues concerning rural-urban migration. The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This implies that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income

Harris-Todaro model of the rural-urban migration process is revisited under an agent-based approach. The migration of the workers is interpreted as a process of social learning by imitation, formalized by a computational model. By simulating this model, we observe a transitional dynamics with continuous growth of the urban fraction of overall population toward an equilibrium. Such an equilibrium is characterized by stabilization of rural-urban expected wages differential (generalized Harris-Todaro equilibrium condition), urban concentration and urban unemployment. These classic results obtained originally by Harris and Todaro are emergent properties of our model.

I. INTRODUCTION

we turn upon the seminal Harris and Todaro work, which together with Todaro is considered one of the starting points of the classic rural-urban migration theory hypothesis and predictions of Harris-Todaro model have been subjected to econometric evaluation and have been corroborated by several studies The key hypothesis of Harris and Todaro are that migrants react mainly to economic incentives, earnings differentials, and the probability of getting a job at the destination have influence on the migraton decision. In other words, these authors posit that rural-urban migration will occur while the urban expected wage exceed the rural wage. From this crucial assumption, as denominated by Harris-Todaro is deduced that the migratory dynamics leads the economic system toward an equilibrium with urban concentration and high urban unemployment.

We analyzed the rural-urban migration by means of an agent-based computational model taking into account the influence of the neighborhood in the migration decision. The inclusion of the influence of neighbors was done via an Ising like model. The economic analogous to the external field in the Ising hamiltonian was the differential of expected wages between urban and rural sectors.

Now, we are motivated by the following question: can the crucial assumption and equilibrium with urban concentration and urban unemployment obtained from the original Harris-Todaro model be generated as emergent properties from the interaction among adaptative agents? In order to answer this question we implemented an agent-based computational model in which workers grope for best sectorial location over time in terms of earnings. The economic system simulated is characterized by the assumption originally made by Harris and Todaro.

THE HARRIS-TODARO MODEL

A. Assumptions

Harris and Todaro studied the migration of workers in a two-sector economic system, namely, rural sector and urban sector. The difference between these sectors are the type of goods produced, the technology of production and the process of wage determination. The rural sector is specialized in the production of agricultural goods. The productive process of this sector can be described by a Cobb-Douglas production function:
where Ya is the production level of the agricultural good, Na is the amount of workers used in the agricultural production, Aa > 0 and 0 < f 0 and 0 < a 0 and g > 0 are a parametric constants. g is the elasticity of p with respect to the ratio Ym/Ya.

The overall population of workers in the economy is N, which is kept constant during the whole period of analysis. By assumption there are only two sectors and rural prices are wholly flexible, which implies that there is full employment in the rural area, i.e., all workers living at the rural sector are employed at any period. Then at any period the following equality is verified

B. Temporary Equilibrium

Given a parametric constant vector (Aa,Am,f,a,r,g), an initial urban population Nu, and a minimum wage wm one can calculate the temporary equilibrium of the economic system by using eqs. (1 – 6).
From eq. (4) one can find the employment level at the manufacturing sector
Replacing eq. (7) in eq. (2) we get the production level of the manufacturing sector
From eq. (6) one can obtain the relation
which is used with eq. (1) to obtain the agricultural production
By using eqs. (5), (8) and (10) the terms of trade are determined
Finally, by using eqs. (3), (9) and (11), the rural wage in units of manufacturated good is obtained
In sum, the vector (Nm,Ym,Na,Ya,p,wa) configures a temporary equilibrium that might be altered whether occurs a migration of workers, induced by the differential of sectorial wages, which changes the sectorial distribution of overall population.

C. The Long Run Equilibrium

Harris and Todaro, in determining the long run equilibrium, i.e., the absence of a net rural-urban migratory flow, argue that the rural workers, in their decision on migrating to the urban area, estimate the expected urban wage, , defined as:
The ratio Nm/Nu, which is the employment rate, is an estimative of the probability that a worker living at urban sector gets a job in this sector.
As mentioned before, the key assumption of the model of Harris and Todaro is that there will be a migratory flow from the rural to the urban sector while the expected urban wage is higher than the rural wage. Thus, the long run equilibrium is attained when the urban worker population reaches a level such that the expected urban wage equates the rural wage:
This equality is known in the economic literature as the Harris-Todaro condition. Harris and Todaro argue that the differential of expected wages in eq. (14) can be a constant value d ¹ 0. When this differential reaches d, the net migration ceases. This generalized Harris-Todaro condition can be expressed as follows:
The level of the urban population that satisfies the eq. (15), i.e., the equilibrium urban share = /N, is determined from the solution of the equation resulting from substitution of equations (12), (13) in eq. (15):
The solution of eq. (16) is parametrized by the vector (Aa,Am,r,g,a,f,wm).
Harris and Todaro [1], in order to evaluate the stability of the long run equilibrium, postulate a mechanism of adjustment that is based on the following function of sign preservation:
The differential equation that governs the state transition in the model of Harris and Todaro is obtained by replacing equations (12), (13) in eq. (17). Based on this postulated adjustment process, Harris and Todaro [1] show that the long run equilibrium is globally asymptotically stable. This means that the economy would tend to long run equilibrium with unemployment in the urban sector generated by the presence of a relatively high minimum wage for all possible initial conditions. From now on we will refer to the long run equilibrium simply as equilibrium.

Based on the numerical solutions of eq. (16) one can evaluate the impact that the variation of the minimum wage and the elasticity of the terms of trade on the equilibrium. In Fig. 1 we see that under the hypothesis of a Cobb-Douglas technology, the equilibrium urban share, , uses the labor demand on the manufacturing sector what results in higher unemployment rates in the equilibrium.

nges in the elasticity of the terms of trade alter slightly the equilibrium urban share and unemployment rate. A net migration toward urban sector shift the terms of trade to higher values. The greater g the greater this shift, what cause an increase in the rural wage in units of manufacturing good, becoming the urban sector less attractive.

III. HARRIS-TODARO AGENT-BASED MODEL

In this section we describe the implementation of the computational model we proposed, as well as the aggregate patterns obtained numerically and the comparison with the respective analytical results.

A. Computational Implementation

Initially, workers are randomly placed in a square lattice with linear dimension L = 500. The reference values of the parameters used for these simulations are the same done to evaluate the equilibrium of the Harris-Todaro model, namely, Aa = 1.0, Am = 1.0, f = 0.3, a = 0.7, r = 1.0 and g = 1.0. The value of the minimum wage used is wm = 0.8 and the initial urban fraction of the total population is nu = 0.2, where nu = Nu/N is the normalized urban population also called urban share. The initial value nu = 0.2 is in agreement with historical data of developing economies. Given these parameters, one can calculate the vector which characterizes temporary equilibrium of the system by using eqs. (7 – 12).

By using eq. (7), the employment level of the urban sector, Nm, is obtained. If nu Nm/N there will be a fraction of Nm/Nu workers employed, which earn the minimum wage, wi = wm, and (1-Nm/Nu) workers unemployed, which earn a wage wi = 0.

Each worker can be selected to review his sectorial location with probability a, called activity . Therefore, in each time step only a fraction of workers becomes potential migrants, going through the sectorial location reviewing process. Potential migrants will determine their satisfaction level of being in the current sector by comparing their earnings, wi, among nearest neighbors.

The potential migrant starts the comparison process with a initial satisfaction level si = 0. When wi > wneighbor the satisfaction level si is added in one unit; if wi < wneighbor, si is diminished in one unit; if wi = wneighbor, si does not change. After the worker has passed through the reviewing process his/her satisfaction level is checked. The migration will occur only if si < 0, what means that the worker's i earnings is less than the most of his/her nearest neighbors.

After all the potential migrants complete the reviewing process and have decided migrate or not, a new configuration of the system is set. Therefore, once again a new temporary equilibrium of the system is calculated by using eqs. (8 – 12). The whole procedure is repeated until a pre-set number of steps is reached. It is important to emphasize that Nm is kept constant throughout the simulation. Its given by eq. (7) which depends on the technological parameters, a,Am, and the minimum wage, wm, which are constants too.

B. Analysis of the Emergent Properties

In this section we develop the analysis of the long run aggregate regularities of Harris-Todaro agent-based computational model. These long run properties will be compared between the solution of the analytical model and simulations.

show the basic characteristics of the transitional dynamics and long run equilibrium generated by simulations. When the economic system has a low initial urban share, nu = 0:2 or nu = 0:3, there is a net migration toward urban sector. This migration takes the urban sector from a full employment situation to an unemployment one. The positive differential of expected wages that pulls workers to the urban sector diminishes. However, if the economic system initiates with a high urban share, nu = 0:8, or nu = 0:9 there is net flow of migration toward rural sector in such a way that the unemployment rate of the urban sector decreases

In this case, the differential of expected wages is negative. In an economy mainly rural (nu < 0:5), the transitional dynamics characterized by a continuous growth of population of the urban sector with a differential of expected wages relatively high is followed by the stabilization of rural-urban differential of expected wages. In other words, the generalized Harris-Todaro condition, eq. (15), arises as a long run equilibrium result of the agent-based migratory dynamics.

Figure 3 also shows that even after the urban share has reached an stable average value, there are small fluctuations around this average. Therefore, differently from the original Harris-Todaro model, our computational model shows in the long run equilibrium the reverse migration. This phenomenon has been observed in developing countries.
for a given value of a, the variation of wm practically does not change the equilibrium values of the urban share, the differential of expected wages and the unemployment rate. However, for a given wm, higher values of a make the urban sector less attractive due the reduction of the employment level. This causes a lower equilibrium urban share, a higher unemployment rate and a gap in the convergence of the expected wages.

The equilibrium values of the urban share, the differential of expected wages and unemployment rate do not have a strong dependence with wm. However, variations in g for a fixedwm, dramatically change the equilibrium values of the variable mentioned before. Higher values of g generate a lower urban concentration, a higher gap in the expected wages and a higher unemployment rate in the equilibrium.
The convergence of migratory dynamics for a urban share, compatible with historical data, is robust in relation to the variation of the key technological parameters, a and f. The impact of the variation of these parameters in the values of the equilibrium differential of expected wages, ( – wa), and the equilibrium urban unemployment rate, (1-Nm=Nu).

CONCLUSION

The dispersed and non-coordinated individual migration decisions, made based on local information, generate aggregate regularities. Firstly, the crucial assumption of Harris and Todaro, the principle that rural-urban migration will occur while the urban expected wage exceed the rural wage, comes out as spontaneous upshot of interaction among adaptative agents.

Secondly, the migratory dynamics generated by agents that seek to adaptate to the economic environment that they co-create leads the economy toward a long run equilibrium characterized by urban concentration with urban unemployment. When this long run equilibrium is reached, the generalized Harris-Todaro condition is satisfied, i.e., there is a stabilization of the rural-urban expected wage differential.

Thirdly, the impact of the minimum wage and elasticity of terms of trade in a long run equilibrium obtained by simulations are in agreement with the predictions of the original Harris-Todaro model with Cobb-Douglas technology.

Finally, the simulations showed an aggregated pattern not found in the original Harris-Todaro model. There is the possibility of small fluctuations of the urban share around an average value. This phenomenon is known as reverse migration.

Acknowledgments

Aquino L. Espíndola thanks CAPES for the financial support. Jaylson J. Silveira acknowledges research grants from CNPq. T. J. P. Penna thanks CNPq for the fellowship.

To

13. Okpor Martha Ashinedu says:

Name: OKPOR MARTHA ASHINEDU
Reg No: 2017/241430
Email: marthaokpor2017@gmail.com
THE LEWIS-FEI-RANIS SURPLUS LABOUR THEORY
The two economists John Fei and Gustav Ranis presented the dual economy model in this article “The theory of Economic Development”, also known as the surplus labour model. There was a flaw in Lewis model that it did not pay attention to the importance of agricultural sector in promoting industrial growth. But Fei- Ran is model of dual economy explains how the increased productivity in agricultural sector would become helpful in promoting industrial sector. In this respect, it presents three stages whereby underdeveloped countries move from stagnation to self- sustained economic growth.

ASSUMPTIONS OF THE FEI-RANIS MODEL INCLUDE;
1) Supply of labour is fixed.
2) Population growth is an exogenous phenomenon
3) Constant return to scale with labour works as a variable factor.
4) No accumulation of capital in agricultural sector except land reclamation
5) The output in agricultural sector is a function of land and labour only.
6) Industrial sector is a function of capital and labour alone.
7) Land has no role as a factor of production.
8) Marginal product of labour becomes zero at some point. If the population is excess the quantity where MPL becomes zero, then labour can be transfered to industrial sector without any loss of agricultural production.

On the basis of the above cited assumptions, the development of labour surplus can be divided into three phases;
a) In the first phase, there are disguised unemployed workers who are not contributing to agricultural production and can be easily shifted to industrial sector at a constant institutional wage.
b) In the second stage, agricultural workers who are adding to agricultural output but produce less than the institutional wage they get. This type of workers can be transferred to industrial sector.
c) The third stage is the stage of self- sustained growth, it starts where workers are adding to agricultural output and produce more than the institutional wages they get.

COMPARISON OF THE FEI-RANIS MODEL TO THE REAL WORLD
The Fei-Ranis model assume a close model and hence there is no presence of foreign trade in the economy, which is unrealistic as food or raw materials can not be imported. Like in Japan, the country imported cheap farm materials from other countries and this made better the country’s terms of trade. Also the model failed to recognize the sluggish economic situation prevailing in the developing countries(eg Nigeria). If they had thoroughly scrutinized the existing nature and causes of it, they would have found that the existing agricultural backwardness was due to institutional structure, primarily the system of feudalism that prevailed. While mentioning the role of agricultural productivity for economic development, the model failed to mention the need for capital. Although it is important to create surplus, it is equally important to maintain it through technical progress, which is possible through capital accumulation, but the Fei- Ranis model considers only labour and output as factors of production. The model assumes the MPL=0. The underdeveloped countries mostly exhibit seasonality on food production especially during favourable climatic conditions, say that of harvesting or sowing, MPL would definitely be greater than zero. The model assumed that the supply of land is fixed, but this is not try as supply of land can be increased in the long-run.

HARRIS- TODARO THEORY OF MIGRATION
John R. Harris and Michael P. Todaro presented this model of migration in 1970. The main assumption of this model is that the migration decision is based on expected wage differentials between rural and urban areas rather than actual wage differentials. In the model, an equilibrium is reached when the expected wage in urban areas is equal to the marginal product of an agricultural labour. The model assumes that unemployment is non-existent in the rural agricultural sector. It is also assumed that the rural agricultural production and the subsequent labour market is perfectly competitive. As a result, the agricultural rural wage is equal to agricultural marginal production.

In equilibrium, the rural to urban migration rate will be zero since the expected rural income equals the expected urban income. However there will be positive unemployment in the urban sector.
For the formal statement of the Harris- Todaro model let;
wr= wage rate in rural sector
wu= wage rate in urban area
le= number of jobs available in urban sector
lus= Total number of jobs seekers in the urban sectors.
Rural to urban migration will take place if; wr (le/lus)wu
There for equilibrium is established where; wr = (le/ lus)wu
No rural to urban migration will take place in this condition.

COMPARISON OF HARRIS- TODARO MODEL OF MIGRATION TO THE REAL WORLD
We have derived one necessary and sufficient condition under which the increase in capital stock does not increase unemployment in the urban area. This condition concerns he relationship between the institutionally and legally set minimum wage in the urban area and agricultural productivity in the rural area. Unsurprisingly, if agricultural productivity rises as well as income in rural aras, rural workers have no need to migrate to the urban sector to find jobs and face the risk of unemployment.
It has been observed in Asian countries that, particularly in the urban sector, concentrated improvement of social capital such as harbors, roads, and industrial parks gives rise to Todaro paradox. In the case of Metro Cebu, the Philippines, the Todaro paradox occurred in the 1990s. As the Metro Cebu economy developed with ODA projects supported by the Japanese Government, workers from surrounding areas migrated to the region and increased urban unemployment. Therefore, when social infrastructure improvement is implemented, improvement of the agricultural infrastructure should be carried out simultaneously to increase agricultural productivity. By so doing, it becomes possible to avoid a disruptive influx of workers from rural to urban areas.

LIMITATIONS OF THE MODEL
a) It assumes potential migrants are risk neutral, as they are indifferent between a certain expected rural income and an uncertain expected urban income of the same magnitude.
b) The model assumes that labour has perfect information about market wages in rural and urban sectors, which is impractical given the prevalent illiteracy among rural people.
c) The reflection of economic realities by this assumption is questionable; poor migrants will likely be risk averse and require a significantly greater expected urban income to migrate.

14. Nwaankpa Lilian Ugomma says:

Nwankpa Lilian Ugomma
Reg no:2017/244743
Dept:Social science Education(Economics Edu)
HARRIS-TODARO MODEL OF MIGRATION
INTRODUCTION
The Harris–Todaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and welfare economics to explain some of the issues concerning rural-urban migration.
In this easy we turn upon the seminal Harris and Todaro work, which together with Todaro is considered one of the starting points of the classic rural-urban migration theory. The hypothesis and predictions of Harris-Todaro model have been subjected to econometric evaluation and have been corroborated by several studies. The key hypothesis of Harris and Todaro are that migrants react mainly to economic incentives, earnings differentials, and the probability of getting a job at the destination have influence on the migraton decision. In other words, these authors posit that rural-urban migration will occur while the urban expected wage exceed the rural wage. From this crucial assumption, as denominated by Harris-Todaro, is deduced that the migratory dynamics leads the economic system toward an equilibrium with urban concentration and high urban unemployment.
In the model, an equilibrium is reached when the expected wage in urban areas (actual wage adjusted for the unemployment rate), is equal to the marginal product of an agricultural worker. The model assumes that unemployment is non-existent in the rural agricultural sector. It is also assumed that rural agricultural production and the subsequent labor market is perfectly competitive. As a result, the agricultural rural wage is equal to agricultural marginal productivity. In equilibrium, the rural to urban migration rate will be zero since the expected rural income equals the expected urban income. However, in this equilibrium there will be positive unemployment in the urban sector. The model explains internal migration in China as the regional income gap has been proved to be a primary drive of rural-urban migration, while urban unemployment is local governments’ main concern in many cities.
COMPARISON OF THIS MODEL TO LEWIS-FEY MODEL
Here, we will discuss about the model of labour migration and reallocation.
Employment policy in developing countries like India cannot be formulated and implemented without answering a basic question, viz., how can underutilised labour be used in a development strategy? Ragnar Nurkse and W. A. Lewis asserted that large numbers of people remain engaged in work which adds nothing to national output. Nurkse saw the reallocation of a surplus labour to more productive uses, especially labour-intensive construction projects, as a major source of capital formation and economic growth.
Lewis envisaged a similar reallocation process but he pictured the ‘capitalist sector’, essentially industry, as the principal employer of surplus labour. Both theories regarded the labour reallocation process as nearly costless but they worried about how to capture from the agricultural sector the food necessary to feed the transferred workers.
While criticising the Lewis model J. R. Harris and M. P. Todaro have developed a new model of economic development which is relevant for labour surplus countries like India. It is the best known model of internal migration in the context of present-day developing countries. The model has focused on migration of labour from rural to urban areas induced by certain incentives. They have referred to two types of migration—induced migration and internal migration.
According to this model migrating workers are essentially participants in a lottery of relatively high-paid jobs in the towns. When new urban jobs are created the lottery becomes more attractive to potential migrants. Depending on their responsiveness to this improved opportunity, more than one worker are likely to migrate for each job created. If so, the output foregone may be that of two or more agricultural workers, not just one. If the migrants bring some of their family members to urban areas more output will be lost. The reason is that the wife and children of migrants find fewer employment opportunities in towns than in the rural areas because they do not have land in the towns on which to grow food.
MODELS AND ASSUMPTIONS
The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This implies that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.
CRITIQUES OF THE STANDARD HARRIS-TODARO MODEL AND ITS POLICY IMPLICATIONS
The Todaro Paradox conveyed the message that internal migration can be harmful because it exacerbates urban unemployment. Given the high unemployment rates and significant migration to cities in developing countries, this idea has certainly inspired many governments to implement restrictive policies even though the empirical validity of the Harris-Todaro model and of the Todaro paradox are not clearly established. In any case, the Harris-Todaro model suffers from theoretical oversimplifications, among which several are likely to overestimate the link between migration and urban unemployment. The critiques revolve around six major points:
1. The Harris-Todaro framework is only a static model describing migration, which is a dynamic phenomenon by nature. Even though the model can be thought of as representing a steady state equilibrium, this is a limitation. Furthermore, the formalization is made in a partial equilibrium context which greatly weakens the justifications for policy recommendations.
2. Important aspects are absent from the standard Harris-Todaro model, including the probable heterogeneity of migrants which is not accounted for, risk aversion which could dampen migration incentives and render the Todaro paradox even less likely to occur, the possibility of job search in the urban area from the rural area, the possibility of return migration, or the existence of rural unemployment. In fact, the Harris-Todaro is almost silent about what happens in the rural areas.
3. The assumption that urban workers are either employed in the manufacturing sector or unemployed has been criticized as too simplistic even though, in the authors’ minds, it was implicit that unemployment could also be interpreted as underemployment in the informal sector. Cole and Sanders (1985) have criticized the Harris-Todaro model for not explicitly modeling the subsistence sector employing uneducated migrants, arguing that it flawed the job selection process and expected income calculations if, by lack of qualification, uneducated migrants could not find a job in the modern urban sector.
4. The job rationing mechanism or hiring model hypothesized is not realistic. In particular, assuming random job selection in each period overestimates the likelihood of finding a job. Stieglitz (1974) suggests that the employment probability might vary in a non-monotonic way with the duration of the stay in the city: it could increase in the first periods when migrants form social networks in the city, and then decrease in the later periods because of deteriorating human capital or because of bad signaling.
5. The Harris-Todaro model assumes that the urban wage is exogenously set above the endogenous rural wage since it must be that w > f’a(L’a) for (2.3) to hold. The assumption that wages are high find several explanations ranging from the existence of trade unions to the agglomeration of economic activities. It is confirmed in practice,since wages are often reported three to four times higher in urban areas than in rural areas (Todaro, 2000). What is more problematic, however, is the assumption that the urban wage is fixed, especially in the presence of an informal sector as typical of many developing economies. In fact, the argument of a minimum wage should only hold for low wages in the formal sector, unless remunerations in the informal sector align themselves with those in the formal sector (due to the competition for labor between employers).14 In addition, the wage in the Harris-Todaro model is not related to unemployment in any manner. If the urban wage tends to decrease with an increase in the unemployment rate as argued by Hoddinott (1996) in his study on urban African labor markets, then this would tend to reduce the expected earnings differential in the transition towards the equilibrium in the model. This gives another reason why migration flows could be overestimated, making the Todaro paradox even less likely to occur.
6. The assumption of migration led by expected income differentials may overlook other important elements in the migration decision. In particular, it has been observed that migration can occur even when the urban expected income is below the rural income, which is clearly inconsistent with the income differential approach adopted by the Harris-Todaro model (see Katz and Stark 1986a). In view of these critiques, the policy implications derived from the Harris-Todaro model i.e. to restrict the rural to urban migration are much weaker. In particular, there are several reasons that qualify the justifications of restrictive migration policies. First, Todarian models only focus on urban labor markets whereas national governments should be concerned with whether overall national employment (i.e. including rural areas) has improved. Second, as observed by Stark (1991), in a general equilibrium perspective, the migration of labor between rural and urban areas may reflect a disequilibrium in another market, for instance poorly-functioning capital markets in rural areas, which can induce migration and should therefore be addressed. Third, it cannot be ruled out that migration may have a positive impact on rural areas, possibly by raising productivity, allowing exchanges with urban areas, and generating income for rural development.
CONCLUSION
What policies can be adopted to make a dent on the problem of employment? The preceding analysis suggests a two pronged policy strategy. The first component of the policy framework must deal with the adoption, enactment and implementation of a set of measures that can significantly reduce the wage gap. Since the wage gap can be reduced in either of two ways, i.e. by decreasing the urban wage, holding the average rural income constant; or by increasing rural incomes faster than the urban real wage, the question would arise as to which of these is more desirable. There are many reasons, I wish to argue, to recommend the latter, i.e. narrowing the wage gap by increasing rural incomes and not by reducing urban incomes. First, the increase in rural incomes while holding urban wages from falling would impart an overall impetus to the levels of aggregate demand in the economy. This will be beneficial in sustaining rapid economic growth in the macroeconomy, as has been pointed by other scholars (Nagaraj, 2017). Second, the relative increase in rural incomes will reduce levels of overall inequality in the distribution of income even as average incomes of the poorest and most vulnerable rise. This would be construed as an overall increase in economic welfare by most economists and policy makers.

15. Onyekanma Chidinma Cynthia says:

NAME: ONYEKANMA CHIDINMA CYNTHIA
REG.NO. 2017/249569
DEPARTMENT: ECONOMICS
EMAIL: cchidinma96@gmail.com
HARRIS-TODARO’S MIGRATION THEORY
John R. Harris and Michael P. Todaro developed the Theory of migration. This theory is used in development economics and it illustrates a migrants’ decision on his expected income difference between a rural(agriculture) and urban(manufacturing) areas. The model of rural-urban migration is typically studied in the context of employment and unemployment situation in developing countries. The need of the model is to explain the critical urban unemployment problem in developing countries using Nigeria as case study.
ASSUMPTIONS OF THE MODEL
a. Two sectors: urban (manufacture) and rural (agriculture)
b. Rural-urban migration condition: when urban real wage exceeds real agricultural product
c. No migration cost
d. Perfect competition
e. Cobb-Douglas production function
f. Static approach
g. Low risk

THE DISCOURSE
The fundamental contribution of Harris and Todaro’s rural-urban two sector migration model was to build a model that fit the stylized facts of the labor market. On the lines of the theory, developing countries adopted program on integrated rural development which encouraged an increase in the rural traditional sector wage. The theory proves that the higher the unemployment rate, the lower is the probability of new migrants from the countryside actively seeking formal sector employment who are unable to find it.
SIGNIFICANT FINDINGS OF THE THEORY:
First, if the expected urban wage equals rural income, there is no incentive to migrate.
Second, if the expected urban wage is greater than rural income, there is a great incentive to move from rural to urban area.
Third, if the expected urban wage is less than rural incomes, there would be an incentive to move in other direction.
Fourth, the expected urban wage depends on what type of job migrant is engaged in.

IMPACT OF THE THEORY IN NIGERIA
Using Nigeria as a case study, Rural-urban migration is one of the most distressing problems facing the Nigerian socio- economic development. A situation where the desire for better employment, business opportunities and education pushes both young and old out of the rural areas to the urban areas. Rural-urban migration represents a phenomenon of unprecedented movement of people from the rural countryside to the urban cities. Historically, migration existed internally across city boundaries to enable excess labor to be taken slowly from the rural areas to provide workforce for industries in the urban areas and therefore aid industrialization and economic growth. However, over time, the rate of rural-urban migration has rapidly outweighed the rate of job creation in developing and underdeveloped countries( Harris-Todaros’ finding) overstretched available social and infrastructural facilities in the urban areas.
The Haris Todaro’s model will helps policy-makers in Nigeria to avoid two mistakes:
a). One is to assume that development efforts should necessarily be channeled to the sectors where the poor are.
b.) The other is to assume that efforts should necessarily be focused on getting the poor out of the sectors in which they presently are.
FIRST-BEST POLICY
According to the first-best solution labor should be allocated such that:
a) marginal products in agriculture and manufacturing must be equal
b) no unemployment
As Harris and Todaro stated the first –best solution is to subsidize manufacturing (at the rate ZZ’ per man) and restrict migration out of agriculture. Or, subsidize both sectors equally by ZZ’ per man. To finance this subsidy we need to find some sectors that are taxable either directly, or indirectly through trade policy, so that it will not affect supplies of the taxed factors as a result.
CONCLUSION
Harris Todaro model explains some issues of rural-urban migration. This migration happens in case when expected urban income is higher than rural wages. In this case economy may have high rates of unemployment. The equilibrium condition of this model is when expected urban wage is equal to rural wage. When government subsidize manufacturing sector Harris Todaro paradox may happen.
According to the Harris and Todaro, job creation instead of dealing with unemployment problem actually may cause increase of unemployment. This happens when urban-rural wage differential is high enough, so rural workers move to the cities hoping to find a job with high wage. Obviously, not all these workers succeed in finding jobs which leads to unemployment. Another issue is that inducing minimum wages creates labor market distortions. Therefore, policy makers in Nigeria should not set the minimum wage rates. In addition, simulations showed that different policies’ outcomes depend on elasticity of labor demand in different sectors and on marginal product of labor. As Harris and Todaro suggested the first-best policy would be subsidizing manufacturing along with restrictions of rural migration.

2. LEWIS FEI-RANIS MODEL
INTRODUCTION
The Fei–Ranis model of economic growth is a dualism model developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.
SIGNIFICANCE OF AGRICULTURE IN FEI-RANIS MODEL
The Lewis model is criticized on the grounds that it neglects agriculture. Fei– Ranis model goes a step beyond and states that agriculture has a very major role to play in the expansion of the industrial sector. In fact, it says that the rate of growth of the industrial sector … depends on the amount of total agricultural surplus and on the amount of profit that are earned in the industrial sector. So, larger the amount of surplus and the amount of surplus put into productive investment and larger the amount of industrial profits earned, the larger will be the rate of growth of the industrial economy. As the model focuses on the shifting of the focal point of progress from the agricultural to the industrial sector, Fei and Ranis believe that the ideal shifting takes place when the investment funds from surplus and industrial profits are significantly large so as to purchase industrial capital goods like plants and machinery. These capital goods are needed for the creation of employment opportunities. Hence, the condition put by Fei and Ranis for a successful transformation is that Rate of increase of capital stock & rate of employment opportunities > Rate of population growth
IN SUMMARY
For economies in the early stages of development or still developing, such as Nigeria, the rural agricultural sector consists of family farming units, with a hiring principle that is different from that of the firm. Family members work together and share the value of their output. They are paid not the marginal product but the average product of labor. Thus, it is possible that there exists surplus labor in Nigeria and other developing countries. The notions of surplus labor and disguised unemployment have been a central part of development economics since Lewis (1954). With the presence of surplus labor in the traditional sector, the modern sector can expand without increasing labor costs. This process will continue until the surplus labor in the traditional sector is used up. After this point is reached, wages begin to rise consistent with rising marginal productivity, in which the workers in the traditional sector would also be paid in accordance with their marginal product rather than the subsistence wage. At this stage, the dualistic economic structure disappears, replaced by a competitive one-sector economy that can be explained by the neoclassical model.

16. NAME: Obodo chisom jessica
REG NO: 2017/249538
EMAIL: chisom.obodo.249538@unn.edu.ng
WEBSITE: teddy-cilia.simplesite.com

LEWIS-FEI-RANIS MODEL (SURPLUS LABOUR THEORY)
The Lewis (1954) theory of dualistic economic development provides the seminal contribution of theories of economic development particularly for labour-surplus and resource-poor developing countries. In the Lewis theory, the economy is assumed to comprise the agricultural and non-agricultural sectors. The agricultural sector is assumed to have vast amounts of surplus labour that result in an extremely low, close to zero, marginal productivity of labour. The agricultural wage rate is presumed to follow the sharing rule and be equal to average productivity, which is also known as the institutional wage. The non-agricultural sector has an abundance capital and resources relative to labour. It pursues profit and employs labour at a wage rate higher than the agricultural institutional wage by approximately 30 percent (Lewis, 1954, p.150). The non-agricultural sector accumulates capital by drawing surplus labour out of the agricultural sector. The expansion of the non-agricultural sector takes advantage of the infinitely elastic supply of labour from the agricultural sector due to its labour surplus.
The Fei-Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the surplus labour model. It recognizes the presence of a dual economy comprising both of the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the economic development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial sector, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod-Domars model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.
Ranis and Fei (1961) formalized Lewis’s theory by combining it with Rostow’s (1956) three “linear-stages-of-growth” theory. They disassembled Lewis’s two-stage economic development into three phases, defined by the marginal productivity of agricultural labor. They assume the economy to be stagnant in its pre-conditioning stage. The breakout point marks the creation of an infant non-agricultural sector and the entry into phase one. Agricultural labour starts to be reallocated to the non-agricultural sector.

ASSUMPTIONS OF THE MODEL
Some assumptions of the model are; firstly, the modern sector employment creation and labour transfer the rate if capital accumulation in the modern sector. Marginal productivity of labour, henceforth MPL, is positive in the modern sector. Labour could be transferred from the agricultural sector to the modern sector at zero cost, yielding net profits in the industry leading to a higher rate of investment: countries can thus develop rapidly (Todaro and Smith, 2009 pp 118). Secondly, was the notion that surplus labour exists in rural areas, while the urban areas were said to have full employment. This, Todaro said, was because there was over-population in the rural area where MPL is zero. Actual output of labour was used to determine their wages (Todaro and Smith, 2009,pp 118). A popular economist Ishikawa (1975) approves the theory of minimum subsistence level of existence. This is one of the institutional real wages and he defined it as income distribution and principle of employment which says that every family is entitled to at least a minimum wage (Ranis, 2004). Hayami and Kikuchi (1982), using a Neo-classical approach, found that, in Indonesia, wages will never adjust based on labour marginal product but through social conventions.
Thirdly, another important assumption that Lewis made is about savings generated in the capitalist sector and in the subsistence sector. The capitalist sector invests its entire savings for its further expansion. Those in subsistence sector, on the other hand squander away their savings, if any in purchase of jewellery and for construction of temples and so on. The propensity to save of the people in subsistence sector is also lower when compared with that of those in capitalist sector. Lewis in fact so much fascinated by the higher propensity to save of the capitalist sector that he even advocates a transfer of income from the subsistence sector to the capitalist sector. He feels that steps to be taken to raise the rate of savings from 10% to 15% if the development of the economy has to be smooth.

In conclusion, I have shown the main ideas behind the Lewis-Ranis-Fei model and used the consecutive analysis of the model to explain why it is important to invest in both sectors in order to remain on the balanced growth path and maintain the rate of industrialization. Relating this to the Nigerian economy, the existence of surplus labour in agriculture allows the industry to continue to pay the institutional wage and therefore enjoy further profits and continued investment. Also at the same time, as more and more people are moving away from agriculture, there will be some amount of agricultural surplus that can be used up to fuel or lead to further development. This process continues until the surplus labour is absorbed. Hence, saving and investment are a crucial part in the Lewis-Ranis-Fei to support economic development.

HARRIS-TODARO MODEL OF MIGRATION
The Harris–Todaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and welfare economics to explain some of the issues concerning rural-urban migration. The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This implies that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.
In the model, an equilibrium is reached when the expected wage in urban areas (actual wage adjusted for the unemployment rate), is equal to the marginal product of an agricultural worker. The model assumes that unemployment is non-existent in the rural agricultural sector. It is also assumed that rural agricultural production and the subsequent labor market is perfectly competitive. As a result, the agricultural rural wage is equal to agricultural marginal productivity. In equilibrium, the rural to urban migration rate will be zero since the expected rural income equals the expected urban income. However, in this equilibrium there will be positive unemployment in the urban sector.

Assumptions
Harris and Todaro [1] studied the migration of workers in a two-sector economic system, namely, rural sector and urban sector. The difference between these sectors are the type of goods produced, the technology of production and the process of wage determination. The rural sector is specialized in the production of agricultural goods. The productive process of this sector can be described by a Cobb-Douglas production function:
where Ya is the production level of the agricultural good, Na is the amount of workers used in the agricultural production, Aa > 0 and 0 < f 0 and 0 < a 0 and g > 0 are a parametric constants. g is the elasticity of p with respect to the ratio Ym/Ya.

The overall population of workers in the economy is N, which is kept constant during the whole period of analysis. By assumption there are only two sectors and rural prices are wholly flexible, which implies that there is full employment in the rural area, i.e., all workers living at the rural sector are employed at any period. Then at any period the following equality is verified.
Relating to the Nigerian economy,In terms of pro-poor economic growth, the Harris-Todaro model and other multisector-labor-market models can help policy makers avoid two mistakes. One is to assume that development efforts should be channeled to the sectors where the poor are. The other is to assume that efforts should always be focused on getting the poor out of the sectors in which they now are. Careful cost-benefit analysis based on well-specified labor-market models is required to decide among such alternatives.

17. NAME:UGWOKE, NGOZI CHRISTABEL
DEPT: LIBRARY AND INFORMATION SCIENCE
REG NO:2017/244942
LEWIS- FEI – RANIS MODEL
In the mid-1950s, W. Arthur Lewis outlined a model of economic development. At the heart of the model were the dynamics of labour reallocation in a ‘dual economy’ composed of a traditional or subsistence sector and a modern or industrial or capitalist sector. The Lewis model has since become one of the most influential models in development economics and its creator was awarded the Nobel prize in appreciation of it.
Lewis argued that the driver of capital accumulation was a sectoral movement of the factor of production abundant in developing countries, labour, from the ‘traditional’ or ‘non-capitalist’ sector (of low productivity, low wage, priced to average product not marginal product, and thus with widespread disguised unemployment) to the ‘modern’ or ‘capitalist’ sector (of higher productivity and where wages are set by productivity in the ‘subsistence sector’). Crucial is the existence of surplus labour in the traditional or non-capitalist sector. Because of this, wages are set just above subsistence across the whole economy, leading to the transfer of labour over time from traditional or non-capitalist to modern or capitalist sectors and the capture of labour productivity gains to capitalists as profits as these are the source of growth via reinvestment. The floor for wages is institutionally set at subsistence. When the surplus labour disappears an integrated labour market and economy emerge and wages will then start to rise.
In 1954. In his model Lewis divides the economy in an underdeveloped country in two sectors namely the Subsistence sector and the capitalist sector. Subsistence is identified with the agricultural sector of the economy while the capitalist sector implies mainly the manufacturing sector of the economy. Capitalist sector also includes plantations and mining where hired labour is employed for purposes of production. The capitalist sector can either be private or public in nature. Subsistence sector, that the agricultural sector is considered to be labour intensive. It does not use reproducible capital. It uses poor techniques of production and has very low productivity.
The Lewis model was intended as a critique of the neoclassical approach in that labour is available to the modern or capitalist sector of an economy not in a perfectly elastic supply but upward sloping rather than flat, and with a distinction between surplus-producing labour and subsistence labour (the latter of which was a negligible source of net profits for reinvestment, which Lewis saw as the driver for growth). Lewis also rejected the assumptions of neoclassical economists of perfect competition, market clearing and full employment and Lewis made the distinction, noted above, between productive labour, which produced a surplus, and unproductive labour, which did not.
ASSUMPTION OF LEWIS MODEL
(A) Surplus labour in substance sector:
The basic assumption of the model is that there exists surplus labour in the subsistence sectors. It includes labour whose marginal productivity is zero as well as that whose marginal productivity is positive but is less than the institutional wage. This labour comprises farmers, agricultural labourers, petty traders domestic servants and women. The surplus labour in the agriculture sector acts as a source of unlimited supply of labour for the manufacturing sector. By unlimited supply of labour. Lewis means that the supply of labour is perfectly elastic at a particular wages. This particular wage is somewhat higher than the institutional wage which each worker in the agricultural sector gets.
(B) Important of saving:
Another important assumption that Lewis makes is about the savings generated in the capitalist sector and in the subsistence sector. The capitalist sector invests all its savings for its further expansion.Those in the subsistence sector, on the other hand squander away their savings, if any in purchase of jewellery & for construction of temples etc. The propensity to save of the people in subsistence sector is also lower when compared with that of those in the capitalist sector. Lewis so much fascinated by the higher propensity to save of the capitalist sector that he even advocates a transfer of income from the subsistence sector to the capitalist sector. He feels that steps have to be taken to raise the rate of savings from 10% to 15% if the development of the economy has to be smooth.
HOW IT RELATE TO NIGERIA ECONOMY

The Lewis theory of development to the Nigerian economy. Nigeria has both rural and urban sectors that provide for each forward and backward linkages and as such, the two sectors are not mutually exclusive in promoting the economic growth of the country and improving the standard of living of citizens. However, the Federal Government of Nigeria does not necessarily have to move surplus labour that exists in the rural areas to the urban areas but instead infrastructural facilities should be provided equally to both the rural and urban areas of the country.
The Harris-Todaro model of the rural-urban migration process is revisited under an agent-based approach. The migration of the workers is interpreted as a process of social learning by imitation, formalized by a computational model. By simulating this model, we observe a transitional dynamics with continuous growth of the urban fraction of overall population toward an equilibrium. Such an equilibrium is characterized by stabilization of rural-urban expected wages differential (generalized Harris-Todaro equilibrium condition), urban concentration and urban unemployment. These classic results obtained originally by Harris and Todaro are emergent properties of our model.Todaro is considered one of the starting points of the classic rural-urban migration theory . The hypothesis and predictions of Harris-Todaro model have been subjected to econometric evaluation and have been corroborated by several studies. The key hypothesis of Harris and Todaro are that migrants react mainly to economic incentives, earnings differentials, and the probability of getting a job at the destination have influence on the migraton decision. In other words, these authors posit that rural-urban migration will occur while the urban expected wage exceed the rural wage. From this crucial assumption as denominated by Harris-Todaro , is deduced that the migratory dynamics leads the economic system toward an equilibrium with urban concentration and high urban unemployment.
The Harris-Tadora model of the rural-urban migration is a means of an agent-based computational model taking into account the influence of the neighborhood in the migration decision. The inclusion of the influence of neighbors was done via an Ising like model. The economic analogous to the external field in the Ising hamiltonian was the differential of expected wages between urban and rural sectors
ASSUMPTIONS OF HARRIS-TADOR MODEL OF MIGRATION.
A. Assumption.
Harris and Todaro studied the migration of workers in a two-sector economic system, namely, rural sector and urban sector. The difference between these sectors are the type of goods produced, the technology of production and the process of wage determination. The rural sector is specialized in the production of agricultural goods. The productive process of this sector can be described by a Cobb-Douglas production function:

where Ya is the production level of the agricultural good, Na is the amount of workers used in the agricultural production, Aa > 0 and 0 <  0 and 0 <  0 and  > 0 are a parametric constants.  is the elasticity of p with respect to the ratio Ym/Ya.
The overall population of workers in the economy is N, which is kept constant during the whole period of analysis. By assumption there are only two sectors and rural prices are wholly flexible, which implies that there is full employment in the rural area, i.e., all workers living at the rural sector are employed at any period. Then at any period the following equality is verified:

B. Temporary equilibrium.
Given a parametric constant vector (Aa,Am,,,,), an initial urban population Nu, and a minimum wage wm one can calculate the temporary equilibrium of the economic system by using eqs. (1 – 6).
From eq. (4) one can find the employment level at the manufacturing sector

Replacing eq. (7) in eq. (2) we get the production level of the manufacturing sector

From eq. (6) one can obtain the relation

which is used with eq. (1) to obtain the agricultural production

By using eqs. (5), (8) and (10) the terms of trade are determined

Finally, by using eqs. (3), (9) and (11), the rural wage in units of manufacturated good is obtained

In sum, the vector (Nm,Ym,Na,Ya,p,wa) configures a temporary equilibrium that might be altered whether occurs a migration of workers, induced by the differential of sectorial wages, which changes the sectorial distribution of overall population.

18. NAME:UGWOKE NGOZI CHRISTABEL
REGNO:2017/244942
EMAIL:ngozi.ugeoke.244942@unn.edu.ng

LEWIS- FEI – RANIS MODEL
In the mid-1950s, W. Arthur Lewis outlined a model of economic development. At the heart of the model were the dynamics of labour reallocation in a ‘dual economy’ composed of a traditional or subsistence sector and a modern or industrial or capitalist sector. The Lewis model has since become one of the most influential models in development economics and its creator was awarded the Nobel prize in appreciation of it.
Lewis argued that the driver of capital accumulation was a sectoral movement of the factor of production abundant in developing countries, labour, from the ‘traditional’ or ‘non-capitalist’ sector (of low productivity, low wage, priced to average product not marginal product, and thus with widespread disguised unemployment) to the ‘modern’ or ‘capitalist’ sector (of higher productivity and where wages are set by productivity in the ‘subsistence sector’). Crucial is the existence of surplus labour in the traditional or non-capitalist sector. Because of this, wages are set just above subsistence across the whole economy, leading to the transfer of labour over time from traditional or non-capitalist to modern or capitalist sectors and the capture of labour productivity gains to capitalists as profits as these are the source of growth via reinvestment. The floor for wages is institutionally set at subsistence. When the surplus labour disappears an integrated labour market and economy emerge and wages will then start to rise.
In 1954. In his model Lewis divides the economy in an underdeveloped country in two sectors namely the Subsistence sector and the capitalist sector. Subsistence is identified with the agricultural sector of the economy while the capitalist sector implies mainly the manufacturing sector of the economy. Capitalist sector also includes plantations and mining where hired labour is employed for purposes of production. The capitalist sector can either be private or public in nature. Subsistence sector, that the agricultural sector is considered to be labour intensive. It does not use reproducible capital. It uses poor techniques of production and has very low productivity.
The Lewis model was intended as a critique of the neoclassical approach in that labour is available to the modern or capitalist sector of an economy not in a perfectly elastic supply but upward sloping rather than flat, and with a distinction between surplus-producing labour and subsistence labour (the latter of which was a negligible source of net profits for reinvestment, which Lewis saw as the driver for growth). Lewis also rejected the assumptions of neoclassical economists of perfect competition, market clearing and full employment and Lewis made the distinction, noted above, between productive labour, which produced a surplus, and unproductive labour, which did not.

ASSUMPTION OF LEWIS MODEL
(A) Surplus labour in substance sector:
The basic assumption of the model is that there exists surplus labour in the subsistence sectors. It includes labour whose marginal productivity is zero as well as that whose marginal productivity is positive but is less than the institutional wage. This labour comprises farmers, agricultural labourers, petty traders domestic servants and women. The surplus labour in the agriculture sector acts as a source of unlimited supply of labour for the manufacturing sector. By unlimited supply of labour. Lewis means that the supply of labour is perfectly elastic at a particular wages. This particular wage is somewhat higher than the institutional wage which each worker in the agricultural sector gets.
(B) Important of saving:
Another important assumption that Lewis makes is about the savings generated in the capitalist sector and in the subsistence sector. The capitalist sector invests all its savings for its further expansion.Those in the subsistence sector, on the other hand squander away their savings, if any in purchase of jewellery & for construction of temples etc. The propensity to save of the people in subsistence sector is also lower when compared with that of those in the capitalist sector. Lewis so much fascinated by the higher propensity to save of the capitalist sector that he even advocates a transfer of income from the subsistence sector to the capitalist sector. He feels that steps have to be taken to raise the rate of savings from 10% to 15% if the development of the economy has to be smooth.

HOW IT RELATE TO NIGERIA ECONOMY

The Lewis theory of development to the Nigerian economy. Nigeria has both rural and urban sectors that provide for each forward and backward linkages and as such, the two sectors are not mutually exclusive in promoting the economic growth of the country and improving the standard of living of citizens. However, the Federal Government of Nigeria does not necessarily have to move surplus labour that exists in the rural areas to the urban areas but instead infrastructural facilities should be provided equally to both the rural and urban areas of the country.

The Harris-Todaro model of the rural-urban migration process is revisited under an agent-based approach. The migration of the workers is interpreted as a process of social learning by imitation, formalized by a computational model. By simulating this model, we observe a transitional dynamics with continuous growth of the urban fraction of overall population toward an equilibrium. Such an equilibrium is characterized by stabilization of rural-urban expected wages differential (generalized Harris-Todaro equilibrium condition), urban concentration and urban unemployment. These classic results obtained originally by Harris and Todaro are emergent properties of our model.Todaro is considered one of the starting points of the classic rural-urban migration theory . The hypothesis and predictions of Harris-Todaro model have been subjected to econometric evaluation and have been corroborated by several studies. The key hypothesis of Harris and Todaro are that migrants react mainly to economic incentives, earnings differentials, and the probability of getting a job at the destination have influence on the migraton decision. In other words, these authors posit that rural-urban migration will occur while the urban expected wage exceed the rural wage. From this crucial assumption as denominated by Harris-Todaro , is deduced that the migratory dynamics leads the economic system toward an equilibrium with urban concentration and high urban unemployment.
The Harris-Tadora model of the rural-urban migration is a means of an agent-based computational model taking into account the influence of the neighborhood in the migration decision. The inclusion of the influence of neighbors was done via an Ising like model. The economic analogous to the external field in the Ising hamiltonian was the differential of expected wages between urban and rural sectors

ASSUMPTIONS OF HARRIS-TADOR MODEL OF MIGRATION.
A. Assumption.
Harris and Todaro studied the migration of workers in a two-sector economic system, namely, rural sector and urban sector. The difference between these sectors are the type of goods produced, the technology of production and the process of wage determination. The rural sector is specialized in the production of agricultural goods. The productive process of this sector can be described by a Cobb-Douglas production function:

where Ya is the production level of the agricultural good, Na is the amount of workers used in the agricultural production, Aa > 0 and 0 <  0 and 0 <  0 and  > 0 are a parametric constants.  is the elasticity of p with respect to the ratio Ym/Ya.
The overall population of workers in the economy is N, which is kept constant during the whole period of analysis. By assumption there are only two sectors and rural prices are wholly flexible, which implies that there is full employment in the rural area, i.e., all workers living at the rural sector are employed at any period. Then at any period the following equality is verified:

B. Temporary equilibrium.
Given a parametric constant vector (Aa,Am,,,,), an initial urban population Nu, and a minimum wage wm one can calculate the temporary equilibrium of the economic system by using eqs. (1 – 6).
From eq. (4) one can find the employment level at the manufacturing sector

Replacing eq. (7) in eq. (2) we get the production level of the manufacturing sector

From eq. (6) one can obtain the relation

which is used with eq. (1) to obtain the agricultural production

By using eqs. (5), (8) and (10) the terms of trade are determined

Finally, by using eqs. (3), (9) and (11), the rural wage in units of manufacturated good is obtained

In sum, the vector (Nm,Ym,Na,Ya,p,wa) configures a temporary equilibrium that might be altered whether occurs a migration of workers, induced by the differential of sectorial wages, which changes the sectorial distribution of overall population.

19. AKOMA CHIOMA ONYINYE (2017/241339) says:

INTRODUCTION
The Harris-Todaro (1970) model’s key contribution to the field of development economics is by making the migration process a rational choice based on expected earnings. The Harris-Todaro (H-T) model takes most of Lewis models’ assumptions as given, such as the rural sector being characterized by subsistence agriculture, and the urban sector being characterized by modernized industries. The Harris-Todaro model takes a standard two sector model and imposes a higher wage in the urban sector which is higher than equilibrium clearing, while wage in agriculture is flexible. Equilibrium clearing is simply when wage across both sectors equalize, minus movement costs or natural advantages (such as better living environment) in 1 or the other sector. By imposing this higher wage in the urban sector, we no longer have market clearing wage which gives the workers in the rural sector an incentive to migrate to the urban sector. These migrant workers are not guaranteed to find a job in the urban sector. There is a probability that they will end being unemployed or in the informal sector. For modeling simplicity, it is usually assumed that only 1 of these two sectors are in the model. It fits the situation in LDC’s better to assume that an informal sector exists in the urban sector than unemployment. LDC’s are unlikely to have good social safety nets such as welfare benefits, unemployment benefits, and old age security. Without these benefits, workers in urban sector must do some work to keep themselves alive. If they were unable to find a job in the urban formal sector, which is the modern industrial sector, they would be forced to work in the informal sector to keep themselves alive. The informal sector is very primitive; work in this sector is labour intensive with little or no capital endowment. The equilibrium condition of the Harris-Todaro model can be described as the wage in agriculture must be equal to the expected wage in the urban sector. The model in its most basic form ignores disutility from not being at home farm, or cost of mobility, but these omissions do not change the essence of the model, the only implication of this is a downward shift of the urban sector’s expected returns.
The main idea of the Harris-Todaro model is that labour migration in underdeveloped countries is due to rural-urban differences in average expected wages rather than actual wages. The migrants consider the various opportunities of employment available to them in rural and urban sectors and choose the one that maximises their expected wages from migration.The minimum urban wage is substantially higher than the rural wage. If more employment opportunities are created in the urban sector at the minimum wage, the expected will rise and rural-urban migration will increase. Expected wages are measured by the difference in real urban income and rural agricultural income and the probability of a migrant’s getting an urban job.In fact, a migrant compares his expected income for a given time horizon in the urban sector with his prevailing average rural income and migrates if the former is more than the latter.
Thus migration in the Harris-Todaro modal is viewed as the wage or income gap between the urban and the rural sectors. But all migrants cannot be absorbed in the urban sector at high wages. Many fail to find a job and get employment in the informal urban sector at wages which are even lower than in the rural sector. Thus they join the queue of the underemployed or disguised unemployed in the urban sector.
ASSUMPTIONS OF THE MODEL
The Harris-Todaro model is based on the following assumptions:
1. There are two sectors in the economy – the rural or agricultural sector (A) and the urban or manufacturing sector (M).
2. The model operates in the short run.
3. The marginal production of labour in agriculture (MPLA) and of industry (MPLM) are determined by their respective technologies.
4. Capital is available in fixed quantities in the two sectors.
5. There are L workers in economy with LA and LM numbers employed in the rural and urban sectors respectively.
6. The number of urban jobs available (LM) is exogenously fixed. In the rural sector some work is always available. Therefore, the total urban labour force LM comprises L-LAalong with an available supply of rural migrants.
7. The urban wage is fixed at WM and the rural wage at WA, WM> WA.
8. The rural wage equals the rural marginal product of labour and the urban wage is exogenously determined.
9. Rural-urban migration continues so long as the expected urban real income is more that the real agricultural income.
10. The assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This implies that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.
In the model, an equilibrium is reached when the expected wage in urban areas (actual wage adjusted for the unemployment rate), is equal to the marginal product of an agricultural worker. The model assumes that unemployment is non-existent in the rural agricultural sector.
It is also assumed that rural agricultural production and the subsequent labor market is perfectly competitive. As a result, the agricultural rural wage is equal to agricultural marginal productivity. In equilibrium, the rural to urban migration rate will be zero since the expected rural income equals the expected urban income. However, in this equilibrium there will be positive unemployment in the urban sector. The model explains internal migration in China as the regional income gap has been proved to be a primary drive of rural-urban migration, while urban unemployment is local governments’ main concern in many cities.
Conclusion
The Harris-Todaro in essence is an extension of the Lewis model. It simply endogenizes migration decision along with the introduction of a second urban sector. It does not change from the Lewis model in that the fundamental driving force of growth is still technological growth.
For economic development in LDCs, capital accumulation in the urban sector is a crucial element. The accumulated capital forms many production bases and creates job opportunities in the urban sector. At the same time, the increase in employment raises the wage level in the urban sector. In the Harris–Todaro model, the rising urban wage pushes up the expected wage in the urban sector and consequently encourages workers to migrate from the rural sector to the urban sector. If, in the resulting migration, there are more workers than the number of job opportunities created in the urban sector, some will necessarily be unemployed. Occasionally, the increase in unemployment lowers the per-capita income level before the capital is accumulated. This phenomenon is referred to as Todaro paradox. Previous studies have not, however, determined what effect an increase in capital stock in the urban sector has on urban unemployment.

20. Ogbonna Anthony says:

Ogbonna Anthony
2017/243368

Lewis-Fei-Ranis Model of Economic Growth.
One of the best known early theoretical models of development that focused on the structural transformation of a primarily subsistence economy was that formulated by Nobel Laureate W. Arthur Lewis in the mid-1950s, and later modified, formalized, and extended by John Fei and Gustav Ranis. The Lewis two-sector model became the general theory of the 1960s and early 1970s, and it is sometimes still applied, particularly to study the recent growth experience in China and labor markets in other developing countries.
The Fei-Ranis model is an improvement over the lewis model. John Fei and Gustav Ranis analyze the transition process through which an underdeveloped economy hopes to move from a condition of stagnation to one of self-sustained growth.
The theory relates to underdeveloped labor surplus and resources; poor economy in which the vast majority of the population is engaged in agriculture amidst widespread unemployment and high rates of population growth.

ASSUMPTIONS OF THE MODEL

1. There is a dual economy divided into a traditional and stagnant agricultural sector and an active industrial sector.
2. The output of the agricultural sector is a function of land and labor alone.
3. There is no accumulation of capital in agriculture except in the form of land reclamation.
4. Land is fixed in supply.
5. Population growth is taken as an exogenous phenomenon.
The real wage in the industrial sector remains fixed and is equal to the initial level of real income in the agricultural sector. It is called an institutional wage.
6. Workers in either sector consume only agricultural products.
Given these assumptions, Fei and Ranis analyze the development of a labor surplus economy into three phases;
In the first phase, the disguised unemployed workers who are not adding to agricultural output are transferred to the industrial sector at a constant institutional wage.
In the second phase, agricultural workers add to agricultural output but produce less than the institutional wage they get. Such workers are shifted to the industrial sector. If the migration of the workers to the industrial sector continues, a point is eventually reached when farmworkers produce output equal to the institutional wage.
In the third phase, which makes the end of the take-of and the beginning of the self-sustained growth when farmworkers produce more than the institutional wage they get. In this phase, the surplus labor is exhausted and the agricultural sector becomes commercialized.

. HARRIS-TODARO AGENT-BASED MODEL

In this section we describe the implementation of the computational model we proposed, as well as the aggregate patterns obtained numerically and the comparison with the respective analytical results.

A. Computational Implementation

Initially, workers are randomly placed in a square lattice with linear dimension L = 500. The reference values of the parameters used for these simulations are the same done to evaluate the equilibrium of the Harris-Todaro model, namely, Aa = 1.0, Am = 1.0, f = 0.3, a = 0.7, r = 1.0 and g = 1.0. The value of the minimum wage used is wm = 0.8 and the initial urban fraction of the total population is nu = 0.2, where nu = Nu/N is the normalized urban population also called urban share. The initial value nu = 0.2 is in agreement with historical data of developing economies. Given these parameters, one can calculate the vector which characterizes temporary equilibrium of the system by using eqs. (7 – 12).

By using eq. (7), the employment level of the urban sector, Nm, is obtained. If nu Nm/N there will be a fraction of Nm/Nu workers employed, which earn the minimum wage, wi = wm, and (1-Nm/Nu) workers unemployed, which earn a wage wi = 0.

Each worker can be selected to review his sectorial location with probability a, called activity . Therefore, in each time step only a fraction of workers becomes potential migrants, going through the sectorial location reviewing process. Potential migrants will determine their satisfaction level of being in the current sector by comparing their earnings, wi, among nearest neighbors.

The potential migrant starts the comparison process with a initial satisfaction level si = 0. When wi > wneighbor the satisfaction level si is added in one unit; if wi < wneighbor, si is diminished in one unit; if wi = wneighbor, si does not change. After the worker has passed through the reviewing process his/her satisfaction level is checked. The migration will occur only if si < 0, what means that the worker's i earnings is less than the most of his/her nearest neighbors.

After all the potential migrants complete the reviewing process and have decided migrate or not, a new configuration of the system is set. Therefore, once again a new temporary equilibrium of the system is calculated by using eqs. (8 – 12). The whole procedure is repeated until a pre-set number of steps is reached. It is important to emphasize that Nm is kept constant throughout the simulation. Its given by eq. (7) which depends on the technological parameters, a,Am, and the minimum wage, wm, which are constants too.

B. Analysis of the Emergent Properties

In this section we develop the analysis of the long run aggregate regularities of Harris-Todaro agent-based computational model. These long run properties will be compared between the solution of the analytical model and simulations.

show the basic characteristics of the transitional dynamics and long run equilibrium generated by simulations. When the economic system has a low initial urban share, nu = 0:2 or nu = 0:3, there is a net migration toward urban sector. This migration takes the urban sector from a full employment situation to an unemployment one. The positive differential of expected wages that pulls workers to the urban sector diminishes. However, if the economic system initiates with a high urban share, nu = 0:8, or nu = 0:9 there is net flow of migration toward rural sector in such a way that the unemployment rate of the urban sector decreases

In this case, the differential of expected wages is negative. In an economy mainly rural (nu < 0:5), the transitional dynamics characterized by a continuous growth of population of the urban sector with a differential of expected wages relatively high is followed by the stabilization of rural-urban differential of expected wages. In other words, the generalized Harris-Todaro condition, eq. (15), arises as a long run equilibrium result of the agent-based migratory dynamics.

Figure 3 also shows that even after the urban share has reached an stable average value, there are small fluctuations around this average. Therefore, differently from the original Harris-Todaro model, our computational model shows in the long run equilibrium the reverse migration. This phenomenon has been observed in developing countries.
for a given value of a, the variation of wm practically does not change the equilibrium values of the urban share, the differential of expected wages and the unemployment rate. However, for a given wm, higher values of a make the urban sector less attractive due the reduction of the employment level. This causes a lower equilibrium urban share, a higher unemployment rate and a gap in the convergence of the expected wages.

The equilibrium values of the urban share, the differential of expected wages and unemployment rate do not have a strong dependence with wm. However, variations in g for a fixedwm, dramatically change the equilibrium values of the variable mentioned before. Higher values of g generate a lower urban concentration, a higher gap in the expected wages and a higher unemployment rate in the equilibrium.
The convergence of migratory dynamics for a urban share, compatible with historical data, is robust in relation to the variation of the key technological parameters, a and f. The impact of the variation of these parameters in the values of the equilibrium differential of expected wages, ( – wa), and the equilibrium urban unemployment rate, (1-Nm=Nu).

CONCLUSION

The dispersed and non-coordinated individual migration decisions, made based on local information, generate aggregate regularities. Firstly, the crucial assumption of Harris and Todaro, the principle that rural-urban migration will occur while the urban expected wage exceed the rural wage, comes out as spontaneous upshot of interaction among adaptative agents.

OGBONNA ANTHONY CHUKWUDUBEM
2017/243368
Email *
ogbonnatony54@gmail.com

21. Iwu Ifeanyi Julian says:

NAME: IWU IFEANYI JULIAN
REG.NO. 2017/249354
DEPARTMENT: CSS(Economics/Political Science)
EMAIL: iwujulian@gmail.com

Good morning Mr. President and the honourable members of this parliament.

FEI-RANIS MODEL
The Fei-Ranis model assumed a closed economy and from my perspective this hinders growth especially in the industrial sector. And my opinion the the economy should be opened is based on the fact that exports would improve the country’s terms of trade. The Fei-Ranis model also doesn’t take capital into account and does not indicate that the supply of land could be increased in the long run.

HARRIS-TODARO MODEL OF MIGRATION
The Harris-Todaro model of migration believes that the migration decision is based on expected income differentials between rural and urban areas. In my opinion, this model is flawed in that it assumes potential migrants are indifferent between a certain expected rural income and an uncertain expected urban income of the same magnitude and this model doesn’t take into account the urban unemployed living on a zero wage.

22. Ogbonnaya Victor Nnanna says:

NAME: Ogbonnaya Victor Nnanna
Reg no: 2017/249544
Department: Economics
Email: nnanna.ogbonnaya.249544@unn.edu.ng

LEWIS-FEI-RANIS MODEL (SURPLUS LABOUR THEORY)
This model was propounded by two economists Gustav Rani’s and John Fei in the article “The theory of Economic Development” also known as the surplus labour model. The theory relates to underdeveloped labour surplus and resources, poor economy in which the vast majority of the population is engaged in agriculture admits widespread unemployment and high rates of population growth. There exist surplus labour in the subsistence sector and this labour is made available for the industrial and urban sector but at a constant wage determined by minimum level of existence in traditional family farming because of disguised unemployment in agriculture.
ASSUMPTIONS:
They assume the economy has two sectors which are rural and urban sector.
They assume that there is surplus labour in subsistence sector.
They emphasize on the importance of saving in both sector.
Land has no role as a factor of production.
They assume that population growth is an exogenous phenomenon.
They assume that the output in agricultural sector is a function of land and labour only.
CRITICISM
The model ignored the cost involved in training the unskilled workers transferred from the subsistence sector.
The model assumed that besides labour there is an unlimited supply of entrepreneur in the capitalist sector and this is not true in most developed countries.
When labour is transferred from the subsistence sector, share of agricultural output falling to each one left in the agricultural sector will start rising.
The assumption that disguised unemployment exists in the agricultural sector were not accepted by many economists, according to them the production in the subsistence sector will be affected when labour is withdrawn from it.
The model assumed that there already exists a market for the industrial products in the country which is wrong as people of an underdeveloped country may not be able to purchase the products.
It is not easy to transfer labour from the subsistence sector to the capitalist sector by offering them an incentive of a little higher wage and the mobility of labour is very low.
COMPARISON OF THE FEI-RANIS MODEL TO THE REAL WORLD.
The model failed to recognize and put into consideration the sluggish economic situation present in less developed countries (eg Nigeria). If they had considered that they would find out that the agricultural backwardness was a result of the institutional structure that prevailed.
The model also assumed a closed model i.e there is absence of foreign trade in the economy which is unrealistic as raw materials and other products can’t be imported, an example is Japan.
CONCLUSION
These limitations do not undermine the importance of the Fei-Ranis model for the economic development of labour surplus countries. It systematically analyses the development process from the take-off to self sustained growth through the interaction of the agricultural sectors of an underdeveloped economy.

THE HARRIS-TODARO MODEL OF MIGRATION
The Harris-Todaro model is named after John R. Harris and Michael Todaro and was developed in 1970. The model assumes that the migration decision is based on expected income differential between rural and urban areas rather than just wage differential. In this model, an equilibrium is reached when the expected wage in urban areas is equal to the marginal product of an agricultural worker. The model assumes that unemployment is non existent in the rural agricultural sector. It is also assumed that rural agricultural production and the subsequent labour market is perfectly competitive, and this results in equality in the agricultural rural wage and agricultural marginal productivity.
ASSUMPTIONS OF THE HARRIS-TODARO MODEL
There are two sectors in the economy which are the rural and urban sector
The number of urban/manufacturing jobs available is exogenously fixed.
The model operates in the short run.
Capital is available in fixed quantities in the two sectors.
There is perfect competition among producers in both sectors.
The rural wage equals the rural marginal product of labour and the urban wage is exogenously determined.
CRITICISM OF THE HARRIS-TODARO MODEL
This model ignored the cost of rural-urban migration or the relatively higher costs of urban living which the migrants have to incur in the urban sector.
The model ignored the generation of savings as a source of financing subsidy.
The model does not specify alternate policy prescription such as giving a wage subsidy to the urban sector.
The model suggest non-distortionary lump sum tax to finance subsidy, but a lump sum tax is not usually non-distortionary
CONCLUSION
The migratory dynamics generated by agents that seek to adapt to the economic environment that they co-create leads the economy towards a long run equilibrium characterized by urban concentration with urban unemployment. When this is reached, the generalized Harris-Todaro condition is satisfied which is there will be stabilized rural-urban wage differential.

23. Ikechukwu Chizoba Peace
2017/249617
Economics

HARRIS-TODARO MODEL OF MIGRATION
INTRODUCTION
Harris Todaro model was named after John R-Harris and Michael Todaro developed on 1970 and it is used in welfare and development Economics to explain some of the rural-urban migration issues. This model is developed to explain rural-urban migration and it is based on two sector the rural and urban migration. His migration is studied under the context of employment and unemployment in developing countries. The Major scenario in this model is that the determinant of migration process is the differential features between the expected urban and rural wages. Based on the assumption that migration is based primarily on privately rational Economic calculations despite the existence of high urban unemployment, the Harris Todaro model posits that migration happens just in response to urban-rural differences in expected income than the actual earnings. And again that what causes this migration is an increase in a country’s urban population; the natural growth rate of the urban population, the re-classification of rural rural settlements as they grow and hit the magic number that makes them cities and towns, and rural-urban migration. Todaro’s model of migration does not advocate simply the rural-urban wage differences as the basis of migration as is claimed in all migration theories. According to him the migrants are rational in nature and calculative in their decision to shift to a particular city. He did not only take into consideration the wage differences but also the probability of getting a job in the urban area, so to him migration is determined more by rural-urban differences in expected income than the actual earnings.
H-T MODEL;
The model process is revisited under an agent based approach, that some factors are behind the migration of workers. Such factors like social learning by imitation. Todaro model posits that migration decision is based on expected income differentials. The high rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income is much more higher than expected rural income. Migration here depends primarily on the difference in wages between rural and urban labour markets. Where H-T takes urban employment to be Eu, urban unemployment Uu and L the total urban labour force. Put together W superscript ‘e’ and subscript ‘u’ becomes the urban wage times the urban employment rate (W x Eu)
To him there is nothing like unemployment in the rural area which is dominated by agricultural sector, so based on this assumption of rural agricultural production and the subsequent labour market is perfectly competitive, their agricultural wage is said to be equal to their agricultural marginal productivity. Todaro accepts the logistics of Lewis model but only with reservation. He alternates Lewis model based on his assumption that there would exist constant real urban wages until that of rural surplus exhausts. Because he discovered that in almost all the developing countries that the urban wages have been on the rise.
ASSUMPTIONS/ FEATURES
1.Migration decision is based on expected income differentials.
2. Rural labour market is perfectly competitive
3. Rural-urban migration process is revisited under an agent based approach
4. Probability of obtaining urban job is inversely related to the urban unemployment rate.
5. Migration is stimulated primarily by rational Economic consideration.
CRITICISM
Francis Cherunilam commenting on Todaro migration model, writes that while the model is correct holding that there’s no possibility of full employment in urban areas Francis was slightly against this claims and he was like it is not correct to believe that the act of migration is always rational and well calculated. And he also said that Todaro is also wrong in not giving factors in the migration process.
Secondly, the model assumes that employment transfer evolve at the same rate as capital accumulates in the modern sector.
Thirdly, Cole and Sanders (1985) have criticized the Harris Todaro model for not explicitly modelling the subsistence sector employing uneducated migrants, arguing that it flawed the job selection process and expected income calculations if, by lack of qualification, uneducated migrants could not find a job in the modern urban sector.

LEWIS-FEI-RANIS MODEL OF ECONOMIC GROWTH
The Lewis-fei-Ranis model of Economic growth is a dualism model in developmental or welfare Economics that has been developed by John C.H. fei and Gustav Rannis. It is also known as the surplus labour model.
Surplus labour is the key point Karl Marx used in critique of political economy. The term surplus labour means labour performed in excess of the labour needed to produce the means of livelihood of the workers, and surplus in this context means the additional labour a worker has to do in their job beyond earning their keep. This also explains the instability of the capital system, the capitalist pays his workers less than the marginal value of the goods usually only enough to maintain the workers at a subsistence Level.
Lewis model divided the economy of underdeveloped countries into two sectors namely the subsistence and capitalist sector. Capitalist sector is defined as that part of the economy which makes use of reproducible capital and pays capitalist for the use thereof. It is also known as capital intensive system. It also implies mainly the manufacturing sector of the economy
While the subsistence sector is all that part of the economy which does not make use of reproducible capital, it is identified with the agricultural sector of the economy, including petty retail trading, domestic service and the whole range of casual jobs. To Lewis transition from subsistence sector to the capitalist sector does not necessarily involve rural-urban migration. The new version of Lewis model of migration has been coined in terms of sectors of activity rather than the areas of residence, so this did not address the notion of rural-urban migration directly. The subsistence sector is characterized by zero or very low productivity ‘surplus ‘ labour and there is a high productivity in urban industrial sector into which labour from the subsistence sector is generally transferred.
Lewis feels that if a wage higher than the the institutional wage prevailing in the subsistence sector by a certain proportion of the institutional wage is fixed in the capitalist sector will be able to attract an unlimited quantity, the labour from subsistence sector and this will enable the capitalist sector to expand. And this in turns leads to generation of more savings in the capitalist sector.
The model assumed that there exists surplus labour in the subsistence sector. It includes labour whose marginal productivity is zero as well as that whose marginal productivity is positive but is less than the institutional wage.
ASSUMPTIONS
1. Modern sector employment creation and labour transfer rate is proportional to the rate of capital accumulation in the sector. That is MPL is positive in the modern sector and that labour could be transferred to this sector at zero cost.
2. Surplus labour exists in rural areas while the urban areas is said to have full employment
3. Reinvestment of local economy capitalist profits instead of the profits being sent abroad
4. Assumption of diminishing returns in the modern sector; mostly the industrial areas
5. That if a modern labour sector was competitive it is guaranteed a continuous existence of real urban wages to be a point that surplus labour is exhausted in the real sector.
CRITICISM
If marginal productivity of labour in agricultural sector is negligible, zero or negative, it’s obvious that there is a disguised unemployment in agriculture. Surplus labour, wage determination and the mechanism of labour mobility are unclear, and because of this development could not move further, and this has prevented it’s use in empirical research.
Lewis assertion that subsistence sector has surplus labour and capital sector have full employment is not necessarily true because in developing countries, capital sector do not provide full employment.

24. FERDINAND DANIEL NWEKE says:

NAME: FERDINAND DANIEL NWEKE
Reg No: 2017/245020
Email: bookn1991@gmail.com
Lewis- Fei- Ranis model of Economic Growth

The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.

CONCLUSION AND DRAW OPINIONS
Base on this model we can see that nation like Nigeria should invest in both sector to increase it productivity and ensure rapid development of the nation through stopping of transfer of labour from one sector to another , the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply.

Haris Todara model of migration

INTRODUCTION
In this work will are looking at the Harris -Todara Model of migration theory. The hypothesis and predictions of Harris-Todaro model have been subjected to econometric evaluation and have been corroborated by several studies .The key hypothesis of Harris and Todaro are that migrants react mainly to economic incentives, earnings differentials, and the probability of getting a job at the destination have influence on the migration decision. In other words, these authors posit that rural-urban migration will occur while the urban expected wage exceed the rural wage. From this crucial assumption, as denominated by Harris-Todaro , is deduced that the migratory dynamics leads the economic system toward an equilibrium with urban concentration and high urban unemployment
The Harris–Todaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and welfare economics to explain some of the issues concerning rural-urban migration. The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This implies that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.In the model, an equilibrium is reached when the expected wage in urban areas (actual wage adjusted for the unemployment rate), is equal to the marginal product of an agricultural worker.
Assumption
Harris and Todaro studied the migration of workers in a two-sector economic system, namely, rural sector and urban sector. The difference between these sectors are the type of goods produced, the technology of production and the process of wage determination. The rural sector is specialized in the production of agricultural goods. The productive process of this sector can be described by a Cobb-Douglas production function:
where Ya is the production level of the agricultural good, Na is the amount of workers used in the agricultural production, Aa > 0 and 0 < f 0 and 0 0 are a parametric constants. g is the elasticity of p with respect to the ratio Ym/Ya.

The overall population of workers in the economy is N, which is kept constant during the whole period of analysis. By assumption there are only two sectors and rural prices are wholly flexible, which implies that there is full employment in the rural area, i.e., all workers living at the rural sector are employed at any period. Then at any period the following equality is verified.
Relating to the Nigerian economy,In terms of pro-poor economic growth, the Harris-Todaro model and other multisector-labor-market models can help policy makers avoid two mistakes. One is to assume that development efforts should be channeled to the sectors where the poor are. The other is to assume that efforts should always be focused on getting the poor out of the sectors in which they now are. Careful cost-benefit analysis based on well-specified labor-market models is required to decide among such alternatives.

At equilibrium With the random matching of workers to available jobs, the ratio of available jobs to total job seekers gives the probability that any person moving from the agricultural sector to the urban sector will be able to find a job. As a result, in equilibrium, the agricultural wage rate is equal to the expected urban wage rate, which is the urban wage multiplied by the employment rate.

COMPARISON WITH THE REAL WORLD
The successful East Asian Countries of Taiwan, Korea, and Singapore, as well as the not-so successful countries like Brazil, Chile, and several others, is usually the example that is given to explain the comparison of this model with the real world. It is argued (Balassa 1989) that the import-substitution policies in many less-developed countries are based against the primary agricultural sector which is the exporting sector while the export-oriented polices provide similar incentives to the two sectors. Countries that adopt inward-looking strategies, the limitation of the domestic markets and the lack of competition leads to the allocative and technological inefficiency. As in contrast with the onward-looking countries which are able to mobilize domestic resources effectively in the production if goods that are in competition in the wide markets worldwide which would result in technology. It is now in our own opinion that majority of the less-developed countries have approached what is said to be the take-off stage as described by Lewis (1954) and Fei and Ranis (1961) characterized by the rapidly growing economies, transfer of labour from the traditional sector, and the persistent or continuous problems of the high urban unemployment and underemployment rates.
CONCUSSION
1). Urban wages (wu) increase in the urban sector (le), increasing the expected urban income.
2). Agricultural productivity decreases, lowering marginal productivity and wages in the agricultural sector (wr), decreasing the expected rural income.

25. FERDINAND DANIEL NWEKE says:

NAME: FERDINAND DANIEL NWEKE

Reg No: 2017/245020

Email: bookn1991@gmail.com

Lewis- Fei- Ranis model of Economic Growth

The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.

CONCLUSION AND DRAW OPINIONS
Base on this model we can see that nation like Nigeria should invest in both sector to increase it productivity and ensure rapid development of the nation through stopping of transfer of labour from one sector to another , the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply.

Haris Todara model of migration

INTRODUCTION
In this work will are looking at the Harris -Todara Model of migration theory. The hypothesis and predictions of Harris-Todaro model have been subjected to econometric evaluation and have been corroborated by several studies .The key hypothesis of Harris and Todaro are that migrants react mainly to economic incentives, earnings differentials, and the probability of getting a job at the destination have influence on the migration decision. In other words, these authors posit that rural-urban migration will occur while the urban expected wage exceed the rural wage. From this crucial assumption, as denominated by Harris-Todaro , is deduced that the migratory dynamics leads the economic system toward an equilibrium with urban concentration and high urban unemployment
The Harris–Todaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and welfare economics to explain some of the issues concerning rural-urban migration. The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This implies that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.In the model, an equilibrium is reached when the expected wage in urban areas (actual wage adjusted for the unemployment rate), is equal to the marginal product of an agricultural worker.
Assumption
Harris and Todaro studied the migration of workers in a two-sector economic system, namely, rural sector and urban sector. The difference between these sectors are the type of goods produced, the technology of production and the process of wage determination. The rural sector is specialized in the production of agricultural goods. The productive process of this sector can be described by a Cobb-Douglas production function:
where Ya is the production level of the agricultural good, Na is the amount of workers used in the agricultural production, Aa > 0 and 0 < f 0 and 0 0 are a parametric constants. g is the elasticity of p with respect to the ratio Ym/Ya.

The overall population of workers in the economy is N, which is kept constant during the whole period of analysis. By assumption there are only two sectors and rural prices are wholly flexible, which implies that there is full employment in the rural area, i.e., all workers living at the rural sector are employed at any period. Then at any period the following equality is verified.
Relating to the Nigerian economy,In terms of pro-poor economic growth, the Harris-Todaro model and other multisector-labor-market models can help policy makers avoid two mistakes. One is to assume that development efforts should be channeled to the sectors where the poor are. The other is to assume that efforts should always be focused on getting the poor out of the sectors in which they now are. Careful cost-benefit analysis based on well-specified labor-market models is required to decide among such alternatives.

At equilibrium With the random matching of workers to available jobs, the ratio of available jobs to total job seekers gives the probability that any person moving from the agricultural sector to the urban sector will be able to find a job. As a result, in equilibrium, the agricultural wage rate is equal to the expected urban wage rate, which is the urban wage multiplied by the employment rate.

COMPARISON WITH THE REAL WORLD
The successful East Asian Countries of Taiwan, Korea, and Singapore, as well as the not-so successful countries like Brazil, Chile, and several others, is usually the example that is given to explain the comparison of this model with the real world. It is argued (Balassa 1989) that the import-substitution policies in many less-developed countries are based against the primary agricultural sector which is the exporting sector while the export-oriented polices provide similar incentives to the two sectors. Countries that adopt inward-looking strategies, the limitation of the domestic markets and the lack of competition leads to the allocative and technological inefficiency. As in contrast with the onward-looking countries which are able to mobilize domestic resources effectively in the production if goods that are in competition in the wide markets worldwide which would result in technology. It is now in our own opinion that majority of the less-developed countries have approached what is said to be the take-off stage as described by Lewis (1954) and Fei and Ranis (1961) characterized by the rapidly growing economies, transfer of labour from the traditional sector, and the persistent or continuous problems of the high urban unemployment and underemployment rates.

CONCUSSION
1). Urban wages (wu) increase in the urban sector (le), increasing the expected urban income.
2). Agricultural productivity decreases, lowering marginal productivity and wages in the agricultural sector (wr), decreasing the expected rural income.

26. NAME: OKEKE JUDE CHIMOBI

REG NO: 2017/249556

The Lewis-Fei-Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis. It can also be understood as an extension of the Lewis model. The model is also known as the Surplus Labour model that recognizes the presence of a dual economy comprising both the modern and the primitive sectors, and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labour from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labour supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials.

The Lewis model is criticized on the grounds that it neglects agriculture. Fei–Ranis model goes a step beyond and states that agriculture has a very major role to play in the expansion of the industrial sector. In fact, it says that the rate of growth of the industrial sector depends on the amount of total agricultural surplus and on the amount of profits that are earned in the industrial sector. So, larger the amount of surplus and the amount of
surplus put into productive investment and larger the amount of industrial profits earned, the larger will be the rate of growth of the industrial economy. As the model focuses on the shifting of the focal point of progress from the agricultural to the industrial sector, Fei and Ranis believe that the ideal shifting takes place when the investment funds from surplus and industrial profits are sufficiently large so as to purchase industrial capital goods like plants and machinery. These capital goods are needed for the creation of employment opportunities. Hence, the condition put by Fei and Ranis for a successful transformation is that the rate of increase of capital stock & rate of employment opportunities should be greater than the rate of population growth.

ASSUMPTIONS OF THE LEWIS-FEI-RAINIS MODEL
 The model assumes that a developing economy has a surplus of unproductive labour in the agricultural sector.
 Labourers are attracted to the growing manufacturing sector where higher wages are offered.
 Entrepreneurs in the manufacturing sector make profit because they charge a price above the fixed wage rate.
 The model assumes that these profits will be reinvested in the business as a fixed capital.
 An advanced manufacturing sector means an economy has moved from a traditional to an industrialized one.
 According to Lewis, the supply of labour is perfectly elastic. In other words, the supply of labour is greater than demand for labour.
 There is a duel economy i.e., the economy is characterized by a traditional, over-populated rural subsistence sector furnished with zero MPL, and the high productivity modern industrial sector.

STUDY OBSERVATION
Based on the observation of this study, Lewis-Fei-Ranis model of economic growth is considered to be more realistic in comparison to other economic growth models and based on the the fact that some of its assumptions are realistic in an actual economy. The model assumes that a developing economy has a surplus of unproductive labour in the agricultural sector which is true if we consider Nigeria as a case study and some other developing economies like Ghana, Gambia, etc

The model also assume a duel economy i.e., the Industrial and agricultural sector. Lewis believe that workers will move from Agricultural sector to the industrial sector as a result of high wage rate in the industrial sector. this movement or transfer of a good percentage labour force from agricultural to industrial sector is a sign of development and economic growth which is true in many countries like China, India, Turkey etc. In the case Nigeria the Federal Government of Nigeria does not necessarily have to move surplus labour that exists in the rural areas to the urban areas but instead infrastructural facilities should be provided equally to both the rural and urban areas of the country (Balance Growth Theory).

The Harris–Todaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and welfare economics to explain some of the issues concerning rural-urban migration. The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This implies that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.
In the model, an equilibrium is reached when the expected wage in urban areas (actual wage adjusted for the unemployment rate), is equal to the marginal product of an agricultural worker. The model assumes that unemployment is non-existent in the rural agricultural sector. It is also assumed that rural agricultural production and the subsequent labour market is perfectly competitive. As a result, the agricultural rural wage is equal to agricultural marginal productivity. In equilibrium, the rural to urban migration rate will be zero since the expected rural income equals the expected urban income. However, in this equilibrium there will be positive unemployment in the urban sector. The model explains internal migration in China as the regional income gap has been proved to be a primary drive of rural-urban migration, while urban unemployment is local governments’ main concern in many cities.

ASSUMPTIONS OF THE HARRIS-TODAROS MODEL
1. There are two sectors in the economy: the rural or agricultural sector (A) and the urban or manufacturing sector (M).
2. The model operates in the short run.
3. Capital is available in fixed quantities in the two sectors.
4. The number of urban/manufacturing jobs available is exogenously fixed.
5. Rural-urban migration continues so long as the expected urban real income is more than the real agricultural income.
6. The rural wage equals the rural marginal product of labor and the urban wage is exogenously determined.
7. There is perfect competition among producers in both sectors.

MODEL APPLICATION:

The model is applicable to real life economic situation considering that the migratory dynamics generated by agents that seek to adaptate to the economic environment that they co-create leads the economy toward a long run equilibrium characterized by urban concentration with urban unemployment. When this long run equilibrium is reached, the generalized Harris-Todaro condition is satisfied, i.e., there is a stabilization of the rural-urban expected wage differential.

Nigeria government can adopt this theory of economic growth is they wish to reduce the rural-urban migration which is cause by high urban unemployment. To this, the Federal government must carryout more expansionary fiscal policy on the rural areas in Nigeria. This policy with increase the rate of employment in rural areas and also
will increase the expect income of the rural people.

27. Name: Idu Ifeanyi Peculiar
Reg No: 2017/249511
Email: ifeanyipeculiaridu@gmail.com
Blog: iduifeanyi1999.blogspot.com

1. LEWIS-FEI-RANIS MODEL (SURPLUS LABOUR THEORY)
The Fei–Ranis model of economic growth is a dualism model that has been developed by John C.H. Fei and Gustav Rani’s and can be understood as an extension of the lewis model. He takes into account the economic situation of underdeveloped and underemployment of resources. There is surplus labour(marginal productivity is zero) in the agricultural sector and this labour is made available for the industrial and urban sector but at a constant wage. later on, if the surplus labour is been exhausted then only a rising wage rate will draw more labour out of agriculture.
ASSUMPTION (ARGUMENTS)
An economy starts with 2 sectors:A rural agricultural sector and urban industrial sector.
Agriculture generally under-employs workers and marginal productivity of labour is virtually zero.
Transferring workers out of agriculture doesn’t reduce productivity in the whole economy.
Labour is then released for work in the more productive urban sector.
Industrialization is now possible,given the increase in supply of workers who have moved from the land.
Industrial firms starts to make profit which can be re-invested into more industrialization and capital starts to accumulate.
As soon as capital accumulate further economy development can sustain itself.
CRITICISM
Fei-Ranis model was criticized on multiple grounds one of which is that they didn’t pay attention to the slow economic situation in developing countries, they also failed to distinguish between wage labour and household labour which is important in evaluating prices in an underdeveloped economy, they also neglected seasonal unemployment which occurs as a result of seasonal change in labour demand.
In conclusion, the Fei-Ranis model is a dualism model. They are of the view that both the agricultural and the industrial sectors are necessary in order to spur economic development in a developing country. The agricultural sector supplies excess labour to the industrial sector to boost industrial output in order to satisfy the demand. Despite this model lagging in some areas like not having a clear understanding of the sluggish economic situation prevailing in developing countries, its still a realistic model of economic development as its application is seen in our world today, surplus labour in the agricultural sector is reallocated to the industrial sector to enhance productivity without neglecting the agricultural sector, so these two sectors as we can see co-exist in our economy as they both have major roles to play in order to achieve economic development. Hence, the dualistic nature of the model.
2. HARRIS -TODARO MODEL OF MIGRATION
Also known as the structural change model. It focuses on the mechanism by which underdeveloped economy transform their domestic economic structure from heavy emphasis on traditional subsistence agriculture to a more modern urbanized and industrial diverse manufacturing service economy. It also apply tool of neo classical prices and resource allocation theory and modern econometrics to describe how transformation processes take place. By structural transformation that is a way that the contribution to national income by the manufacturing sector surpasses the contribution by agricultural sector.
Michael Todaro (1969) and John Harris (Harris and Todaro 1970) propounded the most notable modern thinking. The Harris-Todaro Model is an equilibrium version of the Todaro Migration Model which explains the rural-urban migration as an economically rational process despite the high urban unemployment. The importance of this was as a result of the Keynesian Revolution which says “equilibrium could occur or come about even when there is a chronic level of unemployment in the urban sector”. This implies that the economy could still be in balance even with the existence of a severe urban unemployment. It has also been deduced that the most important factor why urban population was more than of the rural sector was due to the fact that labour from the rural sector moved to the urban sector to search for better opportunities.
In the situation of a dualistic model, the rural sector is letting go of much labour too quickly while the urban sector is hiring or accepting labour too slowly as it is assumed that the urban sector is capital-intensive (Lewis 1965). Unemployed in the urban area is the cause of poverty and underemployment in the Third World Countries (Lubell 1988). The contribution of Todaro is the introduction of the possibility of employment as a factor in the decision-making process of a potential migrant. He devised what he called a two-stage process in the less-developed countries.
The first stage is characterized by where the labour migrant decides to move from the rural sector for a period of time. The second stage is then reached when that labour migrant has gotten a more permanent job in the modern or urban sector.
According to Todaro, the probability or tendency of getting a job depends on the size of the urban population that is employed, number of newly created jobs in the urban sector, as well as the length or duration a labour migrant has been in that sector. Consequently it implied that according to Todaro, the longer a labour migrant has been in the manufacturing sector, the more likely he or she is to get a job there. An extension of this was done by Harris and Todaro (1970), where they explained that the urban wage is equal to the expected value of the urban wage and this formed the notable Harris-Todaro Equation which is of the form:
Wa = βWm where,
Wa = Flexible wage in the agricultural sector is equal to the value of the marginal product in that sector, β = Probability of employment (dependent on the three (3) factors listed earlier), and Wm = Wage in the manufacturing sector which is assumed fixed or constant institutionally either because of the involvement of the union’s activities or a friendly government towards the workers in the modern sector.
THE BASIC MODEL
The Harris-Todaro Model would be referred to as the H – T Model from henceforth, assume that migration from the rural to the urban areas depends primarily on the difference in wages between the rural and urban labour markets. That is the expected urban wage is the actual urban wage multiplied by the probability of getting a job, or Weu = PWu where,
Weu = Expected Urban Wage and P = Probability of getting a job where P is expressed as: P = where,

Eu = Urban Employment, Uu = Urban Unemployment and L = Total Labour Force. Another assumption of the Harris-Todaro is that all the members of the urban labour force have equal chances of obtaining or getting the jobs available for them. So Weu = Urban Wage multiplied by the Urban Employment Rate.
POLICY IMPLICATIONS OF THE H – T MODEL
The H – T Model has some impressing implications from the policy point of view. Let’s take for an instance, if the government of a country is concerned with fostering industrial development in an urban area, employment would increase and this would lead to an increase in productive of getting urban employment in the minds of the rural inhabitants. Migration to the urban area would then increase and the outcome would be that the unemployment rate in the urban areas would rise more than how it was before the development occurred. Due to this, labour migrants would prefer to accept the wage in the urban informal sector than going back to wait for long for jobs that would not come in time as urban employment is now in equilibrium. However, the effect of this is that the earnings in the urban modern industrial sectors would be more or higher than those in the rural traditional sectors. The long-term solution to this issue would be to fix a wage policy for the two sectors that would reduce the real income differences between the two sectors.
THE ASSUMPTIONS OF THE MODEL
In analyzing the H – T Model, there are some assumptions alongside those listed before which include:
There is fixed amounts of labour (L) and capital (K) factor inputs.
Capital is fully employed but labour unemployment exists in the urban sector due to the fixed urban wage, W is higher than the flexible rural wage, w.

In conclusion, even though this migration creates unemployment and induces informal sector growth, this behavior is economically rational and utility-maximizing in the context of the Harris-Todaro model. As long as the migrating economic agents have complete and accurate information concerning rural and urban wage rates and probabilities of obtaining employment, they will make an expected income-maximizing decision.
Another issue is that inducing minimum wages creates labour market distortions. Therefore, policy makers should not set the minimum wage rate. In addition, simulations showed that different policies’ outcomes depend on elasticity of labour demand in different sectors and on marginal product of labour.
As Harris and Todaro suggested the first-best policy would be subsidizing manufacturing along with restrictions of rural migration.

28. Name: Idu Ifeanyi Peculiar
Reg No: 2017/249511
Email: ifeanyipeculiaridu@gmail.com
Blog: iduifeanyi.blogspot.com

1. LEWIS-FEI-RANIS MODEL (SURPLUS LABOUR THEORY)
The Fei–Ranis model of economic growth is a dualism model that has been developed by John C.H. Fei and Gustav Rani’s and can be understood as an extension of the lewis model. He takes into account the economic situation of underdeveloped and underemployment of resources. There is surplus labour(marginal productivity is zero) in the agricultural sector and this labour is made available for the industrial and urban sector but at a constant wage. later on, if the surplus labour is been exhausted then only a rising wage rate will draw more labour out of agriculture.
ASSUMPTION (ARGUMENTS)
An economy starts with 2 sectors:A rural agricultural sector and urban industrial sector.
Agriculture generally under-employs workers and marginal productivity of labour is virtually zero.
Transferring workers out of agriculture doesn’t reduce productivity in the whole economy.
Labour is then released for work in the more productive urban sector.
Industrialization is now possible,given the increase in supply of workers who have moved from the land.
Industrial firms starts to make profit which can be re-invested into more industrialization and capital starts to accumulate.
As soon as capital accumulate further economy development can sustain itself.
CRITICISM
Fei-Ranis model was criticized on multiple grounds one of which is that they didn’t pay attention to the slow economic situation in developing countries, they also failed to distinguish between wage labour and household labour which is important in evaluating prices in an underdeveloped economy, they also neglected seasonal unemployment which occurs as a result of seasonal change in labour demand.
In conclusion, the Fei-Ranis model is a dualism model. They are of the view that both the agricultural and the industrial sectors are necessary in order to spur economic development in a developing country. The agricultural sector supplies excess labour to the industrial sector to boost industrial output in order to satisfy the demand. Despite this model lagging in some areas like not having a clear understanding of the sluggish economic situation prevailing in developing countries, its still a realistic model of economic development as its application is seen in our world today, surplus labour in the agricultural sector is reallocated to the industrial sector to enhance productivity without neglecting the agricultural sector, so these two sectors as we can see co-exist in our economy as they both have major roles to play in order to achieve economic development. Hence, the dualistic nature of the model.
2. HARRIS -TODARO MODEL OF MIGRATION
Also known as the structural change model. It focuses on the mechanism by which underdeveloped economy transform their domestic economic structure from heavy emphasis on traditional subsistence agriculture to a more modern urbanized and industrial diverse manufacturing service economy. It also apply tool of neo classical prices and resource allocation theory and modern econometrics to describe how transformation processes take place. By structural transformation that is a way that the contribution to national income by the manufacturing sector surpasses the contribution by agricultural sector.
Michael Todaro (1969) and John Harris (Harris and Todaro 1970) propounded the most notable modern thinking. The Harris-Todaro Model is an equilibrium version of the Todaro Migration Model which explains the rural-urban migration as an economically rational process despite the high urban unemployment. The importance of this was as a result of the Keynesian Revolution which says “equilibrium could occur or come about even when there is a chronic level of unemployment in the urban sector”. This implies that the economy could still be in balance even with the existence of a severe urban unemployment. It has also been deduced that the most important factor why urban population was more than of the rural sector was due to the fact that labour from the rural sector moved to the urban sector to search for better opportunities.
In the situation of a dualistic model, the rural sector is letting go of much labour too quickly while the urban sector is hiring or accepting labour too slowly as it is assumed that the urban sector is capital-intensive (Lewis 1965). Unemployed in the urban area is the cause of poverty and underemployment in the Third World Countries (Lubell 1988). The contribution of Todaro is the introduction of the possibility of employment as a factor in the decision-making process of a potential migrant. He devised what he called a two-stage process in the less-developed countries.
The first stage is characterized by where the labour migrant decides to move from the rural sector for a period of time. The second stage is then reached when that labour migrant has gotten a more permanent job in the modern or urban sector.
According to Todaro, the probability or tendency of getting a job depends on the size of the urban population that is employed, number of newly created jobs in the urban sector, as well as the length or duration a labour migrant has been in that sector. Consequently it implied that according to Todaro, the longer a labour migrant has been in the manufacturing sector, the more likely he or she is to get a job there. An extension of this was done by Harris and Todaro (1970), where they explained that the urban wage is equal to the expected value of the urban wage and this formed the notable Harris-Todaro Equation which is of the form:
Wa = βWm where,
Wa = Flexible wage in the agricultural sector is equal to the value of the marginal product in that sector, β = Probability of employment (dependent on the three (3) factors listed earlier), and Wm = Wage in the manufacturing sector which is assumed fixed or constant institutionally either because of the involvement of the union’s activities or a friendly government towards the workers in the modern sector.
THE BASIC MODEL
The Harris-Todaro Model would be referred to as the H – T Model from henceforth, assume that migration from the rural to the urban areas depends primarily on the difference in wages between the rural and urban labour markets. That is the expected urban wage is the actual urban wage multiplied by the probability of getting a job, or Weu = PWu where,
Weu = Expected Urban Wage and P = Probability of getting a job where P is expressed as: P = where,

Eu = Urban Employment, Uu = Urban Unemployment and L = Total Labour Force. Another assumption of the Harris-Todaro is that all the members of the urban labour force have equal chances of obtaining or getting the jobs available for them. So Weu = Urban Wage multiplied by the Urban Employment Rate.
POLICY IMPLICATIONS OF THE H – T MODEL
The H – T Model has some impressing implications from the policy point of view. Let’s take for an instance, if the government of a country is concerned with fostering industrial development in an urban area, employment would increase and this would lead to an increase in productive of getting urban employment in the minds of the rural inhabitants. Migration to the urban area would then increase and the outcome would be that the unemployment rate in the urban areas would rise more than how it was before the development occurred. Due to this, labour migrants would prefer to accept the wage in the urban informal sector than going back to wait for long for jobs that would not come in time as urban employment is now in equilibrium. However, the effect of this is that the earnings in the urban modern industrial sectors would be more or higher than those in the rural traditional sectors. The long-term solution to this issue would be to fix a wage policy for the two sectors that would reduce the real income differences between the two sectors.
THE ASSUMPTIONS OF THE MODEL
In analyzing the H – T Model, there are some assumptions alongside those listed before which include:
There is fixed amounts of labour (L) and capital (K) factor inputs.
Capital is fully employed but labour unemployment exists in the urban sector due to the fixed urban wage, W is higher than the flexible rural wage, w.

In conclusion, even though this migration creates unemployment and induces informal sector growth, this behavior is economically rational and utility-maximizing in the context of the Harris-Todaro model. As long as the migrating economic agents have complete and accurate information concerning rural and urban wage rates and probabilities of obtaining employment, they will make an expected income-maximizing decision.
Another issue is that inducing minimum wages creates labour market distortions. Therefore, policy makers should not set the minimum wage rate. In addition, simulations showed that different policies’ outcomes depend on elasticity of labour demand in different sectors and on marginal product of labour.
As Harris and Todaro suggested the first-best policy would be subsidizing manufacturing along with restrictions of rural migration.

29. Chidera Umelo says:

NAME: CHIDERA NICOLE UMELO
REGISTERATION NUMBER: 2017/249589
EMAIL: nicoleumelo@gmail,com

THE HARRIS- TODARO MODEL OF MIGRATION.
The Harris Todaro model is named after John. R. Harris and Michael Todaro. It was developed in1970. It has been used in development economics and welfare economics to explain some of the issues concerned with rural-urban migration. Its main assumption is that migration decision is based on expected income differences between rural and urban areas and not just wage differences. To them, rural- urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.

THE HISTORICAL CONTEXT OF THE MODEL.
In the 1960’s, the government of Kenya, a newly independent country at the time, faced serious difficulties concerning employment. The unemployment levels in the Kenyan capital city- Nairobi, and other major cities of Kenya at the time had been high and rising. To solve this burgeoning problem agreements were reached in the effect that private and public sector employers in Kenya, agreed to increase their levels of employment if labor unions agreed to hold wages at their current levels as at the time. The expectation of this agreement was that urban unemployment in Kenya would be eradicated or even decreased. However, a cobra effect of this policy agreement was noted in the country. Rather than reduce the high levels of unemployment in Kenya, what these agreements served to achieve was a greater increase in the unemployment levels witnessed in the urban sectors of Kenya. It was as a result of this occurrence that John Harris and Michael Todaro formulated what I now known as the Harris- Todaro model or more formally, the rural- urban migration model.
Apart from the problem of rising unemployment in Kenya, there was also the problem of urban migration. The migration was as a result of the differences in expected wages of the laborers. It was seen that the urban wage was much higher than the rural wages and this was considered as the major cause of unemployment.

AN INDEPTH DISCUSSION OF THE HARRIS TODARO MODEL.
As a result of the Kenyan Paradox, John Harris and Michael Todaro formulated the Harris- Todaro model in 1979. First, the model assumes that the real wages i.e. wages adjusted for the cost of living differences in the country, are higher in urban sector jobs than in rural traditional sector jobs. Again, to be hired in the formal sector jobs, one has to be physically present in the urban sector. As a result of this, more workers search for formal sector jobs than are hired since employers employ a few workers but not all. Hence, the model sought to answer the question of why rural-urban migration is still taking place in spite of the high level of unemployment in the urban sector.
In the model, migration is seen as an economic model that is made based on wages and the probability of unemployment. To make this decision, migrants in the rural areas calculate the expected real income of the urban areas and decide to move if it exceeds the expected real income of the rural areas. The idea behind this model is that the urban minimum wage is higher than the minimum wage paid to the rural labor. This results in a wage difference between both sectors of the economy. To answer the question, rural works continue to migrate to urban areas, despite urban unemployment, as a result of the possibility of higher wages/ earnings in the urban sectors. This migration continues in so far as there is a possibility for workers to increase their earnings in the urban sector. The model is further supported by the fact that some individuals might obtain arranged employment before they leave the rural sector for the urban sector, and even those who do not have an arranged employment may decide to leave the rural sector with the hopes of finding jobs in the urban sector, although most of them would still join the pool of unemployed individuals in the urban sector. This explains the high rate of rural- urban migrants despite the high rate of urban unemployment.

ASSUMPTIONS OF THE HARRIS- TODARO MODEL
The Harris-Todaro model has the following assumptions:
• The economy is a small open economy
• The economy consists of two sectors
a. The agricultural rural sector (sector 1)
b. The manufacturing urban sector (sector 2)
• There are three types of production factors (i.e. factors of production) in the economy;
a. Specific production factor in sector 1 (k1)
b. Specific production factor in sector 2 (k2)
c. Labor (L), which is employed by bot factors and mobile between factors
Note: the specific production factors in each sector (i.e. k1 and k2) are immobile between sectors and k2 consists of not just plants, equipment and machinery, but also social infrastructure such as good roads, airports etc., so that as the social infrastructure increases, k2 also increases.
• Marginal productivity of labor equals the real wage in each sector
• There is mobility of labor between sectors due to the wage gap between sectors.
• The expected wage in each sector is obtained by multiplying the actual wage of each sector (i.e. w1 and w2) by the probability of finding a job in the sector.
• In the model, the probability of finding a job is equal to the rate of employment.
• I the rural sector, it is assumed that wages are flexible. Hence, there is no unemployment I the rural sector and so the probability of obtaining a job in the rural sector is equal to 1 or unity, whereas, in the urban sector, the probability of obtaining a job is less than 1 (or unity). This situation in the urban sector is caused by unemployment.

EXPLANATION OF THE BASIC FORMALISM OF THE HARRIS TODARO MODEL.
Stating the Harris Todaro model in mathematical connotations;
1. Let wA be the real wage rate (also marginal productivity of labor) in the rural agricultural sector.
2. Let wM be the actual real wage rate in the urban manufacturing sector of the economy.
3. Let Le be the number of jobs available in the urban sector, which should be equal to the number of employed urban workers.
4. Let LU, be the total number of job seekers in the urban sector- both employed and unemployed.
5. Let wu be the wage rate in the urban sector that is set by the government, using a minimum wage law (it should be noted that wu is expected to be greater than wu)
Based on the Harris Todaro model, rural-urban migration will only occur if
Wr (Le /LU) × Wu
This means that when the expected rural wage rate is greater than the employment rate (or probability of obtaining an urban job) multiplied by the actual real urban wage rate, then there is greater incentive to work in the rural area than the urban area. Hence, urban-rural migration occurs.
Again, equilibrium occurs when;
Wr = (Le /LU) × Wu
This means that when the expected rural wage rate is equal to the employment rate (or probability of obtaining an urban job) multiplied by the actual real urban wage rate, then the equilibrium condition in the economy has been reached. i.e. there is no incentive for workers to move from urban-rural areas or from rural-urban areas.

THE LEWIS FEI- RANIS MODEL.
The Lewis Fei-Ranis model was developed by John. C.H Fei and Gustav Ranis. The model is believed to e an extension of the Lewis model. The model is also called the surplu labor theory and it emphasizes the presence of a dual economy (i.e. the principle of dualism). this principle states that there are only two sectors of the economy i.e. the modern industrial sector and the primitive agricultural sector. This model also takes into consideration the problems of unemployment and the underemployment of scarce resources. In this theory, the two sectors of the economy coexist together and development of the economy occurs only when there is focus on the development of the modern sector over the rural sector. This development is achieved by transferring labor from the agricultural sector to the industrial sector to increase the industrial output.
The Lewis Fei- Ranis model was developed in 1958 by Lewis and later extended in 1961 by Fei and Ranis. The model assumed a dual economy, comprising of the traditional and the modern sectors. The traditional sector (according to the model), comprises of the agricultural sector with surplus labors, whereas the modern sector comprises of the urban industrial sector with industrial output. According to the model, because the modern sector attracts workers from the rural sector, there is a high rate of rural –urban migration. This is because workers believe that there are better wages, higher incomes and more savings in the urban areas than is attainable in the rural areas. This causes them to move from the rural- urban areas in order to enjoy these advantages. The ensuing migration generates surplus foods, more incomes and more savings and investments among the rural people.
More formally, the Lewis model believed that surplus labor in the developing economies should be reallocated to the capitalist sector i.e. to industries.

30. Izuogu Chiamaka Goodluck
2017/242101
Economics Education
chiamaka.izuogu.242101@unn.edu.ng
Unncareerinfo
LEWIS FEI- RANIS MODEL OF ECONOMIC GROWTH
The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics hithat was developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes into account the economic situation of unemployment and underemployment of resources unlike many other growth models that consider underdeveloped countries to be homogenous in nature.
According to this theory, the primitive sector consists of the existing agricultural sector and the modern sector which is rapidly emerging beginning as small industrial sector. Both the sectors co-exist in the economy and therein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is an augmentation of industrial output. This is done by transfer of labour from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from limitations of labour supply. At the same time, growth in the agricultural sector must not be neglected and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economics of underdeveloped countries.
Thus we find that whereas Lewis had failed to offer a satisfactory explanation of this subsistence sector and ignored the real impact of population growth on the choice of capital intensity on the process of surplus labour absorption. Moreover, FR model emphasized upon the simultaneous growth of agri. and industrial sectors. Thus FR model believes in ‘Balanced Growth’ in the take-off stage. It means that there should be a simultaneous investment in both agri, sector and industrial sector. According to FR model in the beginning the surplus rises; such surplus will be available as a capital in the take-off stage. Some part of this surplus will be used in agri. development, while some part will be reploughed in industrial development. As a result, both agri. and industrial sectors will grow under ‘Balanced Growth’ pattern
Basics of the model
This model is treated as an improvement over Lewis model of unlimited supply of labor.
This theory is concerned with a poor economy which has following properties:
(i) There is an abundance of labour in such UDC and shortage of natural resources.
(ii) The population growth rate is very high which results in mass unemployment in the economy.
(iii) The major share of population is engaged in agriculture. But agriculture sector is stagnant. Hence, the marginal productivity of labour is zero and negative in agriculture sector.
(iv) There are certain non-agrarian sectors in the economy where there is reduced use of capital.
(v) There is a dynamic industrial sector in the economy.
Thus the model suggests that:
“Economic development would be taking place if agricultural laborers are transferred to industrial sector where their productivity will increase”.
As we told earlier that it is a dual economy where there is a stagnant agri. sector and dynamic industrial sector. The situation where MPL – 0, labor can be transferred to industrial sector without any loss in agricultural output. The real wages in industrial sector remains fixed and it is equal to the initial level of real income in agri. sector. Such wages are given the name of institutional wages.
Fei and Ranis emphasized strongly on the industry-agriculture interdependency and said that a robust connectivity between the two would encourage and speedup development. If agricultural labourers look for industrial employment, and industrialists employ more workers by use of larger capital good stock and labour-intensive technology, this connectivity can work between the industrial and agricultural sector. Also, if the surplus owner invests in that section of industrial sector that is close to soil and is in known surroundings, he will most probably choose that productivity out of which future savings can be channelized. Looking at the example of Japan’s dualistic economy in the 19th century the connectivity between the two sectors of Japan was heightened due to the presence of a decentralized rural industry which was often linked to urban production. According to them, economic progress is achieved in dualistic economies of underdeveloped countries through the work of a small number of entrepreneurs who have access to land and decision-making powers and use industrial capital and consumer goods for agricultural practices.
The Lewis model is criticised on the grounds that it neglects agriculture. Fei–Ranis model goes a step beyond and states that agriculture has a very major role to play in the expansion of the industrial sector Thus, this model is treated as an improvement over Lewis model of unlimited supply of labor. The biggest drawback of the Lewis model was the undermining of the role of agriculture in boosting the growth of the industrial sector. In addition to that, he did not acknowledge that the increase in productivity of labour should take place prior to the labour shift between the two sectors. However, They further argued that the model lacked proper application of concentrated analysis to the change that takes place with agricultural development but improvements in agriculture and land use are fundamental to achieving food security, poverty alleviation and overall sustainable development in the Nigeria’s economy

Harris- TODARO Model of Migration
The Harris–Todaro model was named after John R. Harris and Michael Todaro. It is an economic model established in 1970 which was used in development economics and welfare economics to explain some of the issues surrounding rural-urban migration. The model was propounded on the basis of the migration decision on the expected income differentials between rural and urban areas rather than just wage differentials. This depicts that rural-urban migration is the cause of high urban unemployment and can be economically logical if expected urban income exceeds expected rural income. According to Brazilian Journal of Physics, it considered Harris and Todaro’s work together as the starting point of classic rural-urban migration theory which underwent Econometrics evaluation and other several studies.
The H-T model is a pioneering general equilibrium model that describes the labour migration from rural to urban areas due to a wage gap and the existence of urban unemployment and underemployment in developing countries such as Nigeria. Since the publication of Todaro (1969), Harris and Todaro (1970), the model has been used as a basis for further research by mainly theoretical economists concerned with both development economics and international economics.
The most important attribute of this model is that it made it possible for analysts to deal with unemployment, within the framework of general equilibrium, by including unemployed workers who were still waiting for jobs in the urban sector, a factor that had previously been difficult to assess. It gave rise to a more realistic description of developing economies and helped to unfold migration between urban and rural areas theoretically. The H-T model is a particular form of the ‘‘neo-classical two sectors model’’, represented by the ‘‘Heckscher, Ohlin and Samuelson model’’ (known as HOS model), and it can be understood as a ‘‘specific factor model’’ (known as S-F model), established by Jones (1971). In the S-F model, each sector has its own specific production factor which cannot swerve between sectors, and the specific factor endowments are also constant. It has been pin- pointed out by many that economic considerations, or urban-rural wage differentials play a vital role in determining the extent of labor migration and the higher the competitive urban wage is due to a combination of trade-union pressure, nationalistic government pressure on foreign enterprises, and the new social conscience of big entrepreneurs (Lewis 1965).
The Harris-Todaro (1970) model’s major contribution to the field of development economics was by making the migration process a rational choice based on expected earnings. The Harris-Todaro (H-T) model took most of Lewis models’ assumptions as given, such as the rural sector being characterized by subsistence agriculture, and the urban sector being characterized by modernized industries. The Harris-Todaro model takes a standard two sector model and imposes a higher wage in the urban sector which is higher than equilibrium clearing, while wage in agriculture is flexible (Chen,2012).
This model has some characteristics which are:
1. Migration is stimulated by rational economic considerations of relative benefits and costs.
2. Migration depends on expected rather than actual Urban real wage differentials where the expected differential is determined by the interactions of two variables, actual Urban real wage differential and probability of gaining enjoyment in Urban sector.
: 3. Probably of gaining an urban job is directly related to Urban employment rate and inversely to Urban unemployment.
4. Migration rate in excess of Urban job opportunity growth rates are not only possible but also rational. The equation is defined as:
Wa = ( Lf /Lf + Li)Wf + ( Li /Lf + Li)Wi.
Inspite of its popularity among economists, some of the assumptions of the HT model have been subjected to criticism since it was developed. The main critiques are summarized by Williamson (1988) as:
1. The lottery style job allocation excludes investment in job search on the part of the immigrants;
2. The informal sector is not explicitly modelled;
3. There is not enough evidence to support the assumption of a rigid wage in the modern sector. Moreover, besides trade union pressure or minimum wage legislation, the wage differentials among sectors could be explained as well by, say, firm- specific training costs.
4. The issue of discount rates and rational migrants is ignored;
5. The influence on decision making of risk and risk attitudes on the part of the potential immigrants is not included; and
6. Differentials in skill levels among the migrants are not accounted for.
Potential migrants may take a long-term view in arriving at a decision. They may consider that their desireness of obtaining an urban job will be higher after a waiting period of some months. Thus they will compare the present value of the sum of expected urban earnings with that of expected rural earnings. They may be content to accept a low wage in the urban informal sector for some time. This might be a rational decision on a long-term basis. The root of the problem is the large difference between earnings in the modern industrial sector and those in the rural areas. Often the former are well above the market clearing levels for varies reasory. The long-term solution to the problem lies in adopting policies for both urban and rural areas which reduces the real income differences between the two areas. Countries like China, India, Pakistan,,etc makes use of this model and that is why it is labeled as “orthodox” by Corden and Findlay (1971).
I suggest that more juicy paying job opportunities be established in the rural areas by building more industries. The wage rate should be increased in the rural sector which will help reduce the unemployment in the urban areas due to migration especially in Nigeria.
Conclusion
The Harris-Todaro model was a much more difficult model to program. The programmed model solves the wage differential between rural and urban sectors . As an tenet in the Harris-Todaro model, migration decision is derived from the difference between agricultural wage and urban expected wage. The most interesting outcome is without a doubt derived from the H-T experiment where the inter-sectoral terms of trade is explored. Manipulations of terms of trade do not affect migration much at all, which is identical to the findings of the Lewis.

31. NAME: Ogumba Joy Chidinma
REG NO: 2017/242028
EMAIL: williamsjoy77@gmail.com
DEPARTMENT: Education Economics

LEWIS-FEI-RANIS MODEL (SURPLUS LABOUR) AND HOW IT APPLIES TO THE NIGERIAN ECONOMY

The Fei–Ranis model of economic growth is a developmental or welfare economics dualism model developed by John C. H. Fei and Gustav Ranis (1961, 1964, 1997), and can be thought of as an extension of the Lewis model (1954). The Surplus Labour model is another name for it.
Unlike several other growth models that consider underdeveloped countries to be homogeneous in nature, it recognizes the existence of a dual economy that involves both the industrial and primitive markets, as well as the economic situation of unemployment and underemployment of resources. The primitive sector, according to this theory, is the economy’s current agricultural sector, while the modern sector is the rapidly developing yet limited industrial sector. In the economy, all sectors coexist, which is the crux of the development crisis. Only a complete change in the focus of progress from the agricultural to the industrial economy, with an increase in industrial production, will bring about growth. This is accomplished by transferring labour from the agricultural to the manufacturing sectors, demonstrating that developing countries do not face labour shortages. At the same time, agricultural sector growth must not be marginal, and its production must be adequate to provide food and raw materials to the entire economy. When it comes to the economic growth of underdeveloped countries, saving and spending become the guiding forces, just as they do in the Harrod–Domar model.

Basic Arguments of the Lewis-Fei-Ranis Model:

Lewis model is a classical type model which states that unlimited supplies of labour can be had at the prevailing subsistence wages. The industrial and advanced modern sector can be developed on the basis of agriculture to the traditional sector. This can be done by transferring labour from the traditional sector and the modern sector.

Lewis says that the wages in the industrial sector remain constant. Consequently, the capitalists will earn a ‘surplus’. Such surplus will be re-invested in the modern sector leading to absorb the labour which is migrated from the subsistence sector. In this way, the surplus-labour or the labour which were prey to disguised unemployment will get the employment. Thus, both the labour transfer and modern sector employment growth are brought about by output expansion in that sector. The speed with which this expansion occurs is determined by the rate of industrial investment and capital accumulation in the modern sector. Though the wages have been assumed constant, yet Lewis says that the urban wages are at least 30% higher than average rural income to induce the workers to migrate from their home areas.

CONTRIBUTIONS OF THE MODEL
• Fei – Ranis model enables the economy to move smoothly into self-sustained growth.
• Fei and Ranis have further shown that their model satisfies the conditions of balanced growth during the take-off process. Balanced growth requires simultaneous investment in both the agricultural and industrial sectors of the economy.

CRITICISM OF THE MODEL
 Amartya Sen critically appraised that, Fei and Ranis do not distinguish between units of labour hours and units of a number of men, which is crucial for peasant agriculture.
 Amartya Sen further said that following W. A. Lewis, Fei and Ranis assume a horizontal supply curve for labour in the initial phase.
 They develop Nurske’s analysis of “hidden rural savings” in disguised unemployment. What the transferred labourers were consuming prior to their shift from disguised unemployment in the rural sector is now saved and used to provide the wage bill in the industrial sector.
 The commercialisation of Agriculture leads to inflationary pressures in the economy.
 Berry and Solingo in their 1968 paper have criticized this model for its MPL = 0 assumption, and for the assumption that the transfer of labour from the agricultural sector leaves the output in that sector unchanged Phase 1.
 Fei and Ranis assume a close model hence there is no presence of foreign trade in the economy, which is very unrealistic as food or raw materials can not be imported. If we take the example of Japan, the country imported cheap farm products from other countries and this made better the country’s term of trade.

HOW IT APPLIES TO NIGERIA AND CONCLUSION
Having studied the Lewis-Fei-Ranis Model (Surplus Labour) it can be said surplus labour can be gotten when the Agricultural sector is not overlooked or undermined. A country can have surplus labour when the available labour force in its large proportion contributes less input in the economy without any significant increase in the output. A country like this suffers from underdevelopment as its citizens would overtime suffer from underemployment and unemployment thereby affecting the standard of living of the citizens.

A country such as Nigeria is experiencing surplus labour as the number of the willing labour force is greater than the available Industries for production of goods with the available raw materials which has declined over the years as a result of the Rural to Urban Migration over the years and also the Insurgencies in most parts of the country is limiting her agricultural production in the rural areas as the farmers are being chased and killed out of their farms with their crops being destroyed by cattle, thereby reducing its agricultural surplus causing inflation and denying the country the ability to export its products but rather, import goods at a higher rate.

32. Irueforum joseph emeka says:

Name: IRUEFORUM JOSEPH EMEKA
Reg No: 2017/249519
Department: ECONOMICS
Email: Josephirueforum@gmail.com
Course: DEVELOPMENT ECONOMICS ASSGIMENT

LEWIS-FEI-RANIS MODEL (SURPLUS LABOUR THEORY)
One of the early known theory of development focused on structural transformation of subsistence economy formulated by a Nobel laureate W. Arthur Lewis in the mid-1950s. The Fei–Ranis model of economic growth is a dualism model in developmental economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model.
The surplus labor models advanced by Lewis (1954), and expanded upon by Ranis and Fei, described a two-sector economy depicting an initially large traditional sector and a relatively small commercialized sector, with the key feature that the traditional sector does not adhere to the neoclassical full employment labor market clearing assumption. It was sufficient to assume that labor was in excess supply relative to cooperating factors at the prevailing wage and technology, and thus that the commercialized sector faced an essentially infinitely elastic labor supply at any moment in time.
The definition of “labor surplus” does not mean that a substantial portion of the agricultural labor force can be withdrawn without loss of output, i.e., that they have a marginal productivity of zero. Indeed, as Sen and Fei-Ranis outlined, when some workers with low marginal productivity are withdrawn, those who remain are likely to work harder and other technology changes of the reorganization variety are likely to result. As Fei and Ranis emphasized, in addition to this organizational dimension of dualism, there is also an important product dualism to be analyzed, focused on the exchange between the food produced by the non-commercialized agricultural sector and the goods produced by the commercialized non-agricultural sector. The key point here is that agricultural and nonagricultural products cannot really be substituted for each other; in the closed economy, food producing agriculture becomes a necessary condition for industry while the converse does not hold.

The first stage of FEI-RANIS model is closely related to Lewis. Disguised unemployment comes into being because the supply of labor is perfectly elastic and MPL = 0. Therefore, such disguised unemployed are to be transferred to industrial sector at the constant institutional wage.

In the second stage of FEI-RANIS (phase) agricultural workers add to agricultural output but they produce less than institutional wage they get. In other words, in the second stage the labor surplus exists where APL > MPL, but it is not equal to subsistence (institutional) wages. Accordingly, such disguised unemployed also have to be transferred to industrial sector. If the migration to industrial sector continues a situation is eventually reached where the farm workers produce output equal to institutional wages. This would mean that productivity in agricultural sector has gone up.

In the third stage of FEI-RANIS model the take-off situation comes to an end and there begins the era of self-sustained growth where the farm workers produce more than the institutional wage they get. In this stage of economic growth the surplus labor comes to an end and the agricultural sector becomes commercialized sector. All such is explained with the Figures.
Accordingly, they have to be shifted to industrial sector. As labor are transferred to industrial sector a shortage of labor will develop in agricultural sector. In other words, it will be difficult for the industrial sector to get the labor at same prevailing constant wages.

Thus, three major points are highlighted in the surplus labour model:

(i) Growth of agriculture is as important as the growth of industry.

(ii) There should be a balanced growth of agricultural industrial sectors.

(iii) The rate of labor absorption must be higher than the rate of population growth to get out of the “Malthusian population trap”.

This model can be applicable to Nigeria economy, early post independence that is during that time the colonial masters had just introduced a vibrant manufacturing sector and the subsistence agriculture had been fully employed. It was of no use that new school leavers would be employed in the subsistence agricultural sector when there is underemployment in the manufacturing sector. So instead government made policies like increment of scholarship opportunities to increase skilled labour and human capital to meet the need of the manufacturing sector.

HARRIS-TODARO MODEL OF MIGRATION
The economic development of western Europe and the United States was closely associated with the movement of labor from rural to urban areas. For the most part, with a rural sector dominated by agricultural activities and an urban sector focusing on industrialization, overall economic development in these countries was characterized by the gradual reallocation of labor out of agriculture and into industry through rural-urban migration, both internal and international. Urbanization and industrialization were in essence synonymous. This historical model served as a blueprint for structural change in developing countries.
One theory to explain the apparently paradoxical relationship of accelerated rural-urban migration in the context of rising urban unemployment has come to be known as the Todaro migration model and in its equilibrium form as the Harris-Todaro model.
The Harris–Todaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and welfare economics to explain some of the issues concerning rural-urban migration. The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This implies that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.
the Todaro model postulates that migration proceeds in response to urban-rural differences in expected income rather than actual earnings. The fundamental premise is that migrants consider the various labor market opportunities available to them in the rural and urban sectors and choose the one that maximizes their expected gains from migration. In essence, the theory assumes that members of the labor force, both actual and potential, compare their expected incomes for a given time horizon in the urban sector (the difference between returns and costs of migration) with prevailing average rural incomes and migrate if the former exceeds the latter
It is important to recognize, however, that these migration models were developed largely in the context of advanced industrial economies and hence implicitly assume the existence of full or near-full employment. In a full-employment environment, the decision to migrate can be based solely on the desire to secure the highest-paid job wherever it becomes available. Simple economic theory would then indicate that such migration should lead to a reduction in wage differentials through the interaction of the forces of supply and demand, in areas of both emigration and immigration. Unfortunately, such an analysis is not realistic in the context of the institutional and economic framework of most developing nations. First, these countries are beset by a chronic unemployment problem, which means that a typical migrant cannot expect to secure a high-paying urban job immediately. In fact, it is much more likely that on entering the urban labor market, many uneducated, unskilled migrants will either become totally unemployed or will seek casual and part-time employment as vendors, hawkers, repairmen, and itinerant day laborers in the urban traditional or informal sector, where ease of entry, small scale of operation, and relatively competitive price and wage determination prevail. In the case of migrants with considerable human capital in the form of a secondary or university certificate, opportunities are much better, and many will find formal-sector jobs relatively quickly. But they constitute only a small proportion of the total migration stream. Consequently, in deciding to migrate, the individual must balance the probabilities and risks of being unemployed or underemployed for a considerable period of time against the positive urban-rural real income differential. The fact that a typical migrant who gains a modern-sector job can expect to earn twice the annual real income in an urban area than in a rural environment may be of little consequence if the actual probability of his securing the higher-paying job within, say, a one-year period is one chance in five.

To sum up, the Todaro migration model has four basic characteristics: 1. Migration is stimulated primarily by rational economic considerations of relative benefits and costs—mostly financial but also psychological. 2. The decision to migrate depends on expected rather than actual urban-rural real-wage differentials, where the expected differential is determined by the interaction of two variables, the actual urban-rural wage differential and the probability of successfully obtaining employment in the urban sector. 3. The probability of obtaining an urban job is directly related to the urban employment rate and thus inversely related to the urban unemployment rate.
4. Migration rates in excess of urban job opportunity growth rates are not only possible but also rational and even likely in the face of wide urbanrural expected income differentials. High rates of urban unemployment are therefore inevitable outcomes of the serious imbalance of economic opportunities between urban and rural areas in most underdeveloped countries.

The movement from rural area to urban area lead to unemployment in the urban area. This movement is as a result of rational economic decisions makinging by migrants from the rural areas that is they believe that there is higher employment opportunities in this urban area for example, it has become a norm for families in rural parts of Eastern Nigeria to sell family lands and try to accumulate wealth and savings to move one of their male child to an urban area (greener pasture) in other to claim the social mobility ladder but this influx lead to a negative match in the labour market.

33. Nwobodo Ifeanyichukwu Victor says:

NAME: NWOBODO IFEANYICHUKWU VICTOR
Reg no: 2017/249535
Email: nwobodope@gmail.com

HARRIS-TODARO MODEL
According to the Harris-Todaro Model, migration is stimulated primarily by rational economic considerations of relative benefits and costs, mostly financial but also psychological. The decision to migrate depends on expected rather than actual urban-rural real wage differential. Expected urban-rural real wage differential depends not only on the actual differential, but also on the probability to find jobs in the urban sector. Rural-Urban migration is an equilibrium phenomenon which equates rural real income to expected urban real income. Policies designed to reduce urban unemployment may increase it. Migration rates in excess of urban job opportunity growth rates are not only possible but also rational.
For example: the Nigeria migration history has been characterized by rural-urban migration due to dearth of needed infrastructural facilities in the rural areas and alleged prospects of a better life in the urban areas. Such movements contribute to and worsen the unemployment situation in urban centres. Cities such as Lagos, Port Harcourt, Kaduna, Enugu, Benin, and Warri among others, remain chosen destinations for Nigerian labour force, both old and young. Influx into the urban centres leads to population explosion and unintended consequences. Nigerian urban centres are projected to be home to over 200 million people in the next 40 years. Lagos as one of the fastest growing urban centre in the world is expected to take in the biggest chunk of these new arrivals.And this will lead to a negative labour mismatch in these urban areas.

LEWIS-FEI-RANIS MODEL
This model on structural transformation of the subsistence economy. It was formulated by Aurthur Lewis and modified by John Fei and Gustav Ranis. The model assumes the existence of a dual economy consisting of agricultural sector(rural ) and manufacturing sector (urban). According to the model, development can be brought about by complete shift in the focal point from the rural sector to the urban sector such that there is an augmentation of industrial output. This can be achieved by transferring labour from agricultural sector to the manufacturing sector so that there can be no glut in Labour supply in the developing countries and the agricultural sector can in turn produce food and raw material to support the economy as a whole. For example: since precolonial times there has been an influx of labour from agricultural sector to industrial sector. Instead of relying on foreign labour supply, the labour that was once invested in underdeveloped economy go on to gain skills applicable in more industralized sector. That is why there has been a huge increase in indeginous participation in urban economies.

34. OZUEM DEBORAH OGHENEKEVWE says:

NAME: OZUEM DEBORAH OGHENEKEVWE
REG NO: 2017/249572
EMAIL: deborah.ozuem.249572@unn.edu.ng
BLOG: favourdebbie.blogger.com

HARRIS-TODARO MODEL OF MIGRATION
The Harris-Todaro model was named after Prof. John R. Harris and Michael. P. Todaro. It is an economic model developed in 1970 to explain issues concerning rural-urban migration in underdeveloped countries. It generally discusses migration in a two-sector economy i.e. when migration starts and when it will end from a low opportunity area (rural area) to a high opportunity environment (urban area). The difference between these sectors are the type of goods produced, the technology of production and the process of wage determination. It emphasizes the role of economic incentives in the decision of workers to migrate. The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials.
Harris-Todaro model unlike the above models brings into focus the role of economic incentives in the decision of workers to migrate. The migrants consider the various opportunities of employment available to them in rural and urban sectors and choose the one that maximizes their expected wages from migration. The minimum urban wage is substantially higher than the rural wage. If more employment opportunities are created in the urban sector at the urban minimum wage, the expected wage will rise and rural-urban migration will increase. Expected wages are measured by the difference in real urban income and rural agricultural income and the probability of a migrant getting an urban job. In fact, a migrant compares his expected income for a given time horizon in the urban sector with his prevailing average rural income and migrates if the former is more than the latter.
Thus migration in the Harris-Todaro model is viewed as the wage or income gap between the urban and the rural sectors. But all migrants cannot be absorbed in the urban sector at high wages. Many fail to find a job and get employment in the informal urban sector at wages which are even lower than in the rural sector. Thus they join the queue of the underemployment or disguised unemployed in the urban sector.
Some of its basic assumptions include:
1. There are two sectors in the economy – the rural or agricultural sector (A) and the urban or manufacturing sector (M).
2. The model operates in the short run.
3. The marginal production of labour in agriculture and of industry are determined by their respective technologies.
4. Capital is available in fixed quantities in the two sectors.
5. The number of urban jobs available is exogenously fixed. In the rural sector some work is always available.
6. The rural wage equals the rural marginal product of labour and the urban wage is exogenously determined.
7. Rural-urban migration continues so long as the expected urban real income is more that the real agricultural income.
8. Every migrant from the village will not find a job. Because this is the condition, he will always compare the expected urban wage rate with the rural wage rate.

We see that the Harris-Todaro model of migration makes some realistic sense when compared to an actual life scenario. Using the Nigerian economy as a case study, we see that workers in the villages (rural areas) are always optimistic about moving to the towns (urban areas) due to their expectations of urban wage. They usually expect that the difference between their rural wage and the expected urban wage would be high enough to cover their cost of migration (which could be monetary cost or cost measured in terms of opportunity cost e.g. cost of leaving behind families, loved ones and acquaintances). A high expected wage difference between the rural and urban areas will force more workers to migrate to the urban areas and vice versa.
In a situation where the expected wage differential is high, the urban areas will experience excess supply of labour which would consequently lead to a reduction in the actual urban wage. Excess supply of labour pushes down the prevailing wage rate in the urban area and indirectly increases underemployment in the town. Also, there is a very high possibility that not all migrants would find a job in the town. This is because the existing jobs in the town would be unable to go round and absorb the additional supply of labour.
There would be disguised unemployment, underemployment and various social implications such as overpopulation, inadequate social amenities and consequently increased crime rates. When compared to our Nigerian case study, we see that this is an actual representation of the real life situation.

LEWIS-FEI-RANIS MODEL OF ECONOMIC GROWTH (SURPLUS LABOUR THEORY)
William Arthur Lewis, with his most famous published work, “Economic Development with Unlimited Supplies of Labour” and “The Theory of Economic Growth” made a great contribution to the theories of economic development. Based on his findings, Ranis and Fei succeeded to extend the initial Lewis’ model and assessed the changes in the agricultural and industrial labour in more detail.The central idea behind the Lewis model is fairly simple. Lewis divided labour force into two differentiated groups – “subsistence sector” and “capitalist sector” where the former is assumed to contain unlimited supply and consequently, a pool of surplus labour that sets labour-supply conditions for the latter. Subsequently, Ranis’ and Fei’s extension to Lewis’ model can be analysed. They observed the model by assessing the changes in the output and wage as more and more people moved from agriculture to the industry. A new concept was added – namely, disguised unemployment, which appears in the traditional subsistence sector.
The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply.
This theory is concerned with a poor economy which has following properties:
(i) There is an abundance of labor in such underdeveloped countries and shortage of natural resources.
(ii) The population growth rate is very high which results in mass unemployment in the economy.
(iii) The major share of population is engaged in agriculture. But agriculture sector is stagnant. Hence, the marginal productivity of labor is zero and negative in agriculture sector.
(iv) There are certain non-agrarian sectors in the economy where there is reduced use of capital.
(v) There is a dynamic industrial sector in the economy.
Thus the model suggests that “Economic development would be taking place if agricultural laborers are transferred to industrial sector where their productivity will increase”. Fei and Ranis emphasized strongly on the industry-agriculture inter-dependency and said that a robust connectivity between the two would encourage and speedup development. If agricultural laborers look for industrial employment, and industrialists employ more workers by use of larger capital good stock and labor-intensive technology, this connectivity can work between the industrial and agricultural sector. Also, if the surplus owner invests in that section of industrial sector that is close to soil and is in known surroundings, he will most probably choose that productivity out of which future savings can be channelized. They took the example of Japan’s dualistic economy in the 19th century and said that connectivity between the two sectors of Japan was heightened due to the presence of a decentralized rural industry which was often linked to urban production. According to them, economic progress is achieved in dualistic economies of underdeveloped countries through the work of a small number of entrepreneurs who have access to land and decision-making powers and use industrial capital and consumer goods for agricultural practices.
Fei and Ranis develop their dual economy model with the help of three stages of economic growth and these three stages are explained below:
The first stage of Fei-Ranis model is very similar to Lewis. Disguised unemployment comes into being because the supply of labor is perfectly elastic and MPL = 0. Therefore, such disguised unemployed are to be transferred to industrial sector at the constant institutional wage.
In the second stage of Fei-Ranis model (phase) agricultural workers add to agricultural output but they produce less than the institutional wage they get. In other words, in the second stage the labor surplus exists where APL > MPL, but it is not equal to subsistence (institutional) wages. Accordingly, such disguised unemployed also have to be transferred to industrial sector. If the migration to industrial sector continues a situation is eventually reached where the farm workers produce output equal to institutional wages. This would mean that productivity in agricultural sector has gone up. With this the third phase (stage) starts.
In the third stage of Fei-Ranis model the take-off situation comes to an end and there begins the era of self-sustained growth where the farm workers produce more than the institutional wage they get. In this stage of economic growth the surplus labor comes to an end and the agricultural sector becomes commercialized sector.

CONCLUSION:
With the Nigerian economy in view, we find that whereas Lewis had failed to offer a satisfactory explanation of this subsistence sector and ignored the real impact of population growth on the choice of capital intensity on the process of surplus labor absorption. Fei-Ranis model emphasized upon the simultaneous growth of agriculture and industrial sectors. Thus FR model believes in ‘Balanced Growth’ in the take-off stage. It means that there should be a simultaneous investment in both agricultural sector and industrial sector. According to Fei-Ranis model, in the beginning the surplus rises; such surplus will be available as a capital in the take-offstage. Some part of this surplus will be used in agricultural development, while some part will be re-ploughed in industrial development. As a result, both agricultural and industrial sectors will grow under ‘Balanced Growth’ pattern. if the government can simultaneously invest in both sectors, then Nigeria can attain economic development.

35. Ngwu Osita Enoch says:

NGWU OSITA ENOCH
2017/242022
OSITANGWU95@GMAIL.COM
EDUCATION ECONOMICS

Lewis-Fei-Ranis Model (Surplus labour theory).

INTRODUCTION
The Lewis (1954) theory of dualistic economic development provides the seminal contribution to theories of economic development particularly for labour-surplus and resource-poor developing countries. In the Lewis theory, the economy is assumed to comprise the agricultural and non-agricultural sectors. The agricultural sector is assumed to have vast amounts of surplus labour that result in an extremely low, close to zero, marginal productivity of labour. The agricultural wage rate is presumed to follow the sharing rule and be equal to average productivity, which is also known as the institutional wage. The non-agricultural sector has an abundance capital and resources relative to labour. It pursues profit and employs labour at a wage rate higher than the agricultural institutional wage by approximately 30 percent (Lewis, 1954, p.150).
The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output.
HISTORY OF SURPLUS LABOUR THEORY
The historical emergence of surplus labour is, according to Marx, also closely associated with the growth of trade (the economic exchange of goods and services) and with the emergence of a society divided into social classes. As soon as a permanent surplus product can be produced, the moral-political question arises as to how it should be distributed, and for whose benefit surplus-labour should be performed. The strong defeat the weak, and it becomes possible for a social elite to gain control over the surplus-labour and surplus product of the working population; they can live off the labour of others.
Labour which is sufficiently productive so that it can perform surplus labour is, in a cash economy, the material foundation for the appropriation of surplus-value from that labour. How exactly this appropriation will occur, is determined by the prevailing relations of production and the balance of power between social classes.
THE CONCEPT OF SURPLUS LABOUR
The concept of surplus labour is widely discussed among development economics but its specific meaning needs to be defined, especially in technical terms, as many neoclassical economists still doubt the existence of surplus labour in an economy. Defining the source and the extent of surplus labour is then a prerequisite for further study. This section considers the various definitions of surplus labour and clarifies them.
The simple definition of surplus labour implies the existence of a point at which the marginal product of labour becomes zero and labour can be transferred out of the traditional sector without reducing the quantity of output, as noted by Wellisz (1968: 22): The (disguised-unemployment or the Unlimited Supply of Labour) hypothesis claims that in poor, densely populated countries, more people are employed than needed to produce the prevailing output with the existing techniques and the existing supply of non-labour inputs. The ‘surplus’ labour constitutes ‘hidden’ or ‘disguised’ unemployment. Many of the proponents of the hypothesis make the further claim that agricultural output will not decrease, and industrial output will increase, if measures are taken to re-allocate labour from subsistence agriculture (where the surplus is supposed to exist) to industry (where there is no surplus labour).
ASSUMPTIONS OF THE LEWIS-FEI-RANIS MODEL
(A) Surplus Labour in the Subsistence Sectors:
The basic assumption of the model is that there exists surplus labour in the subsistence sectors. It includes labour whose marginal productivity is zero as well as that whose marginal productivity is positive but is less than the institutional wage. This labour comprises farmers, agricultural labourers, petty traders domestic servants and women.
The surplus labour in the agriculture sector acts as a source of unlimited supply of labour for the manufacturing sector. By unlimited supply of labour. Lewis means that the supply of labour is perfectly elastic at a particular wages. This particular wage is somewhat higher than the institutional wage which each worker in the agricultural sector gets.
(B) Importance of Saving:
Another important assumption that Lewis makes is about the savings generated in the capitalist sector and in the subsistence sector. The capitalist sector invests all its savings for its further expansion. Those in the subsistence sector, on the other hand squander away their savings, if any in purchase of jewellery & for construction of temples etc of those in the capitalist sector. Lewis in fact so much fascinated by the higher propensity to save of the capitalist sector that he even advocates a transfer of income from the subsistence sector to the capitalist sector. He feels that steps have to be taken to raise the rate of savings from 10% to 15% if the development of the economy has to be smooth.
COMPARISONS OF THE THEORY OF SURPLUS LABOUR
Surplus labor models are a class of models for analyzing developing countries as dual economies with a modern capitalist sector and a traditional precapitalist sector. The precapitalist sector is viewed as having a large pool (“unlimited supplies”) of labor from which the capitalist sector may draw at constant cost. While these models are often described as finding their inspiration in the old classical economists and Karl Marx, the 1954 model of W. Arthur Lewis and its extensions are technically more neoclassical than truly classical. The Lewis model was elaborated and formalized by many others, most notably John C. H. Fei and Gustav Ranis (1964), with important theoretical contributions from Amartya Sen (1966) and Stephen Marglin (1976). Questions have been raised as to the historical relevance of the neoclassical labor surplus models (Schultz 1964; Myint 1971; Arrighi 1973; Williamson 1985).
CRITICISM
Lewis-Fei-Ranis model of economic growth has been criticized on multiple grounds, although if the model is accepted, then it will have a significant theoretical and policy implications on the underdeveloped countries’ efforts towards development and on the persisting controversial statements regarding the balanced vs. unbalanced growth debate.
It has been asserted that the Lewis-Fei-Ranis model did not have a clear understanding of the sluggish economic situation prevailing in the developing countries. If they had thoroughly scrutinized the existing nature and causes of it, they would have found that the existing agricultural backwardness was due to the institutional structure, primarily the system of feudalism that prevailed.
The Lewis-Fei-Ranis model say, “It has been argued that money is not a simple substitute for physical capital in an aggregate production function. There are reasons to believe that the relationship between money and physical capital could be complementary to one another at some stage of economic development, to the extent that credit policies could play an important part in easing bottlenecks on the growth of agriculture and industry.” This indicates that in the process of development they neglect the role of money and prices. They fail to differ between wage labor and household labor, which is a significant distinction for evaluating prices of dualistic development in an underdeveloped economy.
The Lewis-Fei-Ranis model assume that MPPL is zero during the early phases of economic development, which has been criticized by Harry T.Oshima and some others on the grounds that MPPL of labor is zero only if the agricultural population is very large, and if it is very large, some of that labor will shift to cities in search of jobs. In the short run, this section of labor that has shifted to the cities remains unemployed, but over the long run it is either absorbed by the informal sector, or it returns to the villages and attempts to bring more marginal land into cultivation.
CONCLUSIONS AND RECOMMENDATIONS
Lewis-Fei-Ranis model can be grouped under three instruments; labour force, capital accumulation and integration to the world economy. The main focus in Lewis-Fei-Ranis model was on the reallocation of labour until the turning point is reached, i.e., the time when labour reallocation has outstripped population growth long enough for dualism to atrophy and the economy to become fully commercialized. The model implicitly showed that the traditional sector do not produce any capital accumulation as they are very small and poor. Trade between agriculture and industry as the supply or marketed food falls or the demand for it rises, or both causing the value of marginal product of labour in agriculture to rise.
In sum up, there are several weaknesses of Lewis-Fei-Ranis model that are underlined by many economists. The first and most important is that if marginal productivity of labour in agricultural sector is negligible, zero. Schultz (1964), Sen (1967), Harris and Todaro (1970) and Fields (1975) proved with their empirical results that this cannot happen in agriculture sector. It is obvious that there is a disguised unemployment in agriculture. Particularly, agricultural sector should be considered in two ways: during harvest time and post harvest. If the agricultural surplus is solely considered for the regions where there can be seen harsh winter conditions, it could be accepted of the doctrine of Lewis, otherwise it is irrelevant to say there is a zero marginal productivity for agriculture labours. Also, there are positive opportunity costs, e.g. loss of crops in times of peak harvesting season, labour transfer will reduce agricultural output.
Second, the model employed mostly for the closed economies and gave relatively less information on open economies. Lewis-Fei-Ranis model was criticized as it neglects international trade. The model was to a certain extent supply-oriented, which does not foresee any trade between capital and other sectors. Also it was criticized advocating industrialization and ignores agriculture. If a section of the profit made by the capitalists is not devoted to agricultural development, the process of industrialization would be jeopardized.
Third, Lewis-Fei-Ranis model believed that the more the rate of labour transfer to urban employment, the more the economic grows and more jobs are created. But this is not a common applicable in practice if industrial development involves more intensive use of capital than labour, then the flow of labour from agriculture to industry will simply create more unemployment.
Fourth, the Lewis-Fei-Ranis model would imply that aggregate living standards should not rise as rapidly as productivity until surplus labour is eliminated. However, the evidence on living standards in Latin America during the twentieth century indicates that these have risen in line with productivity, and that the ‘indirect’ components of the real wage (health and education) have actually risen more rapidly that average incomes.
Fifth, the Lewis-Fei-Ranis model stated the wage in industrial sector does not increase before labour surplus is absorbed. But this does not happen in any way in reality as the development of the urban, or industrial, or formal sector can itself lead to the creation of pressure groups and swing the balance of power towards those in that sector, to the detriment of those remaining outside it. The wage in the industrial sector in reality outstandingly rises long before the labour surplus is absorbed.
Haven tested the Lewis-Ranis-Fei theory for developing economy over 1965-2002 we have found that the developing economic growth is mainly attributable to the development of the non-agricultural sector. This is driven by rapid capital accumulation as well as employment growth. The reallocation of labour away from agriculture has made a positive net contribution to rapid economic of the developing economy. The rise in the marginal productivity of agricultural labour indicates the absorption of redundant agricultural labour since the 1978 Economic Reform. However, the marginal productivity of agricultural labour is still lower than the initial low average productivity of agricultural labour. This implies the continued existence of disguised agricultural unemployment. This suggests that the these developing economy has entered the Lewis-Ranis-Fei phase two of development but has not yet achieved phase three. The continuing widening productivity gap between the two sectors calls for the removal of market restrictions and government interventions so as to allow the continued absorption of surplus labour. Several policy recommendations are tentatively suggested. First and foremost, more effort should be made in promoting employment to effectively absorb the remaining labour surplus and promote economic development. This can be achieved by further relaxing the Hukou restrictions on migration, increasing labour market flexibility and improving the allocative efficiency of labour. It can also be achieved by encouraging the development of private enterprise to create more employment opportunities. Second, Government of developing economy should continue implementing the Sunshine Policy, initiated in 2003, designed to provide rudimentary job training, recruitment information and information about conditions in the destination cities to rural migrants. This will not only help facilitate employment of rural migrants but also satisfy the increasing demand for skilled labour in the growing non-agricultural sector. Third, agriculture could be promoted by tax breaks, direct subsidies and most importantly, by removing price controls on agricultural products. Agriculture could thus be commercialised and the economy would enter phase three of economic development.

REFERENCE
Sadik-Zada, Elkhan Richard (2020). “Natural resources, technological progress, and economic modernization”. Review of Development Economics. doi:10.1111/rode.12716.
“Economnics4Development Website”. Surplus Labor Model of Economic Development. Archived from the original on 16 October 2011. Retrieved 12 October 2011.
Thirlwall, A.P (2006). Growth and Development: With Special Reference to Developing Economies. Palgrave Macmillan. ISBN 1-4039-9600-8.
Subrata, Ghatak (2003). Introduction to Developmental Economics. London: Routledge. ISBN 0-415-09722-3.
“Ranis-Fei model vs. Lewis Model” (PDF). Developmentafrique.com. Archived from the original (PDF) on 30 May 2012. Retrieved 14 October 2011.
“American Economic Review”. The Ranis-Fei Model of Economic Development: Comment. 53: 448–452. JSTOR 1809172.
Ranis, Gustav. “Paper on Labor Surplus Economies” (PDF). Retrieved 4 October 2011.
J. Choo, Hakchung. “American Economic Review”. On the Empirical Relevancy of the Rans-Fei Model of Economic Development: Comment. 61: 695–703. JSTOR 1811863.
Misra, Puri, S.K, V.K (2010). Economics of Development and Planning. Mumbai, India: Himalaya Publishing House. pp. 270–279. ISBN 978-81-8488-829-4.

NGWU OSITA ENOCH
2017/242022
OSITANGWU95@GMAIL.COM
EDUCATION ECONOMICS .

Harris-Todaro Model of migration.

INTRODUCTION
Harris and Todaro work, is considered one of the starting points of the classic rural-urban migration theory. The hypothesis and predictions of Harris-Todaro model have been subjected to econometric evaluation and have been corroborated by several studies. The key hypothesis of Harris and Todaro are that migrants react mainly to economic incentives, earnings differentials, and the probability of getting a job at the destination have influence on the migraton decision. In other words, these authors posit that rural-urban migration will occur while the urban expected wage exceed the rural wage. From this crucial assumption, as denominated by Harris-Todaro, is deduced that the migratory dynamics leads the economic system toward an equilibrium with urban concentration and high urban unemployment.
THE HARRIS-TODARO MODEL
Assumptions
Harris and Todaro studied the migration of workers in a two-sector economic system, namely, rural sector and urban sector. The difference between these sectors are the type of goods produced, the technology of production and the process of wage determination. The rural sector is specialized in the production of agricultural goods. The productive process of this sector can be described by a Cobb-Douglas production function: where Ya is the production level of the agricultural good, Na is the amount of workers used in the agricultural production, Aa > 0 and 0 < f 0 and 0 < a < 1 are parametric constants. Both goods and labor markets are perfectly competitive. Nevertheless, there is segmentation in the labor market due to a high minimum urban wage politically determined. In the rural sector, the real wage, perfectly flexible, is equal to the marginal productivity of labor in this sectors where wa is the real wage and p is the price of the agricultural good, both expressed in units of manufactured good.
HARRIS-TODARO AGENT-BASED MODEL
Computational Implementation

Initially, workers are randomly placed in a square lattice with linear dimension L = 500. The reference values of the parameters used for these simulations are the same done to evaluate the equilibrium of the Harris-Todaro model, namely, Aa = 1.0, Am = 1.0, f = 0.3, a = 0.7, r = 1.0 and g = 1.0. The value of the minimum wage used is wm = 0.8 and the initial urban fraction of the total population is nu = 0.2, where nu = Nu/N is the normalized urban population also called urban share. The initial value nu = 0.2 is in agreement with historical data of developing economies. Given these parameters, one can calculate the vector which characterizes temporary equilibrium of the system by using eqs. (7 – 12). By using eq. (7), the employment level of the urban sector, Nm, is obtained. If nu Nm/N there will be a fraction of Nm/Nu workers employed, which earn the minimum wage, wi = wm, and (1-Nm/Nu) workers unemployed, which earn a wage wi = 0. Each worker can be selected to review his sectorial location with probability a, called activity. Therefore, in each time step only a fraction of workers becomes potential migrants, going through the sectorial location reviewing process. Potential migrants will determine their satisfaction level of being in the current sector by comparing their earnings, wi, among nearest neighbors. The potential migrant starts the comparison process with a initial satisfaction level si = 0. When wi > wneighbor the satisfaction level si is added in one unit; if wi < wneighbor, si is diminished in one unit; if wi = wneighbor, si does not change. After the worker has passed through the reviewing process his/her satisfaction level is checked. The migration will occur only if si < 0, what means that the worker's i earnings is less than the most of his/her nearest neighbors. After all the potential migrants complete the reviewing process and have decided migrate or not, a new configuration of the system is set. Therefore, once again a new temporary equilibrium of the system is calculated by using eqs. (8 – 12). The whole procedure is repeated until a pre-set number of steps is reached. It is important to emphasize that Nm is kept constant throughout the simulation. Its given by eq. (7) which depends on the technological parameters, a,Am, and the minimum wage, wm, which are constants too.
In this case, the differential of expected wages is negative. In an economy mainly rural (nu < 0:5), the transitional dynamics characterized by a continuous growth of population of the urban sector with a differential of expected wages relatively high is followed by the stabilization of rural-urban differential of expected wages. In other words, the generalized Harris-Todaro condition, eq. (15), arises as a long run equilibrium result of the agent-based migratory dynamics.
CONCLUSION
In this paper we developed and agent-based computational model which formalizes the rural-urban allocation of workers as a process of social learning by imitation. We analyze a two-sectorial economy composed by adaptative agents, i.e., individuals that grope over time for best sectorial location in terms of earnings. This search is a process of imitation of successful neighbor agents. The dispersed and non-coordinated individual migration decisions, made based on local information, generate aggregate regularities.
Firstly, the crucial assumption of Harris and Todaro, the principle that rural-urban migration will occur while the urban expected wage exceed the rural wage, comes out as spontaneous upshot of interaction among adaptative agents.
Secondly, the migratory dynamics generated by agents that seek to adaptate to the economic environment that they co-create leads the economy toward a long run equilibrium characterized by urban concentration with urban unemployment. When this long run equilibrium is reached, the generalized Harris-Todaro condition is satisfied, i.e., there is a stabilization of the rural-urban expected wage differential.
Thirdly, the impact of the minimum wage and elasticity of terms of trade in a long run equilibrium obtained by simulations are in agreement with the predictions of the original Harris-Todaro model with Cobb-Douglas technology.
Finally, the simulations showed an aggregated pattern not found in the original Harris-Todaro model. There is the possibility of small fluctuations of the urban share around an average value. This phenomenon is known as reverse migration.

REFERENCE

Aquino L. Espíndola thanks CAPES for the financial support. Jaylson J. Silveira acknowledges research grants from CNPq. T. J. P. Penna thanks CNPq for the fellowship.
J. R. Harris and M. P. Todaro, American Economic Review 60, 126 (1970).
M. P. Todaro, American Economic Review 59, 138 (1969).
D. Ray, Development Economics (Princeton: Princeton University Press, 1998).
L. Y. L. Yap, Journal of Development Economics 4, 239 (1977).
D. Mazumdar, Rural-urban Migration in Developing countries. In: Handbook of Regional and Urban Economics, Elsevier, Amsterdam, 1987.
L. Ghatak, P. Levine, and S. Price, Journal of Economics Surveys 10, 159 (1996).
J. G. Willianson, Migration and Urbanization. In: Chenery, H. and Srinivasan, T.N., Handbook of developments economics, Elsevier, Amsterdam, 1988.
J. J. Silveira, A. L. Espíndola, and T. J. P. Penna, physics/0506021, Physica A, to appear.

36. Ngwu Osita Enoch says:

Ngwu Osita Enoch
2017/242022
Ositangwu95@gmail.com
Education Economics

Lewis-Fei-Ranis Model (Surplus labour theory)
INTRODUCTION
The Lewis (1954) theory of dualistic economic development provides the seminal contribution to theories of economic development particularly for labour-surplus and resource-poor developing countries. In the Lewis theory, the economy is assumed to comprise the agricultural and non-agricultural sectors. The agricultural sector is assumed to have vast amounts of surplus labour that result in an extremely low, close to zero, marginal productivity of labour. The agricultural wage rate is presumed to follow the sharing rule and be equal to average productivity, which is also known as the institutional wage. The non-agricultural sector has an abundance capital and resources relative to labour. It pursues profit and employs labour at a wage rate higher than the agricultural institutional wage by approximately 30 percent (Lewis, 1954, p.150).
The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output.
HISTORY OF SURPLUS LABOUR THEORY
The historical emergence of surplus labour is, according to Marx, also closely associated with the growth of trade (the economic exchange of goods and services) and with the emergence of a society divided into social classes. As soon as a permanent surplus product can be produced, the moral-political question arises as to how it should be distributed, and for whose benefit surplus-labour should be performed. The strong defeat the weak, and it becomes possible for a social elite to gain control over the surplus-labour and surplus product of the working population; they can live off the labour of others.
Labour which is sufficiently productive so that it can perform surplus labour is, in a cash economy, the material foundation for the appropriation of surplus-value from that labour. How exactly this appropriation will occur, is determined by the prevailing relations of production and the balance of power between social classes.
THE CONCEPT OF SURPLUS LABOUR
The concept of surplus labour is widely discussed among development economics but its specific meaning needs to be defined, especially in technical terms, as many neoclassical economists still doubt the existence of surplus labour in an economy. Defining the source and the extent of surplus labour is then a prerequisite for further study. This section considers the various definitions of surplus labour and clarifies them.
The simple definition of surplus labour implies the existence of a point at which the marginal product of labour becomes zero and labour can be transferred out of the traditional sector without reducing the quantity of output, as noted by Wellisz (1968: 22): The (disguised-unemployment or the Unlimited Supply of Labour) hypothesis claims that in poor, densely populated countries, more people are employed than needed to produce the prevailing output with the existing techniques and the existing supply of non-labour inputs. The ‘surplus’ labour constitutes ‘hidden’ or ‘disguised’ unemployment. Many of the proponents of the hypothesis make the further claim that agricultural output will not decrease, and industrial output will increase, if measures are taken to re-allocate labour from subsistence agriculture (where the surplus is supposed to exist) to industry (where there is no surplus labour).
ASSUMPTIONS OF THE LEWIS-FEI-RANIS MODEL
(A) Surplus Labour in the Subsistence Sectors:
The basic assumption of the model is that there exists surplus labour in the subsistence sectors. It includes labour whose marginal productivity is zero as well as that whose marginal productivity is positive but is less than the institutional wage. This labour comprises farmers, agricultural labourers, petty traders domestic servants and women.
The surplus labour in the agriculture sector acts as a source of unlimited supply of labour for the manufacturing sector. By unlimited supply of labour. Lewis means that the supply of labour is perfectly elastic at a particular wages. This particular wage is somewhat higher than the institutional wage which each worker in the agricultural sector gets.
(B) Importance of Saving:
Another important assumption that Lewis makes is about the savings generated in the capitalist sector and in the subsistence sector. The capitalist sector invests all its savings for its further expansion. Those in the subsistence sector, on the other hand squander away their savings, if any in purchase of jewellery & for construction of temples etc of those in the capitalist sector. Lewis in fact so much fascinated by the higher propensity to save of the capitalist sector that he even advocates a transfer of income from the subsistence sector to the capitalist sector. He feels that steps have to be taken to raise the rate of savings from 10% to 15% if the development of the economy has to be smooth.
COMPARISONS OF THE THEORY OF SURPLUS LABOUR
Surplus labor models are a class of models for analyzing developing countries as dual economies with a modern capitalist sector and a traditional precapitalist sector. The precapitalist sector is viewed as having a large pool (“unlimited supplies”) of labor from which the capitalist sector may draw at constant cost. While these models are often described as finding their inspiration in the old classical economists and Karl Marx, the 1954 model of W. Arthur Lewis and its extensions are technically more neoclassical than truly classical. The Lewis model was elaborated and formalized by many others, most notably John C. H. Fei and Gustav Ranis (1964), with important theoretical contributions from Amartya Sen (1966) and Stephen Marglin (1976). Questions have been raised as to the historical relevance of the neoclassical labor surplus models (Schultz 1964; Myint 1971; Arrighi 1973; Williamson 1985).
CRITICISM
Lewis-Fei-Ranis model of economic growth has been criticized on multiple grounds, although if the model is accepted, then it will have a significant theoretical and policy implications on the underdeveloped countries’ efforts towards development and on the persisting controversial statements regarding the balanced vs. unbalanced growth debate.
It has been asserted that the Lewis-Fei-Ranis model did not have a clear understanding of the sluggish economic situation prevailing in the developing countries. If they had thoroughly scrutinized the existing nature and causes of it, they would have found that the existing agricultural backwardness was due to the institutional structure, primarily the system of feudalism that prevailed.
The Lewis-Fei-Ranis model say, “It has been argued that money is not a simple substitute for physical capital in an aggregate production function. There are reasons to believe that the relationship between money and physical capital could be complementary to one another at some stage of economic development, to the extent that credit policies could play an important part in easing bottlenecks on the growth of agriculture and industry.” This indicates that in the process of development they neglect the role of money and prices. They fail to differ between wage labor and household labor, which is a significant distinction for evaluating prices of dualistic development in an underdeveloped economy.
The Lewis-Fei-Ranis model assume that MPPL is zero during the early phases of economic development, which has been criticized by Harry T.Oshima and some others on the grounds that MPPL of labor is zero only if the agricultural population is very large, and if it is very large, some of that labor will shift to cities in search of jobs. In the short run, this section of labor that has shifted to the cities remains unemployed, but over the long run it is either absorbed by the informal sector, or it returns to the villages and attempts to bring more marginal land into cultivation.
CONCLUSIONS AND RECOMMENDATIONS
Lewis-Fei-Ranis model can be grouped under three instruments; labour force, capital accumulation and integration to the world economy. The main focus in Lewis-Fei-Ranis model was on the reallocation of labour until the turning point is reached, i.e., the time when labour reallocation has outstripped population growth long enough for dualism to atrophy and the economy to become fully commercialized. The model implicitly showed that the traditional sector do not produce any capital accumulation as they are very small and poor. Trade between agriculture and industry as the supply or marketed food falls or the demand for it rises, or both causing the value of marginal product of labour in agriculture to rise.
In sum up, there are several weaknesses of Lewis-Fei-Ranis model that are underlined by many economists. The first and most important is that if marginal productivity of labour in agricultural sector is negligible, zero. Schultz (1964), Sen (1967), Harris and Todaro (1970) and Fields (1975) proved with their empirical results that this cannot happen in agriculture sector. It is obvious that there is a disguised unemployment in agriculture. Particularly, agricultural sector should be considered in two ways: during harvest time and post harvest. If the agricultural surplus is solely considered for the regions where there can be seen harsh winter conditions, it could be accepted of the doctrine of Lewis, otherwise it is irrelevant to say there is a zero marginal productivity for agriculture labours. Also, there are positive opportunity costs, e.g. loss of crops in times of peak harvesting season, labour transfer will reduce agricultural output.
Second, the model employed mostly for the closed economies and gave relatively less information on open economies. Lewis-Fei-Ranis model was criticized as it neglects international trade. The model was to a certain extent supply-oriented, which does not foresee any trade between capital and other sectors. Also it was criticized advocating industrialization and ignores agriculture. If a section of the profit made by the capitalists is not devoted to agricultural development, the process of industrialization would be jeopardized.
Third, Lewis-Fei-Ranis model believed that the more the rate of labour transfer to urban employment, the more the economic grows and more jobs are created. But this is not a common applicable in practice if industrial development involves more intensive use of capital than labour, then the flow of labour from agriculture to industry will simply create more unemployment.
Fourth, the Lewis-Fei-Ranis model would imply that aggregate living standards should not rise as rapidly as productivity until surplus labour is eliminated. However, the evidence on living standards in Latin America during the twentieth century indicates that these have risen in line with productivity, and that the ‘indirect’ components of the real wage (health and education) have actually risen more rapidly that average incomes.
Fifth, the Lewis-Fei-Ranis model stated the wage in industrial sector does not increase before labour surplus is absorbed. But this does not happen in any way in reality as the development of the urban, or industrial, or formal sector can itself lead to the creation of pressure groups and swing the balance of power towards those in that sector, to the detriment of those remaining outside it. The wage in the industrial sector in reality outstandingly rises long before the labour surplus is absorbed.
Haven tested the Lewis-Ranis-Fei theory for developing economy over 1965-2002 we have found that the developing economic growth is mainly attributable to the development of the non-agricultural sector. This is driven by rapid capital accumulation as well as employment growth. The reallocation of labour away from agriculture has made a positive net contribution to rapid economic of the developing economy. The rise in the marginal productivity of agricultural labour indicates the absorption of redundant agricultural labour since the 1978 Economic Reform. However, the marginal productivity of agricultural labour is still lower than the initial low average productivity of agricultural labour. This implies the continued existence of disguised agricultural unemployment. This suggests that the these developing economy has entered the Lewis-Ranis-Fei phase two of development but has not yet achieved phase three. The continuing widening productivity gap between the two sectors calls for the removal of market restrictions and government interventions so as to allow the continued absorption of surplus labour. Several policy recommendations are tentatively suggested. First and foremost, more effort should be made in promoting employment to effectively absorb the remaining labour surplus and promote economic development. This can be achieved by further relaxing the Hukou restrictions on migration, increasing labour market flexibility and improving the allocative efficiency of labour. It can also be achieved by encouraging the development of private enterprise to create more employment opportunities. Second, Government of developing economy should continue implementing the Sunshine Policy, initiated in 2003, designed to provide rudimentary job training, recruitment information and information about conditions in the destination cities to rural migrants. This will not only help facilitate employment of rural migrants but also satisfy the increasing demand for skilled labour in the growing non-agricultural sector. Third, agriculture could be promoted by tax breaks, direct subsidies and most importantly, by removing price controls on agricultural products. Agriculture could thus be commercialised and the economy would enter phase three of economic development.

REFERENCE
Sadik-Zada, Elkhan Richard (2020). “Natural resources, technological progress, and economic modernization”. Review of Development Economics. doi:10.1111/rode.12716.
“Economnics4Development Website”. Surplus Labor Model of Economic Development. Archived from the original on 16 October 2011. Retrieved 12 October 2011.
Thirlwall, A.P (2006). Growth and Development: With Special Reference to Developing Economies. Palgrave Macmillan. ISBN 1-4039-9600-8.
Subrata, Ghatak (2003). Introduction to Developmental Economics. London: Routledge. ISBN 0-415-09722-3.
“Ranis-Fei model vs. Lewis Model” (PDF). Developmentafrique.com. Archived from the original (PDF) on 30 May 2012. Retrieved 14 October 2011.
“American Economic Review”. The Ranis-Fei Model of Economic Development: Comment. 53: 448–452. JSTOR 1809172.
Ranis, Gustav. “Paper on Labor Surplus Economies” (PDF). Retrieved 4 October 2011.
J. Choo, Hakchung. “American Economic Review”. On the Empirical Relevancy of the Rans-Fei Model of Economic Development: Comment. 61: 695–703. JSTOR 1811863.
Misra, Puri, S.K, V.K (2010). Economics of Development and Planning. Mumbai, India: Himalaya Publishing House. pp. 270–279. ISBN 978-81-8488-829-4.

Harris-Todaro Model of Migration
INTRODUCTION
Harris and Todaro work, is considered one of the starting points of the classic rural-urban migration theory. The hypothesis and predictions of Harris-Todaro model have been subjected to econometric evaluation and have been corroborated by several studies. The key hypothesis of Harris and Todaro are that migrants react mainly to economic incentives, earnings differentials, and the probability of getting a job at the destination have influence on the migraton decision. In other words, these authors posit that rural-urban migration will occur while the urban expected wage exceed the rural wage. From this crucial assumption, as denominated by Harris-Todaro, is deduced that the migratory dynamics leads the economic system toward an equilibrium with urban concentration and high urban unemployment.
THE HARRIS-TODARO MODEL
Assumptions
Harris and Todaro studied the migration of workers in a two-sector economic system, namely, rural sector and urban sector. The difference between these sectors are the type of goods produced, the technology of production and the process of wage determination. The rural sector is specialized in the production of agricultural goods. The productive process of this sector can be described by a Cobb-Douglas production function: where Ya is the production level of the agricultural good, Na is the amount of workers used in the agricultural production, Aa > 0 and 0 < f 0 and 0 < a < 1 are parametric constants. Both goods and labor markets are perfectly competitive. Nevertheless, there is segmentation in the labor market due to a high minimum urban wage politically determined. In the rural sector, the real wage, perfectly flexible, is equal to the marginal productivity of labor in this sectors where wa is the real wage and p is the price of the agricultural good, both expressed in units of manufactured good.
HARRIS-TODARO AGENT-BASED MODEL
Computational Implementation

Initially, workers are randomly placed in a square lattice with linear dimension L = 500. The reference values of the parameters used for these simulations are the same done to evaluate the equilibrium of the Harris-Todaro model, namely, Aa = 1.0, Am = 1.0, f = 0.3, a = 0.7, r = 1.0 and g = 1.0. The value of the minimum wage used is wm = 0.8 and the initial urban fraction of the total population is nu = 0.2, where nu = Nu/N is the normalized urban population also called urban share. The initial value nu = 0.2 is in agreement with historical data of developing economies. Given these parameters, one can calculate the vector which characterizes temporary equilibrium of the system by using eqs. (7 – 12). By using eq. (7), the employment level of the urban sector, Nm, is obtained. If nu Nm/N there will be a fraction of Nm/Nu workers employed, which earn the minimum wage, wi = wm, and (1-Nm/Nu) workers unemployed, which earn a wage wi = 0. Each worker can be selected to review his sectorial location with probability a, called activity. Therefore, in each time step only a fraction of workers becomes potential migrants, going through the sectorial location reviewing process. Potential migrants will determine their satisfaction level of being in the current sector by comparing their earnings, wi, among nearest neighbors. The potential migrant starts the comparison process with a initial satisfaction level si = 0. When wi > wneighbor the satisfaction level si is added in one unit; if wi < wneighbor, si is diminished in one unit; if wi = wneighbor, si does not change. After the worker has passed through the reviewing process his/her satisfaction level is checked. The migration will occur only if si < 0, what means that the worker's i earnings is less than the most of his/her nearest neighbors. After all the potential migrants complete the reviewing process and have decided migrate or not, a new configuration of the system is set. Therefore, once again a new temporary equilibrium of the system is calculated by using eqs. (8 – 12). The whole procedure is repeated until a pre-set number of steps is reached. It is important to emphasize that Nm is kept constant throughout the simulation. Its given by eq. (7) which depends on the technological parameters, a,Am, and the minimum wage, wm, which are constants too.
In this case, the differential of expected wages is negative. In an economy mainly rural (nu < 0:5), the transitional dynamics characterized by a continuous growth of population of the urban sector with a differential of expected wages relatively high is followed by the stabilization of rural-urban differential of expected wages. In other words, the generalized Harris-Todaro condition, eq. (15), arises as a long run equilibrium result of the agent-based migratory dynamics.
CONCLUSION
In this paper we developed and agent-based computational model which formalizes the rural-urban allocation of workers as a process of social learning by imitation. We analyze a two-sectorial economy composed by adaptative agents, i.e., individuals that grope over time for best sectorial location in terms of earnings. This search is a process of imitation of successful neighbor agents. The dispersed and non-coordinated individual migration decisions, made based on local information, generate aggregate regularities.
Firstly, the crucial assumption of Harris and Todaro, the principle that rural-urban migration will occur while the urban expected wage exceed the rural wage, comes out as spontaneous upshot of interaction among adaptative agents.
Secondly, the migratory dynamics generated by agents that seek to adaptate to the economic environment that they co-create leads the economy toward a long run equilibrium characterized by urban concentration with urban unemployment. When this long run equilibrium is reached, the generalized Harris-Todaro condition is satisfied, i.e., there is a stabilization of the rural-urban expected wage differential.
Thirdly, the impact of the minimum wage and elasticity of terms of trade in a long run equilibrium obtained by simulations are in agreement with the predictions of the original Harris-Todaro model with Cobb-Douglas technology.
Finally, the simulations showed an aggregated pattern not found in the original Harris-Todaro model. There is the possibility of small fluctuations of the urban share around an average value. This phenomenon is known as reverse migration.

REFERENCE

Aquino L. Espíndola thanks CAPES for the financial support. Jaylson J. Silveira acknowledges research grants from CNPq. T. J. P. Penna thanks CNPq for the fellowship.
J. R. Harris and M. P. Todaro, American Economic Review 60, 126 (1970).
M. P. Todaro, American Economic Review 59, 138 (1969).
D. Ray, Development Economics (Princeton: Princeton University Press, 1998).
L. Y. L. Yap, Journal of Development Economics 4, 239 (1977).
D. Mazumdar, Rural-urban Migration in Developing countries. In: Handbook of Regional and Urban Economics, Elsevier, Amsterdam, 1987.
L. Ghatak, P. Levine, and S. Price, Journal of Economics Surveys 10, 159 (1996).
J. G. Willianson, Migration and Urbanization. In: Chenery, H. and Srinivasan, T.N., Handbook of developments economics, Elsevier, Amsterdam, 1988.
J. J. Silveira, A. L. Espíndola, and T. J. P. Penna, physics/0506021, Physica A, to appear.

37. NAME: METEKE JOY ORIMUSUE
DEPARTMENT:ECOMOMICS
REG. NO:2017/242430

LEWIS -FEI-RANIS THEORY(SURPLUS LABOUR THEORY)
Lewis (1954) proposed a seminal theory of dualistic economic development for over-populated and under-developed economies with vast amounts of surplus agricultural labour for which he was later to be awarded the 1979 Nobel Prize in Economics. Economic growth in such an economy can be achieved by rapid capital accumulation in the non-agricultural (industrial and service) sector, facilitated by drawing surplus labour in the agricultural sector. In the Lewis theory, an economy transits from the first, labour-surplus “stage” to the second, labour-scarce “stage” of development.The central idea behind the Lewis model is fairly simple. Lewis divided labour force into two differentiated groups – “subsistence sector” and “capitalist sector” where the former is assumed to contain unlimited supply and consequently, a pool of surplus labour that sets labour-supply conditions for the latter.
Assumptions of the Lewis Model
(A) Surplus Labour in the Subsistence Sectors:
The basic assumption of the model is that there exists surplus labour in the subsistence sectors. It includes labour whose marginal productivity is zero as well as that whose marginal productivity is positive but is less than the institutional wage. This labour comprises farmers, agricultural labourers, petty traders domestic servants and women.
(B) Importance of Saving:
Another important assumption that Lewis makes is about the savings generated in the capitalist sector and in the subsistence sector. The capitalist sector invests all its savings for its further expansion.Those in the subsistence sector, on the other hand squander away their savings, if any in purchase of jewellery & for construction of temples etc. The propensity to save of the people in subsistence sector is also lower when compared with that of those in the capitalist sector.
The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model.It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.Ranis and Fei (1961) formalised the Lewis theory and defined three “phases” of dualistic economic development by sub-dividing the first stage in the Lewis model into two phases. Thus, the second labour-scarce stage of the Lewis model corresponds to phase three of the Ranis-Fei model. These three phases, illustrated in Diagram 1below, are distinguished by the marginal productivity of agricultural labour. The entry into each phase is marked three turning points:
• The breakout point leads to phase one growth with redundant agricultural labour.
• The shortage point leads to phase two growth with disguised agricultural unemployment.
• The commercialisation point leads to phase three of self-sustaining economic growth with the commercialisation of the agricultural sector.One of the biggest drawbacks of the Lewis model was the undermining of the role of agriculture in boosting the growth of the industrial sector. In addition to that, he did not acknowledge that the increase in productivity of labor should take place prior to the labor shift between the two sectors. However, these two ideas were taken into account in the Fei–Ranis dual economy model of three growth stages.They further argue that the model lacks in the proper application of concentrated analysis to the change that takes place with agricultural development.
Under competitive assumptions, the real wage rate would fall to zero, but due to the presence of institutional or non-market forces, the institutional wage is sustained. Therefore, there are gains to be had by switching resources away to the industrial sector. Nevertheless, it is generally not likely to happen because the market, left on its own, does not change. If the industrial sector does pay according to marginal product, then, as noted by Ray (1998), there would efficiency gains available as long as the marginal product of the agricultural labour is Gless than the wage, whether it is zero or not. By decreasing the labour force in agriculture by a small amount (whilst still remaining in the surplus labour area), provided that the wage in agriculture does not rise. Since output does not fall, the reduction in the total wage bill gives an economy an agricultural surplus.

RELATING THE MODEL TO NIGERIA ECONOMY
Nigeria has both rural and urban sectors that provide for each forward and backward linkages and as such, the two sectors are not mutually exclusive in promoting the economic growth of the country and improving the standard of living of citizens. However, the Federal Government of Nigeria does not necessarily have to move surplus labour that exists in the rural areas to the urban areas but instead infrastructural facilities should be provided equally to both the rural and urban areas of the country.

HARRIS-TODARO THEORY OF MIGRATION

The Harris–Todaro model, named after John R. Harris and Michael Todaro, is an model developed in 1970 and used in development economics and welfare economics to explain some of the issues concerning rural-urban migration.
The key hypothesis of Harris and Todaro are that migrants react mainly to economic incentives, earnings differentials, and the probability of getting a job at the destination have influence on the migraton decision. In other words, these authors posit that rural-urban migration will occur while the urban expected wage exceed the rural wage. From this crucial assumption as denominated by Harris-Todaro , is deduced that the migratory dynamics leads the economic system toward an equilibrium with urban concentration and high urban unemployment.

ASSUMPTIONS OF THE MODEL
i. Two sectors: urban (manufacture) and rural (agriculture)
ii. Rural-urban migration condition: when urban real wage exceeds real agricultural product
iii.No migration cost
iv. Perfect competition
e. Cobb-Douglas production function.

RELATING THE MODEL TO NIGERIA’S ECONOMY
In cases of pro-poor economic growth, the Harris-Todaro model and other multisector-labor-market models can help policy makers avoid two mistakes. One is to assume that development efforts should be channeled to the sectors where the poor are. The other is to assume that efforts should always be focused on getting the poor out of the sectors in which they now are.

38. OHANADO SHEPHERD IFEANYI 2017/249547 says:

LEWIS-FEI-RANIS MODEL OF ECONOMIC GROWTH
The Fei–Ranis model of economic growth is a dualism model in developmental economics or economic welfare that has been developed by John CH FEI and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model. Rostow Ranis and Fei (1961) formalized Lewis’s theory by combining it with Rostow’s (1956) three “linear-stages-of-growth” theory. They assume the economy to be stagnant in its pre-conditioning stage. The breakout point marks the creation of an infant non-agricultural sector and the entry into phase one. Agricultural labor starts to be reallocated to the non-agricultural sector. Due to the abundance of surplus agricultural labor, its marginal productivity is
Extremely low and average labor productivity defines the agricultural institutional
Wage.
The features of this model is; capital accumulation fuels development of the industrial sector and movement of surplus labor from agriculture sector to industrial
They disassembled Lewis’s two-stage Economic development into three phases, defined by the marginal productivity of Agricultural labor. They assume the economy to be stagnant in its pre-conditioning Stage The capitalist sector can either be private or public in nature
In his model Lewis divides the economy in an underdeveloped country in two sectors namely the Subsistence sector and the capitalist sector. Subsistence is identified with the agricultural sector of the economy while the capitalist sector implies mainly the manufacturing sector of the economy.
The model Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there can be compared to the Harrold Domar model saving and investment become the driving forces when it comes to economic development of underdeveloped countries but the Fei Ranis model is augmentation of industrial output
it affects the Nigeria economy in the sense that industrial sector should get attention more as the world is driving towards industrialization and for one to focus on agricultural sector would be bad best to focus on both sectors to increase labor supply cause an increase in both sectors would reduce unemployment by creating more industrial and agricultural cause the flow of labor to the city and to the industrial sector provides a new gain to society and once surplus labor is exhausted, wages are driven up in both sectors.
And it can be in turn seen that this model can be related to the economy of Nigeria as an increase investment in industry would lead to surplus increase in employment which is one of the major lacking factors in Nigeria and this would in turn lead to an increase in the economy of Nigeria

HARIS-TODARO MODEL OF MIGRATION
The Harris-Todaro model of the rural-urban migration process is revisited under an agent-based approach. … Such an equilibrium is characterized by stabilization of rural-urban expected wages differential (generalized Harris-Todaro equilibrium condition), urban concentration and urban unemployment. The model assumes that unemployment is non-existent in the rural agricultural sector. As a result, the agricultural rural wage is equal to agricultural marginal productivity. In equilibrium, the rural to urban migration rate will be zero since the expected rural income equals the expected urban income. In the Harris–Todaro model, the rising urban wage pushes up the expected wage in the urban sector and consequently encourages workers to migrate from the rural sector to the urban sector.
The model therefore believed that , migration from rural areas to urban areas will increase if:
Urban wages (wu) increase in the urban sector (le), increasing the expected urban income.
Agricultural productivity decreases, lowering marginal productivity and wages in the agricultural sector (wr), decreasing the expected rural income.
However, even though this migration creates unemployment and induces informal sector growth, this behavior is economically rational and utility-maximizing in the context of the Harris–Todaro model. As long as the migrating economic agents have complete and accurate information concerning rural and urban wage rates and probabilities of obtaining employment, they will make an expected income-maximizing decision.
this model can be related to the Nigerian economy in the sense that people would prefer to move from rural to urban areas cause of the income differences and a better life hood and this would lead to a development of urban areas creating avenue for economic growth through development of infrastructure, industries etc. and would in turn lead to economic growth

39. Ezeakudo chinyere Stellamaris says:

Name: Ezeakudo Chinyere Stellamaris
Reg no:2017/249334
E-mail :mariskudos @gmail. Com

Lewis- Fei Ranis model of economic is a growth of a dualism model in developmental economics that has been developed by John. C. H. Fei and Gustavus Ranis. It is also known as the surplus labour model. Which recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and under employment of resources into account, unlike many other growth models that consider under developed countries to be homogeneous in nature. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output . This is done by transfer of labour from the agricultural sector to the industrial one, showing that under developed countries do not suffer from constraints of labour supply.
How this can be applied to the Nigerian economy
1. Improving the standard of living of citizen
2. Promoting the economic growth of the country.
3. Providing equal infrastructural facilities to the both the rural and urban areas of the country.

Harris – Todaro model named after John R. Harris and Michael Todaro is an economic model developed in 1970 and used in development economics and welfare Economics to explain some of the issues concerning rural – urban migration. The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.
How it can be applied to the Nigerian economy
Nigeria favor rural -urban migration. Also Nigerian economy is largely dependent on oil revenue. Which encourage a net movement of people from the rural to urban. The key to resolving issues of rural push is the provision of alternatives that would make rural areas independent of the cities and function more as supporting structure to the cities. Eh Agricultural productivity. Policy development should encourage rural areas to have access to basic amenities and thus allow them to provide value -added services in food security.

40. Ezeakudo chinyere Stellamaris says:

Name: Ezeakudo Chinyere Stellamaris
Reg no:2017/249334
E-mail :mariskudos @gmail. Com

Lewis- Fei Ranis model of economic is a growth of a dualism model in developmental economics that has been developed by John. C. H. Fei and Gustavus Ranis. It is also known as the surplus labour model. Which recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and under employment of resources into account, unlike many other growth models that consider under developed countries to be homogeneous in nature. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output . This is done by transfer of labour from the agricultural sector to the industrial one, showing that under developed countries do not suffer from constraints of labour supply.
How this can be applied to the Nigerian economy
1. Improving the standard of living of citizen
2. Promoting the economic growth of the country.
3. Providing equal infrastructural facilities to the both the rural and urban areas of the country.

Harris – Todaro model named after John R. Harris and Michael Todaro is an economic model developed in 1970 and used in development economics and welfare Economics to explain some of the issues concerning rural – urban migration. The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.
How it can be applied to the Nigerian economy
Nigeria favor rural -urban migration. Also Nigerian economy is largely dependent on oil revenue. Which encourage a net movement of people from the rural to urban. The key to resolving issues of rural push is the provision of alternatives that would make rural areas independent of the cities and function more as supporting structure to the cities. Eh Agricultural productivity. Policy development should encourage rural areas to have access to basic amenities and thus allow them to provide value -added services in food security.

41. Agbo Jennifer Amarachi
2017/249476
jenniferamarachi.agbo@gmail.com
https://agbojenniferamarachi.blogspot.com/?m=1

FIRST TOPIC: HARRIS TODARO MODEL OF MIGRATION.

INTRODUCTION
In reality, it has been confirmed that an economy can develop effectively by transferring a huge amount of its labour from its subsistence otherwise called Agricultural, backward, and informal sector in the rural region to the modern sector or industry. The Rural sector is known to be a sector where the marginal productivity of labour is very low, or even zero, whereas in the modern sector, the marginal productivity of labour is higher, very much positive and greater than zero. The Harris-Todaro model is a model that explains the little dialogue above, and because it deals with two sector in the economy, it is also referred to as a Dualistic Model. According to the Literature of Development Economics, typical dualistic models became popular in the 1950’s. A Dualistic model in development economics contains, two sectors, which are Traditional/ rural or agricultural sector and a modern or manufacturing sector in the urban area.
However, the ground-breaking work of Harris and Todaro in 1970, was brought as a result of what Todaro called “a curious economic phenomenon” in tropical Africa. The phenomenon was a regular and increasing rural urban migration regardless, the existence or presence of higher positive marginal products in agriculture.

MAJOR CONTRIBUTION OF MICHAEL P. TODARO
The introduction of the probability of employment as an element in the decision making process of a potential migrant is considered the main contribution of Todaro. He called his proposal “a more realistic picture of labour migration in less developed countries” that is, a two-stage process.
The First Stage: is where the rural migrant enters the urban area and settles down in traditional urbans sector (the informal sector) for a given or certain period of time.
The Second Stage: it is reached when the migrant finds a more permanent job in the modern sector. Although Todaro and some other authors did not consider the employees of the informal sector, they were seen to be the same with unemployed people in the society, this is because to them they make no income of their own and always have to rely on their relatives for survival.
According to Todaro, the probability of getting a Job is dependent on:
The number of newly recent or newly created jobs in the formal or modern sector/.
The Size of the population Unemployed in the Modern sector.
The length of time a migrant has been in the urban area. It happens that the longer one stays, the greater the chance of finding Job in the urban sector.

HARRIS-TODARO MODEL – AN EXTENSION OF THE TODARO MODEL.

The Harris-Todaro Model is an extension of the Todaro Model. Prof. J.R. Harris and P. Michael Todaro in an article “Migration, Unemployment and Development: A two-Sector Analysis” in 1970 presented a model on rural-urban migration in underdeveloped countries. The core notion of Harris Todaro’s model is that the migration of labour in less developed countries is due to the rural-urban differences in average expected wages rather than actual wages. This means that the migrants will have to consider and weigh the numerous job opportunities that are provided to them in the rural and urban sectors and they will choose the one that gives the highest expected wage from Migration.

The minimum wage which is obtainable in the Urban sector is significantly higher than the rural wage. Therefore, if more job opportunities are created in the urban sector at the minimum wage, the expected wage will rise and rural-urban migration will increase. Expected wages are measured by the differences in real urban income and rural agricultural income and the probability of a migrant’s getting an Urban Job. Thus, migration in the Harris-Todaro model is seen as the wage or income gap between the rural and the urban sectors. However, all the migrants cannot be absorbed simultaneously in the urban sector at that prevailing high wage. So many of them fail to find a job and get employment in the informal urban sector at wages which are even lower than in the rural sector, this means that the number of unemployment will increase in the Urban sector.
The unique concept in the migration flow from rural(Agricultural) areas to urban (Industrial) areas is determined by the difference between expected urban wages and rural wages.

MAIN DISCUSSION OF HARRIS-TODARO MODEL

The ultimate contribution of the Harris-Todaro rural-urban two-sector migration model was to build a model that fit the schematic facts of the labour market. Developing countries implemented program on incorporated rural development which encouraged an increase in the rural traditional sector wage. The theory proves that the higher the Unemployment rate, the lower is the probability of new migrants from the country side actively seeking formal sector employment who are unable to find it.

THE NOTABLE FINDINGS

There is no incentive to migrate if the expected urban wage equals rural income.
There is a great incentive to move from rural to urban area if the expected urban wage is greater than rural income,
There would be an incentive to move in other direction if the expected urban wage is less than rural income.
The expected urban wage depends on what type of Job the migrant is engaged in.

ASSUMPTIONS OF THE HARRIS TODARO MODEL

There are two sectors in the Economy – The rural or agricultural sector (A) and the urban or manufacturing sector (M).

The Model operates in the short run.

The Marginal production of Labour in agriculture (MPLA) and of Industry (MPLM) are determined by their respective technologies.

Available Capital in the two sectors are in fixed quantities.

The number of Urban Jobs available (Lm) is exogenously fixed. In the rural sector some work is always available. Therefore, the total urban labour force Lm comprises L-LA along with an available supply of rural Migrants.

The Urban wage is fixed at Wm and the rural wage at WA , Wm> WA

The rural wage equals the rural marginal product of labour and the urban wage is exogenously determined.

Rural-Urban Migration continues so long as the expected urban real income is more that the real agricultural income.

MAJOR CRITICISMS

The lottery style of Job allocation ignores investment in Job search on the part of the migrants and the informal sector is not clearly modelled.
The assumption of a rigid wage in the modern sector cannot be supported due to lack of evidence. Besides trade union pressure or minimum wage legislation, the wage differentials among sectors could be explained as well by, say. Firm specific training costs.
The issue of discount rates and rational migrants is overlooked and the influence on decision making of risk and risk attitudes on the part of potential migrants is not included.
Differentials in skill levels among the migrants are not accounted for.
Further. Some of the assumptions of the Harris-Todaro model were judged to be too restrictive. The model also assumes that potential migrants are risk neutral where poor migrants will likely be risk averse, as in they are indifferent between a certain expected rural income and uncertain expected urban income of the same magnitude. Also, the assumption that there exist a perfect competition in rural agriculture is not realistic.
However, the main drawback of this model is that it does not incorporate the costs of rural-urban migration or the relatively higher costs of urban living which the migrants have to incur in the urban sector.

CONCLUSION

The Harris-Todaro Model elucidates the issues of rural-urban migration. The equilibrium condition of this model occurs is when the expected urban wage is equal to rural wage. For instance, when government decides to subsidize manufacturing sector Harris-Todaro Paradox may happen. According to the authors job creation instead of dealing with unemployment problem actually may cause increase of unemployment. This happens when urban–rural wage gap is high enough; so rural workers move to the cities hoping to find Job with high wage. However, not all these workers succeed in finding Jobs which leads to Unemployment.

SECOND TOPIC: LEWIS-FEI-RANIS MODEL (SURPLUS LABOUR THEORY)

The Arthur Lewis (1954) theory of dualistic economic development provides the seminal contribution of theories of economic development particularly for labour surplus and resource for poor developing countries. The Economy in the Lewis theory, comprises the agricultural and non-agricultural sectors.

The Agricultural sector is assumed to have huge amounts of surplus labour that results in an extremely low, close to zero, marginal productivity of labour. The agricultural wage rate is pressured to follow the sharing rule and be equal to the average productivity, that is the institutional wage.

The non-agricultural sector has an abundance capital and resources relative to labour. It pursues profit and employs labour at a wage rate higher than the agricultural institutional wage by approximately 30%. It accumulates capital by drawing surplus labour out of the agricultural sector. The expansion of the agricultural sector takes advantage of the infinite elastic supply of labour from the agricultural sector due to its labour surplus. When the surplus labour is exhausted, the labour supply curve in the non-agricultural sector becomes upward sloping. This model is also called Utilization of manpower

Furthermore, Gustav Ranis and John Fei in 1961, formalised and developed Lewis’ theory by combining it with Rostow’s (1956) three “linear stages of growth ” theory. Their significant contribution was the dissembling of Lewis’ two-stage Economic development into 3 phase; defined by the marginal productivity of agricultural labour.

ASSUMPTIONS

The Economy is assumed to be constant in the preconditioning stage. The break out point marks the creation of an infant non-agricultural sector and the entry into phase one.
Agricultural labour starts to be reallocated to the non-agricultural sector. Due to the abidance of surplus agricultural labour, it’s marginal productivity is extremely low and average productivity defines the agricultural institutional wage. When. The redundant agricultural labour force has been reallocated, the agricultural marginal productivity of labour starts to rise but is still lower than the institutional wage.
This marks the shortage point at which the Economy enters phase two of development. During phase two the remaining agricultural unemployment is gradually absorbed.
At the end of this process the Economy reaches the commercialization point and enters phase three where the agricultural labour market is fully commercialised.

Modern Urban industrial sector is characterised by high productivity and employment opportunities.

Output expansion leads labour transfer and Urban employment growth.

The speed which they occur is given by the rate of investment or capital accumulation in the modern sector.

Urban wages would have be at least 30% higher than average rural income to induce workers to migrate from their home areas.

Level of wages in industrial sector is assumed constant. But at this constant wage, the supply of rural labour is considered perfectly elastic.

CRITICISMS OF THE MODEL

It fails to explain the underdevelopment in third world countries in under three aspect:

✓ The model assumes that, the rate of labour transferred employment creation is proportional to the rate of capital accumulation, the faster the rate of capital accumulation, the higher the growth rate of the modern sector and the faster the rate of job creation. Although total Gross National Product would rise, all the extra income and output growth is distributed to the few owners of capital while income levels of the masses of workers remain unchanged, hence no improvement in social welfare.

✓ The model assumes that surplus labour occurs in rural areas while there is full employment in Urban areas, but this is not true with third world countries. There is substantial open unemployment in Urban areas but almost no general surplus labour in rural locations.

✓ The model assumes constant constant real wages in Urban areas, this however is not the case with the developing countries where in most cases real wages both in absolute and relative terms tends to increase.

This model has been applied to analysis for instance the dualistic economic development of China and many other countries.

CONCLUSION

According to this theory, the primitive sector consist of the existing agricultural sector, the modern sector which is rapidly emerging and a small industrial sector. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy such that there is augmentation of industrial output.

This is done by transfer of labour from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labour supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole Economy with food and raw materials.

42. Name: Agbo Jennifer Amarachi
Reg No: 2017/249476
E-mail: jenniferamarachi.agbo@gmail.com

FIRST TOPIC: HARRIS TODARO MODEL OF MIGRATION.

INTRODUCTION
In reality, it has been confirmed that an economy can develop effectively by transferring a huge amount of its labour from its subsistence otherwise called Agricultural, backward, and informal sector in the rural region to the modern sector or industry. The Rural sector is known to be a sector where the marginal productivity of labour is very low, or even zero, whereas in the modern sector, the marginal productivity of labour is higher, very much positive and greater than zero. The Harris-Todaro model is a model that explains the little dialogue above, and because it deals with two sector in the economy, it is also referred to as a Dualistic Model. According to the Literature of Development Economics, typical dualistic models became popular in the 1950’s. A Dualistic model in development economics contains, two sectors, which are Traditional/ rural or agricultural sector and a modern or manufacturing sector in the urban area.
However, the ground-breaking work of Harris and Todaro in 1970, was brought as a result of what Todaro called “a curious economic phenomenon” in tropical Africa. The phenomenon was a regular and increasing rural urban migration regardless, the existence or presence of higher positive marginal products in agriculture.

MAJOR CONTRIBUTION OF MICHAEL P. TODARO
The introduction of the probability of employment as an element in the decision making process of a potential migrant is considered the main contribution of Todaro. He called his proposal “a more realistic picture of labour migration in less developed countries” that is, a two-stage process.
The First Stage: is where the rural migrant enters the urban area and settles down in traditional urbans sector (the informal sector) for a given or certain period of time.
The Second Stage: it is reached when the migrant finds a more permanent job in the modern sector. Although Todaro and some other authors did not consider the employees of the informal sector, they were seen to be the same with unemployed people in the society, this is because to them they make no income of their own and always have to rely on their relatives for survival.
According to Todaro, the probability of getting a Job is dependent on:
The number of newly recent or newly created jobs in the formal or modern sector/.
The Size of the population Unemployed in the Modern sector.
The length of time a migrant has been in the urban area. It happens that the longer one stays, the greater the chance of finding Job in the urban sector.

HARRIS-TODARO MODEL – AN EXTENSION OF THE TODARO MODEL.

The Harris-Todaro Model is an extension of the Todaro Model. Prof. J.R. Harris and P. Michael Todaro in an article “Migration, Unemployment and Development: A two-Sector Analysis” in 1970 presented a model on rural-urban migration in underdeveloped countries. The core notion of Harris Todaro’s model is that the migration of labour in less developed countries is due to the rural-urban differences in average expected wages rather than actual wages. This means that the migrants will have to consider and weigh the numerous job opportunities that are provided to them in the rural and urban sectors and they will choose the one that gives the highest expected wage from Migration.

The minimum wage which is obtainable in the Urban sector is significantly higher than the rural wage. Therefore, if more job opportunities are created in the urban sector at the minimum wage, the expected wage will rise and rural-urban migration will increase. Expected wages are measured by the differences in real urban income and rural agricultural income and the probability of a migrant’s getting an Urban Job. Thus, migration in the Harris-Todaro model is seen as the wage or income gap between the rural and the urban sectors. However, all the migrants cannot be absorbed simultaneously in the urban sector at that prevailing high wage. So many of them fail to find a job and get employment in the informal urban sector at wages which are even lower than in the rural sector, this means that the number of unemployment will increase in the Urban sector.
The unique concept in the migration flow from rural(Agricultural) areas to urban (Industrial) areas is determined by the difference between expected urban wages and rural wages.

MAIN DISCUSSION OF HARRIS-TODARO MODEL

The ultimate contribution of the Harris-Todaro rural-urban two-sector migration model was to build a model that fit the schematic facts of the labour market. Developing countries implemented program on incorporated rural development which encouraged an increase in the rural traditional sector wage. The theory proves that the higher the Unemployment rate, the lower is the probability of new migrants from the country side actively seeking formal sector employment who are unable to find it.

THE NOTABLE FINDINGS

There is no incentive to migrate if the expected urban wage equals rural income.
There is a great incentive to move from rural to urban area if the expected urban wage is greater than rural income,
There would be an incentive to move in other direction if the expected urban wage is less than rural income.
The expected urban wage depends on what type of Job the migrant is engaged in.

ASSUMPTIONS OF THE HARRIS TODARO MODEL

There are two sectors in the Economy – The rural or agricultural sector (A) and the urban or manufacturing sector (M).

The Model operates in the short run.

The Marginal production of Labour in agriculture (MPLA) and of Industry (MPLM) are determined by their respective technologies.

Available Capital in the two sectors are in fixed quantities.

The number of Urban Jobs available (Lm) is exogenously fixed. In the rural sector some work is always available. Therefore, the total urban labour force Lm comprises L-LA along with an available supply of rural Migrants.

The Urban wage is fixed at Wm and the rural wage at WA , Wm> WA

The rural wage equals the rural marginal product of labour and the urban wage is exogenously determined.

Rural-Urban Migration continues so long as the expected urban real income is more that the real agricultural income.

MAJOR CRITICISMS

The lottery style of Job allocation ignores investment in Job search on the part of the migrants and the informal sector is not clearly modelled.
The assumption of a rigid wage in the modern sector cannot be supported due to lack of evidence. Besides trade union pressure or minimum wage legislation, the wage differentials among sectors could be explained as well by, say. Firm specific training costs.
The issue of discount rates and rational migrants is overlooked and the influence on decision making of risk and risk attitudes on the part of potential migrants is not included.
Differentials in skill levels among the migrants are not accounted for.
Further. Some of the assumptions of the Harris-Todaro model were judged to be too restrictive. The model also assumes that potential migrants are risk neutral where poor migrants will likely be risk averse, as in they are indifferent between a certain expected rural income and uncertain expected urban income of the same magnitude. Also, the assumption that there exist a perfect competition in rural agriculture is not realistic.
However, the main drawback of this model is that it does not incorporate the costs of rural-urban migration or the relatively higher costs of urban living which the migrants have to incur in the urban sector.

CONCLUSION

The Harris-Todaro Model elucidates the issues of rural-urban migration. The equilibrium condition of this model occurs is when the expected urban wage is equal to rural wage. For instance, when government decides to subsidize manufacturing sector Harris-Todaro Paradox may happen. According to the authors job creation instead of dealing with unemployment problem actually may cause increase of unemployment. This happens when urban–rural wage gap is high enough; so rural workers move to the cities hoping to find Job with high wage. However, not all these workers succeed in finding Jobs which leads to Unemployment.

SECOND TOPIC: LEWIS-FEI-RANIS MODEL (SURPLUS LABOUR THEORY)

The Arthur Lewis (1954) theory of dualistic economic development provides the seminal contribution of theories of economic development particularly for labour surplus and resource for poor developing countries. The Economy in the Lewis theory, comprises the agricultural and non-agricultural sectors.

The Agricultural sector is assumed to have huge amounts of surplus labour that results in an extremely low, close to zero, marginal productivity of labour. The agricultural wage rate is pressured to follow the sharing rule and be equal to the average productivity, that is the institutional wage.

The non-agricultural sector has an abundance capital and resources relative to labour. It pursues profit and employs labour at a wage rate higher than the agricultural institutional wage by approximately 30%. It accumulates capital by drawing surplus labour out of the agricultural sector. The expansion of the agricultural sector takes advantage of the infinite elastic supply of labour from the agricultural sector due to its labour surplus. When the surplus labour is exhausted, the labour supply curve in the non-agricultural sector becomes upward sloping. This model is also called Utilization of manpower

Furthermore, Gustav Ranis and John Fei in 1961, formalised and developed Lewis’ theory by combining it with Rostow’s (1956) three “linear stages of growth ” theory. Their significant contribution was the dissembling of Lewis’ two-stage Economic development into 3 phase; defined by the marginal productivity of agricultural labour.

ASSUMPTIONS

The Economy is assumed to be constant in the preconditioning stage. The break out point marks the creation of an infant non-agricultural sector and the entry into phase one.
Agricultural labour starts to be reallocated to the non-agricultural sector. Due to the abidance of surplus agricultural labour, it’s marginal productivity is extremely low and average productivity defines the agricultural institutional wage. When. The redundant agricultural labour force has been reallocated, the agricultural marginal productivity of labour starts to rise but is still lower than the institutional wage.
This marks the shortage point at which the Economy enters phase two of development. During phase two the remaining agricultural unemployment is gradually absorbed.
At the end of this process the Economy reaches the commercialization point and enters phase three where the agricultural labour market is fully commercialised.

Modern Urban industrial sector is characterised by high productivity and employment opportunities.

Output expansion leads labour transfer and Urban employment growth.

The speed which they occur is given by the rate of investment or capital accumulation in the modern sector.

Urban wages would have be at least 30% higher than average rural income to induce workers to migrate from their home areas.

Level of wages in industrial sector is assumed constant. But at this constant wage, the supply of rural labour is considered perfectly elastic.

CRITICISMS OF THE MODEL

It fails to explain the underdevelopment in third world countries in under three aspect:

✓ The model assumes that, the rate of labour transferred employment creation is proportional to the rate of capital accumulation, the faster the rate of capital accumulation, the higher the growth rate of the modern sector and the faster the rate of job creation. Although total Gross National Product would rise, all the extra income and output growth is distributed to the few owners of capital while income levels of the masses of workers remain unchanged, hence no improvement in social welfare.

✓ The model assumes that surplus labour occurs in rural areas while there is full employment in Urban areas, but this is not true with third world countries. There is substantial open unemployment in Urban areas but almost no general surplus labour in rural locations.

✓ The model assumes constant constant real wages in Urban areas, this however is not the case with the developing countries where in most cases real wages both in absolute and relative terms tends to increase.

This model has been applied to analysis for instance the dualistic economic development of China and many other countries.

CONCLUSION

According to this theory, the primitive sector consist of the existing agricultural sector, the modern sector which is rapidly emerging and a small industrial sector. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy such that there is augmentation of industrial output.

This is done by transfer of labour from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labour supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole Economy with food and raw materials.

43. NNANYELUGO CHIDERA MICHAEL says:

NAME: NNANYELUGO CHIDERA MICHAEL.
REG. NO: 2017/245023
DEPT: ECONOMICS
Email: chiderannanyelugo@gmail.com

HARRIS-TODARO MODEL OF MIGRATION.

LEWIS – FEI-RANIS MODEL OF MIGRATION OF SURPLUS LABOUR

Harris Todaro Model of Migration
Introduction
The model was an academic investigation to throw light on the events following ‘Tripartite Agreement’ in Kenya. The newly independent Kenya in the 1960s was increasingly facing serious situation of unemployment in the major urban cities. To cope with the situation of unemployment, Tripartite Agreement was signed between the government public sector and the private sector. The agreement increased employment in the industrial jobs in exchange for unions agreeing to hold wages at their current levels. The larger number of employment was expected to reduce unemployment, but it appeared that the urban unemployment had increased following the government’s agreement. Harris and Todaro subsequently formulated a model to explain rural-urban economic preferences to migrate. The distinctive concept in the model is that the rate of migration flow from rural (agricultural) areas to urban (industrial) areas is determined by the difference between expected urban wages and rural wages.
The rural-urban two-sector model centrally holds the following futures: 1) Real wages (adjusted for cost-of-living differences) were higher in urban formal sector jobs than in rural traditional sector jobs. 2) To be hired for a formal sector job, it was necessary to be physically present in the urban areas where the formal sector jobs were located. 3) Consequently, from the first two features, more workers searched for formal sector jobs than were actually hired. Employers hired some of the searchers but not all of them. 4) To maintain equality between the expected wage associated with searching for an urban job and the expected wage associated with taking up a lower-paying rural job, the equilibrium arising in such a setting would be characterized by urban unemployment.
History
The Harris–Todaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and welfare economics to explain some of the issues concerning rural-urban migration. The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This implies that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.
THE HARRIS-TODARO MODEL
A. Assumptions
Harris and Todaro [1] studied the migration of workers in a two-sector economic system, namely, rural sector and urban sector. The difference between these sectors is the type of goods produced, the technology of production and the process of wage determination. The rural sector is specialized in the production of agricultural goods. The productive process of this sector can be described by a Cobb-Douglas production function:

where Ya is the production level of the agricultural good, Na is the amount of workers used in the agricultural production, Aa > 0 and 0 <   0 and 0 <   0 and  > 0 are a parametric constants.  is the elasticity of p with respect to the ratio Ym/Ya.
The overall population of workers in the economy is N, which is kept constant during the whole period of analysis. By assumption there are only two sectors and rural prices are wholly flexible, which implies that there is full employment in the rural area, i.e., all workers living at the rural sector are employed at any period. Then at any period the following equality is verified:

B. Temporary Equilibrium
Given a parametric constant vector (Aa,Am,,,,), an initial urban population Nu, and a minimum wage wm one can calculate the temporary equilibrium of the economic system by using eqs. (1 – 6).
From eq. (4) one can find the employment level at the manufacturing sector

Replacing eq. (7) in eq. (2) we get the production level of the manufacturing sector

From eq. (6) one can obtain the relation

Which is used with eq. (1) to obtain the agricultural production?

By using. Eqs. (5), (8) and (10) the terms of trade are determined

Finally, by using eqs. (3), (9) and (11), the rural wage in units of manufacturated good is obtained

In sum, the vector (Nm,Ym,Na,Ya,p,wa) configures a temporary equilibrium that might be altered whether occurs a migration of workers, induced by the differential of sectorial wages, which changes the sectorial distribution of overall population.
C. The Long Run Equilibrium
Harris and Todaro, in determining the long run equilibrium, i.e., the absence of a net rural-urban migratory flow, argue that the rural workers, in their decision on migrating to the urban area, estimate the expected urban wage, defined as:

The ratio Nm/Nu, which is the employment rate, is an estimative of the probability that a worker living at urban sector gets a job in this sector.
As mentioned before, the key assumption of the model of Harris and Todaro is that there will be a migratory flow from the rural to the urban sector while the expected urban wage is higher than the rural wage. Thus, the long run equilibrium is attained when the urban worker population reaches a level such that the expected urban wage equates the rural wage:

Harris and Todaro [1], in order to evaluate the stability of the long run equilibrium, postulate a mechanism of adjustment that is based on the following function of sign preservation:

The differential equation that governs the state transition in the model of Harris and Todaro is obtained by replacing equations (12), (13) in eq. (17). Based on this postulated adjustment process, Harris and Todaro [1] show that the long run equilibrium is globally asymptotically stable. This means that the economy would tend to long run equilibrium with unemployment in the urban sector generated by the presence of a relatively high minimum wage for all possible initial conditions. From now on we will refer to the long run equilibrium simply as equilibrium.
Based on the numerical solutions of eq. (16) one can evaluate the impact that the variation of the minimum wage and the elasticity of the terms of trade on the equilibrium. In Fig. 1 we see that under the hypothesis of a Cobb-Douglas technology, the equilibrium urban share, , does not depend on the minimum wage wm. However, changes in the value of wm reduces the labor demand on the manufacturing sector what results in higher unemployment rates in the equilibrium.
HARRIS-TODARO AGENT-BASED MODEL
In this section we describe the implementation of the computational model we proposed, as well as the aggregate patterns obtained numerically and the comparison with the respective analytical results.
A. Computational Implementation
Initially, workers are randomly placed in a square lattice with linear dimension L = 500. The reference values of the parameters used for these simulations are the same done to evaluate the equilibrium of the Harris-Todaro model, namely, Aa = 1.0, Am = 1.0, = 0.3,  = 0.7, r = 1.0 and = 1.0. The value of the minimum wage used is wm = 0.8 and the initial urban fraction of the total population is nu = 0.2, where nu = Nu/N is the normalized urban population also called urban share. The initial value nu = 0.2 is in agreement with historical data of developing economies. Given these parameters, one can calculate the vector which characterizes temporary equilibrium of the system by using eqs. (7 – 12).
By using eq. (7), the employment level of the urban sector, Nm, is obtained. If nu  Nm/N there will be a fraction of Nm/Nu workers employed, which earn the minimum wage, wi = wm, and (1-Nm/Nu) workers unemployed, which earn a wage wi = 0.
Each worker can be selected to review his sectorial location with probability a, called activity [11]. Therefore, in each time step only a fraction of workers becomes potential migrants, going through the sectorial location reviewing process. Potential migrants will determine their satisfaction level of being in the current sector by comparing their earnings, wi, among nearest neighbors.
The potential migrant starts the comparison process with a initial satisfaction level si = 0. When wi > wneighbor the satisfaction level si is added in one unit; if wi < wneighbor, si is diminished in one unit; if wi = wneighbor, si does not change. After the worker has passed through the reviewing process his/her satisfaction level is checked. The migration will occur only if si < 0, what means that the worker's i earnings is less than the most of his/her nearest neighbors.
After all the potential migrants complete the reviewing process and have decided migrate or not, a new configuration of the system is set. Therefore, once again a new temporary equilibrium of the system is calculated by using eqs. (8 – 12). The whole procedure is repeated until a pre-set number of steps is reached. It is important to emphasize that Nm is kept constant throughout the simulation. It’s given by eq. (7) which depends on the technological parameters, ,Am, and the minimum wage, wm, which are constants too.
B. Analysis of the Emergent Properties
In this section we develop the analysis of the long run aggregate regularities of Harris-Todaro agent-based computational model. These long run properties will be compared between the solution of the analytical model and simulations we ran.
Figures 3, 4 and 5 show the basic characteristics of the transitional dynamics and long run equilibrium generated by simulations. When the economic system has a low initial urban share, nu = 0:2 or nu = 0:3, there is a net migration toward urban sector. This migration takes the urban sector from a full employment situation to an unemployment one. The positive differential of expected wages that pulls workers to the urban sector diminishes. However, if the economic system initiates with a high urban share, nu = 0:8, or nu = 0:9 there is net flow of migration toward rural sector in such a way that the unemployment rate of the urban sector decreases.
In this case, the differential of expected wages is negative. In an economy mainly rural (nu < 0:5), the transitional dynamics characterized by a continuous growth of population of the urban sector with a differential of expected wages relatively high is followed by the stabilization of rural-urban differential of expected wages. In other words, the generalized Harris-Todaro condition, eq. (15), arises as a long run equilibrium result of the agent-based migratory dynamics.

COMPARISON OF THE MODEL
The models are: 1. Lewis’s Model of Rural-Urban Migration 2. The Fei-Ranis Model on Rural-Urban Migration 3. Harris-Todaro Model of Rural-Urban Migration.
1. Lewis’s Model of Rural-Urban Migration:
Prof. W. Arthur Lewis in his article, “Unlimited Supplies of Labour” has explained the process of migration from rural to urban areas in an underdeveloped economy.An underdeveloped economy is a dual economy having two sectors:
a modern sector, and
an indigenous sector.
Out of these two, the latter is the predominant sector. The capitalist sector is defined as “that part of the economy which uses reproducible capital, pays capitalists for the use thereof and employs wage labour for profit making purposes.”
2. The Fei-Ranis Model on Rural-Urban Migration:
John Fei and Gustav Ranis have presented in an article entitled, “A Theory of Economic Development”, the process of rural-urban migration in underdeveloped countries.
The model is related to an underdeveloped economy having surplus labour but scarcity of capital. The major part of the population is engaged in agriculture which is stagnant. Non-agricultural occupations use small capital. There also exists an industrial sector.
3. Harris-Todaro Model Of Rural-Urban Migration:
Prof. J.R. Harris and P. M. Todaro in an article “Migration, Unemployment and Development: A Two-Sector Analysis” in 1970 presented a model on rural-urban migration in underdeveloped countries.
The main idea of the Harris-Todaro model is that labour migration in underdeveloped countries is due to rural-urban differences in average expected wages rather than actual wages. The migrants consider the various opportunities of employment available to them in rural and urban sectors and choose the one that maximizes their expected wages from migration.
Conclusion
An important aspect of urban unemployment in developing countries is that it is predominantly open. The massive influx of rural migrants in the cities has been instrumental in fostering an overwhelmingly faster population growth in urban areas than in the rural ones. Rural workers are lured to migrate by economic incentives as well as by other attractions of an urbane life. While some of the migrants do manage to secure jobs in industries, the less-fortunate ones get absorbed only in the urban informal sector and the rest wait for their chance to get employment and thus swell the number of open urban unemployment. A substantial portion of the urban population in a country like India is engaged in the informal sector.

LEWIS – FEI-RANIS MODEL OF MIGRATION OF SURPLUS LABOUR
History
The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.
Basic of the Model
One of the biggest drawbacks of the Lewis model was the undermining of the role of agriculture in boosting the growth of the industrial sector. In addition to that, he did not acknowledge that the increase in productivity of labor should take place prior to the labor shift between the two sectors. However, these two ideas were taken into account in the Fei–Ranis dual economy model of three growth stages. They further argue that the model lacks in the proper application of concentrated analysis to the change that takes place with agricultural development in phase 1 of the Fei–Ranis model, the elasticity of the agricultural labor work-force is infinite and as a result, suffers from disguised unemployment. Also, the marginal product of labor is zero. This phase is similar to the Lewis model. In Phase 2 of the model, the agricultural sector sees a rise in productivity and this leads to increased industrial growth such that a base for the next phase is prepared. In Phase 2, agricultural surplus may exist as the increasing average product (AP), higher than the marginal product (MP) and not equal to the subsistence level of wages.
Using the help of the figure on the left, we see that after AD, MP begins to rise, and industrial labor rises from zero to a value equal to AD. AP of agricultural labor is shown by BYZ and we see that this curve falls downward after AD. This fall in AP can be attributed to the fact that as agricultural laborers shift to the industrial sector, the real wage of industrial laborers decreases due to shortage of food supply, since less laborers are now working in the food sector. The decrease in the real wage level decreases the level of profits, and the size of surplus that could have been re-invested for more industrialization. However, as long as surplus exists, growth rate can still be increased without a fall in the rate of industrialization. This re-investment of surplus can be graphically visualized as the shifting of MP curve outwards. In Phase2 the level of disguised unemployment is given by AK. This allows the agricultural sector to give up a part of its labor-force until
{\displaystyle {\text{Phase 1}}:AL({\text{from figure}})=MP=0{\text{ and }}AB({\text{from figure}})=AP\,}
Depiction of phase1, phase2 and phase 3 of the dual economy model using average output
After AD, MP begins to rise, and industrial labor rises from zero to a value equal to AD. AP of agricultural labor is shown by BYZ and we see that this curve falls downward after AD. This fall in AP can be attributed to the fact that as agricultural laborers shift to the industrial sector, the real wage of industrial laborers decreases due to shortage of food supply, since less laborers are now working in the food sector. The decrease in the real wage level decreases the level of profits, and the size of surplus that could have been re-invested for more industrialization. However, as long as surplus exists, growth rate can still be increased without a fall in the rate of industrialization. This re-investment of surplus can be graphically visualized as the shifting of
MP curve outwards. In Phase2 the level of disguised unemployment is given by AK. This allows the agricultural sector to give up a part of its labor-force until the amount of labor that is shifted and the time that this shifting takes depends upon:
The growth of surplus generated within the agricultural sector, and the growth of industrial capital stock dependent on the growth of industrial profits;
The nature of the industry's technical progress and its associated bias;
Growth rate of population.
So, the three fundamental ideas used in this model are:
Agricultural growth and industrial growth are both equally important;
Agricultural growth and industrial growth are balanced;
Only if the rate at which labor is shifted from the agricultural to the industrial sector is greater than the rate of growth of population will the economy be able to lift itself up from the Malthusian population trap.
This shifting of labor can take place by the landlords' investment activities and by the government's fiscal measures. However, the cost of shifting labor in terms of both private and social cost may be high, for example transportation cost or the cost of carrying out construction of buildings. In addition to that, per capita agricultural consumption can increase, or there can exist a wide gap between the wages of the urban and the rural people. These three occurrences- high cost, high consumption and high gap in wages are called as leakages, and leakages prevent the creation of agricultural surplus. In fact, surplus generation might be prevented due to a backward-sloping supply curve of labor as well, which happens when high income-levels are not consumed. This would mean that the productivity of laborers with rise in income will not rise. However, the case of backward-sloping curves is mostly unpractical.
Critism of the Model
Fei–Ranis model of economic growth has been criticized on multiple grounds, although if the model is accepted, then it will have a significant theoretical and policy implications on the underdeveloped countries' efforts towards development and on the persisting controversial statements regarding the balanced vs. unbalanced growth debate.
It has been asserted that Fei and Ranis did not have a clear understanding of the sluggish economic situation prevailing in the developing countries. If they had thoroughly scrutinized the existing nature and causes of it, they would have found that the existing agricultural backwardness was due to the institutional structure, primarily the system of feudalism that prevailed.
Fei and Ranis say, "It has been argued that money is not a simple substitute for physical capital in an aggregate production function. There are reasons to believe that the relationship between money and physical capital could be complementary to one another at some stage of economic development, to the extent that credit policies could play an important part in easing bottlenecks on the growth of agriculture and industry." This indicates that in the process of development they neglect the role of money and prices. They fail to differ between wage labor and household labor, which is a significant distinction for evaluating prices of dualistic development in an underdeveloped economy.
Fei and Ranis assume that MPPL is zero during the early phases of economic development, which has been criticized by Harry T.Oshima and some others on the grounds that MPPL of labor is zero only if the agricultural population is very large, and if it is very large, some of that labor will shift to cities in search of jobs. In the short run, this section of labor that has shifted to the cities remains unemployed, but over the long run it is either absorbed by the informal sector, or it returns to the villages and attempts to bring more marginal land into cultivation. They have also neglected seasonal unemployment, which occurs due to seasonal change in labor demand and is not permanent.
To understand this better, we refer to the graph in this section, which shows Food on the vertical axis and Leisure on the horizontal axis. OS represents the subsistence level of food consumption, or the minimum level of food consumed by agricultural labor that is necessary for their survival. I0 and I1 between the two commodities of food and leisure (of the agriculturists). The origin falls on G, such that OG represents maximum labor and labor input would be measured from the right to the left. The transformation curve SAG falls from A, which indicates that more leisure is being used to same units of land. At A, the marginal transformation between food and leisure and MPL = 0 and the indifference curve I0 is also tangent to the transformation curve at this point. This is the point of leisure satiation.

44. Chigbata Franklin Chigozie says:

NAME: CHIGBATA FRANKLIN CHIGOZIE
REG: 2017/242424
EMAIL:FRANKLIN.CHIGBATA.242424@UNN.EDU.NG
ECO 361

Haris-Todaro Model of Migration
The Harris-Todaro Model was promulgated in the 1970 by two economists John R. Harris and Micheal Todaro. This model is used in development economics to understand the issues with rural urban migration. It has been noticed that for an economy to grow, large number of Labours has to be moved from the traditional sector in rural areas. Where the labour productivity is low or zero to a modern manufacturing sector where the productivity of labour is rising due to capital accumulation in that sector. Here we consider time closed economy that consist of two sector corresponding to rural and modern sector. The total population is assume to be one. The mass of residents it should not be surprising therefore that in the literature of development economics dualistic model is gained popularity over the simple-commodity or singular sector theories. A typical dualistic model in development economic constrains two sectors, a traditional sector in a rural area and manufacturing sector in an urban area. One factor of such rural urban migration is the per capital income differential between two rural and urban areas.
Todaro and Harris set up a seminal framework of migration between rural and urban area. They hypothesis that individual migrant to urban sector with the sum of obtaining employment. The formal sector and that informal sector employment is a transitional phase during which migrants balance the probability of employment against the real income differentials between the urban sector and rural sectors.

THE CORE ARGUMENT, ASSUMPTIONS AND DIAGRAMS OF THE HARRIS-TODARO MODEL
The main core argument of Todaro is the introduction of the probability of employment as an element in the decision making process of a potential migrant. He argues that a more realistic view of labour migration is less developed countries is a two stage process. The first stage rural migrant enter urban area settle in the traditional urban sector in a period of time. The second stage is reached when the migrant find a more permanent job in the modern sector. Todaro dual not consider the informal urban sector explicitly, it employee are underemployed or not different from does that are not employed.
Some of the argument and assumption of Harris and Todaro in the formation of this model. Harris and Todaro studied the migration of workers in a two sectors economic system namely, rural sector and urban sector. The difference between these sectors are the type of goods produced, the technology of production and the production of agricultural goods. The productive process of the sector can be described by a Cobb-Douglas production function.
Ya = Aa Na
Where Ya is the production level of agricultural good. Na is the amount of workers used in the agricultural production, Aa > 0 and 0 < f 0 and 0 < 9 < 1 are parametric constants. Both market are perfectly competitive. Nevertheless, there is segmentation in the labour market due to a high minimum urban wage politically determined.
In the rural sector the real wage is flexible, is equal to the marginal productivity of labour in the sector.
Wa = Aa
Where Na is the real wage and P is the price of the agricultural good both expressed in the units of manufacture
Wa = aAm such Nm Nu
Where Nu is the amount of workers in the urban sector.
This relative price of agriculture good P with respect to the ratio of Ym/Ya
The Temporary Equilibrium is given by a parametric constant vector (Aa, Am, f, a, r, g) an initial urban population Nu and a minimum wage Wm one can calculate the temporary equilibrium of the economic system Nm =
In sum (Nm, Ym, Na, P, Wa) configures a temporary equilibrium that might be altered whether occurs a migration of worker, induced by the differential of sectorial wage which changes the sectoral distribution of overall population.
The long run equilibrium is determined in the Harris – Todaro model. It will absence of a net rural-urban migratory flow. They argue that the rural workers in their decision on migrating to the urban area, estimate the expected urban wage.

Nm/Mu is the ratio of employment rate, it will estimation of the probability that live in the urban area get job in that area or sector
As mention before the key assumption of the model of Harris-Todaro is that there will be a migratory flow from the rural to the urban sector from the rural to the urban sector while the expected urban wage is higher than the rural wage. Thus, the long run equilibrium is attained when the urban worker population reaches a level such that the expected urban wage equates the rural wage.

This equality is known as the Harris-Todaro condition in the economic literature. Harris and Todaro argue that the differential of expected wage can be constant value. When the differential reader ‘d’ the net migration ceases.

Lewis-Fei-Ranis Model of Economic Growth

According to Rains-Fei point shows the Lewis turning point i.e. the point after which the supply curve of labour in the industrial sector will turn upwards. However Lewis himself did not consider this point as the upward turning point.
For him all labour in the agriculture sector whose marginal productivity was either zero or was less than the institutional wage was available to the industrial sector at the institutional wage (or at a rate a little above it,) Fie never pointed out that as soon as the zero value labour was transferred to the industrial sector (i.e. up to the end of phase I in the present model) the supply curve for labour will start turning upwards. For him some other labour too (whose marginal productivity was less than the institutional wage, was also available at a constant wage rate.The reason for this difference in the views of the authors of two models is that unlike Ranis and Fei, Lewis did not take into account the effect of changing terms on trade on the supply price of labour in the industrial sector. He totally ignored it.
Fie assumed as if the wages to the transferred labour will be paid in agricultural products and as the institutional wages fixed in terms of agricultural produce, the labour transferred to the industrial sector will continue to be available at the constant wage rate i.e. that institutional wage.Ranis and Fei, on the other hand assumed that the labour in the industrial sector will be paid, in terms of the industrial products and they had to bring the hanging terms of trade into the picture. So we find that whereas according to Ranis and Fei, Lewis’ turning point appears as soon as phase in their model ends, according to Lewis himself, the turning point will appear at the end of the phase II. If i.e. upto the point where labour in the agricultural sector is paid institutional wages.
Basic Thesis of the Model:
This theory is concerned with a poor economy which has following properties:
(i) There is an abundance of labor in such UDC and shortage of natural resources.
(ii) The population growth rate is very high which results in mass unemployment in the economy.
(iii) The major share of population is engaged in agriculture. But agriculture sector is stagnant. Hence, the marginal productivity of labor is zero and negative in agriculture sector.
(iv) There are certain non-agrarian sectors in the economy where there is reduced use of capital.
(v) There is a dynamic industrial sector in the economy.
Thus the model suggests that, "Economic development would be taking place if agricultural laborers are transferred to industrial sector where their productivity will increase".As we told earlier that it is a dual economy where there is a stagnant agri. sector and dynamic industrial sector. The situation where MPL – 0, labor can be transferred to industrial sector without any loss in agricultural output. The real wages in industrial sector remains fixed and it is equal to the initial level of real income in agri. sector. Such wages are given the name of institutional wages.
Stages of Fei-Ranis Model:
Fei and Ranis develop their dual economy model with the help of three stages of economic growth. They are presented as:
The investment in industrial sector (with the surplus earned) will shift the MP curve outward right as from aa to bb and then to cc. In this way agri. sector will be able to get rid of labor until the MPL = real wages = AB =constant institutional wage (CIW) which is obtained by dividing the total agri. output ORX (b part of Fig) by AD amount of labor. In other words, the slope of ORX curve represents real wage rate. Thus the MPL = CIW where the tangent to the total output line ORX at X is parallel to OX. In the second phase DK amount of labor were employed. But still MPL MPL. It means that in this phase still a certain amount of labor is surplus or they are prey to disguised unemployment.
A. The first stage of FR model is very similar to Lewis. Disguised unemployment comes into being because the supply of labor is perfectly elastic and MPL = 0. Therefore, such disguised unemployed are to be transferred to industrial sector at the constant institutional wage.
B. In the second stage of FR model (phase) agri. workers add to agri. output but they produce less than institutional wage they get. In other words, in the second stage the labor surplus exists where APL > MPL, but it is not equal to subsistence (institutional) wages. Accordingly, such disguised unemployed also have to be transferred to industrial sector. If the migration to industrial sector continues a situation is eventually reached where the farm workers produce output equal to institutional wages. This would mean that productivity in agri. sector has gone up. With this the third phase (stage) starts.
C. In the third stage of FR model the take-off situation comes to an end and there begins the era of self-sustained growth where the farm workers produce more than the institutional wage they get. In this stage of economic growth the surplus labor comes to an end and the agri. sector becomes commercialized sector. All such is explained with the Fig.
The amount and time to re-allocate labor will depend upon:
(i) The rate of growth of industrial capital which depends upon the growth of profits in industrial sector and growth of surplus generated within the agri. sector.
(ii) The nature and bias of technical progress in industry.
(iii) The rate of growth of population. It means that the rate of labor transfer must be in excess of the rate of growth of population.
The three phases of labor transfer are summarized as:
In phase I: MPL = 0 and there exists the surplus labor equal to AD.
In phase II: CIW > MPL > 0 and there exists the open and disguised unemployment equal to AK.
In phase III: MPL > CIW and the economy is fully commercialized and disguised unemployment is exhausted. The supply of labor curve becomes steeper and both agri. and industrial sector compete with each other to get labor.
Thus we find that whereas Lewis had failed to offer a satisfactory explanation of this subsistence sector and ignored the real impact of population growth on the choice of capital intensity on the process of surplus labor absorption. Moreover, FR model emphasized upon the simultaneous growth of agri. and industrial sectors. Thus FR model believes in ‘Balanced Growth’ in the take-off stage. It means that there should be a simultaneous investment in both agri, sector and industrial sector. According to FR model in the beginning the surplus rises; such surplus will bo available as a capital in the take-offstage. Some part of this surplus will be used in agri. development, while some part will be reploughed in industrial development. As a result, both agri. and industrial sectors will grow under ‘Balanced Growth’ pattern.
Thus, three major points are highlighted in the FR mode:
(i) Growth of agri. is as important as the growth of industry.
(ii) There should be a balanced growth of agri and industrial sectors.
(iii) The rate of labor absorption must be higher than the rate of population growth to get out of the “Malthusian Nightmare”.
Criticism:
The FR model is considered to be an improvement over Lewis. This model presents a balanced growth of both the sectors of the economy, the most notable thing for the growth of UDCs. Despite this fact, this model has following shortcomings:
(i) Marginal Productivity of Labor in Phase I: The FR model is of the view that MFL = 0 in the first phase of growth, and the transfer of labor from agri. would not reduce output in the agri. sector in phase I. But the economists like Berry and Soligo are of the view that agri. output in phase I of FR model will not remain constant and may fell under different systems of land tenure, i.e., the peasant proprietorship and share cropping etc.
(ii) Marginal Productivity of Labor is Not Zero: Prof. Jorgenson who has also presented a model of ‘dual economy’ has object FR model’s contention of zero MP in phase I. He says whether MPL will be zero is an empirical issue. During the seasons of sowing and harvesting the MPL > 0. Jorgenson concluded on the basis of Japanese data even for the pre I world war period the supply of labor was not unlimited. Then how MPL can be zero.
(iii) Ignoring The Role of Capital: The FR model concentrated upon land and labor as the determinants of output, ignoring the role of capital. But Profs. Brown, Byres, Frankel, Griffen, Ghatak and Ingersent are of the view that in the UDCs there has occurred what is known as ‘Green Revolution’ in agri. which has promoted the greater use of capital and technology on lands. Consequently, there has been a greater increase in the agri. productivity and agri. incomes.
(iv) Open Economy: FR model ignored the role of foreign trade as it assumed a closed economy model. In the 2nd phase when agri. product decreases the TOT goes against industrial sector. This would occur in the presence of closed economy. But if the model is made open such would not happen as the goods could be imported in the presence of then-scarcity. This was especially observed in case of Japan which imported cheap farm products to improve her TOT (terms of trade).
(v) Supply of Land in Long Run: FR model assumed that in the process of economic development the supply of land remained fixed. But it is not true. The supply of land can be increased in case of long run.
(vi) Commercialization Of Agri. And Inflation: According to FR model when 3rd phase starts the agri. sector becomes commercialized. But it is criticized by saying that this phase does not start so easily The shifting of labor to industrial sector will create labor shortage in agri. sector. This will create shortage of food stuff leading to increase their prices. In this way, the inflation will generate which may obstruct the process of development.
(vii) Low Productivity in Agri Sector: According to Jorgenson it has been observed that there has been a very slow rise in the productivity of agri. sector. Consequently, the surplus will hardly be created in agri. sector. Accordingly, agri. sector will not contribute to development Thus the growth requires that the surplus must be generated and it should persist.
CONCLUSION
We analyse a two-sectorial economy composed by adaptive agent such as the individual that struggle over time for best sectorial location in term of earnings. First the basic assumption that of Harris-Todaro model that rural urban migration will occur while the urban expected wage exceed the rural wage. This on my view is visible or can be seen in the real world when individuals or economic agents see potential in a geographical area, they find to move to migrate in those area. Secondly the migratory dynamics generated by agents that seeking to adapt to the economic environment that they co-create lead the economy toward a long run equilibrium. This is also applicable in the real world were the effect of migration are felt.
Lastly the impact of the minimum wage and elasticity of terms of term in a long run equilibrium obtained by simulations are in agreement with the prediction of the original Harris-Todaro model with the application of the Cobb-Douglas technology.The harris-todaro model is visible in the real world because it applies the neutral principle of rural-urban migration and this make it more application in the real world.

45. Chigbata Franklin Chigozie says:

NAME: CHIGBATA FRANKLIN CHIGOZIE
REG: 2017/242424
EMAIL:FRANKLIN.CHIGBATA.242424@UNN.EDU.NG
ECO 361

Haris-Todaro Model of Migration

The Harris-Todaro Model was promulgated in the 1970 by two economists John R. Harris and Micheal Todaro. This model is used in development economics to understand the issues with rural urban migration. It has been noticed that for an economy to grow, large number of Labours has to be moved from the traditional sector in rural areas. Where the labour productivity is low or zero to a modern manufacturing sector where the productivity of labour is rising due to capital accumulation in that sector. Here we consider time closed economy that consist of two sector corresponding to rural and modern sector. The total population is assume to be one. The mass of residents it should not be surprising therefore that in the literature of development economics dualistic model is gained popularity over the simple-commodity or singular sector theories. A typical dualistic model in development economic constrains two sectors, a traditional sector in a rural area and manufacturing sector in an urban area. One factor of such rural urban migration is the per capital income differential between two rural and urban areas.
Todaro and Harris set up a seminal framework of migration between rural and urban area. They hypothesis that individual migrant to urban sector with the sum of obtaining employment. The formal sector and that informal sector employment is a transitional phase during which migrants balance the probability of employment against the real income differentials between the urban sector and rural sectors.

THE CORE ARGUMENT, ASSUMPTIONS AND DIAGRAMS OF THE HARRIS-TODARO MODEL
The main core argument of Todaro is the introduction of the probability of employment as an element in the decision making process of a potential migrant. He argues that a more realistic view of labour migration is less developed countries is a two stage process. The first stage rural migrant enter urban area settle in the traditional urban sector in a period of time. The second stage is reached when the migrant find a more permanent job in the modern sector. Todaro dual not consider the informal urban sector explicitly, it employee are underemployed or not different from does that are not employed.
Some of the argument and assumption of Harris and Todaro in the formation of this model. Harris and Todaro studied the migration of workers in a two sectors economic system namely, rural sector and urban sector. The difference between these sectors are the type of goods produced, the technology of production and the production of agricultural goods. The productive process of the sector can be described by a Cobb-Douglas production function.
Ya = Aa Na
Where Ya is the production level of agricultural good. Na is the amount of workers used in the agricultural production, Aa > 0 and 0 < f 0 and 0 < 9 < 1 are parametric constants. Both market are perfectly competitive. Nevertheless, there is segmentation in the labour market due to a high minimum urban wage politically determined.
In the rural sector the real wage is flexible, is equal to the marginal productivity of labour in the sector.
Wa = Aa
Where Na is the real wage and P is the price of the agricultural good both expressed in the units of manufacture
Wa = aAm such Nm Nu
Where Nu is the amount of workers in the urban sector.
This relative price of agriculture good P with respect to the ratio of Ym/Ya
The Temporary Equilibrium is given by a parametric constant vector (Aa, Am, f, a, r, g) an initial urban population Nu and a minimum wage Wm one can calculate the temporary equilibrium of the economic system Nm =
In sum (Nm, Ym, Na, P, Wa) configures a temporary equilibrium that might be altered whether occurs a migration of worker, induced by the differential of sectorial wage which changes the sectoral distribution of overall population.
The long run equilibrium is determined in the Harris – Todaro model. It will absence of a net rural-urban migratory flow. They argue that the rural workers in their decision on migrating to the urban area, estimate the expected urban wage.

Nm/Mu is the ratio of employment rate, it will estimation of the probability that live in the urban area get job in that area or sector
As mention before the key assumption of the model of Harris-Todaro is that there will be a migratory flow from the rural to the urban sector from the rural to the urban sector while the expected urban wage is higher than the rural wage. Thus, the long run equilibrium is attained when the urban worker population reaches a level such that the expected urban wage equates the rural wage.

This equality is known as the Harris-Todaro condition in the economic literature. Harris and Todaro argue that the differential of expected wage can be constant value. When the differential reader ‘d’ the net migration ceases.

Lewis-Fei-Ranis Model of Economic Growth

According to Rains-Fei point shows the Lewis turning point i.e. the point after which the supply curve of labour in the industrial sector will turn upwards. However Lewis himself did not consider this point as the upward turning point.
For him all labour in the agriculture sector whose marginal productivity was either zero or was less than the institutional wage was available to the industrial sector at the institutional wage (or at a rate a little above it,) Fie never pointed out that as soon as the zero value labour was transferred to the industrial sector (i.e. up to the end of phase I in the present model) the supply curve for labour will start turning upwards. For him some other labour too (whose marginal productivity was less than the institutional wage, was also available at a constant wage rate.The reason for this difference in the views of the authors of two models is that unlike Ranis and Fei, Lewis did not take into account the effect of changing terms on trade on the supply price of labour in the industrial sector. He totally ignored it.
Fie assumed as if the wages to the transferred labour will be paid in agricultural products and as the institutional wages fixed in terms of agricultural produce, the labour transferred to the industrial sector will continue to be available at the constant wage rate i.e. that institutional wage.Ranis and Fei, on the other hand assumed that the labour in the industrial sector will be paid, in terms of the industrial products and they had to bring the hanging terms of trade into the picture. So we find that whereas according to Ranis and Fei, Lewis’ turning point appears as soon as phase in their model ends, according to Lewis himself, the turning point will appear at the end of the phase II. If i.e. upto the point where labour in the agricultural sector is paid institutional wages.
Basic Thesis of the Model:
This theory is concerned with a poor economy which has following properties:
(i) There is an abundance of labor in such UDC and shortage of natural resources.
(ii) The population growth rate is very high which results in mass unemployment in the economy.
(iii) The major share of population is engaged in agriculture. But agriculture sector is stagnant. Hence, the marginal productivity of labor is zero and negative in agriculture sector.
(iv) There are certain non-agrarian sectors in the economy where there is reduced use of capital.
(v) There is a dynamic industrial sector in the economy.
Thus the model suggests that, "Economic development would be taking place if agricultural laborers are transferred to industrial sector where their productivity will increase".As we told earlier that it is a dual economy where there is a stagnant agri. sector and dynamic industrial sector. The situation where MPL – 0, labor can be transferred to industrial sector without any loss in agricultural output. The real wages in industrial sector remains fixed and it is equal to the initial level of real income in agri. sector. Such wages are given the name of institutional wages.
Stages of Fei-Ranis Model:
Fei and Ranis develop their dual economy model with the help of three stages of economic growth. They are presented as:
The investment in industrial sector (with the surplus earned) will shift the MP curve outward right as from aa to bb and then to cc. In this way agri. sector will be able to get rid of labor until the MPL = real wages = AB =constant institutional wage (CIW) which is obtained by dividing the total agri. output ORX (b part of Fig) by AD amount of labor. In other words, the slope of ORX curve represents real wage rate. Thus the MPL = CIW where the tangent to the total output line ORX at X is parallel to OX. In the second phase DK amount of labor were employed. But still MPL MPL. It means that in this phase still a certain amount of labor is surplus or they are prey to disguised unemployment.
A. The first stage of FR model is very similar to Lewis. Disguised unemployment comes into being because the supply of labor is perfectly elastic and MPL = 0. Therefore, such disguised unemployed are to be transferred to industrial sector at the constant institutional wage.
B. In the second stage of FR model (phase) agri. workers add to agri. output but they produce less than institutional wage they get. In other words, in the second stage the labor surplus exists where APL > MPL, but it is not equal to subsistence (institutional) wages. Accordingly, such disguised unemployed also have to be transferred to industrial sector. If the migration to industrial sector continues a situation is eventually reached where the farm workers produce output equal to institutional wages. This would mean that productivity in agri. sector has gone up. With this the third phase (stage) starts.
C. In the third stage of FR model the take-off situation comes to an end and there begins the era of self-sustained growth where the farm workers produce more than the institutional wage they get. In this stage of economic growth the surplus labor comes to an end and the agri. sector becomes commercialized sector. All such is explained with the Fig.
The amount and time to re-allocate labor will depend upon:
(i) The rate of growth of industrial capital which depends upon the growth of profits in industrial sector and growth of surplus generated within the agri. sector.
(ii) The nature and bias of technical progress in industry.
(iii) The rate of growth of population. It means that the rate of labor transfer must be in excess of the rate of growth of population.
The three phases of labor transfer are summarized as:
In phase I: MPL = 0 and there exists the surplus labor equal to AD.
In phase II: CIW > MPL > 0 and there exists the open and disguised unemployment equal to AK.
In phase III: MPL > CIW and the economy is fully commercialized and disguised unemployment is exhausted. The supply of labor curve becomes steeper and both agri. and industrial sector compete with each other to get labor.
Thus we find that whereas Lewis had failed to offer a satisfactory explanation of this subsistence sector and ignored the real impact of population growth on the choice of capital intensity on the process of surplus labor absorption. Moreover, FR model emphasized upon the simultaneous growth of agri. and industrial sectors. Thus FR model believes in ‘Balanced Growth’ in the take-off stage. It means that there should be a simultaneous investment in both agri, sector and industrial sector. According to FR model in the beginning the surplus rises; such surplus will bo available as a capital in the take-offstage. Some part of this surplus will be used in agri. development, while some part will be reploughed in industrial development. As a result, both agri. and industrial sectors will grow under ‘Balanced Growth’ pattern.
Thus, three major points are highlighted in the FR mode:
(i) Growth of agri. is as important as the growth of industry.
(ii) There should be a balanced growth of agri and industrial sectors.
(iii) The rate of labor absorption must be higher than the rate of population growth to get out of the “Malthusian Nightmare”.
Criticism:
The FR model is considered to be an improvement over Lewis. This model presents a balanced growth of both the sectors of the economy, the most notable thing for the growth of UDCs. Despite this fact, this model has following shortcomings:
(i) Marginal Productivity of Labor in Phase I: The FR model is of the view that MFL = 0 in the first phase of growth, and the transfer of labor from agri. would not reduce output in the agri. sector in phase I. But the economists like Berry and Soligo are of the view that agri. output in phase I of FR model will not remain constant and may fell under different systems of land tenure, i.e., the peasant proprietorship and share cropping etc.
(ii) Marginal Productivity of Labor is Not Zero: Prof. Jorgenson who has also presented a model of ‘dual economy’ has object FR model’s contention of zero MP in phase I. He says whether MPL will be zero is an empirical issue. During the seasons of sowing and harvesting the MPL > 0. Jorgenson concluded on the basis of Japanese data even for the pre I world war period the supply of labor was not unlimited. Then how MPL can be zero.
(iii) Ignoring The Role of Capital: The FR model concentrated upon land and labor as the determinants of output, ignoring the role of capital. But Profs. Brown, Byres, Frankel, Griffen, Ghatak and Ingersent are of the view that in the UDCs there has occurred what is known as ‘Green Revolution’ in agri. which has promoted the greater use of capital and technology on lands. Consequently, there has been a greater increase in the agri. productivity and agri. incomes.
(iv) Open Economy: FR model ignored the role of foreign trade as it assumed a closed economy model. In the 2nd phase when agri. product decreases the TOT goes against industrial sector. This would occur in the presence of closed economy. But if the model is made open such would not happen as the goods could be imported in the presence of then-scarcity. This was especially observed in case of Japan which imported cheap farm products to improve her TOT (terms of trade).
(v) Supply of Land in Long Run: FR model assumed that in the process of economic development the supply of land remained fixed. But it is not true. The supply of land can be increased in case of long run.
(vi) Commercialization Of Agri. And Inflation: According to FR model when 3rd phase starts the agri. sector becomes commercialized. But it is criticized by saying that this phase does not start so easily The shifting of labor to industrial sector will create labor shortage in agri. sector. This will create shortage of food stuff leading to increase their prices. In this way, the inflation will generate which may obstruct the process of development.
(vii) Low Productivity in Agri Sector: According to Jorgenson it has been observed that there has been a very slow rise in the productivity of agri. sector. Consequently, the surplus will hardly be created in agri. sector. Accordingly, agri. sector will not contribute to development Thus the growth requires that the surplus must be generated and it should persist.
CONCLUSION
We analyse a two-sectorial economy composed by adaptive agent such as the individual that struggle over time for best sectorial location in term of earnings. First the basic assumption that of Harris-Todaro model that rural urban migration will occur while the urban expected wage exceed the rural wage. This on my view is visible or can be seen in the real world when individuals or economic agents see potential in a geographical area, they find to move to migrate in those area. Secondly the migratory dynamics generated by agents that seeking to adapt to the economic environment that they co-create lead the economy toward a long run equilibrium. This is also applicable in the real world were the effect of migration are felt.
Lastly the impact of the minimum wage and elasticity of terms of term in a long run equilibrium obtained by simulations are in agreement with the prediction of the original Harris-Todaro model with the application of the Cobb-Douglas technology.The harris-todaro model is visible in the real world because it applies the neutral principle of rural-urban migration and this make it more application in the real world.

46. NAME:METEKE JOY ORIMUSUE
DEPARTMENT: ECONOMICS
REG. NO:2017/242430
EMAIL:joymetex2000@gmail.com
WEBSITE:www.metekejoy01.blogspot.com

LEWIS FEI RANIS THEORY (SURPLUS LABOUR THEORY)

Lewis (1954) proposed a seminal theory of dualistic economic development for over-populated and under-developed economies with vast amounts of surplus agricultural labour for which he was later to be awarded the 1979 Nobel Prize in Economics. Economic growth in such an economy can be achieved by rapid capital accumulation in the non-agricultural (industrial and service) sector, facilitated by drawing surplus labour in the agricultural sector. In the Lewis theory, an economy transits from the first, labour-surplus “stage” to the second, labour-scarce “stage” of development.The central idea behind the Lewis model is fairly simple. Lewis divided labour force into two differentiated groups – “subsistence sector” and “capitalist sector” where the former is assumed to contain unlimited supply and consequently, a pool of surplus labour that sets labour-supply conditions for the latter.
Assumptions of the Lewis Model
(A) Surplus Labour in the Subsistence Sectors:
The basic assumption of the model is that there exists surplus labour in the subsistence sectors. It includes labour whose marginal productivity is zero as well as that whose marginal productivity is positive but is less than the institutional wage. This labour comprises farmers, agricultural labourers, petty traders domestic servants and women.
(B) Importance of Saving:
Another important assumption that Lewis makes is about the savings generated in the capitalist sector and in the subsistence sector. The capitalist sector invests all its savings for its further expansion.Those in the subsistence sector, on the other hand squander away their savings, if any in purchase of jewellery & for construction of temples etc. The propensity to save of the people in subsistence sector is also lower when compared with that of those in the capitalist sector.
The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model.It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.Ranis and Fei (1961) formalised the Lewis theory and defined three “phases” of dualistic economic development by sub-dividing the first stage in the Lewis model into two phases. Thus, the second labour-scarce stage of the Lewis model corresponds to phase three of the Ranis-Fei model. These three phases, illustrated in Diagram 1below, are distinguished by the marginal productivity of agricultural labour. The entry into each phase is marked three turning points:
• The breakout point leads to phase one growth with redundant agricultural labour.
• The shortage point leads to phase two growth with disguised agricultural unemployment.
• The commercialisation point leads to phase three of self-sustaining economic growth with the commercialisation of the agricultural sector.One of the biggest drawbacks of the Lewis model was the undermining of the role of agriculture in boosting the growth of the industrial sector. In addition to that, he did not acknowledge that the increase in productivity of labor should take place prior to the labor shift between the two sectors. However, these two ideas were taken into account in the Fei–Ranis dual economy model of three growth stages.They further argue that the model lacks in the proper application of concentrated analysis to the change that takes place with agricultural development.One of the biggest drawback of the lewis models was the underminig of the role of agriculture in boosting the growth of the industrial sector.In addition to that,he did not acknowledge that the increase in the productivity of labour should take place prior to the laboir shift between two sectors .However,these two ideas were taken into account in the field ranis economic modelof three growth stages:
In phase 1of the model,the elasticity of agricultural labor force is infinite and as a result,suffers from disguised unemployment,that is MPC=0
In phase 2,the agricultural sector sees a rise in the productivity and leads to increased Industrial growth such that a base for the next phase is prepared.Also in phase 2,agricultural surplus may exist as the increasing AP os higher than the MPand not equal to the substitence level of wages .
Phase 3is the point where the economy becomes completely commercialised in the absence of disisguised employment .Lewis fei ranis model according to Chen(2005) should be considered a classical model because of the usage of industrial wage .

RELATING THE MODEL TO NIGERIA’S ECONOMY
The government should invest on activities that promote agricultural gains and leads to pro poor growth.They should broadly align agricultural spending and policy priorities in order to stimulate qualitative growth in the sector of growing financial support to farmers.

HARRIS TODARO MODEL OF MIGRATION
The Harris Todaro model was named after John.R.Harris and Michael Todaro,is an economic model developed in 1970and used in development economics and welfare economics to explain some of the issues concerning rural urban migration.The major assumption of this model is that migration decision is based on expected income differentials between rural urban migration in a context of high urban unemployment can ecomomically rational if expected urban income exceeds expected rural income .Harris Todaro model studied the dual sector:rural and urban sector .The difference between them is the type of good produced,technology of production and the process of wage determination.This can be explained using the cobb douglas production function ;Ya=AaNa′.
The key hypothesis of Harris Todaro are that migrants react mainly to economic incentives ,earnings differencials and the probability of getting a job at the influence on the migration decision.

RELATING MODEL TO NIGERIA ECONOMY
I’m term of pro poor economic growth,the Harris Todaro model and other multi sector labor market can help policy makers avoid two mistakes; one is to assume that development effort should be channled to sectors where the poor are .The other is to assume that effort should always be focused on getting the poor out of the sectors which they now are . Careful cost benefits analysis based on well specified labour market models is required to decide among such alternatives .

47. NAME:METEKE JOY ORIMUSUE
DEPARTMENT: ECONOMICS
REG. NO:2017/242430
EMAIL:joymetex2000@gmail.com
WEBSITE:www.metekejoy01.blogspot.com

LEWIS FEI RANIS THEORY (SURPLUS LABOUR THEORY)

Lewis (1954) proposed a seminal theory of dualistic economic development for over-populated and under-developed economies with vast amounts of surplus agricultural labour for which he was later to be awarded the 1979 Nobel Prize in Economics. Economic growth in such an economy can be achieved by rapid capital accumulation in the non-agricultural (industrial and service) sector, facilitated by drawing surplus labour in the agricultural sector. In the Lewis theory, an economy transits from the first, labour-surplus “stage” to the second, labour-scarce “stage” of development.The central idea behind the Lewis model is fairly simple. Lewis divided labour force into two differentiated groups – “subsistence sector” and “capitalist sector” where the former is assumed to contain unlimited supply and consequently, a pool of surplus labour that sets labour-supply conditions for the latter.
Assumptions of the Lewis Model
(A) Surplus Labour in the Subsistence Sectors:
The basic assumption of the model is that there exists surplus labour in the subsistence sectors. It includes labour whose marginal productivity is zero as well as that whose marginal productivity is positive but is less than the institutional wage. This labour comprises farmers, agricultural labourers, petty traders domestic servants and women.
(B) Importance of Saving:
Another important assumption that Lewis makes is about the savings generated in the capitalist sector and in the subsistence sector. The capitalist sector invests all its savings for its further expansion.Those in the subsistence sector, on the other hand squander away their savings, if any in purchase of jewellery & for construction of temples etc. The propensity to save of the people in subsistence sector is also lower when compared with that of those in the capitalist sector.
The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model.It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.Ranis and Fei (1961) formalised the Lewis theory and defined three “phases” of dualistic economic development by sub-dividing the first stage in the Lewis model into two phases. Thus, the second labour-scarce stage of the Lewis model corresponds to phase three of the Ranis-Fei model. These three phases, illustrated in Diagram 1below, are distinguished by the marginal productivity of agricultural labour. The entry into each phase is marked three turning points:
• The breakout point leads to phase one growth with redundant agricultural labour.
• The shortage point leads to phase two growth with disguised agricultural unemployment.
• The commercialisation point leads to phase three of self-sustaining economic growth with the commercialisation of the agricultural sector.One of the biggest drawbacks of the Lewis model was the undermining of the role of agriculture in boosting the growth of the industrial sector. In addition to that, he did not acknowledge that the increase in productivity of labor should take place prior to the labor shift between the two sectors. However, these two ideas were taken into account in the Fei–Ranis dual economy model of three growth stages.They further argue that the model lacks in the proper application of concentrated analysis to the change that takes place with agricultural development.One of the biggest drawback of the lewis models was the underminig of the role of agriculture in boosting the growth of the industrial sector.In addition to that,he did not acknowledge that the increase in the productivity of labour should take place prior to the laboir shift between two sectors .However,these two ideas were taken into account in the field ranis economic modelof three growth stages:
In phase 1of the model,the elasticity of agricultural labor force is infinite and as a result,suffers from disguised unemployment,that is MPC=0
In phase 2,the agricultural sector sees a rise in the productivity and leads to increased Industrial growth such that a base for the next phase is prepared.Also in phase 2,agricultural surplus may exist as the increasing AP os higher than the MPand not equal to the substitence level of wages .
Phase 3is the point where the economy becomes completely commercialised in the absence of disisguised employment .Lewis fei ranis model according to Chen(2005) should be considered a classical model because of the usage of industrial wage .

RELATING THE MODEL TO NIGERIA’S ECONOMY
The government should invest on activities that promote agricultural gains and leads to pro poor growth.They should broadly align agricultural spending and policy priorities in order to stimulate qualitative growth in the sector of growing financial support to farmers.

HARRIS TODARO MODEL OF MIGRATION
The Harris Todaro model was named after John.R.Harris and Michael Todaro,is an economic model developed in 1970and used in development economics and welfare economics to explain some of the issues concerning rural urban migration.The major assumption of this model is that migration decision is based on expected income differentials between rural urban migration in a context of high urban unemployment can ecomomically rational if expected urban income exceeds expected rural income .Harris Todaro model studied the dual sector:rural and urban sector .The difference between them is the type of good produced,technology of production and the process of wage determination.This can be explained using the cobb douglas production function ;Ya=AaNa′.
The key hypothesis of Harris Todaro are that migrants react mainly to economic incentives ,earnings differencials and the probability of getting a job at the influence on the migration decision.

RELATING MODEL TO NIGERIA ECONOMY
I’m term of pro poor economic growth,the Harris Todaro model and other multi sector labor market can help policy makers avoid two mistakes; one is to assume that development effort should be channled to sectors where the poor are .The other is to assume that effort should always be focused on getting the poor out of the sectors which they now are . Careful cost benefits analysis based on well specified labour market models is required to decide among such alternatives .

48. NAME:METEKE JOY ORIMUSUE
DEPARTMENT:ECONOMICS
REG.NO:2017/242430
EMAIL:joymetex2000@gmail.com
BLOG WEBSITE:metekejoy01.blogspot.com

LEWIS-FEI-RANIS THEORY(SURPLUS LABOUR THEORY)
Lewis (1954) proposed a seminal theory of dualistic economic development for over-populated and under-developed economies with vast amounts of surplus agricultural labour for which he was later to be awarded the 1979 Nobel Prize in Economics. Economic growth in such an economy can be achieved by rapid capital accumulation in the non-agricultural (industrial and service) sector, facilitated by drawing surplus labour in the agricultural sector. In the Lewis theory, an economy transits from the first, labour-surplus “stage” to the second, labour-scarce “stage” of development.The central idea behind the Lewis model is fairly simple. Lewis divided labour force into two differentiated groups – “subsistence sector” and “capitalist sector” where the former is assumed to contain unlimited supply and consequently, a pool of surplus labour that sets labour-supply conditions for the latter.
Assumptions of the Lewis Model
(A) Surplus Labour in the Subsistence Sectors:
The basic assumption of the model is that there exists surplus labour in the subsistence sectors. It includes labour whose marginal productivity is zero as well as that whose marginal productivity is positive but is less than the institutional wage. This labour comprises farmers, agricultural labourers, petty traders domestic servants and women.
(B) Importance of Saving:
Another important assumption that Lewis makes is about the savings generated in the capitalist sector and in the subsistence sector. The capitalist sector invests all its savings for its further expansion.Those in the subsistence sector, on the other hand squander away their savings, if any in purchase of jewellery & for construction of temples etc. The propensity to save of the people in subsistence sector is also lower when compared with that of those in the capitalist sector.
The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model.It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.Ranis and Fei (1961) formalised the Lewis theory and defined three “phases” of dualistic economic development by sub-dividing the first stage in the Lewis model into two phases. Thus, the second labour-scarce stage of the Lewis model corresponds to phase three of the Ranis-Fei model. These three phases, illustrated in Diagram 1below, are distinguished by the marginal productivity of agricultural labour. The entry into each phase is marked three turning points:
• The breakout point leads to phase one growth with redundant agricultural labour.
• The shortage point leads to phase two growth with disguised agricultural unemployment.
• The commercialisation point leads to phase three of self-sustaining economic growth with the commercialisation of the agricultural sector.One of the biggest drawbacks of the Lewis model was the undermining of the role of agriculture in boosting the growth of the industrial sector. In addition to that, he did not acknowledge that the increase in productivity of labor should take place prior to the labor shift between the two sectors. However, these two ideas were taken into account in the Fei–Ranis dual economy model of three growth stages.They further argue that the model lacks in the proper application of concentrated analysis to the change that takes place with agricultural development. One of the biggest drawbacks of the Lewis model was the undermining of the role of agriculture in boosting the growth of the industrial sector. In addition to that, he did not acknowledge that the increase in productivity of labor should take place prior to the labor shift between the two sectors. However, these two ideas were taken into account in the Fei–Ranis dual economy model of three growth stages.[4] They further argue that the model lacks in the proper application of concentrated analysis to the change that takes place with agricultural development[5] In Phase 1 of the Fei–Ranis model, the elasticity of the agricultural labor work-force is infinite and as a result, suffers from disguised unemployment. Also, the marginal product of labor is zero. This phase is similar to the Lewis model. In Phase 2 of the model, the agricultural sector sees a rise in productivity and this leads to increased industrial growth such that a base for the next phase is prepared. In Phase 2, agricultural surplus may exist as the increasing average product (AP), higher than the marginal product (MP) and not equal to the subsistence level of wages.Phase 3 begins from the point of commercialization which is at K in the Figure. This is the point where the economy becomes completely commercialized in the absence of disguised unemployment. The supply curve of labor in Phase 3 is steeper and both the sectors start bidding equally for labor.

The amount of labor that is shifted and the time that this shifting takes depends upon:The growth of surplus generated within the agricultural sector, and the growth of industrial capital stock dependent on the growth of industrial profits;
The nature of the industry’s technical progress and its associated bias;
Growth rate of population.
So, the three fundamental ideas used in this model are:

1.Agricultural growth and industrial growth are both equally important;
2.Agricultural growth and industrial growth are balanced;
3. Only if the rate at which labor is shifted from the agricultural to the industrial sector is greater than the rate of growth of population will the economy be able to lift itself up from the Malthusian population trap.

HARRIS TODARO THEORY OF MIGRATION
The Harris–Todaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and welfare economics to explain some of the issues concerning rural-urban migration. The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This implies that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.In the model, an equilibrium is reached when the expected wage in urban areas (actual wage adjusted for the unemployment rate), is equal to the marginal product of an agricultural worker. The model assumes that unemployment is non-existent in the rural agricultural sector. It is also assumed that rural agricultural production and the subsequent labor market is perfectly competitive. As a result, the agricultural rural wage is equal to agricultural marginal productivity. In equilibrium, the rural to urban migration rate will be zero since the expected rural income equals the expected urban income. However, in this equilibrium there will be positive unemployment in the urban sector. The model explains internal migration in China as the regional income gap has been proved to be a primary drive of rural-urban migration, while urban unemployment is local governments’ main concern in many cities.migration from rural areas to urban areas will increase if:
1.Urban wages (wu) increase in the urban sector (le), increasing the expected urban income.
2.Agricultural productivity decreases, lowering marginal productivity and wages in the agricultural sector (wr), decreasing the expected rural income.
However, even though this migration creates unemployment and induces informal sector growth, this behavior is economically rational and utility-maximizing in the context of the Harris–Todaro model. As long as the migrating economic agents have complete and accurate information concerning rural and urban wage rates and probabilities of obtaining employment, they will make an expected income-maximizing decision.

RELATION TO NIGERIA ECONOMY
According to this model migrating workers in developing countries sich as Nigeria are essentially participants in a lottery of relatively high-paid jobs in the towns. When new urban jobs are created the lottery becomes more attractive to potential migrants. Depending on their responsiveness to this improved opportnity, more than one worker are likely to migrate for each job created.

If so, the output foregone may be that of two or more agricultural workers, not just one. If the migrants bring some of their family members to urban areas more output will be lost. The reason is that the wife and children of migrants find fewer employment opportunities in towns than in the rural areas because they do not have land in the towns on which to grow food.

49. NAME: ANACHUNAM DABERECHI MARYJANE
REG NO: 2017/241448
EMAIL: daberechi.anachunam.241448@unn.edu.ng
BLOG: maryjaneanachunam.wordpress.com

AN ESSAY ON LEWIS-FEI-RANIS MODEL (SURPLUS LABOUR THEORY) AND HARRIS-TODARO MODEL OF MIGRATION

LEWIS-FEI-RANIS MODEL (SURPLUS LABOUR THEORY)

William Arthur Lewis, with his most famous published work, “Economic Development with Unlimited Supplies of Labour” (Manchester School, May 1954) and “The Theory of Economic Growth” (Allen and Unwin, 1955), made a great contribution to the theories of economic development. Based on his findings, Ranis and Fei succeeded to extend the initial Lewis’ model and assessed the changes in the agricultural and industrial labour in more detail. (Ukessays, 2018)
The central idea behind the Lewis model is fairly simple. Lewis divided the labour force into two differentiated groups – “subsistence sector” and “capitalist sector” where the former is assumed to contain unlimited supply and consequently, a pool of surplus labour[1] that sets labour-supply conditions for the latter. The concept of a dual economy is heavily criticised.(Ukessays, 2018)

Subsequently, Ranis’ and Fei’s extension to Lewis’ model can be analysed. They observed the model by reading it from left to right and assessed the changes in the output and wage as more and more people moved from agriculture to the industry. A new concept was added – namely, disguised unemployment, which appears in the traditional subsistence sector. The marginal product of labour, which is observed as the slope of the production function, in the agricultural sector is lower than in industry (Ukessays, 2018)

The Lewis-Ranis-Fei model

The Lewis (1954) theory of dualistic economic development provides the seminal
contribution to theories of economic development particularly for labour-surplus and
resource-poor developing countries. In the Lewis theory, the economy is assumed to
comprise the agricultural and non-agricultural sectors. The agricultural sector is
assumed to have vast amounts of surplus labour that result in an extremely low, close to
zero, marginal productivity of labour. The agricultural wage rate is presumed to follow
the sharing rule and be equal to average productivity, which is also known as the
institutional wage. The non-agricultural sector has an abundance capital and resources
relative to labour. It pursues profit and employs labour at a wage rate higher than the
agricultural institutional wage by approximately 30 percent (Lewis, 1954, p.150). The
non-agricultural sector accumulates capital by drawing surplus labour out of the
agricultural sector. The expansion of the non-agric ultural sector takes advantage of the
infinitely elastic supply of labour from the agricultural sector due to its labour surplus.
When the surplus labour is exhausted, the labour supply curve in the non-agricultural
sector becomes upward-sloping.
Ranis and Fei (1961) formalised Lewis’s theory by combining it with Rostow’s
(1956) three “linear-stages-of-growth” theory. They disassembled Lewis’s two-stage
economic development into three phases, defined by the marginal productivity of
agricultural labour. They assume the economy to be stagnant in its pre-conditioning
stage. The breakout point marks the creation of an infant non-agricultural sector and the
entry into phase one. Agricultural labour starts to be reallocated to the non-agricultural
sector. Due to the abundance of surplus agricultural labour, its marginal productivity is
extremely low and average labour productivity defines the agricultural institutional
wage. When the redundant agricultural labour force has been reallocated, the
agricultural marginal productivity of labour starts to rise but is still lower than the
institutional wage. This marks the shortage point a t which the economy enters phase two of development. During phase two the remaining agricultural unemployment is
gradually absorbed. At the end of this process the economy reaches the
commercialisation point and enters phase three where the agricultural labour market is
fully commercialised ( Marco G. Ercolani and Zheng Wei, 2010).

To conclude, having shown the main ideas behind the Lewis-Ranis-Fei model . Using Nigeria as a case study, it is important to invest in both sectors in order to remain on the balanced growth path and maintain the rate of industrialization. The existence of surplus labour in agriculture allows the industry to continue to pay the institutional wage and therefore enjoy further profits and continued investment. At the same time, as more and more people are moving away from agriculture, there will be some amount of agricultural surplus that can be used up to fuel further development. This process continues until the surplus labour is absorbed. Hence, saving and investment are a crucial part in the Lewis-Ranis-Fei to support economic development (Ukessays, 2018).

HARRIS-TODARO MODEL OF MIGRATION

John R. Harris and Michael P. Todaro presented the work Two sector modelin American
Economic Association, 1970. This model is an important study in the field encompassing rural-urban
migration.

The main idea of the Harris-Todaro model is that labour migration in underdeveloped countries is due to rural-urban differences in average expected wages rather than actual wages. The migrants consider the various opportunities of employment available to them in rural and urban sectors and choose the one that maximises their expected wages from migration (Divisha s, 2017).
The minimum urban wage is substantially higher than the rural wage. If more employment opportunities are created in the urban sector at the minimum wage, the expected will rise and rural-urban migration will increase. Expected wages are measured by the difference in real urban income and rural agricultural income and the probability of a migrants getting an urban job.
In fact, a migrant compares his expected income for a given time horizon in the urban sector with his prevailing average rural income and migrates if the former is more than the latter.
Thus migration in the Harris-Todaro modal is viewed as the wage or income gap between the urban and the rural sectors. But all migrants cannot be absorbed in the urban sector at high wages. Many fail to find a job and get employment in the informal urban sector at wages which are even lower than in the rural sector. Thus they join the queue of the underemployed or disguised unemployed in the urban sector (Divisha s, 2017)

Assumptions of the Model:

The Harris-Todaro model is based on the following assumptions:
1. There are two sectors in the economy – the rural or agricultural sector (A) and the urban or manufacturing sector (M).
2. The model operates in the short run.
3. The marginal production of labour in agriculture (MPLA) and of industry (MPLM) are determined by their respective technologies.
4. Capital is available in fixed quantities in the two sectors.
5. There are L workers in economy with LA and LM numbers employed in the rural and urban sectors respectively.
6. The number of urban jobs available (LM) is exogenously fixed. In the rural sector some work is always available. Therefore, the total urban labour force LM comprises L-LAalong with an available supply of rural migrants.
7. The urban wage is fixed at WM and the rural wage at WA, WM>WA.
8. The rural wage equals the rural marginal product of labour and the urban wage is exogenously determined.
9. Rural-urban migration continues so long as the expected urban real income is more that the real agricultural income.

At the core of the Harris-Todaro model were the following features. First, real wages (adjusted for cost-of-living differences) are higher in urban formal-sector jobs than in rural traditional-sector jobs. Second, to be hired for a formal-sector job, one has to be physically present in the urban areas where the formal-sector jobs are located. Third, and as a consequence of the first two features, more workers search for formal-sector jobs than are hired, employers hire some of the job seekers but not all of them, and those not hired end up unemployed. Fourth, for equality to be maintained between the expected wage associated with searching for an urban job and the expected wage associated with taking up a lower-paying rural job, the equilibrium arising in such a setting is characterized by urban unemployment. And fifth, any temporary difference in the expected wages between one sector and another is eroded as workers migrate from the low-expected-wage labor market to the high-expected-wage labor market.

Starting from the assumption that migration is based primarily on privately rational economic calculations despite the existence of high urban unemployment, the Todaro model postulates that migration proceeds in response to urban-rural differences in expected rather than actual earnings. The fundamental premise is that as decision-makers migrants consider the various labor-market opportunities available to them as, say, between the rural and urban sectors, choosing the one that maximizes their “expected” gains from migration. Expected gains are measured by the difference in real incomes between rural and urban work opportunities and the probability of a new migrant’s obtaining urban job. The “thought process” of the Todaro model can be explained as follows. Suppose the average unskilled or semiskilled rural worker has a choice between being a farm laborer (or working his own land) for an annual average real income of, say, 50 units per year, and migrating to the city where a worker with his skill or educational background can obtain wage employment yielding an annual real income of, say, 100 units. The worker should seek the higher-paying urban job. It is important to recognize, however, that these migration models were developed largely in the context of advanced industrial economies and, as such, implicitly assumed the existence of full or near-full employment in urban areas. In a full-employment environment the decision to migrate can in fact be predicated solely on securing the highest-paying job wherever it becomes available, other factors being held constant. Simple economic theory would then indicate that such migration should lead to a reduction in wage differentials through geographic changes in supply and demand, both in areas of out-migration (where incomes rise) and in points of in-migration (where they fall). Unfortunately, such an analysis is not very realistic in the context of the institutional and economic framework of most Third World nations. First of all, these countries are beset by a chronic and serious problem of urban surplus labor, so that many migrants cannot expect to secure high-paying urban jobs immediately upon arrival. In fact, it is much more likely that upon entering the urban labor market many migrants will either become totally unemployed or will seek casual and parttime employment in the urban traditional sector for some time.
Consequently, in his decision to migrate the individual must in effect balance the probabilities and risks of being unemployed or underemployed for a considerable period of time against the positive urban-rural real-income differential. That it is possible for our hypothetical migrant to earn twice as much annual real income in an urban area as in his rural environment may be of little consequence if his actual probability of securing the higher-paying job within a year is one chance in five. In such a situation the migrant’s actual probability of being successful in securing the higherpaying urban job is 20%, so that his “expected” urban income for the one-year period is in fact 20 units, not the 100 units that a migrant in a full-employment urban environment might expect to receive. Thus, with a one-period time horizon and a probability of success of 20% it would be irrational for this migrant to seek an urban job even though the differential between urban and rural earnings capacity is 100%. On the other hand, if the probability of success were, say, 60%, so that the expected urban income is 60 units, it would be entirely rational for such a migrant with his one-period time horizon to try his luck in the urban job “lottery” even though urban unemployment may be extremely high. Returning now to the more realistic situation of longer time horizons for potential migrants, especially considering that the vast majority are between the ages of 15 and 24, It is argued that the decision to migrate should be represented on the basis of a “permanent income” calculation. If the migrant anticipates a relatively low probability of finding regular wage employment in the initial period but expects this probability to increase over time as he is able to broaden his urban contacts, then it would still be rational for him to migrate even though expected urban income during the initial period or periods might be lower than expected rural income. As long as the present value of the net stream of expected urban income over the migrant’s planning horizon exceeds that of the expected rural income, the decision to migrate is economically justified. Rather than wage adjustments bringing about an equilibrium between urban and rural incomes, as would be the case in a competitive model, it is further argued that rural-urban migration itself must act as the ultimate equilibrating force. With urban wages assumed to be inflexible in a downward direction, rural and urban “expected” incomes can be equalized only by falling urban job probabilities resulting from rising urban unemployment. For example, if average rural wages are 60 units and urban wages are institutionally set at a level of 120 units, then in a one-period model a 50% urban unemployment rate would be necessary to vitiate the private profitability of further migration. Since expected incomes are defined in terms of both wages and employment probabilities, argument is that it is not only possible but likely to have continued migration in spite of the existence of sizable rates of urban unemployment. In the above numerical example, migration would continue even if the urban unemployment rate were 30 or 40%.

Conclusion
In the Harris–Todaro model, the rising urban wage pushes up the expected wage in the urban sector and consequently encourages workers to migrate from the rural sector to the urban sector. If, in the resulting migration, there are more workers than the number of job opportunities created in the urban sector, some will necessarily be unemployed which is the case in Nigeria when people leave rural areas to go to bigger cities like Lagos and end up being unemployed. Occasionally, the increase in unemployment lowers the per-capita income level before the capital is accumulated. This phenomenon is referred to as Todaro paradox.
If there is a necessary and sufficient condition under which the increase in capital stock does not increase unemployment in the urban area. This condition concerns the relationship between the institutionally and legally set minimum wage in the urban area and increased agricultural productivity in the rural area, that is there is an institutionally set minimum wage in urban areas (eg Lagos) that can’t be manipulated while the government works harder to develop the agricultural sector. Unsurprisingly, if agricultural productivity rises and income in the rural area increases, rural workers have no need to migrate to the urban sector to find jobs and face the risk of unemployment.

50. NAME: ANACHUNAM DABERECHI MARYJANE
REG NO: 2017/241448
EMAIL: daberechi.anachunam.241448@unn.edu.ng
BLOG: maryjaneanachunam.wordpress.com

AN ESSAY ON LEWIS-FEI-RANIS MODEL (SURPLUS LABOUR THEORY) AND HARRIS-TODARO MODEL OF MIGRATION

LEWIS-FEI-RANIS MODEL (SURPLUS LABOUR THEORY)

William Arthur Lewis, in his work, “Economic Development with Unlimited Supplies of Labour” (Manchester School, May 1954) and “The Theory of Economic Growth” (Allen and Unwin, 1955), made a great contribution to the theories of economic development. Based on his findings, Ranis and Fei succeeded to extend the initial Lewis’ model and assessed the changes in the agricultural and industrial labour in more detail. (Ukessays, 2018)
The central idea behind the Lewis model is fairly simple. Lewis divided the labour force into two differentiated groups – “subsistence sector” and “capitalist sector” where the former is assumed to contain unlimited supply and consequently, a pool of surplus labour[1] that sets labour-supply conditions for the latter. The concept of a dual economy is heavily criticised.(Ukessays, 2018)

Subsequently, Ranis’ and Fei’s extension to Lewis’ model can be analysed. They observed the model by reading it from left to right and assessed the changes in the output and wage as more and more people moved from agriculture to the industry. A new concept was added – namely, disguised unemployment, which appears in the traditional subsistence sector. The marginal product of labour, which is observed as the slope of the production function, in the agricultural sector is lower than in industry (Ukessays, 2018)

The Lewis-Ranis-Fei model

The Lewis (1954) theory of dualistic economic development provides the seminal
contribution to theories of economic development particularly for labour-surplus and
resource-poor developing countries. In the Lewis theory, the economy is assumed to
comprise the agricultural and non-agricultural sectors. The agricultural sector is
assumed to have vast amounts of surplus labour that result in an extremely low, close to
zero, marginal productivity of labour. The agricultural wage rate is presumed to follow
the sharing rule and be equal to average productivity, which is also known as the
institutional wage. The non-agricultural sector has an abundance capital and resources
relative to labour. It pursues profit and employs labour at a wage rate higher than the
agricultural institutional wage by approximately 30 percent (Lewis, 1954, p.150). The
non-agricultural sector accumulates capital by drawing surplus labour out of the
agricultural sector. The expansion of the non-agric ultural sector takes advantage of the
infinitely elastic supply of labour from the agricultural sector due to its labour surplus.
When the surplus labour is exhausted, the labour supply curve in the non-agricultural
sector becomes upward-sloping.
Ranis and Fei (1961) formalised Lewis’s theory by combining it with Rostow’s
(1956) three “linear-stages-of-growth” theory. They disassembled Lewis’s two-stage
economic development into three phases, defined by the marginal productivity of
agricultural labour. They assume the economy to be stagnant in its pre-conditioning
stage. The breakout point marks the creation of an infant non-agricultural sector and the
entry into phase one. Agricultural labour starts to be reallocated to the non-agricultural
sector. Due to the abundance of surplus agricultural labour, its marginal productivity is
extremely low and average labour productivity defines the agricultural institutional
wage. When the redundant agricultural labour force has been reallocated, the
agricultural marginal productivity of labour starts to rise but is still lower than the
institutional wage. This marks the shortage point a t which the economy enters phase two of development. During phase two the remaining agricultural unemployment is
gradually absorbed. At the end of this process the economy reaches the
commercialisation point and enters phase three where the agricultural labour market is
fully commercialised ( Marco G. Ercolani and Zheng Wei, 2010).

To conclude, having shown the main ideas behind the Lewis-Ranis-Fei model . Using Nigeria as a case study, it is important to invest in both sectors in order to remain on the balanced growth path and maintain the rate of industrialization. The existence of surplus labour in agriculture allows the industry to continue to pay the institutional wage and therefore enjoy further profits and continued investment. At the same time, as more and more people are moving away from agriculture, there will be some amount of agricultural surplus that can be used up to fuel further development. This process continues until the surplus labour is absorbed. Hence, saving and investment are a crucial part in the Lewis-Ranis-Fei to support economic development (Ukessays, 2018).

HARRIS-TODARO MODEL OF MIGRATION

John R. Harris and Michael P. Todaro presented the work Two sector modelin American
Economic Association, 1970. This model is an important study in the field encompassing rural-urban
migration.

The main idea of the Harris-Todaro model is that labour migration in underdeveloped countries is due to rural-urban differences in average expected wages rather than actual wages. The migrants consider the various opportunities of employment available to them in rural and urban sectors and choose the one that maximises their expected wages from migration (Divisha s, 2017).
The minimum urban wage is substantially higher than the rural wage. If more employment opportunities are created in the urban sector at the minimum wage, the expected will rise and rural-urban migration will increase. Expected wages are measured by the difference in real urban income and rural agricultural income and the probability of a migrants getting an urban job.
In fact, a migrant compares his expected income for a given time horizon in the urban sector with his prevailing average rural income and migrates if the former is more than the latter.
Thus migration in the Harris-Todaro modal is viewed as the wage or income gap between the urban and the rural sectors. But all migrants cannot be absorbed in the urban sector at high wages. Many fail to find a job and get employment in the informal urban sector at wages which are even lower than in the rural sector. Thus they join the queue of the underemployed or disguised unemployed in the urban sector (Divisha s, 2017)

Assumptions of the Model:

The Harris-Todaro model is based on the following assumptions:
1. There are two sectors in the economy – the rural or agricultural sector (A) and the urban or manufacturing sector (M).
2. The model operates in the short run.
3. The marginal production of labour in agriculture (MPLA) and of industry (MPLM) are determined by their respective technologies.
4. Capital is available in fixed quantities in the two sectors.
5. There are L workers in economy with LA and LM numbers employed in the rural and urban sectors respectively.
6. The number of urban jobs available (LM) is exogenously fixed. In the rural sector some work is always available. Therefore, the total urban labour force LM comprises L-LAalong with an available supply of rural migrants.
7. The urban wage is fixed at WM and the rural wage at WA, WM>WA.
8. The rural wage equals the rural marginal product of labour and the urban wage is exogenously determined.
9. Rural-urban migration continues so long as the expected urban real income is more that the real agricultural income.

. At the core of the Harris-Todaro model were the following features. First, real wages (adjusted for cost-of-living differences) are higher in urban formal-sector jobs than in rural traditional-sector jobs. Second, to be hired for a formal-sector job, one has to be physically present in the urban areas where the formal-sector jobs are located. Third, and as a consequence of the first two features, more workers search for formal-sector jobs than are hired, employers hire some of the job seekers but not all of them, and those not hired end up unemployed. Fourth, for equality to be maintained between the expected wage associated with searching for an urban job and the expected wage associated with taking up a lower-paying rural job, the equilibrium arising in such a setting is characterized by urban unemployment. And fifth, any temporary difference in the expected wages between one sector and another is eroded as workers migrate from the low-expected-wage labor market to the high-expected-wage labor market.
Starting from the assumption that migration is based primarily on privately rational economic calculations despite the existence of high urban unemployment, the Todaro model postulates that migration proceeds in response to urban-rural differences in expected rather than actual earnings. The fundamental premise is that as decision-makers migrants consider the various labor-market opportunities available to them as, say, between the rural and urban sectors, choosing the one that maximizes their “expected” gains from migration. Expected gains are measured by the difference in real incomes between rural and urban work opportunities and the probability of a new migrant’s obtaining urban job. The “thought process” of the Todaro model can be explained as follows. Suppose the average unskilled or semiskilled rural worker has a choice between being a farm laborer (or working his own land) for an annual average real income of, say, 50 units per year, and migrating to the city where a worker with his skill or educational background can obtain wage employment yielding an annual real income of, say, 100 units. The worker should seek the higher-paying urban job. It is important to recognize, however, that these migration models were developed largely in the context of advanced industrial economies and, as such, implicitly assumed the existence of full or near-full employment in urban areas. In a full-employment environment the decision to migrate can in fact be predicated solely on securing the highest-paying job wherever it becomes available, other factors being held constant. Simple economic theory would then indicate that such migration should lead to a reduction in wage differentials through geographic changes in supply and demand, both in areas of out-migration (where incomes rise) and in points of in-migration (where they fall). Unfortunately, such an analysis is not very realistic in the context of the institutional and economic framework of most Third World nations. First of all, these countries are beset by a chronic and serious problem of urban surplus labor, so that many migrants cannot expect to secure high-paying urban jobs immediately upon arrival. In fact, it is much more likely that upon entering the urban labor market many migrants will either become totally unemployed or will seek casual and parttime employment in the urban traditional sector for some time.
Consequently, in his decision to migrate the individual must in effect balance the probabilities and risks of being unemployed or underemployed for a considerable period of time against the positive urban-rural real-income differential. That it is possible for our hypothetical migrant to earn twice as much annual real income in an urban area as in his rural environment may be of little consequence if his actual probability of securing the higher-paying job within a year is one chance in five. In such a situation the migrant’s actual probability of being successful in securing the higherpaying urban job is 20%, so that his “expected” urban income for the one-year period is in fact 20 units, not the 100 units that a migrant in a full-employment urban environment might expect to receive. Thus, with a one-period time horizon and a probability of success of 20% it would be irrational for this migrant to seek an urban job even though the differential between urban and rural earnings capacity is 100%. On the other hand, if the probability of success were, say, 60%, so that the expected urban income is 60 units, it would be entirely rational for such a migrant with his one-period time horizon to try his luck in the urban job “lottery” even though urban unemployment may be extremely high. Returning now to the more realistic situation of longer time horizons for potential migrants, especially considering that the vast majority are between the ages of 15 and 24, It is argued that the decision to migrate should be represented on the basis of a “permanent income” calculation. If the migrant anticipates a relatively low probability of finding regular wage employment in the initial period but expects this probability to increase over time as he is able to broaden his urban contacts, then it would still be rational for him to migrate even though expected urban income during the initial period or periods might be lower than expected rural income. As long as the present value of the net stream of expected urban income over the migrant’s planning horizon exceeds that of the expected rural income, the decision to migrate is economically justified. Rather than wage adjustments bringing about an equilibrium between urban and rural incomes, as would be the case in a competitive model, it is further argued that rural-urban migration itself must act as the ultimate equilibrating force. With urban wages assumed to be inflexible in a downward direction, rural and urban “expected” incomes can be equalized only by falling urban job probabilities resulting from rising urban unemployment. For example, if average rural wages are 60 units and urban wages are institutionally set at a level of 120 units, then in a one-period model a 50% urban unemployment rate would be necessary to vitiate the private profitability of further migration. Since expected incomes are defined in terms of both wages and employment probabilities, argument is that it is not only possible but likely to have continued migration in spite of the existence of sizable rates of urban unemployment. In the above numerical example, migration would continue even if the urban unemployment rate were 30 or 40%.

Conclusion
In the Harris–Todaro model, the rising urban wage pushes up the expected wage in the urban sector and consequently encourages workers to migrate from the rural sector to the urban sector. If, in the resulting migration, there are more workers than the number of job opportunities created in the urban sector, some will necessarily be unemployed which is the case in Nigeria when people leave rural areas to go to bigger cities like Lagos and end up being unemployed. Occasionally, the increase in unemployment lowers the per-capita income level before the capital is accumulated. This phenomenon is referred to as Todaro paradox.
If there is a necessary and sufficient condition under which the increase in capital stock does not increase unemployment in the urban area. This condition concerns the relationship between the institutionally and legally set minimum wage in the urban area and increased agricultural productivity in the rural area, that is there is an institutionally set minimum wage in urban areas (eg Lagos) that can’t be manipulated while the government works harder to develop the agricultural sector. Unsurprisingly, if agricultural productivity rises and income in the rural area increases, rural workers have no need to migrate to the urban sector to find jobs and face the risk of unemployment.

51. Anopueme Franklin Ifeanyi
2017/249485
http://www.franklin.anopueme.249485@unn.edu.ng
http://www.franksempire.wordpress.com

1. The Lewis–Fei–Ranis model of economic growth is a dualism model in development economics and welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both sectors co-exist in the economy, and according to the model, development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one.

Features of the Lewis–Fei–Ranis Model
This theory is concerned with a poor economy which has following properties:
(i) There is an abundance of labor and shortage of natural resources.
(ii) The population growth rate is very high which results in mass unemployment in the economy.
(iii) The major share of population is engaged in agriculture. But agriculture sector is stagnant. Hence, the marginal productivity of labor is zero and negative in agriculture sector.
(iv) There are certain non-agrarian sectors in the economy where there is reduced use of capital.
(v) There is a dynamic industrial sector in the economy.

Assumptions
(i) The increase in net income in the agricultural sector, and the growth of industrial capital depends on the growth of industrial profits.
(ii)Agricultural growth and industrial growth are both equally important.
(iii)Agricultural growth and industrial growth are balanced.

Conclusion
In examining the initial role of the Agricultural sector in Nigeria, the sector is seen to be an indispensable sector in establishing the framework for national economic growth. Hence, increased agricultural production is expected to be a core pre-requisite for rapid economic growth in a developing nation like Nigeria, and the Lewis–Fei–Ranis growth model acknowledges the Agricultural sector, as a sector responsible for driving rapid, positive economic growth. On the other hand, The Industrial sector is also a worthy sector that drives economic growth, because it houses so many sectors and sub sectors responsible for pushing the economy forward. The Lewis–Fei–Ranis already applies in the Nigerian economy, because there has been a recorded shift of investment and dependency from the Agricultural sector to the industrial sector. Nigeria have undoubtedly prioritized crude oil, which is a product of the industrial sector, to be it’s major source of national revenue.

2. The Harris-Todaro model which was named after John Robert Harris and Michael Todaro, is an economic model developed in 1970 and used in the development of economics and welfare economics to explain some of the issues concerning rural / urban migration. The main assumption of the Harris Todaro model is that the migration decision is based on expected income differences between rural and urban areas rather than just wage distinctive.

Features of the Model
Harris and Todaro subsequently formulated a model to explain rural urban economic preferences to migrate. The distinctive concept in the model is that the rate of migration flow from rural (agricultural) areas as to urban (industrial) areas is determined by the difference between expected urban wages and rural wages.
The rural urban two sector model centrally holds the following features:
(i) Real wages (adjusted for cost of living differences) were higher in urban formal sector jobs than in rural traditional sector jobs.
(ii) To be hired for a formal sector job, it was necessary to be physically present in the urban areas there the formal sector jobs were located.
(iii) Consequently, from the first two features, more workers searched for formal sector jobs than were actually hired. Employers hired some of the researchers but not all of them.
(iv) To maintain equality between the expected wage associated with searching for an urban job and the expected wage associated with taking up a lower paying rural job, the equilibrium arising in such a setting would be characterized by urban unemployment.
(v) Any temporary difference in the expected wages between one sector and another would be eroded as workers migrate from the low expected wage labor market to the high expected wage.

General Assumptions of the Model
The assumptions of Haris-Todaro model of migration include the following:
(i) Two sectors; urban (manufacture) and rural (agriculture)
(ii) No migration cost
(iii) Perfect competition
(iv) Cobb Douglas production function
(v) Static approach
(vi) Low risk aversion

Conclusion
The Harris-Todaro model can be applied in Nigeria by determining what causes people to migrate from rural to urban areas. It is no longer news that the salaries paid to workers in cities are higher than the ones paid in the rural areas, and this can be noted as one the reasons making people to migrate into the urban areas hoping to get a lucrative job. The possibility of getting a lucrative job depends on the size of unemployment in relation to the number of employed workers in the industrial sector of the Nigerian economy.

52. UDUMA IKECHUKWU OBASI says:

NAME: UDUMA IKECHUKWU OBASI
REG: 2017/241441
EMAIL: ikechukwuuduma9@gmail.com

LEWIS-RANIS-FEI MODEL:
(SURPLUS LABOUR)

The Lewis (1954) theory of dualistic economic development provides the seminal
contribution to theories of economic development particularly for labour-surplus and resource-poor developing countries. In the Lewis theory, the economy is assumed to
comprise the agricultural and non-agricultural sectors. The agricultural sector is assumed to have vast amounts of surplus labour that result in an extremely low, close to zero, marginal productivity of labour. The agricultural wage rate is presumed to follow
the sharing rule and be equal to average productivity, which is also known as the institutional wage. The non-agricultural sector has an abundance capital and resources relative to labour. It pursues profit and employs labour at a wage rate higher than the agricultural institutional wage by approximately 30 percent (Lewis, 1954, ). The non-agricultural sector accumulates capital by drawing surplus labour out of the agricultural sector. The expansion of the non-agricultural sector takes advantage of the infinitely elastic supply of labour from the agricultural sector due to its labour surplus.
When the surplus labour is exhausted, the labour supply curve in the non-agricultural
sector becomes upward-sloping. Ranis and Fei (1961) formalised Lewis’s theory by combining it with Rostow’s (1956) three “linear-stages-of-growth” theory. They disassembled Lewis’s two-stage economic development into three phases, defined by the marginal productivity of agricultural labour. They assume the economy to be stagnant in its pre-conditioning stage. The breakout point marks the creation of an infant non-agricultural sector and the entry into phase one. Agricultural labour starts to be reallocated to the non-agricultural sector. Due to the abundance of surplus agricultural labour, its marginal productivity is extremely low and average labour productivity defines the agricultural institutional wage. When the redundant agricultural labour force has been reallocated, the agricultural marginal productivity of labour starts to rise but is still lower than the institutional wage. This marks the shortage point at which the economy enters phase two of development. During phase two the remaining agricultural unemployment is gradually absorbed. At the end of this process the economy reaches the commercialisation point and enters phase three where the agricultural labour market is fully commercialised

CONCLUSION AND POLICY RECOMMENDATIONS:

Having tested the Lewis-Ranis-Fei theory for the Chinese economy over 1965-2002 we will in the case of this study substitute the economy of Nigeria to that of China and implement the policy recommendations therein.The test shows that China’s economic growth is mainly attributable to the development of the non-agricultural sector(which is similar to that of Nigeria). This is driven by rapid capital accumulation as well as
employment growth. The reallocation of labour away from agriculture has made a
positive net contribution to China’s rapid economic growth by around 1.23 percent. The
rise in the marginal productivity of agricultural labour indicates the absorption of
redundant agricultural labour since the 1978 Economic Reform. However, the marginal
productivity of agricultural labour is still lower than the initial low average productivity
of agricultural labour. This implies the continued existence of disguised agricultural
unemployment. This suggests that the Chinese economy has entered the
Lewis-Ranis-Fei phase two of development but has not yet achieved phase three. The
continuing widening productivity gap between the two sectors calls for the removal of
market restrictions and government interventions so as to allow the continued
absorption of surplus labour.
Several policy recommendations are tentatively suggested. First and foremost, more
effort should be made in promoting employment to effectively absorb the remaining
labour surplus and promote China’s economic development. This can be achieved by
further relaxing the Hukou restrictions on migration, increasing labour market flexibility
and improving the allocative efficiency of labour. It can also be achieved by
encouraging the development of private enterprise to create more employment
opportunities. Second, China’s government should continue implementing the Sunshine
Policy, initiated in 2003, designed to provide rudimentary job training, recruitment
information and information about conditions in the destination cities to rural migrants.
This will not only help facilitate employment of rural migrants but also satisfy the
increasing demand for skilled labour in the growing non-agricultural sector. Third,
agriculture could be promoted by tax breaks, direct subsidies and most importantly, by
removing price controls on agricultural products. Agriculture could thus be
commercialised and the economy would enter phase three of economic development.

HARRIS TODARO MIGRATION MODEL:

In the 1960s the government of newly independent Kenya faced a difficult situation: Unemployment in Nairobi and other major cities was high and apparently rising. To cope with this problem, Tripartite Agreements were reached in which private-sector and public-sector employers agreed to increase employment in exchange for unions agreeing to hold wages at their current levels. The larger number of jobs was expected to reduce unemployment. However, in the event, urban unemployment appeared to have increased following the Tripartite Agreements rather than decreased, as far as anyone could tell.
In light of these events, John Harris and Michael Todaro formulated the Harris-Todaro model to explain the puzzle. At the core of the Harris-Todaro model were the following features. First, real wages (adjusted for cost-of-living differences) are higher in urban formal-sector jobs than in rural traditional-sector jobs. Second, to be hired for a formal-sector job, one has to be physically present in the urban areas where the formal-sector jobs are located. Third, and as a consequence of the first two features, more workers search for formal-sector jobs than are hired, employers hire some of the job seekers but not all of them, and those not hired end up unemployed. Fourth, for equality to be maintained between the expected wage associated with searching for an urban job and the expected wage associated with taking up a lower-paying rural job, the equilibrium arising in such a setting is characterized by urban unemployment. And fifth, any temporary difference in the expected wages between one sector and another is eroded as workers migrate from the low-expected-wage labor market to the high-expected-wage labor market.
The Harris-Todaro model produced two powerful policy results. The first concerns the policy of formal-sector job creation to employ the unemployed (who, in the Harris-Todaro model, are all in urban areas, because that is where the formal-sector jobs are assumed to be located). Such a policy, they concluded, would increase the formalsector labor force by more than the number of new jobs created, thereby raising the number of urban unemployed. Thus, the solution to urban unemployment is not to create urban employment.
The second policy option that Harris and Todaro considered was a policy of rural development. If such a program could increase the rural traditional-sector wage, unemployment would then fall. Thus, in the Harris-Todaro model, the solution to urban unemployment is rural development.
Soon after the model was published, the government of Kenya followed the Harris-Todaro precepts by putting into place an integrated program of rural development. The result was that unemployment in Kenya fell.
Harris and Todaros fundamental contribution was building a model that fit the stylized facts of the labor market they were analyzing and that was based on sound micro foundations. The fact that the model remains part of the economists intellectual toolkit today is a tribute to its basic insight and enduring analytic power.

The original model has been both simplified for some purposes and expanded for others by later contributors, including Stiglitz, Bell, Khan, Anand and Joshi, Bourguignon, Corden and Findlay, and others (Fields 2005). Harris and Todaro formulated general processes for determining prices of the products produced by the two sectors and also for determining a rural-sector wage that varies inversely with the number of people in the rural sector. A simplified version of the Harris-Todaro model was developed in which product prices and rural-sector wages are taken as constant. Numerous additional analytic and policy results were derived in the simplified Harris-Todaro model. At the same time, some of the assumptions of the Harris-Todaro model were judged to be too restrictive, and so the model was generalized in the years that followed to nest their specific formulation within a broader framework. The initial Harris-Todaro model has been extended to allow for on-the-job search from a rural agriculture setting, the existence of an urban informal sector, preferential hiring of the better-educated, employment fixity, duality of production conditions and earnings levels within the rural sector, capital mobility, endogenous urban wage setting, risk aversion, and a system of demand for goods, among other factors.
As an early multisector labor-market model, the Harris-Todaro model set forth a principal alternative framework for policy analysis. It showed how employment and wage levels in one labor market reflect supply, demand, and institutional conditions not only in that labor market but also in other labor markets.
In terms of pro-poor economic growth, the Harris-Todaro model and other multisector-labor-market models can help policy makers avoid two mistakes. One is to assume that development efforts should be channeled to the sectors where the poor are. The other is to assume that efforts should always be focused on getting the poor out of the sectors in which they now are. Careful cost-benefit analysis based on well-specified
labor-market models is required to decide among such alternatives.

FINDINGS AND RECOMMENDATIONS:

The fundamental contribution of Harris and Todaros rural-urban two sector migration model was to build a model that fit the stylized facts of the labour market. On the lines of the theory, developing countries (e.g Nigeria) adopted program on integrated rural development which could encouraged an increase in the rural traditional sector wage. The theory proves that the higher the unemployment rate, the lower is the probability of new migrants from the countryside actively seeking formal sector employment who are unable to find it. The significant findings of the theory are:
first, if the expected urban wage equals rural income, there is no incentive to migrate.
Second, if the expected urban wage is greater than rural income, there is a great incentive to move from rural to urban area.
Third, if the expected urban wage is less than rural incomes, there would be an incentive to move in other direction.
Fourth, the expected urban wage depends on what type of job migrant is engaged in. Therefore, the Haris Todaros model helps policy-makers to avoid two mistakes. One is to assume that development efforts should necessarily be channeled to the sectors where the poor are. The other is to assume that efforts should necessarily be focused on getting the poor out of the sectors in which they presently are.
Thus, recommended policies should be the ones poised to eradicate both poverty level and unemployment rate among the dwellers of rural areas. Reduction/ eradication of poverty in the form of poor wage gain will on the other hand reduce the incentive of moving to the urban areas for greener pasture search such that the problems of high immigration rate will be avoided.

53. Ngene Michael C. says:

Name: Ngene Michael C.
Reg no: 2017/246022
Dept: Economies
Email: michaelchinecherem1997@gmail.com

Lewis-Fei-Ranis Model of Economic Growth

Introduction
Lewis (1954) proposed a seminal theory of dualistic economic development for
over-populated and under-developed economies with vast amounts of surplus agricultural labour for which he was later to be awarded the 1979 Nobel Prize in Economics. Economic growth in such an economy can be achieved by rapid capitala ccumulation in the non-agricultural (industrial and service) sector, facilitated by drawing surplus labour in the agricultural sector. In the Lewis theory, an economy transits from the first, labour-surplus “stage” to the second, labour-scarce “stage” of development. Later, Ranis and Fei (1961) formalised the Lewis theory and defined three “phases” of dualistic economic development by sub-dividing the first stage in the Lewis model into two phases. Thus, the second labour-scarce stage of the Lewis model corresponds to the phase three of the Ranis-Fei model. into which each phase marked three turning points which are :
• The breakout point leads to phase one growth with redundant agricultural labour.
• The shortage point leads to phase two growth with disguised agricultural unemployment.
• The commercialisation point leads to phase three of self-sustaining economic growth with the commercialisation of the agricultural sector.
The Lewis-Ranis-Fei theory of dualistic economic development therefore provides a
suitable theoretical framework for studying the growth path of labour-surplus in developing economies such as China. The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature.
According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector in the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.
Fei-Ranis (F-R) Model of Dual Economy:
The two economists John Fei and Gustav Ranis presented their dual economy model. There was a flaw in Lewis model that it did not pay enough attention to the importance of agricultural sector in promoting industrial growth. But Fei-Ranis (F-R) model of dual economy explains how the increased productivity in the agricultural sector would become helpful in promoting the industrial sector. In this respect, it presents three stages whereby a UDC moves from stagnation to self-sustained economic growth. Thus, this model is treated as an improvement over Lewis model of unlimited supply of labor.
Thus the model suggests that:
“Economic development would be taking place if agricultural laborers are transferred to industrial sector where their productivity will increase”.
As we told earlier that it is a dual economy where there is a stagnant agri. sector and dynamic industrial sector. The situation where MPL – 0, labor can be transferred to industrial sector without any loss in agricultural output. The real wages in industrial sector remains fixed and it is equal to the initial level of real income in agri. sector. Such wages are given the name of institutional wages.

Conclusion and policy recommendations
Having tested the Lewis-Ranis-Fei theory for the Nigerian economy we have found that Nigeria’s economic growth is mainly attributable to the development of the non-agricultural sector. This is driven by rapid capital accumulation as well as
employment growth. The reallocation of labour away from agriculture has made a
positive net contribution to Nigeria’s rapid economic growth by around 1.23 percent.
The rise in the marginal productivity of agricultural labour indicates the absorption of
redundant agricultural labour since the 1978 Economic Reform. However, the marginal
productivity of agricultural labour is still lower than the initial low average productivity
of agricultural labour. This suggests that the Nigerian economy has entered the
Lewis-Ranis-Fei phase two of development but has not yet achieved phase three.
Several policy recommendations are tentatively suggested. First and foremost, more
effort should be made in promoting employment to effectively absorb the remaining
labour surplus and promote Nigeria economic development. Secondly,
agriculture could be promoted by tax breaks, direct subsidies and most importantly, by
removing price controls on agricultural products. Agriculture could thus be commercialised and the economy would enter phase three of economic development.

Haris-Todaro Model of Migration

The Harris–Todaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and welfare economics to explain some of the issues concerning rural-urban migration. The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This implies that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.
In the model, an equilibrium is reached when the expected wage in urban areas (actual wage adjusted for the unemployment rate), is equal to the marginal product of an agricultural worker. The model assumes that unemployment is non-existent in the rural agricultural sector. It is also assumed that rural agricultural production and the subsequent labor market is perfectly competitive. As a result, the agricultural rural wage is equal to agricultural marginal productivity. In equilibrium, the rural to urban migration rate will be zero since the expected rural income equals the expected urban income. However, in this equilibrium there will be positive unemployment in the urban sector. The model explains internal migration in China as the regional income gap has been proved to be a primary drive of rural-urban migration, while urban unemployment is local governments’ main concern in many cities.

Conclusions
Therefore, migration from rural areas to urban areas will increase in Nigeria if:
Urban wages (wu) increase in the urban sector (le), increasing the expected urban income.
Agricultural productivity decreases, lowering marginal productivity and wages in the agricultural sector (wr), decreasing the expected rural income.
However, even though this migration creates unemployment and induces informal sector growth, this behavior is economically rational and utility-maximizing in the context of the Harris–Todaro model. As long as the migrating economic agents have complete and accurate information concerning rural and urban wage rates and probabilities of obtaining employment, they will make an expected income-maximizing decision.

54. INTRODUCTION
The Harris Todaro Model which was named after John R. Harris and Michael Todaro is an economic analytical model developed in 1970 and is used in development economics and welfare economics to explain and analyze some of the issues that concerns rural-urban migration. The main assumption of the Harris Todaro’s model is that the migration decision is mainly based on the expected income differentials between rural and urban areas rather than just wage differentials. This implies that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income. Harris Todaro migration theory is considered one of the starting points of the classic rural-urban migration theory.
The hypothesis and predictions of Harris-Todaro model have been subjected to econometric evaluation and have been corroborated by several studies. The key hypothesis of Harris and Todaro are that migrants react mainly to economic incentives, earnings differentials, and the probability of getting a job at the destination have influence on the migraton decision. In other words, these authors posit that rural-urban migration will occur while the urban expected wage exceeds the rural wage. From this crucial assumption, as denominated by Harris-Todaro, is deduced that the migratory dynamics leads the economic system towards equilibrium with urban concentration and high urban unemployment. In our previous works we analyzed the rural-urban migration by means of an agent-based computational model taking into account the influence of the neighborhood in the migration decision. The inclusion of the influence of neighbors was done via an Ising like model. The economic analogous to the external field in the Ising Hamiltonian was the differential of expected wages between urban and rural sectors. Therefore, in theses works the crucial assumption of Harris and Todaro were taken for granted.
Now, we are motivated by the following question: can the crucial assumption and equilibrium with urban concentration and urban unemployment obtained from the original Harris-Todaro model be generated as emergent properties from the interaction among adaptive agents? In order to answer this question we implemented an agent-based computational model in which workers grope for best sectorial location over time in terms of earnings. The economic system simulated is characterized by the assumption originally made by Harris and Todaro.
The paper is arranged as follows. Section describes the analytical Harris-Todaro model showing its basic equilibrium properties. In Section we present the implementation of the computational model via an agent-based simulation and compare its aggregate regularities with the analytical equilibrium properties. Section shows concluding remarks.

THE HARRIS-TODARO MODEL
A. Assumptions
Harris and Todaro studied the migration of workers in a two-sector economic system, namely, rural sector and urban sector. The differences between these sectors are the type of goods produced, the technology of production and the process of wage determination. The rural sector is specialized in the production of agricultural goods. The productive process of this sector can be described by a Cobb-Douglas production function:

where Ya is the production level of the agricultural good, Na is the amount of workers used in the agricultural production, Aa > 0 and 0 < f 0 and 0 < a 0 and g > 0 are a parametric constants. g is the elasticity of p with respect to the ratio Ym/Ya.
The overall population of workers in the economy is N, which is kept constant during the whole period of analysis. By assumption there are only two sectors and rural prices are wholly flexible, which implies that there is full employment in the rural area, i.e., all workers living at the rural sector are employed at any period. Then at any period the following equality is verified:

B. Temporary Equilibrium: Given a parametric constant vector (Aa,Am,f,a,r,g), an initial urban population Nu, and a minimum wage wm one can calculate the temporary equilibrium of the economic system by using eqs. (1 – 6).
From eq. (4) one can find the employment level at the manufacturing sector

Replacing eq. (7) in eq. (2) we get the production level of the manufacturing sector

From eq. (6) one can obtain the relation

which is used with eq. (1) to obtain the agricultural production

By using eqs. (5), (8) and (10) the terms of trade are determined

Finally, by using eqs. (3), (9) and (11), the rural wage in units of manufacturated good is obtained

In sum, the vector (Nm,Ym,Na,Ya,p,wa) configures a temporary equilibrium that might be altered whether occurs a migration of workers, induced by the differential of sectorial wages, which changes the sectorial distribution of overall population.

C. The Long Run Equilibrium: Harris and Todaro, in determining the long run equilibrium, i.e., the absence of a net rural-urban migratory flow, argue that the rural workers, in their decision on migrating to the urban area, estimate the expected urban wage, , defined as:

The ratio Nm/Nu, which is the employment rate, is an estimative of the probability that a worker living at urban sector gets a job in this sector.
As mentioned before, the key assumption of the model of Harris and Todaro is that there will be a migratory flow from the rural to the urban sector while the expected urban wage is higher than the rural wage. Thus, the long run equilibrium is attained when the urban worker population reaches a level such that the expected urban wage equates the rural wage:

This equality is known in the economic literature as the Harris-Todaro condition. Harris and Todaro argue that the differential of expected wages in eq. (14) can be a constant value d ¹ 0. When this differential reaches d, the net migration ceases. This generalized Harris-Todaro condition can be expressed as follows:

The level of the urban population that satisfies the eq. (15), i.e., the equilibrium urban share = /N, is determined from the solution of the equation resulting from substitution of equations (12), (13) in eq. (15):

The solution of eq. (16) is parametrized by the vector (Aa,Am,r,g,a,f,wm).
Harris and Todaro [1], in order to evaluate the stability of the long run equilibrium, postulate a mechanism of adjustment that is based on the following function of sign preservation:

The differential equation that governs the state transition in the model of Harris and Todaro is obtained by replacing equations (12), (13) in eq. (17). Based on this postulated adjustment process, Harris and Todaro show that the long run equilibrium is globally asymptotically stable. This means that the economy would tend to long run equilibrium with unemployment in the urban sector generated by the presence of a relatively high minimum wage for all possible initial conditions. From now on we will refer to the long run equilibrium simply as equilibrium. Based on the numerical solutions of eq. (16) one can evaluate the impact that the variation of the minimum wage and the elasticity of the terms of trade on the equilibrium. In Fig. 1 we see that under the hypothesis of a Cobb-Douglas technology, the equilibrium urban share, , does not depend on the minimum wage wm. However, changes in the value of wm reduces the labor demand on the manufacturing sector what results in higher unemployment rates in the equilibrium.
In turn, as seen in Fig. 2, changes in the elasticity of the terms of trade alter slightly the equilibrium urban share and unemployment rate. A net migration toward urban sector shift the terms of trade to higher values. The greater g the greater this shift, what cause an increase in the rural wage in units of manufacturing good, becoming the urban sector less attractive

APPLICATION OF HARRIS TODARO MODEL OF MIGRATION

Harris Todaro model of migration is applicable to real life economic situation due to the fact that immigrants from rural areas would want to be part of the economic activities of the society and by wanting to make their life much better would move to urban areas and this would lead the economy toward a long run equilibrium characterized by urban concentration with urban unemployment. When this long run equilibrium is reached, the generalized Harris-Todaro condition is satisfied, i.e., there is a stabilization of the rural-urban expected wage differential.

Nigeria government can use this theory of economic growth if they wish to reduce the rural-urban migration which is cause by high urban unemployment. To this, the government can make possible more expansionary fiscal policy on the rural areas in Nigeria. This policy with increase the rate of employment in rural areas and also
will increase the expect income of the rural people.

55. Ngene Michael C. says:

Name: Ngene Michael C.
Reg no: 2017/246022
Dept: Economies
Email: michaelchinecherem1997@gmail.com

Lewis-Fei-Ranis Model of Economic Growth

Introduction
Lewis (1954) proposed a seminal theory of dualistic economic development for
over-populated and under-developed economies with vast amounts of surplus agricultural labour for which he was later to be awarded the 1979 Nobel Prize in Economics. Economic growth in such an economy can be achieved by rapid capitala ccumulation in the non-agricultural (industrial and service) sector, facilitated by drawing surplus labour in the agricultural sector. In the Lewis theory, an economy transits from the first, labour-surplus “stage” to the second, labour-scarce “stage” of development. Later, Ranis and Fei (1961) formalised the Lewis theory and defined three “phases” of dualistic economic development by sub-dividing the first stage in the Lewis model into two phases. Thus, the second labour-scarce stage of the Lewis model corresponds to the phase three of the Ranis-Fei model. into which each phase marked three turning points which are :
• The breakout point leads to phase one growth with redundant agricultural labour.
• The shortage point leads to phase two growth with disguised agricultural unemployment.
• The commercialisation point leads to phase three of self-sustaining economic growth with the commercialisation of the agricultural sector.
The Lewis-Ranis-Fei theory of dualistic economic development therefore provides a
suitable theoretical framework for studying the growth path of labour-surplus in developing economies such as China. The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature.
According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector in the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.
Fei-Ranis (F-R) Model of Dual Economy:
The two economists John Fei and Gustav Ranis presented their dual economy model. There was a flaw in Lewis model that it did not pay enough attention to the importance of agricultural sector in promoting industrial growth. But Fei-Ranis (F-R) model of dual economy explains how the increased productivity in the agricultural sector would become helpful in promoting the industrial sector. In this respect, it presents three stages whereby a UDC moves from stagnation to self-sustained economic growth. Thus, this model is treated as an improvement over Lewis model of unlimited supply of labor.
Thus the model suggests that:
“Economic development would be taking place if agricultural laborers are transferred to industrial sector where their productivity will increase”.
As we told earlier that it is a dual economy where there is a stagnant agri. sector and dynamic industrial sector. The situation where MPL – 0, labor can be transferred to industrial sector without any loss in agricultural output. The real wages in industrial sector remains fixed and it is equal to the initial level of real income in agri. sector. Such wages are given the name of institutional wages.

Conclusion And Comparison To The Real World.
Having tested the Lewis-Ranis-Fei theory for the Nigerian economy we have found that Nigeria’s economic growth is mainly attributable to the development of the non-agricultural sector. This is driven by rapid capital accumulation as well as
employment growth. The reallocation of labour away from agriculture has made a
positive net contribution to Nigeria’s rapid economic growth by around 1.23 percent.
The rise in the marginal productivity of agricultural labour indicates the absorption of
redundant agricultural labour since the 1978 Economic Reform. However, the marginal
productivity of agricultural labour is still lower than the initial low average productivity
of agricultural labour. This suggests that the Nigerian economy has entered the
Lewis-Ranis-Fei phase two of development but has not yet achieved phase three.
Several policy recommendations are tentatively suggested. First and foremost, more
effort should be made in promoting employment to effectively absorb the remaining
labour surplus and promote Nigeria economic development. Secondly,
agriculture could be promoted by tax breaks, direct subsidies and most importantly, by
removing price controls on agricultural products. Agriculture could thus be commercialised and the economy would enter phase three of economic development.

Haris-Todaro Model of Migration

The Harris–Todaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and welfare economics to explain some of the issues concerning rural-urban migration. The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This implies that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.
In the model, an equilibrium is reached when the expected wage in urban areas (actual wage adjusted for the unemployment rate), is equal to the marginal product of an agricultural worker. The model assumes that unemployment is non-existent in the rural agricultural sector. It is also assumed that rural agricultural production and the subsequent labor market is perfectly competitive. As a result, the agricultural rural wage is equal to agricultural marginal productivity. In equilibrium, the rural to urban migration rate will be zero since the expected rural income equals the expected urban income. However, in this equilibrium there will be positive unemployment in the urban sector. The model explains internal migration in China as the regional income gap has been proved to be a primary drive of rural-urban migration, while urban unemployment is local governments’ main concern in many cities.

Conclusions
Therefore, migration from rural areas to urban areas will increase in Nigeria if:
Urban wages (wu) increase in the urban sector (le), increasing the expected urban income.
Agricultural productivity decreases, lowering marginal productivity and wages in the agricultural sector (wr), decreasing the expected rural income.
However, even though this migration creates unemployment and induces informal sector growth, this behavior is economically rational and utility-maximizing in the context of the Harris–Todaro model. As long as the migrating economic agents have complete and accurate information concerning rural and urban wage rates and probabilities of obtaining employment, they will make an expected income-maximizing decision.

56. ODOH CHUKWUNONSO MICHAEL says:

The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model.
It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature.
One of the best known early theoretical models of development that focused on the structural transformation of a primarily subsistence economy was that formulated by Nobel Laureate W. Arthur Lewis in the mid-1950s, and later modified, formalized, and extended by John Fei and Gustav Ranis. The Lewis two-sector model became the general theory of the 1960s and early 1970s, and it is sometimes still applied, particularly to study the recent growth experience in China and labor markets in other developing countries.
The Fei-Ranis model is an improvement over the lewis model. John Fei and Gustav Ranis analyze the transition process through which an underdeveloped economy hopes to move from a condition of stagnation to one of self-sustained growth.
The theory relates to underdeveloped labor surplus and resources; poor economy in which the vast majority of the population is engaged in agriculture amidst widespread unemployment and high rates of population growth.

ASSUMPTIONS OF THE MODEL

1. There is a dual economy divided into a traditional and stagnant agricultural sector and an active industrial sector.
2. The output of the agricultural sector is a function of land and labor alone.
3. There is no accumulation of capital in agriculture except in the form of land reclamation.
4. Land is fixed in supply.
5. Population growth is taken as an exogenous phenomenon.
The real wage in the industrial sector remains fixed and is equal to the initial level of real income in the agricultural sector. It is called an institutional wage.
6. Workers in either sector consume only agricultural products.
Given these assumptions, Fei and Ranis analyze the development of a labor surplus economy into three phases;
In the first phase, the disguised unemployed workers who are not adding to agricultural output are transferred to the industrial sector at a constant institutional wage.
In the second phase, agricultural workers add to agricultural output but produce less than the institutional wage they get. Such workers are shifted to the industrial sector. If the migration of the workers to the industrial sector continues, a point is eventually reached when farmworkers produce output equal to the institutional wage.
In the third phase, which makes the end of the take-of and the beginning of the self-sustained growth when farmworkers produce more than the institutional wage they get. In this phase, the surplus labor is exhausted and the agricultural sector becomes commercialized.

. HARRIS-TODARO AGENT-BASED MODEL

In this section we describe the implementation of the computational model we proposed, as well as the aggregate patterns obtained numerically and the comparison with the respective analytical results.

A. Computational Implementation

Initially, workers are randomly placed in a square lattice with linear dimension L = 500. The reference values of the parameters used for these simulations are the same done to evaluate the equilibrium of the Harris-Todaro model, namely, Aa = 1.0, Am = 1.0, f = 0.3, a = 0.7, r = 1.0 and g = 1.0. The value of the minimum wage used is wm = 0.8 and the initial urban fraction of the total population is nu = 0.2, where nu = Nu/N is the normalized urban population also called urban share. The initial value nu = 0.2 is in agreement with historical data of developing economies. Given these parameters, one can calculate the vector which characterizes temporary equilibrium of the system by using eqs. (7 – 12).

By using eq. (7), the employment level of the urban sector, Nm, is obtained. If nu Nm/N there will be a fraction of Nm/Nu workers employed, which earn the minimum wage, wi = wm, and (1-Nm/Nu) workers unemployed, which earn a wage wi = 0.

Each worker can be selected to review his sectorial location with probability a, called activity . Therefore, in each time step only a fraction of workers becomes potential migrants, going through the sectorial location reviewing process. Potential migrants will determine their satisfaction level of being in the current sector by comparing their earnings, wi, among nearest neighbors.

The potential migrant starts the comparison process with a initial satisfaction level si = 0. When wi > wneighbor the satisfaction level si is added in one unit; if wi < wneighbor, si is diminished in one unit; if wi = wneighbor, si does not change. After the worker has passed through the reviewing process his/her satisfaction level is checked. The migration will occur only if si < 0, what means that the worker's i earnings is less than the most of his/her nearest neighbors.

After all the potential migrants complete the reviewing process and have decided migrate or not, a new configuration of the system is set. Therefore, once again a new temporary equilibrium of the system is calculated by using eqs. (8 – 12). The whole procedure is repeated until a pre-set number of steps is reached. It is important to emphasize that Nm is kept constant throughout the simulation. Its given by eq. (7) which depends on the technological parameters, a,Am, and the minimum wage, wm, which are constants too.

B. Analysis of the Emergent Properties

In this section we develop the analysis of the long run aggregate regularities of Harris-Todaro agent-based computational model. These long run properties will be compared between the solution of the analytical model and simulations.

show the basic characteristics of the transitional dynamics and long run equilibrium generated by simulations. When the economic system has a low initial urban share, nu = 0:2 or nu = 0:3, there is a net migration toward urban sector. This migration takes the urban sector from a full employment situation to an unemployment one. The positive differential of expected wages that pulls workers to the urban sector diminishes. However, if the economic system initiates with a high urban share, nu = 0:8, or nu = 0:9 there is net flow of migration toward rural sector in such a way that the unemployment rate of the urban sector decreases

In this case, the differential of expected wages is negative. In an economy mainly rural (nu < 0:5), the transitional dynamics characterized by a continuous growth of population of the urban sector with a differential of expected wages relatively high is followed by the stabilization of rural-urban differential of expected wages. In other words, the generalized Harris-Todaro condition, eq. (15), arises as a long run equilibrium result of the agent-based migratory dynamics.

Figure 3 also shows that even after the urban share has reached an stable average value, there are small fluctuations around this average. Therefore, differently from the original Harris-Todaro model, our computational model shows in the long run equilibrium the reverse migration. This phenomenon has been observed in developing countries.
for a given value of a, the variation of wm practically does not change the equilibrium values of the urban share, the differential of expected wages and the unemployment rate. However, for a given wm, higher values of a make the urban sector less attractive due the reduction of the employment level. This causes a lower equilibrium urban share, a higher unemployment rate and a gap in the convergence of the expected wages.

The equilibrium values of the urban share, the differential of expected wages and unemployment rate do not have a strong dependence with wm. However, variations in g for a fixedwm, dramatically change the equilibrium values of the variable mentioned before. Higher values of g generate a lower urban concentration, a higher gap in the expected wages and a higher unemployment rate in the equilibrium.
The convergence of migratory dynamics for a urban share, compatible with historical data, is robust in relation to the variation of the key technological parameters, a and f. The impact of the variation of these parameters in the values of the equilibrium differential of expected wages, ( – wa), and the equilibrium urban unemployment rate, (1-Nm=Nu).

CONCLUSION

The dispersed and non-coordinated individual migration decisions, made based on local information, generate aggregate regularities. Firstly, the crucial assumption of Harris and Todaro, the principle that rural-urban migration will occur while the urban expected wage exceed the rural wage, comes out as spontaneous upshot of interaction among adaptative agents.

ODOH CHUKWUNONSO MICHAEL
2017/249541

57. Ngwu Osita Enoch says:

Ngwu Osita Enoch
2017/242022
Ositangwu95@gmail.com
Education Economics

Lewis-Fei-Ranis Model (Surplus labour theory)
INTRODUCTION
The Lewis (1954) theory of dualistic economic development provides the seminal contribution to theories of economic development particularly for labour-surplus and resource-poor developing countries. In the Lewis theory, the economy is assumed to comprise the agricultural and non-agricultural sectors. The agricultural sector is assumed to have vast amounts of surplus labour that result in an extremely low, close to zero, marginal productivity of labour. The agricultural wage rate is presumed to follow the sharing rule and be equal to average productivity, which is also known as the institutional wage. The non-agricultural sector has an abundance capital and resources relative to labour. It pursues profit and employs labour at a wage rate higher than the agricultural institutional wage by approximately 30 percent (Lewis, 1954, p.150).
The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output.
HISTORY OF SURPLUS LABOUR THEORY
The historical emergence of surplus labour is, according to Marx, also closely associated with the growth of trade (the economic exchange of goods and services) and with the emergence of a society divided into social classes. As soon as a permanent surplus product can be produced, the moral-political question arises as to how it should be distributed, and for whose benefit surplus-labour should be performed. The strong defeat the weak, and it becomes possible for a social elite to gain control over the surplus-labour and surplus product of the working population; they can live off the labour of others.
Labour which is sufficiently productive so that it can perform surplus labour is, in a cash economy, the material foundation for the appropriation of surplus-value from that labour. How exactly this appropriation will occur, is determined by the prevailing relations of production and the balance of power between social classes.
THE CONCEPT OF SURPLUS LABOUR
The concept of surplus labour is widely discussed among development economics but its specific meaning needs to be defined, especially in technical terms, as many neoclassical economists still doubt the existence of surplus labour in an economy. Defining the source and the extent of surplus labour is then a prerequisite for further study. This section considers the various definitions of surplus labour and clarifies them.
The simple definition of surplus labour implies the existence of a point at which the marginal product of labour becomes zero and labour can be transferred out of the traditional sector without reducing the quantity of output, as noted by Wellisz (1968: 22): The (disguised-unemployment or the Unlimited Supply of Labour) hypothesis claims that in poor, densely populated countries, more people are employed than needed to produce the prevailing output with the existing techniques and the existing supply of non-labour inputs. The ‘surplus’ labour constitutes ‘hidden’ or ‘disguised’ unemployment. Many of the proponents of the hypothesis make the further claim that agricultural output will not decrease, and industrial output will increase, if measures are taken to re-allocate labour from subsistence agriculture (where the surplus is supposed to exist) to industry (where there is no surplus labour).
ASSUMPTIONS OF THE LEWIS-FEI-RANIS MODEL
(A) Surplus Labour in the Subsistence Sectors:
The basic assumption of the model is that there exists surplus labour in the subsistence sectors. It includes labour whose marginal productivity is zero as well as that whose marginal productivity is positive but is less than the institutional wage. This labour comprises farmers, agricultural labourers, petty traders domestic servants and women.
The surplus labour in the agriculture sector acts as a source of unlimited supply of labour for the manufacturing sector. By unlimited supply of labour. Lewis means that the supply of labour is perfectly elastic at a particular wages. This particular wage is somewhat higher than the institutional wage which each worker in the agricultural sector gets.
(B) Importance of Saving:
Another important assumption that Lewis makes is about the savings generated in the capitalist sector and in the subsistence sector. The capitalist sector invests all its savings for its further expansion. Those in the subsistence sector, on the other hand squander away their savings, if any in purchase of jewellery & for construction of temples etc of those in the capitalist sector. Lewis in fact so much fascinated by the higher propensity to save of the capitalist sector that he even advocates a transfer of income from the subsistence sector to the capitalist sector. He feels that steps have to be taken to raise the rate of savings from 10% to 15% if the development of the economy has to be smooth.
COMPARISONS OF THE THEORY OF SURPLUS LABOUR
Surplus labor models are a class of models for analyzing developing countries as dual economies with a modern capitalist sector and a traditional precapitalist sector. The precapitalist sector is viewed as having a large pool (“unlimited supplies”) of labor from which the capitalist sector may draw at constant cost. While these models are often described as finding their inspiration in the old classical economists and Karl Marx, the 1954 model of W. Arthur Lewis and its extensions are technically more neoclassical than truly classical. The Lewis model was elaborated and formalized by many others, most notably John C. H. Fei and Gustav Ranis (1964), with important theoretical contributions from Amartya Sen (1966) and Stephen Marglin (1976). Questions have been raised as to the historical relevance of the neoclassical labor surplus models (Schultz 1964; Myint 1971; Arrighi 1973; Williamson 1985).
CRITICISM
Lewis-Fei-Ranis model of economic growth has been criticized on multiple grounds, although if the model is accepted, then it will have a significant theoretical and policy implications on the underdeveloped countries’ efforts towards development and on the persisting controversial statements regarding the balanced vs. unbalanced growth debate.
It has been asserted that the Lewis-Fei-Ranis model did not have a clear understanding of the sluggish economic situation prevailing in the developing countries. If they had thoroughly scrutinized the existing nature and causes of it, they would have found that the existing agricultural backwardness was due to the institutional structure, primarily the system of feudalism that prevailed.
The Lewis-Fei-Ranis model say, “It has been argued that money is not a simple substitute for physical capital in an aggregate production function. There are reasons to believe that the relationship between money and physical capital could be complementary to one another at some stage of economic development, to the extent that credit policies could play an important part in easing bottlenecks on the growth of agriculture and industry.” This indicates that in the process of development they neglect the role of money and prices. They fail to differ between wage labor and household labor, which is a significant distinction for evaluating prices of dualistic development in an underdeveloped economy.
The Lewis-Fei-Ranis model assume that MPPL is zero during the early phases of economic development, which has been criticized by Harry T.Oshima and some others on the grounds that MPPL of labor is zero only if the agricultural population is very large, and if it is very large, some of that labor will shift to cities in search of jobs. In the short run, this section of labor that has shifted to the cities remains unemployed, but over the long run it is either absorbed by the informal sector, or it returns to the villages and attempts to bring more marginal land into cultivation.
CONCLUSIONS AND RECOMMENDATIONS
Lewis-Fei-Ranis model can be grouped under three instruments; labour force, capital accumulation and integration to the world economy. The main focus in Lewis-Fei-Ranis model was on the reallocation of labour until the turning point is reached, i.e., the time when labour reallocation has outstripped population growth long enough for dualism to atrophy and the economy to become fully commercialized. The model implicitly showed that the traditional sector do not produce any capital accumulation as they are very small and poor. Trade between agriculture and industry as the supply or marketed food falls or the demand for it rises, or both causing the value of marginal product of labour in agriculture to rise.
In sum up, there are several weaknesses of Lewis-Fei-Ranis model that are underlined by many economists. The first and most important is that if marginal productivity of labour in agricultural sector is negligible, zero. Schultz (1964), Sen (1967), Harris and Todaro (1970) and Fields (1975) proved with their empirical results that this cannot happen in agriculture sector. It is obvious that there is a disguised unemployment in agriculture. Particularly, agricultural sector should be considered in two ways: during harvest time and post harvest. If the agricultural surplus is solely considered for the regions where there can be seen harsh winter conditions, it could be accepted of the doctrine of Lewis, otherwise it is irrelevant to say there is a zero marginal productivity for agriculture labours. Also, there are positive opportunity costs, e.g. loss of crops in times of peak harvesting season, labour transfer will reduce agricultural output.
Second, the model employed mostly for the closed economies and gave relatively less information on open economies. Lewis-Fei-Ranis model was criticized as it neglects international trade. The model was to a certain extent supply-oriented, which does not foresee any trade between capital and other sectors. Also it was criticized advocating industrialization and ignores agriculture. If a section of the profit made by the capitalists is not devoted to agricultural development, the process of industrialization would be jeopardized.
Third, Lewis-Fei-Ranis model believed that the more the rate of labour transfer to urban employment, the more the economic grows and more jobs are created. But this is not a common applicable in practice if industrial development involves more intensive use of capital than labour, then the flow of labour from agriculture to industry will simply create more unemployment.
Fourth, the Lewis-Fei-Ranis model would imply that aggregate living standards should not rise as rapidly as productivity until surplus labour is eliminated. However, the evidence on living standards in Latin America during the twentieth century indicates that these have risen in line with productivity, and that the ‘indirect’ components of the real wage (health and education) have actually risen more rapidly that average incomes.
Fifth, the Lewis-Fei-Ranis model stated the wage in industrial sector does not increase before labour surplus is absorbed. But this does not happen in any way in reality as the development of the urban, or industrial, or formal sector can itself lead to the creation of pressure groups and swing the balance of power towards those in that sector, to the detriment of those remaining outside it. The wage in the industrial sector in reality outstandingly rises long before the labour surplus is absorbed.
Haven tested the Lewis-Ranis-Fei theory for developing economy over 1965-2002 we have found that the developing economic growth is mainly attributable to the development of the non-agricultural sector. This is driven by rapid capital accumulation as well as employment growth. The reallocation of labour away from agriculture has made a positive net contribution to rapid economic of the developing economy. The rise in the marginal productivity of agricultural labour indicates the absorption of redundant agricultural labour since the 1978 Economic Reform. However, the marginal productivity of agricultural labour is still lower than the initial low average productivity of agricultural labour. This implies the continued existence of disguised agricultural unemployment. This suggests that the these developing economy has entered the Lewis-Ranis-Fei phase two of development but has not yet achieved phase three. The continuing widening productivity gap between the two sectors calls for the removal of market restrictions and government interventions so as to allow the continued absorption of surplus labour. Several policy recommendations are tentatively suggested. First and foremost, more effort should be made in promoting employment to effectively absorb the remaining labour surplus and promote economic development. This can be achieved by further relaxing the Hukou restrictions on migration, increasing labour market flexibility and improving the allocative efficiency of labour. It can also be achieved by encouraging the development of private enterprise to create more employment opportunities. Second, Government of developing economy should continue implementing the Sunshine Policy, initiated in 2003, designed to provide rudimentary job training, recruitment information and information about conditions in the destination cities to rural migrants. This will not only help facilitate employment of rural migrants but also satisfy the increasing demand for skilled labour in the growing non-agricultural sector. Third, agriculture could be promoted by tax breaks, direct subsidies and most importantly, by removing price controls on agricultural products. Agriculture could thus be commercialised and the economy would enter phase three of economic development.

REFERENCE
Sadik-Zada, Elkhan Richard (2020). “Natural resources, technological progress, and economic modernization”. Review of Development Economics. doi:10.1111/rode.12716.
“Economnics4Development Website”. Surplus Labor Model of Economic Development. Archived from the original on 16 October 2011. Retrieved 12 October 2011.
Thirlwall, A.P (2006). Growth and Development: With Special Reference to Developing Economies. Palgrave Macmillan. ISBN 1-4039-9600-8.
Subrata, Ghatak (2003). Introduction to Developmental Economics. London: Routledge. ISBN 0-415-09722-3.
“Ranis-Fei model vs. Lewis Model” (PDF). Developmentafrique.com. Archived from the original (PDF) on 30 May 2012. Retrieved 14 October 2011.
“American Economic Review”. The Ranis-Fei Model of Economic Development: Comment. 53: 448–452. JSTOR 1809172.
Ranis, Gustav. “Paper on Labor Surplus Economies” (PDF). Retrieved 4 October 2011.
J. Choo, Hakchung. “American Economic Review”. On the Empirical Relevancy of the Rans-Fei Model of Economic Development: Comment. 61: 695–703. JSTOR 1811863.
Misra, Puri, S.K, V.K (2010). Economics of Development and Planning. Mumbai, India: Himalaya Publishing House. pp. 270–279. ISBN 978-81-8488-829-4.

Ngwu Osita Enoch
2017/242022
Ositangwu95@gmail.com
Education Economics

Harris-Todaro Model of Migration
INTRODUCTION
Harris and Todaro work, is considered one of the starting points of the classic rural-urban migration theory. The hypothesis and predictions of Harris-Todaro model have been subjected to econometric evaluation and have been corroborated by several studies. The key hypothesis of Harris and Todaro are that migrants react mainly to economic incentives, earnings differentials, and the probability of getting a job at the destination have influence on the migraton decision. In other words, these authors posit that rural-urban migration will occur while the urban expected wage exceed the rural wage. From this crucial assumption, as denominated by Harris-Todaro, is deduced that the migratory dynamics leads the economic system toward an equilibrium with urban concentration and high urban unemployment.
THE HARRIS-TODARO MODEL
Assumptions
Harris and Todaro studied the migration of workers in a two-sector economic system, namely, rural sector and urban sector. The difference between these sectors are the type of goods produced, the technology of production and the process of wage determination. The rural sector is specialized in the production of agricultural goods. The productive process of this sector can be described by a Cobb-Douglas production function: where Ya is the production level of the agricultural good, Na is the amount of workers used in the agricultural production, Aa > 0 and 0 < f 0 and 0 < a < 1 are parametric constants. Both goods and labor markets are perfectly competitive. Nevertheless, there is segmentation in the labor market due to a high minimum urban wage politically determined. In the rural sector, the real wage, perfectly flexible, is equal to the marginal productivity of labor in this sectors where wa is the real wage and p is the price of the agricultural good, both expressed in units of manufactured good.
HARRIS-TODARO AGENT-BASED MODEL
Computational Implementation

Initially, workers are randomly placed in a square lattice with linear dimension L = 500. The reference values of the parameters used for these simulations are the same done to evaluate the equilibrium of the Harris-Todaro model, namely, Aa = 1.0, Am = 1.0, f = 0.3, a = 0.7, r = 1.0 and g = 1.0. The value of the minimum wage used is wm = 0.8 and the initial urban fraction of the total population is nu = 0.2, where nu = Nu/N is the normalized urban population also called urban share. The initial value nu = 0.2 is in agreement with historical data of developing economies. Given these parameters, one can calculate the vector which characterizes temporary equilibrium of the system by using eqs. (7 – 12). By using eq. (7), the employment level of the urban sector, Nm, is obtained. If nu Nm/N there will be a fraction of Nm/Nu workers employed, which earn the minimum wage, wi = wm, and (1-Nm/Nu) workers unemployed, which earn a wage wi = 0. Each worker can be selected to review his sectorial location with probability a, called activity. Therefore, in each time step only a fraction of workers becomes potential migrants, going through the sectorial location reviewing process. Potential migrants will determine their satisfaction level of being in the current sector by comparing their earnings, wi, among nearest neighbors. The potential migrant starts the comparison process with a initial satisfaction level si = 0. When wi > wneighbor the satisfaction level si is added in one unit; if wi < wneighbor, si is diminished in one unit; if wi = wneighbor, si does not change. After the worker has passed through the reviewing process his/her satisfaction level is checked. The migration will occur only if si < 0, what means that the worker's i earnings is less than the most of his/her nearest neighbors. After all the potential migrants complete the reviewing process and have decided migrate or not, a new configuration of the system is set. Therefore, once again a new temporary equilibrium of the system is calculated by using eqs. (8 – 12). The whole procedure is repeated until a pre-set number of steps is reached. It is important to emphasize that Nm is kept constant throughout the simulation. Its given by eq. (7) which depends on the technological parameters, a,Am, and the minimum wage, wm, which are constants too.
In this case, the differential of expected wages is negative. In an economy mainly rural (nu < 0:5), the transitional dynamics characterized by a continuous growth of population of the urban sector with a differential of expected wages relatively high is followed by the stabilization of rural-urban differential of expected wages. In other words, the generalized Harris-Todaro condition, eq. (15), arises as a long run equilibrium result of the agent-based migratory dynamics.
CONCLUSION
In this paper we developed and agent-based computational model which formalizes the rural-urban allocation of workers as a process of social learning by imitation. We analyze a two-sectorial economy composed by adaptative agents, i.e., individuals that grope over time for best sectorial location in terms of earnings. This search is a process of imitation of successful neighbor agents. The dispersed and non-coordinated individual migration decisions, made based on local information, generate aggregate regularities.
Firstly, the crucial assumption of Harris and Todaro, the principle that rural-urban migration will occur while the urban expected wage exceed the rural wage, comes out as spontaneous upshot of interaction among adaptative agents.
Secondly, the migratory dynamics generated by agents that seek to adaptate to the economic environment that they co-create leads the economy toward a long run equilibrium characterized by urban concentration with urban unemployment. When this long run equilibrium is reached, the generalized Harris-Todaro condition is satisfied, i.e., there is a stabilization of the rural-urban expected wage differential.
Thirdly, the impact of the minimum wage and elasticity of terms of trade in a long run equilibrium obtained by simulations are in agreement with the predictions of the original Harris-Todaro model with Cobb-Douglas technology.
Finally, the simulations showed an aggregated pattern not found in the original Harris-Todaro model. There is the possibility of small fluctuations of the urban share around an average value. This phenomenon is known as reverse migration.

REFERENCE

Aquino L. Espíndola thanks CAPES for the financial support. Jaylson J. Silveira acknowledges research grants from CNPq. T. J. P. Penna thanks CNPq for the fellowship.
J. R. Harris and M. P. Todaro, American Economic Review 60, 126 (1970).
M. P. Todaro, American Economic Review 59, 138 (1969).
D. Ray, Development Economics (Princeton: Princeton University Press, 1998).
L. Y. L. Yap, Journal of Development Economics 4, 239 (1977).
D. Mazumdar, Rural-urban Migration in Developing countries. In: Handbook of Regional and Urban Economics, Elsevier, Amsterdam, 1987.
L. Ghatak, P. Levine, and S. Price, Journal of Economics Surveys 10, 159 (1996).
J. G. Willianson, Migration and Urbanization. In: Chenery, H. and Srinivasan, T.N., Handbook of developments economics, Elsevier, Amsterdam, 1988.
J. J. Silveira, A. L. Espíndola, and T. J. P. Penna, physics/0506021, Physica A, to appear.

58. Ngwu Osita Enoch says:

Ngwu Osita Enoch
2017/242022
Ositangwu95@gmail.com
Education Economics

Lewis-Fei-Ranis Model (Surplus Labour Theory)
INTRODUCTION
The Lewis (1954) theory of dualistic economic development provides the seminal contribution to theories of economic development particularly for labour-surplus and resource-poor developing countries. In the Lewis theory, the economy is assumed to comprise the agricultural and non-agricultural sectors. The agricultural sector is assumed to have vast amounts of surplus labour that result in an extremely low, close to zero, marginal productivity of labour. The agricultural wage rate is presumed to follow the sharing rule and be equal to average productivity, which is also known as the institutional wage. The non-agricultural sector has an abundance capital and resources relative to labour. It pursues profit and employs labour at a wage rate higher than the agricultural institutional wage by approximately 30 percent (Lewis, 1954, p.150).
The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output.
HISTORY OF SURPLUS LABOUR THEORY
The historical emergence of surplus labour is, according to Marx, also closely associated with the growth of trade (the economic exchange of goods and services) and with the emergence of a society divided into social classes. As soon as a permanent surplus product can be produced, the moral-political question arises as to how it should be distributed, and for whose benefit surplus-labour should be performed. The strong defeat the weak, and it becomes possible for a social elite to gain control over the surplus-labour and surplus product of the working population; they can live off the labour of others.
Labour which is sufficiently productive so that it can perform surplus labour is, in a cash economy, the material foundation for the appropriation of surplus-value from that labour. How exactly this appropriation will occur, is determined by the prevailing relations of production and the balance of power between social classes.
THE CONCEPT OF SURPLUS LABOUR
The concept of surplus labour is widely discussed among development economics but its specific meaning needs to be defined, especially in technical terms, as many neoclassical economists still doubt the existence of surplus labour in an economy. Defining the source and the extent of surplus labour is then a prerequisite for further study. This section considers the various definitions of surplus labour and clarifies them.
The simple definition of surplus labour implies the existence of a point at which the marginal product of labour becomes zero and labour can be transferred out of the traditional sector without reducing the quantity of output, as noted by Wellisz (1968: 22): The (disguised-unemployment or the Unlimited Supply of Labour) hypothesis claims that in poor, densely populated countries, more people are employed than needed to produce the prevailing output with the existing techniques and the existing supply of non-labour inputs. The ‘surplus’ labour constitutes ‘hidden’ or ‘disguised’ unemployment. Many of the proponents of the hypothesis make the further claim that agricultural output will not decrease, and industrial output will increase, if measures are taken to re-allocate labour from subsistence agriculture (where the surplus is supposed to exist) to industry (where there is no surplus labour).
ASSUMPTIONS OF THE LEWIS-FEI-RANIS MODEL
(A) Surplus Labour in the Subsistence Sectors:
The basic assumption of the model is that there exists surplus labour in the subsistence sectors. It includes labour whose marginal productivity is zero as well as that whose marginal productivity is positive but is less than the institutional wage. This labour comprises farmers, agricultural labourers, petty traders domestic servants and women.
The surplus labour in the agriculture sector acts as a source of unlimited supply of labour for the manufacturing sector. By unlimited supply of labour. Lewis means that the supply of labour is perfectly elastic at a particular wages. This particular wage is somewhat higher than the institutional wage which each worker in the agricultural sector gets.
(B) Importance of Saving:
Another important assumption that Lewis makes is about the savings generated in the capitalist sector and in the subsistence sector. The capitalist sector invests all its savings for its further expansion. Those in the subsistence sector, on the other hand squander away their savings, if any in purchase of jewellery & for construction of temples etc of those in the capitalist sector. Lewis in fact so much fascinated by the higher propensity to save of the capitalist sector that he even advocates a transfer of income from the subsistence sector to the capitalist sector. He feels that steps have to be taken to raise the rate of savings from 10% to 15% if the development of the economy has to be smooth.
COMPARISONS OF THE THEORY OF SURPLUS LABOUR
Surplus labor models are a class of models for analyzing developing countries as dual economies with a modern capitalist sector and a traditional precapitalist sector. The precapitalist sector is viewed as having a large pool (“unlimited supplies”) of labor from which the capitalist sector may draw at constant cost. While these models are often described as finding their inspiration in the old classical economists and Karl Marx, the 1954 model of W. Arthur Lewis and its extensions are technically more neoclassical than truly classical. The Lewis model was elaborated and formalized by many others, most notably John C. H. Fei and Gustav Ranis (1964), with important theoretical contributions from Amartya Sen (1966) and Stephen Marglin (1976). Questions have been raised as to the historical relevance of the neoclassical labor surplus models (Schultz 1964; Myint 1971; Arrighi 1973; Williamson 1985).
CRITICISM
Lewis-Fei-Ranis model of economic growth has been criticized on multiple grounds, although if the model is accepted, then it will have a significant theoretical and policy implications on the underdeveloped countries’ efforts towards development and on the persisting controversial statements regarding the balanced vs. unbalanced growth debate.
It has been asserted that the Lewis-Fei-Ranis model did not have a clear understanding of the sluggish economic situation prevailing in the developing countries. If they had thoroughly scrutinized the existing nature and causes of it, they would have found that the existing agricultural backwardness was due to the institutional structure, primarily the system of feudalism that prevailed.
The Lewis-Fei-Ranis model say, “It has been argued that money is not a simple substitute for physical capital in an aggregate production function. There are reasons to believe that the relationship between money and physical capital could be complementary to one another at some stage of economic development, to the extent that credit policies could play an important part in easing bottlenecks on the growth of agriculture and industry.” This indicates that in the process of development they neglect the role of money and prices. They fail to differ between wage labor and household labor, which is a significant distinction for evaluating prices of dualistic development in an underdeveloped economy.
The Lewis-Fei-Ranis model assume that MPPL is zero during the early phases of economic development, which has been criticized by Harry T.Oshima and some others on the grounds that MPPL of labor is zero only if the agricultural population is very large, and if it is very large, some of that labor will shift to cities in search of jobs. In the short run, this section of labor that has shifted to the cities remains unemployed, but over the long run it is either absorbed by the informal sector, or it returns to the villages and attempts to bring more marginal land into cultivation.
CONCLUSIONS AND RECOMMENDATIONS
Lewis-Fei-Ranis model can be grouped under three instruments; labour force, capital accumulation and integration to the world economy. The main focus in Lewis-Fei-Ranis model was on the reallocation of labour until the turning point is reached, i.e., the time when labour reallocation has outstripped population growth long enough for dualism to atrophy and the economy to become fully commercialized. The model implicitly showed that the traditional sector do not produce any capital accumulation as they are very small and poor. Trade between agriculture and industry as the supply or marketed food falls or the demand for it rises, or both causing the value of marginal product of labour in agriculture to rise.
In sum up, there are several weaknesses of Lewis-Fei-Ranis model that are underlined by many economists. The first and most important is that if marginal productivity of labour in agricultural sector is negligible, zero. Schultz (1964), Sen (1967), Harris and Todaro (1970) and Fields (1975) proved with their empirical results that this cannot happen in agriculture sector. It is obvious that there is a disguised unemployment in agriculture. Particularly, agricultural sector should be considered in two ways: during harvest time and post harvest. If the agricultural surplus is solely considered for the regions where there can be seen harsh winter conditions, it could be accepted of the doctrine of Lewis, otherwise it is irrelevant to say there is a zero marginal productivity for agriculture labours. Also, there are positive opportunity costs, e.g. loss of crops in times of peak harvesting season, labour transfer will reduce agricultural output.
Second, the model employed mostly for the closed economies and gave relatively less information on open economies. Lewis-Fei-Ranis model was criticized as it neglects international trade. The model was to a certain extent supply-oriented, which does not foresee any trade between capital and other sectors. Also it was criticized advocating industrialization and ignores agriculture. If a section of the profit made by the capitalists is not devoted to agricultural development, the process of industrialization would be jeopardized.
Third, Lewis-Fei-Ranis model believed that the more the rate of labour transfer to urban employment, the more the economic grows and more jobs are created. But this is not a common applicable in practice if industrial development involves more intensive use of capital than labour, then the flow of labour from agriculture to industry will simply create more unemployment.
Fourth, the Lewis-Fei-Ranis model would imply that aggregate living standards should not rise as rapidly as productivity until surplus labour is eliminated. However, the evidence on living standards in Latin America during the twentieth century indicates that these have risen in line with productivity, and that the ‘indirect’ components of the real wage (health and education) have actually risen more rapidly that average incomes.
Fifth, the Lewis-Fei-Ranis model stated the wage in industrial sector does not increase before labour surplus is absorbed. But this does not happen in any way in reality as the development of the urban, or industrial, or formal sector can itself lead to the creation of pressure groups and swing the balance of power towards those in that sector, to the detriment of those remaining outside it. The wage in the industrial sector in reality outstandingly rises long before the labour surplus is absorbed.
Haven tested the Lewis-Ranis-Fei theory for developing economy over 1965-2002 we have found that the developing economic growth is mainly attributable to the development of the non-agricultural sector. This is driven by rapid capital accumulation as well as employment growth. The reallocation of labour away from agriculture has made a positive net contribution to rapid economic of the developing economy. The rise in the marginal productivity of agricultural labour indicates the absorption of redundant agricultural labour since the 1978 Economic Reform. However, the marginal productivity of agricultural labour is still lower than the initial low average productivity of agricultural labour. This implies the continued existence of disguised agricultural unemployment. This suggests that the these developing economy has entered the Lewis-Ranis-Fei phase two of development but has not yet achieved phase three. The continuing widening productivity gap between the two sectors calls for the removal of market restrictions and government interventions so as to allow the continued absorption of surplus labour. Several policy recommendations are tentatively suggested. First and foremost, more effort should be made in promoting employment to effectively absorb the remaining labour surplus and promote economic development. This can be achieved by further relaxing the Hukou restrictions on migration, increasing labour market flexibility and improving the allocative efficiency of labour. It can also be achieved by encouraging the development of private enterprise to create more employment opportunities. Second, Government of developing economy should continue implementing the Sunshine Policy, initiated in 2003, designed to provide rudimentary job training, recruitment information and information about conditions in the destination cities to rural migrants. This will not only help facilitate employment of rural migrants but also satisfy the increasing demand for skilled labour in the growing non-agricultural sector. Third, agriculture could be promoted by tax breaks, direct subsidies and most importantly, by removing price controls on agricultural products. Agriculture could thus be commercialised and the economy would enter phase three of economic development.

REFERENCE
Sadik-Zada, Elkhan Richard (2020). “Natural resources, technological progress, and economic modernization”. Review of Development Economics. doi:10.1111/rode.12716.
“Economnics4Development Website”. Surplus Labor Model of Economic Development. Archived from the original on 16 October 2011. Retrieved 12 October 2011.
Thirlwall, A.P (2006). Growth and Development: With Special Reference to Developing Economies. Palgrave Macmillan. ISBN 1-4039-9600-8.
Subrata, Ghatak (2003). Introduction to Developmental Economics. London: Routledge. ISBN 0-415-09722-3.
“Ranis-Fei model vs. Lewis Model” (PDF). Developmentafrique.com. Archived from the original (PDF) on 30 May 2012. Retrieved 14 October 2011.
“American Economic Review”. The Ranis-Fei Model of Economic Development: Comment. 53: 448–452. JSTOR 1809172.
Ranis, Gustav. “Paper on Labor Surplus Economies” (PDF). Retrieved 4 October 2011.
J. Choo, Hakchung. “American Economic Review”. On the Empirical Relevancy of the Rans-Fei Model of Economic Development: Comment. 61: 695–703. JSTOR 1811863.
Misra, Puri, S.K, V.K (2010). Economics of Development and Planning. Mumbai, India: Himalaya Publishing House. pp. 270–279. ISBN 978-81-8488-829-4.

59. Anachunam Daberechi MaryJane says:

NAME: ANACHUNAM DABERECHI MARYJANE
REG NO: 2017/241448
EMAIL: daberechi.anachunam.241448@unn.edu.ng
BLOG: maryjaneanachunam.wordpress.com

AN ESSAY ON LEWIS-FEI-RANIS MODEL (SURPLUS LABOUR THEORY) AND HARRIS-TODARO MODEL OF MIGRATION

LEWIS-FEI-RANIS MODEL (SURPLUS LABOUR THEORY)

William Arthur Lewis, with his most famous published work, “Economic Development with Unlimited Supplies of Labour” (Manchester School, May 1954) and “The Theory of Economic Growth” (Allen and Unwin, 1955), made a great contribution to the theories of economic development. Based on his findings, Ranis and Fei succeeded to extend the initial Lewis’ model and assessed the changes in the agricultural and industrial labour in more detail. (Ukessays, 2018)
The central idea behind the Lewis model is fairly simple. Lewis divided the labour force into two differentiated groups – “subsistence sector” and “capitalist sector” where the former is assumed to contain unlimited supply and consequently, a pool of surplus labour[1] that sets labour-supply conditions for the latter. The concept of a dual economy is heavily criticised.(Ukessays, 2018)

Subsequently, Ranis’ and Fei’s extension to Lewis’ model can be analysed. They observed the model by reading it from left to right and assessed the changes in the output and wage as more and more people moved from agriculture to the industry. A new concept was added – namely, disguised unemployment, which appears in the traditional subsistence sector. The marginal product of labour, which is observed as the slope of the production function, in the agricultural sector is lower than in industry (Ukessays, 2018)

The Lewis-Ranis-Fei model

The Lewis (1954) theory of dualistic economic development provides the seminal
contribution to theories of economic development particularly for labour-surplus and
resource-poor developing countries. In the Lewis theory, the economy is assumed to
comprise the agricultural and non-agricultural sectors. The agricultural sector is
assumed to have vast amounts of surplus labour that result in an extremely low, close to
zero, marginal productivity of labour. The agricultural wage rate is presumed to follow
the sharing rule and be equal to average productivity, which is also known as the
institutional wage. The non-agricultural sector has an abundance capital and resources
relative to labour. It pursues profit and employs labour at a wage rate higher than the
agricultural institutional wage by approximately 30 percent (Lewis, 1954, p.150). The
non-agricultural sector accumulates capital by drawing surplus labour out of the
agricultural sector. The expansion of the non-agric ultural sector takes advantage of the
infinitely elastic supply of labour from the agricultural sector due to its labour surplus.
When the surplus labour is exhausted, the labour supply curve in the non-agricultural
sector becomes upward-sloping.
Ranis and Fei (1961) formalised Lewis’s theory by combining it with Rostow’s
(1956) three “linear-stages-of-growth” theory. They disassembled Lewis’s two-stage
economic development into three phases, defined by the marginal productivity of
agricultural labour. They assume the economy to be stagnant in its pre-conditioning
stage. The breakout point marks the creation of an infant non-agricultural sector and the
entry into phase one. Agricultural labour starts to be reallocated to the non-agricultural
sector. Due to the abundance of surplus agricultural labour, its marginal productivity is
extremely low and average labour productivity defines the agricultural institutional
wage. When the redundant agricultural labour force has been reallocated, the
agricultural marginal productivity of labour starts to rise but is still lower than the
institutional wage. This marks the shortage point a t which the economy enters phase two of development. During phase two the remaining agricultural unemployment is
gradually absorbed. At the end of this process the economy reaches the
commercialisation point and enters phase three where the agricultural labour market is
fully commercialised ( Marco G. Ercolani and Zheng Wei, 2010).

To conclude, having shown the main ideas behind the Lewis-Ranis-Fei model . Using Nigeria as a case study, it is important to invest in both sectors in order to remain on the balanced growth path and maintain the rate of industrialization. The existence of surplus labour in agriculture allows the industry to continue to pay the institutional wage and therefore enjoy further profits and continued investment. At the same time, as more and more people are moving away from agriculture, there will be some amount of agricultural surplus that can be used up to fuel further development. This process continues until the surplus labour is absorbed. Hence, saving and investment are a crucial part in the Lewis-Ranis-Fei to support economic development (Ukessays, 2018).

HARRIS-TODARO MODEL OF MIGRATION

John R. Harris and Michael P. Todaro presented the work Two sector modelin American
Economic Association, 1970. This model is an important study in the field encompassing rural-urban
migration.

The main idea of the Harris-Todaro model is that labour migration in underdeveloped countries is due to rural-urban differences in average expected wages rather than actual wages. The migrants consider the various opportunities of employment available to them in rural and urban sectors and choose the one that maximises their expected wages from migration (Divisha s, 2017).
The minimum urban wage is substantially higher than the rural wage. If more employment opportunities are created in the urban sector at the minimum wage, the expected will rise and rural-urban migration will increase. Expected wages are measured by the difference in real urban income and rural agricultural income and the probability of a migrants getting an urban job.
In fact, a migrant compares his expected income for a given time horizon in the urban sector with his prevailing average rural income and migrates if the former is more than the latter.
Thus migration in the Harris-Todaro modal is viewed as the wage or income gap between the urban and the rural sectors. But all migrants cannot be absorbed in the urban sector at high wages. Many fail to find a job and get employment in the informal urban sector at wages which are even lower than in the rural sector. Thus they join the queue of the underemployed or disguised unemployed in the urban sector (Divisha s, 2017)

Assumptions of the Model:

The Harris-Todaro model is based on the following assumptions:
1. There are two sectors in the economy – the rural or agricultural sector (A) and the urban or manufacturing sector (M).
2. The model operates in the short run.
3. The marginal production of labour in agriculture (MPLA) and of industry (MPLM) are determined by their respective technologies.
4. Capital is available in fixed quantities in the two sectors.
5. There are L workers in economy with LA and LM numbers employed in the rural and urban sectors respectively.
6. The number of urban jobs available (LM) is exogenously fixed. In the rural sector some work is always available. Therefore, the total urban labour force LM comprises L-LAalong with an available supply of rural migrants.
7. The urban wage is fixed at WM and the rural wage at WA, WM>WA.
8. The rural wage equals the rural marginal product of labour and the urban wage is exogenously determined.
9. Rural-urban migration continues so long as the expected urban real income is more that the real agricultural income.

. At the core of the Harris-Todaro model were the following features. First, real wages (adjusted for cost-of-living differences) are higher in urban formal-sector jobs than in rural traditional-sector jobs. Second, to be hired for a formal-sector job, one has to be physically present in the urban areas where the formal-sector jobs are located. Third, and as a consequence of the first two features, more workers search for formal-sector jobs than are hired, employers hire some of the job seekers but not all of them, and those not hired end up unemployed. Fourth, for equality to be maintained between the expected wage associated with searching for an urban job and the expected wage associated with taking up a lower-paying rural job, the equilibrium arising in such a setting is characterized by urban unemployment. And fifth, any temporary difference in the expected wages between one sector and another is eroded as workers migrate from the low-expected-wage labor market to the high-expected-wage labor market.
Starting from the assumption that migration is based primarily on privately rational economic calculations despite the existence of high urban unemployment, the Todaro model postulates that migration proceeds in response to urban-rural differences in expected rather than actual earnings. The fundamental premise is that as decision-makers migrants consider the various labor-market opportunities available to them as, say, between the rural and urban sectors, choosing the one that maximizes their “expected” gains from migration. Expected gains are measured by the difference in real incomes between rural and urban work opportunities and the probability of a new migrant’s obtaining urban job. The “thought process” of the Todaro model can be explained as follows. Suppose the average unskilled or semiskilled rural worker has a choice between being a farm laborer (or working his own land) for an annual average real income of, say, 50 units per year, and migrating to the city where a worker with his skill or educational background can obtain wage employment yielding an annual real income of, say, 100 units. The worker should seek the higher-paying urban job. It is important to recognize, however, that these migration models were developed largely in the context of advanced industrial economies and, as such, implicitly assumed the existence of full or near-full employment in urban areas. In a full-employment environment the decision to migrate can in fact be predicated solely on securing the highest-paying job wherever it becomes available, other factors being held constant. Simple economic theory would then indicate that such migration should lead to a reduction in wage differentials through geographic changes in supply and demand, both in areas of out-migration (where incomes rise) and in points of in-migration (where they fall). Unfortunately, such an analysis is not very realistic in the context of the institutional and economic framework of most Third World nations. First of all, these countries are beset by a chronic and serious problem of urban surplus labor, so that many migrants cannot expect to secure high-paying urban jobs immediately upon arrival. In fact, it is much more likely that upon entering the urban labor market many migrants will either become totally unemployed or will seek casual and parttime employment in the urban traditional sector for some time.
Consequently, in his decision to migrate the individual must in effect balance the probabilities and risks of being unemployed or underemployed for a considerable period of time against the positive urban-rural real-income differential. That it is possible for our hypothetical migrant to earn twice as much annual real income in an urban area as in his rural environment may be of little consequence if his actual probability of securing the higher-paying job within a year is one chance in five. In such a situation the migrant’s actual probability of being successful in securing the higherpaying urban job is 20%, so that his “expected” urban income for the one-year period is in fact 20 units, not the 100 units that a migrant in a full-employment urban environment might expect to receive. Thus, with a one-period time horizon and a probability of success of 20% it would be irrational for this migrant to seek an urban job even though the differential between urban and rural earnings capacity is 100%. On the other hand, if the probability of success were, say, 60%, so that the expected urban income is 60 units, it would be entirely rational for such a migrant with his one-period time horizon to try his luck in the urban job “lottery” even though urban unemployment may be extremely high. Returning now to the more realistic situation of longer time horizons for potential migrants, especially considering that the vast majority are between the ages of 15 and 24, It is argued that the decision to migrate should be represented on the basis of a “permanent income” calculation. If the migrant anticipates a relatively low probability of finding regular wage employment in the initial period but expects this probability to increase over time as he is able to broaden his urban contacts, then it would still be rational for him to migrate even though expected urban income during the initial period or periods might be lower than expected rural income. As long as the present value of the net stream of expected urban income over the migrant’s planning horizon exceeds that of the expected rural income, the decision to migrate is economically justified. Rather than wage adjustments bringing about an equilibrium between urban and rural incomes, as would be the case in a competitive model, it is further argued that rural-urban migration itself must act as the ultimate equilibrating force. With urban wages assumed to be inflexible in a downward direction, rural and urban “expected” incomes can be equalized only by falling urban job probabilities resulting from rising urban unemployment. For example, if average rural wages are 60 units and urban wages are institutionally set at a level of 120 units, then in a one-period model a 50% urban unemployment rate would be necessary to vitiate the private profitability of further migration. Since expected incomes are defined in terms of both wages and employment probabilities, argument is that it is not only possible but likely to have continued migration in spite of the existence of sizable rates of urban unemployment. In the above numerical example, migration would continue even if the urban unemployment rate were 30 or 40%.

Conclusion
In the Harris–Todaro model, the rising urban wage pushes up the expected wage in the urban sector and consequently encourages workers to migrate from the rural sector to the urban sector. If, in the resulting migration, there are more workers than the number of job opportunities created in the urban sector, some will necessarily be unemployed which is the case in Nigeria when people leave rural areas to go to bigger cities like Lagos and end up being unemployed. Occasionally, the increase in unemployment lowers the per-capita income level before the capital is accumulated. This phenomenon is referred to as Todaro paradox.
If there is a necessary and sufficient condition under which the increase in capital stock does not increase unemployment in the urban area. This condition concerns the relationship between the institutionally and legally set minimum wage in the urban area and increased agricultural productivity in the rural area, that is there is an institutionally set minimum wage in urban areas (eg Lagos) that can’t be manipulated while the government works harder to develop the agricultural sector. Unsurprisingly, if agricultural productivity rises and income in the rural area increases, rural workers have no need to migrate to the urban sector to find jobs and face the risk of unemployment.

60. Name :Okaforukwu chizaram sandra
Reg no : 2017/249551
E-mail: okagrt01@gmail.com

THE HARRIS-TODARO MODEL
The Harris–Todaro model, named after John R. Harris and Michael Todaro, is a 1970s economic model used in development economics and welfare economics to describe some of the problems surrounding rural-urban migration. The model’s key assumption is that migration decisions are based on projected income differentials between rural and urban areas rather than simply wage differentials. This implies that rural-urban migration can be economically acceptable in a context of high urban unemployment if projected urban income exceeds expected rural income. A new pattern of economic development that is relevant for labor surplus nations such as India has been developed by J. R. Harris and M. P. Todaro. The model focuses on labor migration from rural to urban areas, which is caused by certain incentives. Under this model, migrant employees are mainly involved in a lottery of high-paid jobs in cities. For each job created, more than one worker may migrate, which would result in a loss of output if migrants take some family members into the urban zone.
Assumption of the model .
The formal statement of the equilibrium condition of the Harris–Todaro model is as follows:
 Let wr be the wage rate (marginal productivity of labor) in the rural agricultural sector.
 Let le be the total number of available jobs in the urban sector, which should be equal to the number of urban employees employed.
 Let lus be the total number of job seekers, employed and unemployed, in the urban sector.
 Let wu be the wage rate in the urban sector, which the government might likely set with a minimum wage rule.
Rural-to-urban migration will occur if and only if the following conditions are met:
Rural to urban migration will take place if:
wrle/lus(wu)
At equilibrium,
wr=le/lus(wu)
The ratio of available jobs to total job seekers provides the likelihood that any person moving from the agricultural sector to the urban sector will be able to find employment. As a result, in equilibrium, the agricultural wage rate equals the estimated urban wage rate, which is calculated by multiplying the urban wage by the job rate.
Internal Migration:
The model explains why the high observed levels of small-scale urban migration in most developing countries are economically quite natural. In this model, the main motivating force behind migration is the expected real wage differential between urban and rural areas. First, the potential migrant calculates the actual revenue for a job in the urban area with his current endeavor. Then he compares the expected revenue to what he hopes to get in rural areas. His decision to migrate depends on the difference.
800 = 0.4 x 2000
If the likelihood was 0.8, the anticipated income would be 1600 (= 0.8 x 2000). (Naturally, the costs of transfer may be added to this one.) The model thus focuses on the role of economic stimulus in the decision on migration. Migration in any given time then depends on three factors:
1. The salary gap between urban and rural areas,
2. The rate of urban work and
3. The receptivity of potential migrants to the opportunities created as a result.
Theoretical Implication of the Model:
The cost of opportunities and the value in the next best alternative use is an important part of the social cost of each input. Work hired for a formal urban sector project could also be drawn from the informal urban sector. Some analysts think that the wage paid to incidental farm workers is a good measure of the social cost of unqualified labor. However, this measure probably underpins the true social cost, which other compounds are likely to be significant, although a good indicator of the yield foregone by labor reallocation. In an analysis of the labor reallocation that is likely to take place during eco-work, the Harris-Todaro model integrates both forces.

The Policy Implications of the Model:
The root of the problem is the big difference in income between the modern industrial and rural sectors. The former often go far beyond the clearing levels of the market for different restructuring measures. The long-term solution to the problem is that of adopting urban as well as rural policy that reduces the real income gaps between the two areas. From a political point of view, the H-T model has far-reaching consequences. It can be applied to the development of policies to promote urban development and industrial employment. The effect would be to improve urban employment’s subjective productivity.
Critics of the model
Internal migration, according to the Todaro Paradox, can be harmful because it exacerbates urban unemployment. Given high unemployment rates and significant migration to cities in developing countries, this idea has undoubtedly inspired many governments to implement restrictive policies, despite the fact that the empirical validity of the Harris-Todaro model and the Todaro paradox is not well established. In any case, the Harris-Todaro model suffers from theoretical oversimplifications, several of which are likely to exaggerate the relationship between migration and urban unemployment. Six major points are raised in the criticisms:
1. The Harris-Todaro framework is only a static model describing migration, which is a dynamic phenomenon by nature.Even though the model can be thought of as representing a steady state equilibrium, this is a limitation
2. .Furthermore, the formalization is made in a partial equilibrium context which greatly weakens the justifications for policy recommendations.
3. Important aspects are absent from the standard Harris-Todaro model, including the probable heterogeneity of migrants which is not accounted for, risk aversion which could dampen migration incentives and render the Todaro paradox even less likely to occur, the possibility of job search in the urban area from the rural area, the possibility of return migration, or the existence of rural unemployment.In fact, the Harris-Todaro is almost silent about what happens in the rural areas.
4. The job rationing mechanism or hiring model hypothesized is not realistic.In particular, assuming random job selection in each period overestimates the likelihood of finding a job.
5. Stiglitz (1974) suggests that the employment probability might vary in a non-monotonic way with the duration of the stay in the city: it could increase in the first periods when migrants form social networks in the city, and then decrease in the later periods because of deteriorating human capital or because of bad signaling.
6. The Harris-Todaro model assumes that the urban wage is exogenously set above the endogenous rural wage since it must be that w > f’R(LR) for (2.3) to hold.The assumption that wages are high find several explanations ranging from the existence of trade unions to the agglomeration of economic activities.
Given these criticisms, the policy implications of the Harris-Todaro model — namely, limiting rural-to-urban migration — are much weaker. Several factors, in particular, qualify the justifications for restrictive migration policies. To begin, Todarian models only consider urban labor markets, whereas national governments should consider whether overall national employment (including rural areas) has improved. Second, as Stark (1991) observed, in a general equilibrium perspective, labor migration between rural and urban areas may reflect a market disequilibrium. It cannot be ruled out that migration has a positive impact on rural areas, possibly by increasing productivity, allowing exchanges with urban areas, and generating income for rural development. Fourth, restrictions on rural-urban migration could be extremely detrimental. We have seen that, from the perspective of the Lewis model, migration controls are labor market constraints that may prevent developing countries from launching labor-intensive industries that could alleviate poverty. Last but not least, mobility is a fundamental human right, and denying it is difficult to justify. The only economic justification for restricting migration flows is that migrants do not contribute to the economy.
Conclusions
This survey has reviewed theoretical and empirical models of internal migration in developing countries. On the big question — should rural to urban migration be discouraged, tolerated, or encouraged — the broad assessment is that restrictions in general are not desirable.In principle, the Todarian models can be used for policy analysis in situations where urban unemployment arising from rapid rural to urban migration is a concern. However, the empirical literature has not been convincing in assessing whether the conditions formed has also been complex so that these tests are no more convincing than the tests for the Todaro paradox were met in the real world. Empirically testing the Harris-Todaro the conditions for the Todaro paradox to hold.
microeconomic evidence consistent with the migration incentives present in the Harris- Todaro model, measuring for instance how rural dwellers respond to an increase in the wage differential. But this type of evidence does not provide a real test of the link between urban unemployment and migration. In other words, the validity of the model has not been clearly established even though it certainly influenced policies for decades.
Many countries have implemented policies aimed at forbidding migration from rural to urban areas. In South Africa, the Apartheid system (1948-1994) used extreme controls to monitor what was meant to be the temporary migration of rural workers to cities. In Indonesia, the ‘transmigration program’, a policy of resettlement from high to low- density areas has been implemented over several decades, resulting in the relocation of more than eight million people between 1969 and 1995 (Humanitarian Policy and Conflict Research, 2002). Similarly, in China, the Hukou or household registration system initiated in 1955 required that all residents live in the places where they were born and obtain permissions to move. Until the 1970s, migrants were even transferred back to their village in order to prevent ‘over- urbanization’. Some of these programs did meet their objectives of restricting rural to urban migration, but very few have been subjected to a rigorous analysis of their welfare costs. Au and Henderson (2006)’s empirical finding suggest that migration restrictions in China have maintained surplus labor in rural areas and led to insufficient agglomeration of economic activity in cities, resulting in GDP losses.

61. NAME : Okaforukwu chizaram sandra

Reg no : 2017/249551

Email: okagrt01@gmail.com

THE HARRIS-TODARO MODEL ON THE THEORY OF MIGRATION
The Harris–Todaro model, named after John R. Harris and Michael Todaro, is a 1970s economic model used in development economics and welfare economics to describe some of the problems surrounding rural-urban migration. The model’s key assumption is that migration decisions are based on projected income differentials between rural and urban areas rather than simply wage differentials. This implies that rural-urban migration can be economically acceptable in a context of high urban unemployment if projected urban income exceeds expected rural income. A new pattern of economic development that is relevant for labor surplus nations such as India has been developed by J. R. Harris and M. P. Todaro. The model focuses on labor migration from rural to urban areas, which is caused by certain incentives. Under this model, migrant employees are mainly involved in a lottery of high-paid jobs in cities. For each job created, more than one worker may migrate, which would result in a loss of output if migrants take some family members into the urban zone.

ASSUMPTIONS OF THE MODEL
The formal statement of the equilibrium condition of the Harris–Todaro model is as follows:
 Let wr be the wage rate (marginal productivity of labor) in the rural agricultural sector.
 Let le be the total number of available jobs in the urban sector, which should be equal to the number of urban employees employed.
 Let lus be the total number of job seekers, employed and unemployed, in the urban sector.
 Let wu be the wage rate in the urban sector, which the government might likely set with a minimum wage rule.
Rural-to-urban migration will occur if and only if the following conditions are met:
Rural to urban migration will take place if:
wrle/lus(wu)
At equilibrium,
wr=le/lus(wu)
The ratio of available jobs to total job seekers provides the likelihood that any person moving from the agricultural sector to the urban sector will be able to find employment. As a result, in equilibrium, the agricultural wage rate equals the estimated urban wage rate, which is calculated by multiplying the urban wage by the job rate.

INTERNAL MIGRATION
The model explains why the high observed levels of small-scale urban migration in most developing countries are economically quite natural. In this model, the main motivating force behind migration is the expected real wage differential between urban and rural areas. First, the potential migrant calculates the actual revenue for a job in the urban area with his current endeavor. Then he compares the expected revenue to what he hopes to get in rural areas. His decision to migrate depends on the difference.
800 = 0.4 x 2000
If the likelihood was 0.8, the anticipated income would be 1600 (= 0.8 x 2000). (Naturally, the costs of transfer may be added to this one.) The model thus focuses on the role of economic stimulus in the decision on migration. Migration in any given time then depends on three factors:
1. The salary gap between urban and rural areas,
2. The rate of urban work and
3. The receptivity of potential migrants to the opportunities created as a result.

THEORETICAL IMPLICATION OF THE MODEL
The cost of opportunities and the value in the next best alternative use is an important part of the social cost of each input. Work hired for a formal urban sector project could also be drawn from the informal urban sector. Some analysts think that the wage paid to incidental farm workers is a good measure of the social cost of unqualified labor. However, this measure probably underpins the true social cost, which other compounds are likely to be significant, although a good indicator of the yield foregone by labor reallocation. In an analysis of the labor reallocation that is likely to take place during eco-work, the Harris-Todaro model integrates both forces.

THE POLICY IMPLICATION OF THE MODEL
The root of the problem is the big difference in income between the modern industrial and rural sectors. The former often go far beyond the clearing levels of the market for different restructuring measures. The long-term solution to the problem is that of adopting urban as well as rural policy that reduces the real income gaps between the two areas. From a political point of view, the H-T model has far-reaching consequences. It can be applied to the development of policies to promote urban development and industrial employment. The effect would be to improve urban employment’s subjective productivity.

CRITICS OF THE MODEL
Internal migration, according to the Todaro Paradox, can be harmful because it exacerbates urban unemployment. Given high unemployment rates and significant migration to cities in developing countries, this idea has undoubtedly inspired many governments to implement restrictive policies, despite the fact that the empirical validity of the Harris-Todaro model and the Todaro paradox is not well established. In any case, the Harris-Todaro model suffers from theoretical oversimplifications, several of which are likely to exaggerate the relationship between migration and urban unemployment. Six major points are raised in the criticisms:
1. The Harris-Todaro framework is only a static model describing migration, which is a dynamic phenomenon by nature.Even though the model can be thought of as representing a steady state equilibrium, this is a limitation
2. .Furthermore, the formalization is made in a partial equilibrium context which greatly weakens the justifications for policy recommendations.
3. Important aspects are absent from the standard Harris-Todaro model, including the probable heterogeneity of migrants which is not accounted for, risk aversion which could dampen migration incentives and render the Todaro paradox even less likely to occur, the possibility of job search in the urban area from the rural area, the possibility of return migration, or the existence of rural unemployment.In fact, the Harris-Todaro is almost silent about what happens in the rural areas.
4. The job rationing mechanism or hiring model hypothesized is not realistic.In particular, assuming random job selection in each period overestimates the likelihood of finding a job.
5. Stiglitz (1974) suggests that the employment probability might vary in a non-monotonic way with the duration of the stay in the city: it could increase in the first periods when migrants form social networks in the city, and then decrease in the later periods because of deteriorating human capital or because of bad signaling.
6. The Harris-Todaro model assumes that the urban wage is exogenously set above the endogenous rural wage since it must be that w > f’R(LR) for (2.3) to hold.The assumption that wages are high find several explanations ranging from the existence of trade unions to the agglomeration of economic activities.
Given these criticisms, the policy implications of the Harris-Todaro model — namely, limiting rural-to-urban migration — are much weaker. Several factors, in particular, qualify the justifications for restrictive migration policies. To begin, Todarian models only consider urban labor markets, whereas national governments should consider whether overall national employment (including rural areas) has improved. Second, as Stark (1991) observed, in a general equilibrium perspective, labor migration between rural and urban areas may reflect a market disequilibrium. It cannot be ruled out that migration has a positive impact on rural areas, possibly by increasing productivity, allowing exchanges with urban areas, and generating income for rural development. Fourth, restrictions on rural-urban migration could be extremely detrimental. We have seen that, from the perspective of the Lewis model, migration controls are labor market constraints that may prevent developing countries from launching labor-intensive industries that could alleviate poverty. Last but not least, mobility is a fundamental human right, and denying it is difficult to justify. The only economic justification for restricting migration flows is that migrants do not contribute to the economy.

CONCLUSIONS
This survey has reviewed theoretical and empirical models of internal migration in developing countries. On the big question — should rural to urban migration be discouraged, tolerated, or encouraged — the broad assessment is that restrictions in general are not desirable.In principle, the Todarian models can be used for policy analysis in situations where urban unemployment arising from rapid rural to urban migration is a concern. However, the empirical literature has not been convincing in assessing whether the conditions formed has also been complex so that these tests are no more convincing than the tests for the Todaro paradox were met in the real world. Empirically testing the Harris-Todaro the conditions for the Todaro paradox to hold.
microeconomic evidence consistent with the migration incentives present in the Harris- Todaro model, measuring for instance how rural dwellers respond to an increase in the wage differential. But this type of evidence does not provide a real test of the link between urban unemployment and migration. In other words, the validity of the model has not been clearly established even though it certainly influenced policies for decades.
Many countries have implemented policies aimed at forbidding migration from rural to urban areas. In South Africa, the Apartheid system (1948-1994) used extreme controls to monitor what was meant to be the temporary migration of rural workers to cities. In Indonesia, the ‘transmigration program’, a policy of resettlement from high to low- density areas has been implemented over several decades, resulting in the relocation of more than eight million people between 1969 and 1995 (Humanitarian Policy and Conflict Research, 2002). Similarly, in China, the Hukou or household registration system initiated in 1955 required that all residents live in the places where they were born and obtain permissions to move. Until the 1970s, migrants were even transferred back to their village in order to prevent ‘over- urbanization’. Some of these programs did meet their objectives of restricting rural to urban migration, but very few have been subjected to a rigorous analysis of their welfare costs. Au and Henderson (2006)’s empirical finding suggest that migration restrictions in China have maintained surplus labor in rural areas and led to insufficient agglomeration of economic activity in cities, resulting in GDP losses.

62. NAME: Okaforukwu chizaram sandra

Reg no : 2017/249551

Department : Economics

Email: okagrt01@gmail.com

LEWIS FEI RANIS MODEL ON THEORY OF SURPLUS LABOUR

INTRODUCTION
The Fei–Ranis model of economic growth has been designed by John C. Fei and Gustav Ranis and is an extension of the Lewis Model. It is a model of duality in development economics or social economy. The Surplus Labor model is also known. It recognize the presence, in contrast to many other growth models that consider underdeveloped countries homogenous in nature, of a dual economy that involves both the modern and primitive sectors. It takes into account the economic situation of unemployment and underutilization of resources. According to these theories, the primitive sector is made up of the existing agricultural sector in the economy and that is the rapidly emerging but small industrial sector in the modern sector. Development can only result from a complete shift from the agricultural to the industrial economy in the main focus, so that industrial production increases. The work is transferred from the agricultural sector to the industrial sector, which demonstrates that underdeveloped countries do not suffer from labor supply constraints. At the same time, there should also be no negligible growth in the agricultural sector and sufficient output to support the whole economy with food and raw materials. Saving and investment, as in the Harrod–Domar model, become driving forces in the economic development of developing countries.
The Lewis theory was formalized by Ranis and Fei (1961), who identified three “phases” of economic growth. Three turning points mark the start of each phase: The Lewis model’s second labor-scarce stage corresponds to phase three of ranis fei model .
 Phase one growth occurs as a result of the breakout stage, which is fueled by agricultural labor that is no longer required.
 As a result of the shortage stage, phase two development occurs, with disguised agricultural unemployment.
 With the commercialization of the agricultural sector, the commercialization stage contributes to phase three of self-sustaining economic development.
As a result, the Lewis-Ranis-Fei theory of dualistic economic development is a good theoretical paradigm for analyzing the growth direction of labor-surplus emerging economies like China and other developing countries.

BASICS OF THE MODEL
One of Lewis’ greatest disadvantages was that agriculture’s role is being undermined in boosting the growth of the industry. Moreover, he did not recognize that an increase in labor productivity should occur before the shift of labor between the two sectors. In Fei–Ranis’ dual economic model with three stages of growth, both these ideas were taken into account. They argue further that the model does not apply concentrates on the change that occurs with agricultural development properly. The elasticity of the farm workforce is endless in Phase 1 of the Fei–Ranis model, which results in disguised unemployment. Furthermore, the marginal labor product is zero. The Lewis model resembles this phase. In Phase 2 of the model, productivity in the agricultural sector rises, leading to increased industrial growth in a way that creates a basis for the next phase. Agricultural surpluses can exceed the marginal product (MP) and are not equal to subsistence wages in phase 2 as the increasing average product (AP).
Using the help of the figure on the left, we see that
Phase 1:AL(from figure)=MP=0and AB(from figure)=AP
The figure of AD labor may be shifted from the farm sector without a decrease in output, according to Fei and Ranis. It therefore represents overwork.
Phase2:AP>MP
Following AD, the MP starts to increase and the industrial work increases from 0 to AD. BYZ demonstrates AP of agricultural work and we see that the curve falls downwards after AD. This fall in the AP can be due to the decline in the real salaries of industrial workers due to the food shortage, given the fact that fewer workers are working in the food industry. The reduction in real wages reduces profit levels and the surplus volume that could have been reinvested for greater industrialization. As long as there is surplus, however, growth can still be increased without an industrialization rate decline. This surplus reinvestment can be visualized graphically as the MP curve shifts outside. In phase 2, AK is responsible for the level of covert unemployment. This allows the farm sector to surrender part of its workforce until
MP=Real wages=AB=Constant institutional wages(CIW)
Phase 3 begins from the marketing point at K in the figure. This is where, in the absence of covert unemployment, the economy is fully commercialized. In Phase 3, labor supply curve is steeper and both sectors begin to bid for work equally.
Phase3:MP>CIW
The amount of work that is shifted and the time it takes for this shift is:
 Surplus growth in the farming sector and industrial capital stock growth dependent on industrial profit growth;
 the nature and associated prejudice of the technological progress of the industry;
 Population growth rate.
The three basic ideas in this model are as follows:
1. Both agricultural and industrial growth are equally important;
2. agricultural and industrial growth are equitable;
3. The economy will only be able to rise from the Malthusian population trap when the labor rate moves from agriculture to the industrial sector is higher than the population rate of growth.
This work shift can occur through investments of landlords and fiscal measures by the government. However, both private and social costs may be high for shifting work, for example transportation costs or construction costs. Moreover, farm consumption per capita may increase, or a broad difference between the wages of the rural and the urban population may exist. Three of these are called leakage, which prevent the creation of an agricultural surplus. They include high costs, a high consumption, and a high wage gap. Indeed, a reverse supply curve of work could also prevent surplus generation, which occurs when high levels of income are not consumed. This means that workers with higher earnings will not increase their productivity. The case of reverse curves is, however, generally impractical.
Fei and Ranis said that a robust connectivity between the two would encourage and speedup development. They took the example of Japan’s dualistic economy in the 19th century, where rural industry was often linked to urban production. According to them, economic progress is achieved in dualistic economies of underdeveloped countries through the work of a small number of entrepreneurs who have access to land and decision-making powers.

ASSUMPTIONS OF THE MODEL

Fei–Ranis model of economic growth has been criticized on multiple grounds.which are
• It has been claimed that the slow economic situation in the developing world was not clearly understood by Fei and Ranis. Had the existing nature and causes been thoroughly examined, they would have discovered the current backwardness of agriculture due to the institutional structure, primarily the feudal system.
• Fei and Ranis say money is not a simple substitute for physical capital in an aggregate production function. Credit policies could play an important part in easing bottlenecks on the growth of agriculture and industry. They fail to differ between wage labor and household labor, which is a significant distinction for evaluating prices of dualistic development in an underdeveloped economy.
• In the earliest stages of economic development, which Harry T.Oshima and some others have criticized, Fei and Ranis assume that MPPL is nil only when the agricultural population is very large and that if it is extremely large, some work will be moved towards the urban centers in search of jobs. In the short term, this part of the work which has shifted to the cities remains unemployed, but it is either absorbed in the informal sector or re-enters the towns and tries to cultivate more marginal land. Seasonal unemployment is also overlooked because of seasonal changes in demand for labor and is not permanent.
To better understand this, we refer to the graph showing vertical axis food and horizontal axis recreation in this section. The level of food consumption in subsistence is OS. The SAG curve for transformation falls from A, indicating more leisure is used for the same land units. At A the marginal change between food and leisure and MPL = 0 is also tangent with the transforming curve at this point. Leisure satiation or leisure as an inferior good is an extreme case. Berry and Soligo in their 1968 paper have criticized this model for its MPL=0 assumption. In normal cases, the output would decline with shift of labor to the industrial sector. This is because, a fall in the per capita output would mean fall in consumption in a way that it would be lesser than the subsistence level, and the level of labor input per head would either rise or fall. They show that the output changes, and may fall under various land tenure systems, unless the following situations arise. The graph above shows food and leisure as two commodities of the agriculturalists’ consumption. Food is on the vertical axis, and leisure on the horizontal axis. OS represents the minimum level of food consumption, or the minimum amount of food consumed by agricultural labor that is necessary for their survival. The transformation curve SAG falls from A, which indicates that more leisure is being used to same units of land.
1. The lower good category is leisure
2. Satisfaction with leisure is present.
3. The substitutions for food and leisure are perfect, and for all actual income levels the marginal substitution rate is constant.
If the MPL>0 option is not valid now, and the MPL=0 option is invalid as a perfect substitute for food and leisure. Therefore, leisure as a lower good is the only viable option.
The Fei-Ranis model considers only labor and output as factors of production. Fei and Ranis assume a close model and hence there is no presence of foreign trade in the economy. The reluctant expansionary growth in the industrial sector of underdeveloped countries can be attributed to the lagging growth of subsistence agriculture. There is complete negligence of terms of trade between agriculture and industry, foreign exchange, money and price. Stagnation has not been taken into consideration, and no distinction is made between labor through family and labor through wages. The question of whether MPL = 0 is that of an empirical one, and MPL would definitely be greater than zero during favorable climatic conditions, say that of harvesting or sowing, MPL definitely would be higher than zero.

COMPARISON/CONCLUSIONS

We attempt to describe the basic outlines of the development model of the labor surplus and to address criticisms of this model, certain ‘red herrings,’ readily addressed by the micro econometric branch of neo-classical economics, and others.
The key question is whether wages are neo-classically determined or in the earliest stages of development through a negotiating process. We conclude that the neo-classical school which finds inelastic labor supply curves is concerned with the static cross-sectional analysis of labor supply in the farm industry, whereas the labor surplus model is concerned with the tracing of a dynamic reallocation of labor in the dual economy from a subsistence to a neo-classical organized sector. The attack on the model of labor surplus by the neo-classical school is therefore not justified. We deal with various problems and ships pass through the night.
The article follows marshaling data of a certain number of developing countries in the field of labor surpluses which demonstrate that institutional wages lag behind changes in productivity during the unqualified process of labor redistribution on the road to “a turning point” where, decades of intersectoral balanced growth resulted in unskilled labour shortages and the economy lost its dual nature.
Nonetheless, the Lewis fei ranis model provides a framework for understanding economic development in developing countries, as long as structural transformation can occur in a variety of ways.

63. Ngwu Osita Enoch says:

Nice

64. NGWU OSITA ENOCH says:

NGWU OSITA ENOCH
2017/242022
Ositangwu95@gmail.com
Education Economics

LEWIS-FEI-RANIS MODEL (SURPLUS LABOUR THEORY)
INTRODUCTION
The Lewis (1954) theory of dualistic economic development provides the seminal contribution to theories of economic development particularly for labour-surplus and resource-poor developing countries. In the Lewis theory, the economy is assumed to comprise the agricultural and non-agricultural sectors. The agricultural sector is assumed to have vast amounts of surplus labour that result in an extremely low, close to zero, marginal productivity of labour. The agricultural wage rate is presumed to follow the sharing rule and be equal to average productivity, which is also known as the institutional wage. The non-agricultural sector has an abundance capital and resources relative to labour. It pursues profit and employs labour at a wage rate higher than the agricultural institutional wage by approximately 30 percent (Lewis, 1954, p.150).
The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output.
HISTORY OF SURPLUS LABOUR THEORY
The historical emergence of surplus labour is, according to Marx, also closely associated with the growth of trade (the economic exchange of goods and services) and with the emergence of a society divided into social classes. As soon as a permanent surplus product can be produced, the moral-political question arises as to how it should be distributed, and for whose benefit surplus-labour should be performed. The strong defeat the weak, and it becomes possible for a social elite to gain control over the surplus-labour and surplus product of the working population; they can live off the labour of others.
Labour which is sufficiently productive so that it can perform surplus labour is, in a cash economy, the material foundation for the appropriation of surplus-value from that labour. How exactly this appropriation will occur, is determined by the prevailing relations of production and the balance of power between social classes.
THE CONCEPT OF SURPLUS LABOUR
The concept of surplus labour is widely discussed among development economics but its specific meaning needs to be defined, especially in technical terms, as many neoclassical economists still doubt the existence of surplus labour in an economy. Defining the source and the extent of surplus labour is then a prerequisite for further study. This section considers the various definitions of surplus labour and clarifies them.
The simple definition of surplus labour implies the existence of a point at which the marginal product of labour becomes zero and labour can be transferred out of the traditional sector without reducing the quantity of output, as noted by Wellisz (1968: 22): The (disguised-unemployment or the Unlimited Supply of Labour) hypothesis claims that in poor, densely populated countries, more people are employed than needed to produce the prevailing output with the existing techniques and the existing supply of non-labour inputs. The ‘surplus’ labour constitutes ‘hidden’ or ‘disguised’ unemployment. Many of the proponents of the hypothesis make the further claim that agricultural output will not decrease, and industrial output will increase, if measures are taken to re-allocate labour from subsistence agriculture (where the surplus is supposed to exist) to industry (where there is no surplus labour).
ASSUMPTIONS OF THE LEWIS-FEI-RANIS MODEL
(A) Surplus Labour in the Subsistence Sectors:
The basic assumption of the model is that there exists surplus labour in the subsistence sectors. It includes labour whose marginal productivity is zero as well as that whose marginal productivity is positive but is less than the institutional wage. This labour comprises farmers, agricultural labourers, petty traders domestic servants and women.
The surplus labour in the agriculture sector acts as a source of unlimited supply of labour for the manufacturing sector. By unlimited supply of labour. Lewis means that the supply of labour is perfectly elastic at a particular wages. This particular wage is somewhat higher than the institutional wage which each worker in the agricultural sector gets.
(B) Importance of Saving:
Another important assumption that Lewis makes is about the savings generated in the capitalist sector and in the subsistence sector. The capitalist sector invests all its savings for its further expansion. Those in the subsistence sector, on the other hand squander away their savings, if any in purchase of jewellery & for construction of temples etc of those in the capitalist sector. Lewis in fact so much fascinated by the higher propensity to save of the capitalist sector that he even advocates a transfer of income from the subsistence sector to the capitalist sector. He feels that steps have to be taken to raise the rate of savings from 10% to 15% if the development of the economy has to be smooth.
COMPARISONS OF THE THEORY OF SURPLUS LABOUR
Surplus labor models are a class of models for analyzing developing countries as dual economies with a modern capitalist sector and a traditional precapitalist sector. The precapitalist sector is viewed as having a large pool (“unlimited supplies”) of labor from which the capitalist sector may draw at constant cost. While these models are often described as finding their inspiration in the old classical economists and Karl Marx, the 1954 model of W. Arthur Lewis and its extensions are technically more neoclassical than truly classical. The Lewis model was elaborated and formalized by many others, most notably John C. H. Fei and Gustav Ranis (1964), with important theoretical contributions from Amartya Sen (1966) and Stephen Marglin (1976). Questions have been raised as to the historical relevance of the neoclassical labor surplus models (Schultz 1964; Myint 1971; Arrighi 1973; Williamson 1985).
CRITICISM
Lewis-Fei-Ranis model of economic growth has been criticized on multiple grounds, although if the model is accepted, then it will have a significant theoretical and policy implications on the underdeveloped countries’ efforts towards development and on the persisting controversial statements regarding the balanced vs. unbalanced growth debate.
It has been asserted that the Lewis-Fei-Ranis model did not have a clear understanding of the sluggish economic situation prevailing in the developing countries. If they had thoroughly scrutinized the existing nature and causes of it, they would have found that the existing agricultural backwardness was due to the institutional structure, primarily the system of feudalism that prevailed.
The Lewis-Fei-Ranis model say, “It has been argued that money is not a simple substitute for physical capital in an aggregate production function. There are reasons to believe that the relationship between money and physical capital could be complementary to one another at some stage of economic development, to the extent that credit policies could play an important part in easing bottlenecks on the growth of agriculture and industry.” This indicates that in the process of development they neglect the role of money and prices. They fail to differ between wage labor and household labor, which is a significant distinction for evaluating prices of dualistic development in an underdeveloped economy.
The Lewis-Fei-Ranis model assume that MPPL is zero during the early phases of economic development, which has been criticized by Harry T.Oshima and some others on the grounds that MPPL of labor is zero only if the agricultural population is very large, and if it is very large, some of that labor will shift to cities in search of jobs. In the short run, this section of labor that has shifted to the cities remains unemployed, but over the long run it is either absorbed by the informal sector, or it returns to the villages and attempts to bring more marginal land into cultivation.
CONCLUSIONS AND RECOMMENDATIONS
Lewis-Fei-Ranis model can be grouped under three instruments; labour force, capital accumulation and integration to the world economy. The main focus in Lewis-Fei-Ranis model was on the reallocation of labour until the turning point is reached, i.e., the time when labour reallocation has outstripped population growth long enough for dualism to atrophy and the economy to become fully commercialized. The model implicitly showed that the traditional sector do not produce any capital accumulation as they are very small and poor. Trade between agriculture and industry as the supply or marketed food falls or the demand for it rises, or both causing the value of marginal product of labour in agriculture to rise.
In sum up, there are several weaknesses of Lewis-Fei-Ranis model that are underlined by many economists. The first and most important is that if marginal productivity of labour in agricultural sector is negligible, zero. Schultz (1964), Sen (1967), Harris and Todaro (1970) and Fields (1975) proved with their empirical results that this cannot happen in agriculture sector. It is obvious that there is a disguised unemployment in agriculture. Particularly, agricultural sector should be considered in two ways: during harvest time and post harvest. If the agricultural surplus is solely considered for the regions where there can be seen harsh winter conditions, it could be accepted of the doctrine of Lewis, otherwise it is irrelevant to say there is a zero marginal productivity for agriculture labours. Also, there are positive opportunity costs, e.g. loss of crops in times of peak harvesting season, labour transfer will reduce agricultural output.
Second, the model employed mostly for the closed economies and gave relatively less information on open economies. Lewis-Fei-Ranis model was criticized as it neglects international trade. The model was to a certain extent supply-oriented, which does not foresee any trade between capital and other sectors. Also it was criticized advocating industrialization and ignores agriculture. If a section of the profit made by the capitalists is not devoted to agricultural development, the process of industrialization would be jeopardized.
Third, Lewis-Fei-Ranis model believed that the more the rate of labour transfer to urban employment, the more the economic grows and more jobs are created. But this is not a common applicable in practice if industrial development involves more intensive use of capital than labour, then the flow of labour from agriculture to industry will simply create more unemployment.
Fourth, the Lewis-Fei-Ranis model would imply that aggregate living standards should not rise as rapidly as productivity until surplus labour is eliminated. However, the evidence on living standards in Latin America during the twentieth century indicates that these have risen in line with productivity, and that the ‘indirect’ components of the real wage (health and education) have actually risen more rapidly that average incomes.
Fifth, the Lewis-Fei-Ranis model stated the wage in industrial sector does not increase before labour surplus is absorbed. But this does not happen in any way in reality as the development of the urban, or industrial, or formal sector can itself lead to the creation of pressure groups and swing the balance of power towards those in that sector, to the detriment of those remaining outside it. The wage in the industrial sector in reality outstandingly rises long before the labour surplus is absorbed.
Haven tested the Lewis-Ranis-Fei theory for developing economy over 1965-2002 we have found that the developing economic growth is mainly attributable to the development of the non-agricultural sector. This is driven by rapid capital accumulation as well as employment growth. The reallocation of labour away from agriculture has made a positive net contribution to rapid economic of the developing economy. The rise in the marginal productivity of agricultural labour indicates the absorption of redundant agricultural labour since the 1978 Economic Reform. However, the marginal productivity of agricultural labour is still lower than the initial low average productivity of agricultural labour. This implies the continued existence of disguised agricultural unemployment. This suggests that the these developing economy has entered the Lewis-Ranis-Fei phase two of development but has not yet achieved phase three. The continuing widening productivity gap between the two sectors calls for the removal of market restrictions and government interventions so as to allow the continued absorption of surplus labour. Several policy recommendations are tentatively suggested. First and foremost, more effort should be made in promoting employment to effectively absorb the remaining labour surplus and promote economic development. This can be achieved by further relaxing the Hukou restrictions on migration, increasing labour market flexibility and improving the allocative efficiency of labour. It can also be achieved by encouraging the development of private enterprise to create more employment opportunities. Second, Government of developing economy should continue implementing the Sunshine Policy, initiated in 2003, designed to provide rudimentary job training, recruitment information and information about conditions in the destination cities to rural migrants. This will not only help facilitate employment of rural migrants but also satisfy the increasing demand for skilled labour in the growing non-agricultural sector. Third, agriculture could be promoted by tax breaks, direct subsidies and most importantly, by removing price controls on agricultural products. Agriculture could thus be commercialised and the economy would enter phase three of economic development.

REFERENCE
Sadik-Zada, Elkhan Richard (2020). “Natural resources, technological progress, and economic modernization”. Review of Development Economics. doi:10.1111/rode.12716.
“Economnics4Development Website”. Surplus Labor Model of Economic Development. Archived from the original on 16 October 2011. Retrieved 12 October 2011.
Thirlwall, A.P (2006). Growth and Development: With Special Reference to Developing Economies. Palgrave Macmillan. ISBN 1-4039-9600-8.
Subrata, Ghatak (2003). Introduction to Developmental Economics. London: Routledge. ISBN 0-415-09722-3.
“Ranis-Fei model vs. Lewis Model” (PDF). Developmentafrique.com. Archived from the original (PDF) on 30 May 2012. Retrieved 14 October 2011.
“American Economic Review”. The Ranis-Fei Model of Economic Development: Comment. 53: 448–452. JSTOR 1809172.
Ranis, Gustav. “Paper on Labor Surplus Economies” (PDF). Retrieved 4 October 2011.
J. Choo, Hakchung. “American Economic Review”. On the Empirical Relevancy of the Rans-Fei Model of Economic Development: Comment. 61: 695–703. JSTOR 1811863.
Misra, Puri, S.K, V.K (2010). Economics of Development and Planning. Mumbai, India: Himalaya Publishing House. pp. 270–279. ISBN 978-81-8488-829-4.

NGWU OSITA ENOCH
2017/242022
Ositangwu95@gmail.com
Education Economics

Harris-Todaro Model of Migration
INTRODUCTION
Harris and Todaro work, is considered one of the starting points of the classic rural-urban migration theory. The hypothesis and predictions of Harris-Todaro model have been subjected to econometric evaluation and have been corroborated by several studies. The key hypothesis of Harris and Todaro are that migrants react mainly to economic incentives, earnings differentials, and the probability of getting a job at the destination have influence on the migraton decision. In other words, these authors posit that rural-urban migration will occur while the urban expected wage exceed the rural wage. From this crucial assumption, as denominated by Harris-Todaro, is deduced that the migratory dynamics leads the economic system toward an equilibrium with urban concentration and high urban unemployment.
THE HARRIS-TODARO MODEL
Assumptions
Harris and Todaro studied the migration of workers in a two-sector economic system, namely, rural sector and urban sector. The difference between these sectors are the type of goods produced, the technology of production and the process of wage determination. The rural sector is specialized in the production of agricultural goods. The productive process of this sector can be described by a Cobb-Douglas production function: where Ya is the production level of the agricultural good, Na is the amount of workers used in the agricultural production, Aa > 0 and 0 < f 0 and 0 < a < 1 are parametric constants. Both goods and labor markets are perfectly competitive. Nevertheless, there is segmentation in the labor market due to a high minimum urban wage politically determined. In the rural sector, the real wage, perfectly flexible, is equal to the marginal productivity of labor in this sectors where wa is the real wage and p is the price of the agricultural good, both expressed in units of manufactured good.
HARRIS-TODARO AGENT-BASED MODEL
Computational Implementation

Initially, workers are randomly placed in a square lattice with linear dimension L = 500. The reference values of the parameters used for these simulations are the same done to evaluate the equilibrium of the Harris-Todaro model, namely, Aa = 1.0, Am = 1.0, f = 0.3, a = 0.7, r = 1.0 and g = 1.0. The value of the minimum wage used is wm = 0.8 and the initial urban fraction of the total population is nu = 0.2, where nu = Nu/N is the normalized urban population also called urban share. The initial value nu = 0.2 is in agreement with historical data of developing economies. Given these parameters, one can calculate the vector which characterizes temporary equilibrium of the system by using eqs. (7 – 12). By using eq. (7), the employment level of the urban sector, Nm, is obtained. If nu Nm/N there will be a fraction of Nm/Nu workers employed, which earn the minimum wage, wi = wm, and (1-Nm/Nu) workers unemployed, which earn a wage wi = 0. Each worker can be selected to review his sectorial location with probability a, called activity. Therefore, in each time step only a fraction of workers becomes potential migrants, going through the sectorial location reviewing process. Potential migrants will determine their satisfaction level of being in the current sector by comparing their earnings, wi, among nearest neighbors. The potential migrant starts the comparison process with a initial satisfaction level si = 0. When wi > wneighbor the satisfaction level si is added in one unit; if wi < wneighbor, si is diminished in one unit; if wi = wneighbor, si does not change. After the worker has passed through the reviewing process his/her satisfaction level is checked. The migration will occur only if si < 0, what means that the worker's i earnings is less than the most of his/her nearest neighbors. After all the potential migrants complete the reviewing process and have decided migrate or not, a new configuration of the system is set. Therefore, once again a new temporary equilibrium of the system is calculated by using eqs. (8 – 12). The whole procedure is repeated until a pre-set number of steps is reached. It is important to emphasize that Nm is kept constant throughout the simulation. Its given by eq. (7) which depends on the technological parameters, a,Am, and the minimum wage, wm, which are constants too.
In this case, the differential of expected wages is negative. In an economy mainly rural (nu < 0:5), the transitional dynamics characterized by a continuous growth of population of the urban sector with a differential of expected wages relatively high is followed by the stabilization of rural-urban differential of expected wages. In other words, the generalized Harris-Todaro condition, eq. (15), arises as a long run equilibrium result of the agent-based migratory dynamics.
CONCLUSION
In this paper we developed and agent-based computational model which formalizes the rural-urban allocation of workers as a process of social learning by imitation. We analyze a two-sectorial economy composed by adaptative agents, i.e., individuals that grope over time for best sectorial location in terms of earnings. This search is a process of imitation of successful neighbor agents. The dispersed and non-coordinated individual migration decisions, made based on local information, generate aggregate regularities.
Firstly, the crucial assumption of Harris and Todaro, the principle that rural-urban migration will occur while the urban expected wage exceed the rural wage, comes out as spontaneous upshot of interaction among adaptative agents.
Secondly, the migratory dynamics generated by agents that seek to adaptate to the economic environment that they co-create leads the economy toward a long run equilibrium characterized by urban concentration with urban unemployment. When this long run equilibrium is reached, the generalized Harris-Todaro condition is satisfied, i.e., there is a stabilization of the rural-urban expected wage differential.
Thirdly, the impact of the minimum wage and elasticity of terms of trade in a long run equilibrium obtained by simulations are in agreement with the predictions of the original Harris-Todaro model with Cobb-Douglas technology.
Finally, the simulations showed an aggregated pattern not found in the original Harris-Todaro model. There is the possibility of small fluctuations of the urban share around an average value. This phenomenon is known as reverse migration.

REFERENCE

Aquino L. Espíndola thanks CAPES for the financial support. Jaylson J. Silveira acknowledges research grants from CNPq. T. J. P. Penna thanks CNPq for the fellowship.
J. R. Harris and M. P. Todaro, American Economic Review 60, 126 (1970).
M. P. Todaro, American Economic Review 59, 138 (1969).
D. Ray, Development Economics (Princeton: Princeton University Press, 1998).
L. Y. L. Yap, Journal of Development Economics 4, 239 (1977).
D. Mazumdar, Rural-urban Migration in Developing countries. In: Handbook of Regional and Urban Economics, Elsevier, Amsterdam, 1987.
L. Ghatak, P. Levine, and S. Price, Journal of Economics Surveys 10, 159 (1996).
J. G. Willianson, Migration and Urbanization. In: Chenery, H. and Srinivasan, T.N., Handbook of developments economics, Elsevier, Amsterdam, 1988.
J. J. Silveira, A. L. Espíndola, and T. J. P. Penna, physics/0506021, Physica A, to appear.

65. Ugwu Chidimma Joy says:

LEWIS-FEI-RANIS MODEL OF SURPLUS LABOUR THEORY:
The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.

Assumptions of the Model:
This theory is concerned with a poor economy which has following properties:
(I) There is an abundance of labor in such Underdeveloped countries and shortage of natural resources.
(ii) The population growth rate is very high which results in mass unemployment in the economy.
(iii) The major share of population is engaged in agriculture. But agriculture sector is stagnant. Hence, the marginal productivity of labor is zero and negative in agriculture sector.
(iv) There are certain non-agrarian sectors in the economy where there is reduced use of capital.
(v) There is a dynamic industrial sector in the economy.
Thus the model suggests that:
“Economic development would be taking place if agricultural laborers are transferred to industrial sector where their productivity will increase”.
As we told earlier that it is a dual economy where there is a stagnant agricultural sector and dynamic industrial sector. The situation where MPL – 0, labor can be transferred to industrial sector without any loss in agricultural output. The real wages in industrial sector remains fixed and it is equal to the initial level of real income in agricultural sector. Such wages are given the name of institutional wages.
CONCLUSION: Using China as a Case Study.
The Chinese experience China’s dualistic economic development China has had a long history of dualistic economic development. According to Putterman (1992), prior to the 1978 Economic Reform, the rural agricultural sector was run using collective farms and wages were set by the government. In the urban industrial sector, the pursuit of profit was allowed. The 1978 Economic Reform has not brought this dualistic structure to an end. Instead it has allowed the urban sector to develop further by creating an expanding service sector and a new class of town-village enterprises.
Thus, the dualistic structure involves the agricultural sector in rural areas and the non-agricultural sector mainly concentrated in urban areas. Specifically, the agricultural sector includes farming, animal husbandry, forestry and fishery. The non-agricultural sector includes construction, industry (i.e. manufacturing, mining and quarrying, electricity, gas and water supply), transport, post and telecommunication services, wholesale and retail trade and catering services. The output of town-village owned enterprises is included in the non-agricultural sector, though they are in semi-urban locations.
Economic growth in China is largely driven by the non-agricultural sector and less so by that of the agricultural sector.

HARRIS-TODARO MODEL OF MIGRATION.
The Harris–Todaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and welfare economics to explain some of the issues concerning rural-urban migration. The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This implies that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.
In the model, an equilibrium is reached when the expected wage in urban areas (actual wage adjusted for the unemployment rate), is equal to the marginal product of an agricultural worker. The model assumes that unemployment is non-existent in the rural agricultural sector. It is also assumed that rural agricultural production and the subsequent labor market is perfectly competitive. As a result, the agricultural rural wage is equal to agricultural marginal productivity. In equilibrium, the rural to urban migration rate will be zero since the expected rural income equals the expected urban income. However, in this equilibrium there will be positive unemployment in the urban sector. The model explains internal migration in China as the regional income gap has been proved to be a primary drive of rural-urban migration, while urban unemployment is local governments’ main concern in many cities.

The formal statement of the equilibrium condition of the Harris–Todaro model is as follows:

* Let wr be the wage rate (marginal productivity of labor) in the rural agricultural sector.
* Let le be the total number of jobs available in the urban sector, which should be equal to the number of employed urban workers.
* Let lus be the total number of job seekers, employed and unemployed, in the urban sector.
* Let wu be the wage rate in the urban sector, which could possibly be set by government with a minimum wage law.

Rural to urban migration will take place if:

* wage rate(wr) Le÷Lus×Wu

At equilibrium,

* wage rate(wr) =Le÷Lus×Wu
With the random matching of workers to available jobs, the ratio of available jobs to total job seekers gives the probability that any person moving from the agricultural sector to the urban sector will be able to find a job. As a result, in equilibrium, the agricultural wage rate is equal to the expected urban wage rate, which is the urban wage mutiplied by the employment rate.

Therefore, migration from rural areas to urban areas will increase if:

Urban wages (wu) increase in the urban sector (le), increasing the expected urban income.
Agricultural productivity decreases, lowering marginal productivity and wages in the agricultural sector (wr), decreasing the expected rural income.
However, even though this migration creates unemployment and induces informal sector growth, this behavior is economically rational and utility-maximizing in the context of the Harris–Todaro model. As long as the migrating economic agents have complete and accurate information concerning rural and urban wage rates and probabilities of obtaining employment, they will make an expected income-maximizing decision.

CONCLUSION
The fact that Nigeria has one of the highest growth rates in the world cannot be over- emphasized. Using the census figure of 140 million according to the national population census of 2006, over 70% of Nigeria is in the rural areas. A resultant of this growth has led to rapid urbanization and an enormous increase in the population leaving rural areas and now living in urban centers. Demographic, environmental and economic issues become primary areas of concern with the rapid growth of Nigerian urban centers and its attendant effect on rural areas. Policy makers and urban planners are faced with the worries these factors are placing on existing infrastructure and services. While various environmental and socio-economic factors are easily associated with the rapid rural- urban migration trends in Nigeria, it is of utmost importance to identify their impact/implications and developing strategies to combat their effects. This paper therefore ague for rural development as a panacea for rural-urban migration in Nigeria.

Rural-Urban Migration in Nigeria, Implication on the Development of the Society: Anambra State as the Focus of the Study.
This paper examines the implication of rural- urban migration on Nigeria Society using Anambra state as focus of the study. Cities have been growing both through natural increase and through stampede from rural areas in Nigeria. People migrate to urban areas based on the prevailing conditions they fund themselves and the reasons for the migration vary from one individual to another depending on the situation that informs the decision to migrate. In most rural areas, the effect of rural-urban migration was a rapid deterioration of the rural economy leading to poverty and food scarcity. The cause of the phenomenon has been described as the push factors in the rural areas and the pull factors in the urban areas. The objective of this paper is to identify the implication of rural-urban migration on Nigeria society. It is a survey research. Thus, 1200 questionnaire were distributed among the selected local governments in Anambra State. The analysis was run using Runs test and mode analysis. The result of the analysis found the effect of people migrating from rural areas to urban centres on the society to include: increase in prostitution in the urban centres; increase in squalor settlement in the urban centres; and people are doing all sorts of odd jobs in order to survive in urban centres. The paper therefore recommends that the government should make and implement a policy on provision of functional social amenities such as electricity, pipe borne water etc. in the rural areas. Good schools and qualified teachers should be made available in the rural areas and establishment of industries in both rural and urban areas that will to an extent accommodate unemployed youths.

66. AN ESSAY ON THE HARRIS -TODARO MODEL OF MIGRATION.
A) INTRODUCTION
TheHarris-todaro model is an economic model developed in 1970 and used in development and welfare economics to explain some of the issues concerning rural-urban migration.
The advocates of this model John R. Harris and Michael Todaro posited the major assumption of this model, that usf based on differences in expected income between the rural and urban areas rather than just wage differences.
This implies that rural-urban migration in this context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.

B) ASSUMPTIONS OF THE MODEL.
The H-T model is based on the Assumption that the premise that a fixed wage leads to an outlook of misrepresentation and urban unemployment.
The H-T model presupposes that the fixed wage in one sector is added to the Assumption of the S.F model, which is done by introducing the concept of expected wage in the urban sector. The economy in his model consist of two sectors, one is the agricultural sector and the other is a manufacturing sector. The economy considered in the model is a small open economy. There are 3 kinds of production factors, specific production factors in sector 1, k1, production factors in sector 2, k2 and Labour (L) which is employed in both sectors and mobile between sectors.
In the HOS model, the capital Labour ratio are in a one to one relation with the relative price of product. However in the H-T model, there relations among variables are not in a one to one relationship. This makes H-T model more suitable for describing developing countries. This feature also gives the impression that the H-T model depends only on the supply side of the model and ignores the demand side. It is possible for workers to move freely to the wage gap between sectors. In other words, workers move to the higher wage sector by comparing their expected wages in sector 1 and 2. In both sectors, the expected wage is defined by multiplying wi (I=1,2) by the probability of finding a job in the sector.

C) CRITICISM
Cole and Sanders(1985) have criticised the Harris-Todaro model explicitly modeling the subsistence sector employing uneducated migrants arguing that it flawed the job selection process and expected income calculations if by lack of qualification, uneducated migrants couldn’t find a job in the modern urban sector.
D) POLICY IMPLICATIONS
The Todaro paradox Conveyed the message that internal migration can be harmful because it exacerbate urban unemployment. The idea has certainly inspired many government to implement restrictive policies even though the empirical validity of the Harris-todaro model. and the Todaro paradox are not clearly established given the high unemployment rates and significant migration in developing countries. The Harris-Todaro model suffers from theoritical oversimplification, among which several are likely to overestimate the link between migration and urban unemployment.

E) LIMITATIONS OF THE MODEL
1. The model assumes that Labour has a perfect knowledge about market wages which is impractical given the high rate of illiteracy among the rural people.
2. The reflection of economic realities by this Assumption is questionable, poor migrants will likely be risk averse (i.e having a strong dislike for risk) and require a significant greater expected urban income to migrate.
3) They assume that potential migrants are indifferent to a certain expected rural income and unexpected urban income of the same magnitude.

F) IMPACT OF THE THEORY IN NIGERIA
Using Nigeria as a case study, rural-urban migration is one of the most distressing problems facing the Nigerian socio-economic development. A situation where the desire for better employment, business opportunities and education pushes both Young and old not of the rural areas to the urban areas.
Rural-urban migration represents a volume of movement of people from the rural countryside to the urban cities.
Historically, migration existed in the form of transferring uneducated workers from the rural sector to the urban sector to function in the industries so s to increase industrial output.
This Harris-Todaro model will help policy makers in Nigeria to avoid two mistakes
a) To assume that efforts should necessarily be focused on getting the poor out of the sector in which they presently are.
b) The other one is to assume that development efforts should necessarily be channeled to the sectors where the poor are.

AN ESSAY ON THE LEWIS FEI-RANIS MODEL(SURPLUS LABOUR THEORY)
A) INTRODUCTION
The Lewis fei-Ranis model of economic growth developed by John C.H Fei and Gustav Ranis and can be seen as an extension of the Lewis model developed by W. Arthur Lewis is a dualism model in both development and welfare economics.it is also known as surplus Labour model. It recognizes the presence of dual economy comprising both the modern and the primitive sector and takes into consideration, the agricultural and modern economics respectively. It takes into consideration, the economic situation of unemployment and underemployment of resources. This model don’t consider underdeveloped countries to be homogenous unlike other models.
Both sectors (agricultural and modern) in the economy coexist. This is where the crux of the development problem lies. According to the6, Development can be brought about only by a complete shift in the social point of progress from the agricultural to the industrial economy, such that there’s increase in industrial output. According to them, underdeveloped countries don’t suffer from Labour constraint, so they advocate the transfer of labour from the agricultural no sector to the industrial sector. At the same time, growth in the agricultural sector shouldn’t be neglected and it’s output should be sufficient enough since they provide the economy with amount of food and raw materials.

B) BASIS OF THE MODEL
The biggest disadvantage of the Lewis-fei Ranis model was the undermining of the role of agriculture in boosting the growth of the industrial sector. In addition to that, He didn’t acknowledge that the increase in the productivity of labour should take place prior to the Labour shift between the two sectors
However, these two ideas where taken into account in the fei-Ranis dual economy model of three growth stages.
The further argued that the model lacks in the proper application of concentrated analysis to the change that takes place with agricultural development.
In Phase 1of the fei-Ranis model, the workforce is infinite and as a result suffers from disguised unemployment. Also, the marginal product of labour is zero. This phase is similar to the Lewis model .
In Phase 2 of the model, the agricultural sector sees a rise in productivity and this leads to increased in agricultural sector sees a rise in productivity and this leads to increased industrial growth such that’s base for the next phase is prepared. In Phase 2, Agricultural surplus may exist as the increasing average product AP, higher than the marginal product MP and not equal to the subsistence level of wages.
The amount of Labour that is shifted and the time that the shifting takes place depends on
1. Growth of surplus generated in the agricultural sector.
2. The Nature of the industry’s technical Progress.
3. Growth of population
and so, The three fundamental ideas used in the model are;
1. Agricultural growth and industrial growth are equally important.
2. Agricultural growth and industrial growth are balanced.
3. Only if the rate at which Labour is shifted from the agricultural to the industrial sector is greater than the economy be able to free itself from the Malthusian population trap.
The shifting of Labour can take place by the landlords investment activities and by the government’s Fiscal measures.
However, the cost of shifting Labour in terms of both private and social cost may be high. For example, the cost of carrying out construction of buildings.

C) ASSUMPTION OF THE LEWIS MODEL
A) The existence of the surplus Labour in the agricultural sector. It includes Labour whose marginal productivity is zero and as well as the existence of redundancy on the part of the agricultural sector. The Labour consist Farmers, agricultural Labourers, petty traders domestic servant and women. The excess Labour bin the agricultural sector serves as a source of supply to the industrial sector and they are the major source of supply to the industrial sector.
By unlimited supply of labour. Lewis means that the supply of Labour is perfectly elastic at a particular wage. This particular wage is somewhat higher than the institutional wage. Which each worker in the agricultural sector.

B) Another important assumption that Lewis makes us about the savings generated in the capitalist sector and in the subsistence sector. The capitalist sector invests all there savings for it’s further expansion, those in the subsistence sector on the other hand squander away their savings, if any in purchase of jewellery and for construction of example.
The propensity to save in the subsistent sector is quite lower than the propensity to save in the industrial sector. The Lewis further posits that the subsistence sector should transfer their income to the industrial sector so as to increase the rate of savings in the economy and ensure development in the economy.

C) HOW IT RELATES TO THE NIGERIAN ECONOMY
The Nigerian economy consist of both the agricultural band industrial sector that provide each functions for the growth and development of the economy. These two sectors are not mutually exclusive vin promoting the economic growth of the country and improving the standard of living of citizens. However, the federal government of Nigeria doesn’t necessarily have to move surplus Labour that exists in the rural areas to the urban areas but instead infrastructural facilities should be provided equally to both the agricultural and modern sectors of the economy.

• Name: ILLO MARYANN EBUBECHUKWU
REG NO:2017/249350
DEPARTMENT: COMBINED SOCIAL SCIENCE (ECONOMICS AND SOCIOLOGY)
E MAIL: ebubeillo2000@gmail.com
Blog: illoebube.blogspot.com

AN ESSAY ON THE HARRIS -TODARO MODEL OF MIGRATION.
A) INTRODUCTION
TheHarris-todaro model is an economic model developed in 1970 and used in development and welfare economics to explain some of the issues concerning rural-urban migration.
The advocates of this model John R. Harris and Michael Todaro posited the major assumption of this model, that usf based on differences in expected income between the rural and urban areas rather than just wage differences.
This implies that rural-urban migration in this context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.

B) ASSUMPTIONS OF THE MODEL.
The H-T model is based on the Assumption that the premise that a fixed wage leads to an outlook of misrepresentation and urban unemployment.
The H-T model presupposes that the fixed wage in one sector is added to the Assumption of the S.F model, which is done by introducing the concept of expected wage in the urban sector. The economy in his model consist of two sectors, one is the agricultural sector and the other is a manufacturing sector. The economy considered in the model is a small open economy. There are 3 kinds of production factors, specific production factors in sector 1, k1, production factors in sector 2, k2 and Labour (L) which is employed in both sectors and mobile between sectors.
In the HOS model, the capital Labour ratio are in a one to one relation with the relative price of product. However in the H-T model, there relations among variables are not in a one to one relationship. This makes H-T model more suitable for describing developing countries. This feature also gives the impression that the H-T model depends only on the supply side of the model and ignores the demand side. It is possible for workers to move freely to the wage gap between sectors. In other words, workers move to the higher wage sector by comparing their expected wages in sector 1 and 2. In both sectors, the expected wage is defined by multiplying wi (I=1,2) by the probability of finding a job in the sector.

C) CRITICISM
Cole and Sanders(1985) have criticised the Harris-Todaro model explicitly modeling the subsistence sector employing uneducated migrants arguing that it flawed the job selection process and expected income calculations if by lack of qualification, uneducated migrants couldn’t find a job in the modern urban sector.
D) POLICY IMPLICATIONS
The Todaro paradox Conveyed the message that internal migration can be harmful because it exacerbate urban unemployment. The idea has certainly inspired many government to implement restrictive policies even though the empirical validity of the Harris-todaro model. and the Todaro paradox are not clearly established given the high unemployment rates and significant migration in developing countries. The Harris-Todaro model suffers from theoritical oversimplification, among which several are likely to overestimate the link between migration and urban unemployment.

E) LIMITATIONS OF THE MODEL
1. The model assumes that Labour has a perfect knowledge about market wages which is impractical given the high rate of illiteracy among the rural people.
2. The reflection of economic realities by this Assumption is questionable, poor migrants will likely be risk averse (i.e having a strong dislike for risk) and require a significant greater expected urban income to migrate.
3) They assume that potential migrants are indifferent to a certain expected rural income and unexpected urban income of the same magnitude.

F) IMPACT OF THE THEORY IN NIGERIA
Using Nigeria as a case study, rural-urban migration is one of the most distressing problems facing the Nigerian socio-economic development. A situation where the desire for better employment, business opportunities and education pushes both Young and old not of the rural areas to the urban areas.
Rural-urban migration represents a volume of movement of people from the rural countryside to the urban cities.
Historically, migration existed in the form of transferring uneducated workers from the rural sector to the urban sector to function in the industries so s to increase industrial output.
This Harris-Todaro model will help policy makers in Nigeria to avoid two mistakes
a) To assume that efforts should necessarily be focused on getting the poor out of the sector in which they presently are.
b) The other one is to assume that development efforts should necessarily be channeled to the sectors where the poor are.

AN ESSAY ON THE LEWIS FEI-RANIS MODEL(SURPLUS LABOUR THEORY)
A) INTRODUCTION
The Lewis fei-Ranis model of economic growth developed by John C.H Fei and Gustav Ranis and can be seen as an extension of the Lewis model developed by W. Arthur Lewis is a dualism model in both development and welfare economics.it is also known as surplus Labour model. It recognizes the presence of dual economy comprising both the modern and the primitive sector and takes into consideration, the agricultural and modern economics respectively. It takes into consideration, the economic situation of unemployment and underemployment of resources. This model don’t consider underdeveloped countries to be homogenous unlike other models.
Both sectors (agricultural and modern) in the economy coexist. This is where the crux of the development problem lies. According to the6, Development can be brought about only by a complete shift in the social point of progress from the agricultural to the industrial economy, such that there’s increase in industrial output. According to them, underdeveloped countries don’t suffer from Labour constraint, so they advocate the transfer of labour from the agricultural no sector to the industrial sector. At the same time, growth in the agricultural sector shouldn’t be neglected and it’s output should be sufficient enough since they provide the economy with amount of food and raw materials.

B) BASIS OF THE MODEL
The biggest disadvantage of the Lewis-fei Ranis model was the undermining of the role of agriculture in boosting the growth of the industrial sector. In addition to that, He didn’t acknowledge that the increase in the productivity of labour should take place prior to the Labour shift between the two sectors
However, these two ideas where taken into account in the fei-Ranis dual economy model of three growth stages.
The further argued that the model lacks in the proper application of concentrated analysis to the change that takes place with agricultural development.
In Phase 1of the fei-Ranis model, the workforce is infinite and as a result suffers from disguised unemployment. Also, the marginal product of labour is zero. This phase is similar to the Lewis model .
In Phase 2 of the model, the agricultural sector sees a rise in productivity and this leads to increased in agricultural sector sees a rise in productivity and this leads to increased industrial growth such that’s base for the next phase is prepared. In Phase 2, Agricultural surplus may exist as the increasing average product AP, higher than the marginal product MP and not equal to the subsistence level of wages.
The amount of Labour that is shifted and the time that the shifting takes place depends on
1. Growth of surplus generated in the agricultural sector.
2. The Nature of the industry’s technical Progress.
3. Growth of population
and so, The three fundamental ideas used in the model are;
1. Agricultural growth and industrial growth are equally important.
2. Agricultural growth and industrial growth are balanced.
3. Only if the rate at which Labour is shifted from the agricultural to the industrial sector is greater than the economy be able to free itself from the Malthusian population trap.
The shifting of Labour can take place by the landlords investment activities and by the government’s Fiscal measures.
However, the cost of shifting Labour in terms of both private and social cost may be high. For example, the cost of carrying out construction of buildings.

C) ASSUMPTION OF THE LEWIS MODEL
A) The existence of the surplus Labour in the agricultural sector. It includes Labour whose marginal productivity is zero and as well as the existence of redundancy on the part of the agricultural sector. The Labour consist Farmers, agricultural Labourers, petty traders domestic servant and women. The excess Labour bin the agricultural sector serves as a source of supply to the industrial sector and they are the major source of supply to the industrial sector.
By unlimited supply of labour. Lewis means that the supply of Labour is perfectly elastic at a particular wage. This particular wage is somewhat higher than the institutional wage. Which each worker in the agricultural sector.

B) Another important assumption that Lewis makes us about the savings generated in the capitalist sector and in the subsistence sector. The capitalist sector invests all there savings for it’s further expansion, those in the subsistence sector on the other hand squander away their savings, if any in purchase of jewellery and for construction of example.
The propensity to save in the subsistent sector is quite lower than the propensity to save in the industrial sector. The Lewis further posits that the subsistence sector should transfer their income to the industrial sector so as to increase the rate of savings in the economy and ensure development in the economy.

C) HOW IT RELATES TO THE NIGERIAN ECONOMY
The Nigerian economy consist of both the agricultural band industrial sector that provide each functions for the growth and development of the economy. These two sectors are not mutually exclusive vin promoting the economic growth of the country and improving the standard of living of citizens. However, the federal government of Nigeria doesn’t necessarily have to move surplus Labour that exists in the rural areas to the urban areas but instead infrastructural facilities should be provided equally to both the agricultural and modern sectors of the economy.

67. Okoronkwo chibuzo jonah
2017/249400
chibuzojonah08@gmail.com

LEWIS-FEI-RANIS MODEL (SURPLUS LABOUR THEORY)

The two economists John Fei and Gustav Ranis presented their dual economy model. There was a flaw in Lewis model that it did not pay enough attention to the importance of agri. sector in promoting industrial growth. But Fei-Ranis (FR) model of dual economy explains how the increased productivity in agri. sector would become helpful in promoting industrial sector. In this respect, it presents three stages whereby a UDC moves from stagnation to self-sustained economic growth.
HOW THE MODEL APPLICABLE TO REAL WORLD SOCIETY
In this model we see that there is surplus of workers in the rural areas – excess of workers without work in the rural areas and they begin to migrate to the urban area. The migration of these workers create some sort of equilibrium where full employment occurs in both the rural and urban areas meaning there is less people who are unemployed in the rural areas now and same time there is full employment in the urban areas so we see that rural to urban migration benefits both sectors (Agricultural and industrial) and in the absence of labour this will also increase wages in the both areas because labour becomes more valueable.

HARIS-TODARO MODEL OF MIGRATION
The Harris-Todaro model assumes that migration from rural to urban areas depends primarily on the difference in wages between the rural and urban labour markets.

68. NAME:METEKE JOY ORIMUSUE
DEPARTMENT:ECONOMICS
REG.NO:2017/242430
EMAIL:joymetex2000@gmail.com
BLOG WEBSITE:metekejoy01.blogspot.com

LEWIS-FEI-RANIS THEORY(SURPLUS LABOUR THEORY)
Lewis (1954) proposed a seminal theory of dualistic economic development for over-populated and under-developed economies with vast amounts of surplus agricultural labour for which he was later to be awarded the 1979 Nobel Prize in Economics. Economic growth in such an economy can be achieved by rapid capital accumulation in the non-agricultural (industrial and service) sector, facilitated by drawing surplus labour in the agricultural sector. In the Lewis theory, an economy transits from the first, labour-surplus “stage” to the second, labour-scarce “stage” of development.The central idea behind the Lewis model is fairly simple. Lewis divided labour force into two differentiated groups – “subsistence sector” and “capitalist sector” where the former is assumed to contain unlimited supply and consequently, a pool of surplus labour that sets labour-supply conditions for the latter.
Assumptions of the Lewis Model
(A) Surplus Labour in the Subsistence Sectors:
The basic assumption of the model is that there exists surplus labour in the subsistence sectors. It includes labour whose marginal productivity is zero as well as that whose marginal productivity is positive but is less than the institutional wage. This labour comprises farmers, agricultural labourers, petty traders domestic servants and women.
(B) Importance of Saving:
Another important assumption that Lewis makes is about the savings generated in the capitalist sector and in the subsistence sector. The capitalist sector invests all its savings for its further expansion.Those in the subsistence sector, on the other hand squander away their savings, if any in purchase of jewellery & for construction of temples etc. The propensity to save of the people in subsistence sector is also lower when compared with that of those in the capitalist sector.
The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model.It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.Ranis and Fei (1961) formalised the Lewis theory and defined three “phases” of dualistic economic development by sub-dividing the first stage in the Lewis model into two phases. Thus, the second labour-scarce stage of the Lewis model corresponds to phase three of the Ranis-Fei model. These three phases, illustrated in Diagram 1below, are distinguished by the marginal productivity of agricultural labour. The entry into each phase is marked three turning points:
• The breakout point leads to phase one growth with redundant agricultural labour.
• The shortage point leads to phase two growth with disguised agricultural unemployment.
• The commercialisation point leads to phase three of self-sustaining economic growth with the commercialisation of the agricultural sector.One of the biggest drawbacks of the Lewis model was the undermining of the role of agriculture in boosting the growth of the industrial sector. In addition to that, he did not acknowledge that the increase in productivity of labor should take place prior to the labor shift between the two sectors. However, these two ideas were taken into account in the Fei–Ranis dual economy model of three growth stages.They further argue that the model lacks in the proper application of concentrated analysis to the change that takes place with agricultural development. One of the biggest drawbacks of the Lewis model was the undermining of the role of agriculture in boosting the growth of the industrial sector. In addition to that, he did not acknowledge that the increase in productivity of labor should take place prior to the labor shift between the two sectors. However, these two ideas were taken into account in the Fei–Ranis dual economy model of three growth stages.[4] They further argue that the model lacks in the proper application of concentrated analysis to the change that takes place with agricultural development[5] In Phase 1 of the Fei–Ranis model, the elasticity of the agricultural labor work-force is infinite and as a result, suffers from disguised unemployment. Also, the marginal product of labor is zero. This phase is similar to the Lewis model. In Phase 2 of the model, the agricultural sector sees a rise in productivity and this leads to increased industrial growth such that a base for the next phase is prepared. In Phase 2, agricultural surplus may exist as the increasing average product (AP), higher than the marginal product (MP) and not equal to the subsistence level of wages.Phase 3 begins from the point of commercialization which is at K in the Figure. This is the point where the economy becomes completely commercialized in the absence of disguised unemployment. The supply curve of labor in Phase 3 is steeper and both the sectors start bidding equally for labor.

The amount of labor that is shifted and the time that this shifting takes depends upon:The growth of surplus generated within the agricultural sector, and the growth of industrial capital stock dependent on the growth of industrial profits;
The nature of the industry’s technical progress and its associated bias;
Growth rate of population.
So, the three fundamental ideas used in this model are:

1.Agricultural growth and industrial growth are both equally important;
2.Agricultural growth and industrial growth are balanced;
3. Only if the rate at which labor is shifted from the agricultural to the industrial sector is greater than the rate of growth of population will the economy be able to lift itself up from the Malthusian population trap.

HARRIS TODARO THEORY OF MIGRATION
The Harris–Todaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and welfare economics to explain some of the issues concerning rural-urban migration. The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This implies that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.In the model, an equilibrium is reached when the expected wage in urban areas (actual wage adjusted for the unemployment rate), is equal to the marginal product of an agricultural worker. The model assumes that unemployment is non-existent in the rural agricultural sector. It is also assumed that rural agricultural production and the subsequent labor market is perfectly competitive. As a result, the agricultural rural wage is equal to agricultural marginal productivity. In equilibrium, the rural to urban migration rate will be zero since the expected rural income equals the expected urban income. However, in this equilibrium there will be positive unemployment in the urban sector. The model explains internal migration in China as the regional income gap has been proved to be a primary drive of rural-urban migration, while urban unemployment is local governments’ main concern in many cities.migration from rural areas to urban areas will increase if:
1.Urban wages (wu) increase in the urban sector (le), increasing the expected urban income.
2.Agricultural productivity decreases, lowering marginal productivity and wages in the agricultural sector (wr), decreasing the expected rural income.
However, even though this migration creates unemployment and induces informal sector growth, this behavior is economically rational and utility-maximizing in the context of the Harris–Todaro model. As long as the migrating economic agents have complete and accurate information concerning rural and urban wage rates and probabilities of obtaining employment, they will make an expected income-maximizing decision.

RELATION TO NIGERIA ECONOMY
According to this model migrating workers in developing countries sich as Nigeria are essentially participants in a lottery of relatively high-paid jobs in the towns. When new urban jobs are created the lottery becomes more attractive to potential migrants. Depending on their responsiveness to this improved opportnity, more than one worker are likely to migrate for each job created.

If so, the output foregone may be that of two or more agricultural workers, not just one. If the migrants bring some of their family members to urban areas more output will be lost. The reason is that the wife and children of migrants find fewer employment opportunities in towns than in the rural areas because they do not have land in the towns on which to grow food.

NAME:METEKE JOY ORIMUSUE
DEPARTMENT:ECONOMICS
REG.NO:2017/242430
EMAIL:joymetex2000@gmail.com
BLOG WEBSITE:metekejoy01.blogspot.com

LEWIS-FEI-RANIS THEORY(SURPLUS LABOUR THEORY)
Lewis (1954) proposed a seminal theory of dualistic economic development for over-populated and under-developed economies with vast amounts of surplus agricultural labour for which he was later to be awarded the 1979 Nobel Prize in Economics. Economic growth in such an economy can be achieved by rapid capital accumulation in the non-agricultural (industrial and service) sector, facilitated by drawing surplus labour in the agricultural sector. In the Lewis theory, an economy transits from the first, labour-surplus “stage” to the second, labour-scarce “stage” of development.The central idea behind the Lewis model is fairly simple. Lewis divided labour force into two differentiated groups – “subsistence sector” and “capitalist sector” where the former is assumed to contain unlimited supply and consequently, a pool of surplus labour that sets labour-supply conditions for the latter.
Assumptions of the Lewis Model
(A) Surplus Labour in the Subsistence Sectors:
The basic assumption of the model is that there exists surplus labour in the subsistence sectors. It includes labour whose marginal productivity is zero as well as that whose marginal productivity is positive but is less than the institutional wage. This labour comprises farmers, agricultural labourers, petty traders domestic servants and women.
(B) Importance of Saving:
Another important assumption that Lewis makes is about the savings generated in the capitalist sector and in the subsistence sector. The capitalist sector invests all its savings for its further expansion.Those in the subsistence sector, on the other hand squander away their savings, if any in purchase of jewellery & for construction of temples etc. The propensity to save of the people in subsistence sector is also lower when compared with that of those in the capitalist sector.
The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model.It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.Ranis and Fei (1961) formalised the Lewis theory and defined three “phases” of dualistic economic development by sub-dividing the first stage in the Lewis model into two phases. Thus, the second labour-scarce stage of the Lewis model corresponds to phase three of the Ranis-Fei model. These three phases, illustrated in Diagram 1below, are distinguished by the marginal productivity of agricultural labour. The entry into each phase is marked three turning points:
• The breakout point leads to phase one growth with redundant agricultural labour.
• The shortage point leads to phase two growth with disguised agricultural unemployment.
• The commercialisation point leads to phase three of self-sustaining economic growth with the commercialisation of the agricultural sector.One of the biggest drawbacks of the Lewis model was the undermining of the role of agriculture in boosting the growth of the industrial sector. In addition to that, he did not acknowledge that the increase in productivity of labor should take place prior to the labor shift between the two sectors. However, these two ideas were taken into account in the Fei–Ranis dual economy model of three growth stages.They further argue that the model lacks in the proper application of concentrated analysis to the change that takes place with agricultural development. One of the biggest drawbacks of the Lewis model was the undermining of the role of agriculture in boosting the growth of the industrial sector. In addition to that, he did not acknowledge that the increase in productivity of labor should take place prior to the labor shift between the two sectors. However, these two ideas were taken into account in the Fei–Ranis dual economy model of three growth stages.[4] They further argue that the model lacks in the proper application of concentrated analysis to the change that takes place with agricultural development[5] In Phase 1 of the Fei–Ranis model, the elasticity of the agricultural labor work-force is infinite and as a result, suffers from disguised unemployment. Also, the marginal product of labor is zero. This phase is similar to the Lewis model. In Phase 2 of the model, the agricultural sector sees a rise in productivity and this leads to increased industrial growth such that a base for the next phase is prepared. In Phase 2, agricultural surplus may exist as the increasing average product (AP), higher than the marginal product (MP) and not equal to the subsistence level of wages.Phase 3 begins from the point of commercialization which is at K in the Figure. This is the point where the economy becomes completely commercialized in the absence of disguised unemployment. The supply curve of labor in Phase 3 is steeper and both the sectors start bidding equally for labor.

The amount of labor that is shifted and the time that this shifting takes depends upon:The growth of surplus generated within the agricultural sector, and the growth of industrial capital stock dependent on the growth of industrial profits;
The nature of the industry’s technical progress and its associated bias;
Growth rate of population.
So, the three fundamental ideas used in this model are:

1.Agricultural growth and industrial growth are both equally important;
2.Agricultural growth and industrial growth are balanced;
3. Only if the rate at which labor is shifted from the agricultural to the industrial sector is greater than the rate of growth of population will the economy be able to lift itself up from the Malthusian population trap.

HARRIS TODARO THEORY OF MIGRATION
The Harris–Todaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and welfare economics to explain some of the issues concerning rural-urban migration. The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This implies that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.In the model, an equilibrium is reached when the expected wage in urban areas (actual wage adjusted for the unemployment rate), is equal to the marginal product of an agricultural worker. The model assumes that unemployment is non-existent in the rural agricultural sector. It is also assumed that rural agricultural production and the subsequent labor market is perfectly competitive. As a result, the agricultural rural wage is equal to agricultural marginal productivity. In equilibrium, the rural to urban migration rate will be zero since the expected rural income equals the expected urban income. However, in this equilibrium there will be positive unemployment in the urban sector. The model explains internal migration in China as the regional income gap has been proved to be a primary drive of rural-urban migration, while urban unemployment is local governments’ main concern in many cities.migration from rural areas to urban areas will increase if:
1.Urban wages (wu) increase in the urban sector (le), increasing the expected urban income.
2.Agricultural productivity decreases, lowering marginal productivity and wages in the agricultural sector (wr), decreasing the expected rural income.
However, even though this migration creates unemployment and induces informal sector growth, this behavior is economically rational and utility-maximizing in the context of the Harris–Todaro model. As long as the migrating economic agents have complete and accurate information concerning rural and urban wage rates and probabilities of obtaining employment, they will make an expected income-maximizing decision.

RELATION TO NIGERIA ECONOMY
According to this model migrating workers in developing countries sich as Nigeria are essentially participants in a lottery of relatively high-paid jobs in the towns. When new urban jobs are created the lottery becomes more attractive to potential migrants. Depending on their responsiveness to this improved opportnity, more than one worker are likely to migrate for each job created.

If so, the output foregone may be that of two or more agricultural workers, not just one. If the migrants bring some of their family members to urban areas more output will be lost. The reason is that the

NAME:METEKE JOY ORIMUSUE
DEPARTMENT:ECONOMICS
REG.NO:2017/242430
EMAIL:joymetex2000@gmail.com
BLOG WEBSITE:metekejoy01.blogspot.com

LEWIS-FEI-RANIS THEORY(SURPLUS LABOUR THEORY)
Lewis (1954) proposed a seminal theory of dualistic economic development for over-populated and under-developed economies with vast amounts of surplus agricultural labour for which he was later to be awarded the 1979 Nobel Prize in Economics. Economic growth in such an economy can be achieved by rapid capital accumulation in the non-agricultural (industrial and service) sector, facilitated by drawing surplus labour in the agricultural sector. In the Lewis theory, an economy transits from the first, labour-surplus “stage” to the second, labour-scarce “stage” of development.The central idea behind the Lewis model is fairly simple. Lewis divided labour force into two differentiated groups – “subsistence sector” and “capitalist sector” where the former is assumed to contain unlimited supply and consequently, a pool of surplus labour that sets labour-supply conditions for the latter.
Assumptions of the Lewis Model
(A) Surplus Labour in the Subsistence Sectors:
The basic assumption of the model is that there exists surplus labour in the subsistence sectors. It includes labour whose marginal productivity is zero as well as that whose marginal productivity is positive but is less than the institutional wage. This labour comprises farmers, agricultural labourers, petty traders domestic servants and women.
(B) Importance of Saving:
Another important assumption that Lewis makes is about the savings generated in the capitalist sector and in the subsistence sector. The capitalist sector invests all its savings for its further expansion.Those in the subsistence sector, on the other hand squander away their savings, if any in purchase of jewellery & for construction of temples etc. The propensity to save of the people in subsistence sector is also lower when compared with that of those in the capitalist sector.
The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model.It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.Ranis and Fei (1961) formalised the Lewis theory and defined three “phases” of dualistic economic development by sub-dividing the first stage in the Lewis model into two phases. Thus, the second labour-scarce stage of the Lewis model corresponds to phase three of the Ranis-Fei model. These three phases, illustrated in Diagram 1below, are distinguished by the marginal productivity of agricultural labour. The entry into each phase is marked three turning points:
• The breakout point leads to phase one growth with redundant agricultural labour.
• The shortage point leads to phase two growth with disguised agricultural unemployment.
• The commercialisation point leads to phase three of self-sustaining economic growth with the commercialisation of the agricultural sector.One of the biggest drawbacks of the Lewis model was the undermining of the role of agriculture in boosting the growth of the industrial sector. In addition to that, he did not acknowledge that the increase in productivity of labor should take place prior to the labor shift between the two sectors. However, these two ideas were taken into account in the Fei–Ranis dual economy model of three growth stages.They further argue that the model lacks in the proper application of concentrated analysis to the change that takes place with agricultural development. One of the biggest drawbacks of the Lewis model was the undermining of the role of agriculture in boosting the growth of the industrial sector. In addition to that, he did not acknowledge that the increase in productivity of labor should take place prior to the labor shift between the two sectors. However, these two ideas were taken into account in the Fei–Ranis dual economy model of three growth stages.[4] They further argue that the model lacks in the proper application of concentrated analysis to the change that takes place with agricultural development[5] In Phase 1 of the Fei–Ranis model, the elasticity of the agricultural labor work-force is infinite and as a result, suffers from disguised unemployment. Also, the marginal product of labor is zero. This phase is similar to the Lewis model. In Phase 2 of the model, the agricultural sector sees a rise in productivity and this leads to increased industrial growth such that a base for the next phase is prepared. In Phase 2, agricultural surplus may exist as the increasing average product (AP), higher than the marginal product (MP) and not equal to the subsistence level of wages.Phase 3 begins from the point of commercialization which is at K in the Figure. This is the point where the economy becomes completely commercialized in the absence of disguised unemployment. The supply curve of labor in Phase 3 is steeper and both the sectors start bidding equally for labor.

The amount of labor that is shifted and the time that this shifting takes depends upon:The growth of surplus generated within the agricultural sector, and the growth of industrial capital stock dependent on the growth of industrial profits;
The nature of the industry’s technical progress and its associated bias;
Growth rate of population.
So, the three fundamental ideas used in this model are:

1.Agricultural growth and industrial growth are both equally important;
2.Agricultural growth and industrial growth are balanced;
3. Only if the rate at which labor is shifted from the agricultural to the industrial sector is greater than the rate of growth of population will the economy be able to lift itself up from the Malthusian population trap.

HARRIS TODARO THEORY OF MIGRATION
The Harris–Todaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and welfare economics to explain some of the issues concerning rural-urban migration. The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This implies that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.In the model, an equilibrium is reached when the expected wage in urban areas (actual wage adjusted for the unemployment rate), is equal to the marginal product of an agricultural worker. The model assumes that unemployment is non-existent in the rural agricultural sector. It is also assumed that rural agricultural production and the subsequent labor market is perfectly competitive. As a result, the agricultural rural wage is equal to agricultural marginal productivity. In equilibrium, the rural to urban migration rate will be zero since the expected rural income equals the expected urban income. However, in this equilibrium there will be positive unemployment in the urban sector. The model explains internal migration in China as the regional income gap has been proved to be a primary drive of rural-urban migration, while urban unemployment is local governments’ main concern in many cities.migration from rural areas to urban areas will increase if:
1.Urban wages (wu) increase in the urban sector (le), increasing the expected urban income.
2.Agricultural productivity decreases, lowering marginal productivity and wages in the agricultural sector (wr), decreasing the expected rural income.
However, even though this migration creates unemployment and induces informal sector growth, this behavior is economically rational and utility-maximizing in the context of the Harris–Todaro model. As long as the migrating economic agents have complete and accurate information concerning rural and urban wage rates and probabilities of obtaining employment, they will make an expected income-maximizing decision.

RELATION TO NIGERIA ECONOMY
According to this model migrating workers in developing countries sich as Nigeria are essentially participants in a lottery of relatively high-paid jobs in the towns. When new urban jobs are created the lottery becomes more attractive to potential migrants. Depending on their responsiveness to this improved opportnity, more than one worker are likely to migrate for each job created.

If so, the output foregone may be that of two or more agricultural workers, not just one. If the migrants bring some of their family members to urban areas more output will be lost. The reason is that the wife and children of migrants find fewer employment opportunities in towns than in the rural areas because they do not have land in the towns on which to grow food. and children of migrants find fewer employment opportunities in towns than in the rural areas because they do not have land in the towns on which to grow food.

69. NAME:METEKE JOY ORIMUSUE
DEPARTMENT:ECONOMICS
REG.NO:2017/242430
EMAIL:joymetex2000@gmail.com
BLOG WEBSITE:metekejoy01.blogspot.com

LEWIS-FEI-RANIS THEORY(SURPLUS LABOUR THEORY)
Lewis (1954) proposed a seminal theory of dualistic economic development for over-populated and under-developed economies with vast amounts of surplus agricultural labour for which he was later to be awarded the 1979 Nobel Prize in Economics. Economic growth in such an economy can be achieved by rapid capital accumulation in the non-agricultural (industrial and service) sector, facilitated by drawing surplus labour in the agricultural sector. In the Lewis theory, an economy transits from the first, labour-surplus “stage” to the second, labour-scarce “stage” of development.The central idea behind the Lewis model is fairly simple. Lewis divided labour force into two differentiated groups – “subsistence sector” and “capitalist sector” where the former is assumed to contain unlimited supply and consequently, a pool of surplus labour that sets labour-supply conditions for the latter.
Assumptions of the Lewis Model
(A) Surplus Labour in the Subsistence Sectors:
The basic assumption of the model is that there exists surplus labour in the subsistence sectors. It includes labour whose marginal productivity is zero as well as that whose marginal productivity is positive but is less than the institutional wage. This labour comprises farmers, agricultural labourers, petty traders domestic servants and women.
(B) Importance of Saving:
Another important assumption that Lewis makes is about the savings generated in the capitalist sector and in the subsistence sector. The capitalist sector invests all its savings for its further expansion.Those in the subsistence sector, on the other hand squander away their savings, if any in purchase of jewellery & for construction of temples etc. The propensity to save of the people in subsistence sector is also lower when compared with that of those in the capitalist sector.
The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model.It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.Ranis and Fei (1961) formalised the Lewis theory and defined three “phases” of dualistic economic development by sub-dividing the first stage in the Lewis model into two phases. Thus, the second labour-scarce stage of the Lewis model corresponds to phase three of the Ranis-Fei model. These three phases, illustrated in Diagram 1below, are distinguished by the marginal productivity of agricultural labour. The entry into each phase is marked three turning points:
• The breakout point leads to phase one growth with redundant agricultural labour.
• The shortage point leads to phase two growth with disguised agricultural unemployment.
• The commercialisation point leads to phase three of self-sustaining economic growth with the commercialisation of the agricultural sector.One of the biggest drawbacks of the Lewis model was the undermining of the role of agriculture in boosting the growth of the industrial sector. In addition to that, he did not acknowledge that the increase in productivity of labor should take place prior to the labor shift between the two sectors. However, these two ideas were taken into account in the Fei–Ranis dual economy model of three growth stages.They further argue that the model lacks in the proper application of concentrated analysis to the change that takes place with agricultural development. One of the biggest drawbacks of the Lewis model was the undermining of the role of agriculture in boosting the growth of the industrial sector. In addition to that, he did not acknowledge that the increase in productivity of labor should take place prior to the labor shift between the two sectors. However, these two ideas were taken into account in the Fei–Ranis dual economy model of three growth stages.[4] They further argue that the model lacks in the proper application of concentrated analysis to the change that takes place with agricultural development[5] In Phase 1 of the Fei–Ranis model, the elasticity of the agricultural labor work-force is infinite and as a result, suffers from disguised unemployment. Also, the marginal product of labor is zero. This phase is similar to the Lewis model. In Phase 2 of the model, the agricultural sector sees a rise in productivity and this leads to increased industrial growth such that a base for the next phase is prepared. In Phase 2, agricultural surplus may exist as the increasing average product (AP), higher than the marginal product (MP) and not equal to the subsistence level of wages.Phase 3 begins from the point of commercialization which is at K in the Figure. This is the point where the economy becomes completely commercialized in the absence of disguised unemployment. The supply curve of labor in Phase 3 is steeper and both the sectors start bidding equally for labor.

The amount of labor that is shifted and the time that this shifting takes depends upon:The growth of surplus generated within the agricultural sector, and the growth of industrial capital stock dependent on the growth of industrial profits;
The nature of the industry’s technical progress and its associated bias;
Growth rate of population.
So, the three fundamental ideas used in this model are:

1.Agricultural growth and industrial growth are both equally important;
2.Agricultural growth and industrial growth are balanced;
3. Only if the rate at which labor is shifted from the agricultural to the industrial sector is greater than the rate of growth of population will the economy be able to lift itself up from the Malthusian population trap.

HARRIS TODARO THEORY OF MIGRATION
The Harris–Todaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and welfare economics to explain some of the issues concerning rural-urban migration. The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This implies that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.In the model, an equilibrium is reached when the expected wage in urban areas (actual wage adjusted for the unemployment rate), is equal to the marginal product of an agricultural worker. The model assumes that unemployment is non-existent in the rural agricultural sector. It is also assumed that rural agricultural production and the subsequent labor market is perfectly competitive. As a result, the agricultural rural wage is equal to agricultural marginal productivity. In equilibrium, the rural to urban migration rate will be zero since the expected rural income equals the expected urban income. However, in this equilibrium there will be positive unemployment in the urban sector. The model explains internal migration in China as the regional income gap has been proved to be a primary drive of rural-urban migration, while urban unemployment is local governments’ main concern in many cities.migration from rural areas to urban areas will increase if:
1.Urban wages (wu) increase in the urban sector (le), increasing the expected urban income.
2.Agricultural productivity decreases, lowering marginal productivity and wages in the agricultural sector (wr), decreasing the expected rural income.
However, even though this migration creates unemployment and induces informal sector growth, this behavior is economically rational and utility-maximizing in the context of the Harris–Todaro model. As long as the migrating economic agents have complete and accurate information concerning rural and urban wage rates and probabilities of obtaining employment, they will make an expected income-maximizing decision.

RELATION TO NIGERIA ECONOMY
According to this model migrating workers in developing countries sich as Nigeria are essentially participants in a lottery of relatively high-paid jobs in the towns. When new urban jobs are created the lottery becomes more attractive to potential migrants. Depending on their responsiveness to this improved opportnity, more than one worker are likely to migrate for each job created.

If so, the output foregone may be that of two or more agricultural workers, not just one. If the migrants bring some of their family members to urban areas more output will be lost. The reason is that the wife and children of migrants find fewer employment opportunities in towns than in the rural areas because they do not have land in the towns on which to grow food.

70. NAME:METEKE JOY ORIMUSUE
DEPARTMENT:ECONOMICS
REG.NO:2017/242430
EMAIL:joymetex2000@gmail.com
WEBSITE: metekejoy01.blogspot.com

LEWIS-FEI-RANIS THEORY(SURPLUS LABOUR THEORY)
Lewis (1954) proposed a seminal theory of dualistic economic development for over-populated and under-developed economies with vast amounts of surplus agricultural labour for which he was later to be awarded the 1979 Nobel Prize in Economics. Economic growth in such an economy can be achieved by rapid capital accumulation in the non-agricultural (industrial and service) sector, facilitated by drawing surplus labour in the agricultural sector. In the Lewis theory, an economy transits from the first, labour-surplus “stage” to the second, labour-scarce “stage” of development.The central idea behind the Lewis model is fairly simple. Lewis divided labour force into two differentiated groups – “subsistence sector” and “capitalist sector” where the former is assumed to contain unlimited supply and consequently, a pool of surplus labour that sets labour-supply conditions for the latter.
Assumptions of the Lewis Model
(A) Surplus Labour in the Subsistence Sectors:
The basic assumption of the model is that there exists surplus labour in the subsistence sectors. It includes labour whose marginal productivity is zero as well as that whose marginal productivity is positive but is less than the institutional wage. This labour comprises farmers, agricultural labourers, petty traders domestic servants and women.
(B) Importance of Saving:
Another important assumption that Lewis makes is about the savings generated in the capitalist sector and in the subsistence sector. The capitalist sector invests all its savings for its further expansion.Those in the subsistence sector, on the other hand squander away their savings, if any in purchase of jewellery & for construction of temples etc. The propensity to save of the people in subsistence sector is also lower when compared with that of those in the capitalist sector.
The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model.It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.Ranis and Fei (1961) formalised the Lewis theory and defined three “phases” of dualistic economic development by sub-dividing the first stage in the Lewis model into two phases. Thus, the second labour-scarce stage of the Lewis model corresponds to phase three of the Ranis-Fei model. These three phases, illustrated in Diagram 1below, are distinguished by the marginal productivity of agricultural labour. The entry into each phase is marked three turning points:
• The breakout point leads to phase one growth with redundant agricultural labour.
• The shortage point leads to phase two growth with disguised agricultural unemployment.
• The commercialisation point leads to phase three of self-sustaining economic growth with the commercialisation of the agricultural sector.One of the biggest drawbacks of the Lewis model was the undermining of the role of agriculture in boosting the growth of the industrial sector. In addition to that, he did not acknowledge that the increase in productivity of labor should take place prior to the labor shift between the two sectors. However, these two ideas were taken into account in the Fei–Ranis dual economy model of three growth stages.They further argue that the model lacks in the proper application of concentrated analysis to the change that takes place with agricultural development. One of the biggest drawbacks of the Lewis model was the undermining of the role of agriculture in boosting the growth of the industrial sector. In addition to that, he did not acknowledge that the increase in productivity of labor should take place prior to the labor shift between the two sectors. However, these two ideas were taken into account in the Fei–Ranis dual economy model of three growth stages.[4] They further argue that the model lacks in the proper application of concentrated analysis to the change that takes place with agricultural development[5] In Phase 1 of the Fei–Ranis model, the elasticity of the agricultural labor work-force is infinite and as a result, suffers from disguised unemployment. Also, the marginal product of labor is zero. This phase is similar to the Lewis model. In Phase 2 of the model, the agricultural sector sees a rise in productivity and this leads to increased industrial growth such that a base for the next phase is prepared. In Phase 2, agricultural surplus may exist as the increasing average product (AP), higher than the marginal product (MP) and not equal to the subsistence level of wages.Phase 3 begins from the point of commercialization which is at K in the Figure. This is the point where the economy becomes completely commercialized in the absence of disguised unemployment. The supply curve of labor in Phase 3 is steeper and both the sectors start bidding equally for labor.

The amount of labor that is shifted and the time that this shifting takes depends upon:The growth of surplus generated within the agricultural sector, and the growth of industrial capital stock dependent on the growth of industrial profits;
The nature of the industry’s technical progress and its associated bias;
Growth rate of population.
So, the three fundamental ideas used in this model are:

1.Agricultural growth and industrial growth are both equally important;
2.Agricultural growth and industrial growth are balanced;
3. Only if the rate at which labor is shifted from the agricultural to the industrial sector is greater than the rate of growth of population will the economy be able to lift itself up from the Malthusian population trap.

HARRIS TODARO THEORY OF MIGRATION
The Harris–Todaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and welfare economics to explain some of the issues concerning rural-urban migration. The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This implies that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.In the model, an equilibrium is reached when the expected wage in urban areas (actual wage adjusted for the unemployment rate), is equal to the marginal product of an agricultural worker. The model assumes that unemployment is non-existent in the rural agricultural sector. It is also assumed that rural agricultural production and the subsequent labor market is perfectly competitive. As a result, the agricultural rural wage is equal to agricultural marginal productivity. In equilibrium, the rural to urban migration rate will be zero since the expected rural income equals the expected urban income. However, in this equilibrium there will be positive unemployment in the urban sector. The model explains internal migration in China as the regional income gap has been proved to be a primary drive of rural-urban migration, while urban unemployment is local governments’ main concern in many cities.migration from rural areas to urban areas will increase if:
1.Urban wages (wu) increase in the urban sector (le), increasing the expected urban income.
2.Agricultural productivity decreases, lowering marginal productivity and wages in the agricultural sector (wr), decreasing the expected rural income.
However, even though this migration creates unemployment and induces informal sector growth, this behavior is economically rational and utility-maximizing in the context of the Harris–Todaro model. As long as the migrating economic agents have complete and accurate information concerning rural and urban wage rates and probabilities of obtaining employment, they will make an expected income-maximizing decision.

RELATION TO NIGERIA ECONOMY
According to this model migrating workers in developing countries sich as Nigeria are essentially participants in a lottery of relatively high-paid jobs in the towns. When new urban jobs are created the lottery becomes more attractive to potential migrants. Depending on their responsiveness to this improved opportnity, more than one worker are likely to migrate for each job created.

If so, the output foregone may be that of two or more agricultural workers, not just one. If the migrants bring some of their family members to urban areas more output will be lost. The reason is that the wife and children of migrants find fewer employment opportunities in towns than in the rural areas because they do not have land in the towns on which to grow food.

71. NWAFOR CLARA DABELECHI says:

NAME: NWAFOR CLARA DABELECHI
REG. NO. 2017/249534
Email: Clara.daberechi.249534@unn.edu.ng

Harris-Todaro model of migration
The Harris-Todaro model of migration is an economic model developed in the 1970 by John Harris and Michael Todaro used in development economics and welfare economics to explain issues relating to rural urban migration. Harris and Todaro studied the migration of workers in a two-sector economic system, namely, rural sector and the urban sector. The differences between these sectors are type of goods produced, the technology of production and the process of wage determination. The rural sector is specialized in the production of agricultural goods while the urban sector has formal and informal jobs.
The assumptions of the Harris-Todaro model
Migration decisions are based on the expected income differentials between rural and urban areas rather than just wage differential.
Unemployment does not exist in the rural agricultural sector.
It also assumes that rural agricultural production and the subsequent labor market is perfectly competitive.
The urban wage is institutionally and legally fixed, so that as a result of the migration of workers, if there are more workers than the number of new jobs, some workers would necessarily be unemployed. They have to enter the urban informal sector and be unemployed or underemployed there.
Labour Market friction
The Crucial assumption is that urban formal wages are fixed and higher than agricultural wage for the same type of worker. This is caused by
Urban formal jobs as government showcase i.e. government could use these formal jobs as a showoff to the world that people are well off at least in the capital city
Efficiency wages: an argument that there is a want to have the highest productive workers whom put in a lot of effort
Union bargaining power: i.e. bargaining power by unions that push up wages in the formal sector.
Labour market regulation :regulations in the labour market that might restrict the number of jobs and thereby pushing up wages
The Harris-Todaro model produced two powerful policy results. The first concerns the policy of formal-sector job creation to employ the unemployed (who, in the Harris-Todaro model, are all in urban areas, because that is where the formal-sector jobs are assumed to be located). They concluded that such a policy would increase the formal sector labor force by more than the number of new jobs created, thereby raising the number of urban unemployed. Thus, the solution to urban unemployment is not to create urban employment. The second policy option that Harris and Todaro considered was a policy of rural development. If such a program could increase the rural traditional-sector wage, unemployment would then fall. Thus, in the Harris-Todaro model, the solution to urban unemployment is rural development.
In countries like Nigeria where people migrate from the rural areas to the urban area in search of more paying jobs thereby causing unemployment in the urban areas since workers available are more than available jobs. According to the Harris-Todaro model, increasing jobs in the urban sector will not reduce unemployment; hence the solution to unemployment is the development of the rural areas such that people do not need to migrate to the urban areas.

Lewis Fei-Ranis model
The Fei-Ranis model of economic growth is an economic model developed by John C. H. Fei and Gustav Ranis used in developmental economics or welfare economics. It is an extension of the Lewis model and also known as the Surplus Labor model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account. The model explains how the increased productivity in agricultural sector would become helpful in promoting industrial sector. Development can be brought about only by a complete shift from the agricultural economy to the industrial economy, such that there is increase in the industrial output. This can be achieved by transfer of labor from the agricultural sector to the industrial sector; this means that underdeveloped countries do not suffer from limited labor supply. At the same time, growth in the agricultural sector must not be out looked and its output should be enough to support the whole economy with food and raw materials. The model is concerned with a poor economy which has the following properties:
There is an abundance of labor in such underdeveloped countries and shortage of natural resources.
The population growth rate is very high which results in mass unemployment in the economy.
The major share of population is engaged in agriculture. But the agricultural sector is stagnant. Hence, the marginal productivity of labor is zero and negative in agriculture sector.
There are certain non-agrarian sectors in the economy where there is reduced use of capital.
There is a dynamic industrial sector in the economy.
The model presents three stages whereby an underdeveloped country moves from stagnation to self sustained economic growth. These stages are:
Phase I: Disguised unemployment comes into being because the supply of labor is perfectly elastic and MPL = 0. Therefore, such disguised unemployed are to be transferred to industrial sector at the constant institutional wage. Phase II: Agricultural workers add to Agricultural output but they produce less than the institutional wage they get. Which means that in the second stage the labor surplus exists where APL > MPL, but it is not equal to subsistence (institutional) wages. Accordingly, such disguised unemployed also have to be transferred to industrial sector. If the migration to industrial sector continues a situation is eventually reached where the farm workers produce output equal to institutional wages. This would mean that productivity in Agricultural sector has gone up. Phase III: In the third stage of Fei-Ranis model, the take-off situation comes to an end and there begins the stage of self-sustained growth where the farm workers produce more than the institutional wage they get. In this stage of economic growth the surplus labor comes to an end and the Agricultural sector becomes commercialized sector.
From the analysis above, it is observed that the model supports the balanced growth of the economy, that is, it gives a satisfactory explanation of the agricultural and the industrial sector. It also recognizes the real impact of population growth on the choice of capital intensity on the process of surplus labor absorption.
In a developing country like Nigeria, the fei-ranis model suggests that development could only be achieved by shifting surplus labour from agricultural sector to the industrial sector while growing both sectors simultaneously. It means that there should be a simultaneous investment in both agricultural sector and industrial sector such that even though there is a shift to the industrial sector, the agricultural sector will still be given enough attention to be able to produce food and raw materials for the industrial sector. The result therefore will be that both agricultural and industrial sectors will grow under ‘Balanced Growth’ pattern.

72. NWAFOR CLARA DABELECHI says:

NAME: NWAFOR CLARA DABELECHI
REG NO. 2017/249534
EMAIL: Clara.daberechi.249534@unn.edu.ng

Harris-Todaro model of migration
The Harris-Todaro model of migration is an economic model developed in the 1970 by John Harris and Michael Todaro used in development economics and welfare economics to explain issues relating to rural urban migration. Harris and Todaro studied the migration of workers in a two-sector economic system, namely, rural sector and the urban sector. The differences between these sectors are type of goods produced, the technology of production and the process of wage determination. The rural sector is specialized in the production of agricultural goods while the urban sector has formal and informal jobs.
The assumptions of the Harris-Todaro model
Migration decisions are based on the expected income differentials between rural and urban areas rather than just wage differential.
Unemployment does not exist in the rural agricultural sector.
It also assumes that rural agricultural production and the subsequent labor market is perfectly competitive.
The urban wage is institutionally and legally fixed, so that as a result of the migration of workers, if there are more workers than the number of new jobs, some workers would necessarily be unemployed. They have to enter the urban informal sector and be unemployed or underemployed there.
Labour Market friction
The Crucial assumption is that urban formal wages are fixed and higher than agricultural wage for the same type of worker. This is caused by
Urban formal jobs as government showcase i.e. government could use these formal jobs as a showoff to the world that people are well off at least in the capital city
Efficiency wages: an argument that there is a want to have the highest productive workers whom put in a lot of effort
Union bargaining power: i.e. bargaining power by unions that push up wages in the formal sector.
Labour market regulation :regulations in the labour market that might restrict the number of jobs and thereby pushing up wages
The Harris-Todaro model produced two powerful policy results. The first concerns the policy of formal-sector job creation to employ the unemployed (who, in the Harris-Todaro model, are all in urban areas, because that is where the formal-sector jobs are assumed to be located). They concluded that such a policy would increase the formal sector labor force by more than the number of new jobs created, thereby raising the number of urban unemployed. Thus, the solution to urban unemployment is not to create urban employment. The second policy option that Harris and Todaro considered was a policy of rural development. If such a program could increase the rural traditional-sector wage, unemployment would then fall. Thus, in the Harris-Todaro model, the solution to urban unemployment is rural development.
In countries like Nigeria where people migrate from the rural areas to the urban area in search of more paying jobs thereby causing unemployment in the urban areas since workers available are more than available jobs. According to the Harris-Todaro model, increasing jobs in the urban sector will not reduce unemployment; hence the solution to unemployment is the development of the rural areas such that people do not need to migrate to the urban areas.

Lewis Fei-Ranis model
The Fei-Ranis model of economic growth is an economic model developed by John C. H. Fei and Gustav Ranis used in developmental economics or welfare economics. It is an extension of the Lewis model and also known as the Surplus Labor model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account. The model explains how the increased productivity in agricultural sector would become helpful in promoting industrial sector. Development can be brought about only by a complete shift from the agricultural economy to the industrial economy, such that there is increase in the industrial output. This can be achieved by transfer of labor from the agricultural sector to the industrial sector; this means that underdeveloped countries do not suffer from limited labor supply. At the same time, growth in the agricultural sector must not be out looked and its output should be enough to support the whole economy with food and raw materials. The model is concerned with a poor economy which has the following properties:
There is an abundance of labor in such underdeveloped countries and shortage of natural resources.
The population growth rate is very high which results in mass unemployment in the economy.
The major share of population is engaged in agriculture. But the agricultural sector is stagnant. Hence, the marginal productivity of labor is zero and negative in agriculture sector.
There are certain non-agrarian sectors in the economy where there is reduced use of capital.
There is a dynamic industrial sector in the economy.
The model presents three stages whereby an underdeveloped country moves from stagnation to self sustained economic growth. These stages are:
Phase I: Disguised unemployment comes into being because the supply of labor is perfectly elastic and MPL = 0. Therefore, such disguised unemployed are to be transferred to industrial sector at the constant institutional wage. Phase II: Agricultural workers add to Agricultural output but they produce less than the institutional wage they get. Which means that in the second stage the labor surplus exists where APL > MPL, but it is not equal to subsistence (institutional) wages. Accordingly, such disguised unemployed also have to be transferred to industrial sector. If the migration to industrial sector continues a situation is eventually reached where the farm workers produce output equal to institutional wages. This would mean that productivity in Agricultural sector has gone up. Phase III: In the third stage of Fei-Ranis model, the take-off situation comes to an end and there begins the stage of self-sustained growth where the farm workers produce more than the institutional wage they get. In this stage of economic growth the surplus labor comes to an end and the Agricultural sector becomes commercialized sector.
From the analysis above, it is observed that the model supports the balanced growth of the economy, that is, it gives a satisfactory explanation of the agricultural and the industrial sector. It also recognizes the real impact of population growth on the choice of capital intensity on the process of surplus labor absorption. In a developing country like Nigeria, the fei-ranis model suggests that development could only be achieved by shifting surplus labour from agricultural sector to the industrial sector while growing both sectors simultaneously. It means that there should be a simultaneous investment in both agricultural sector and industrial sector such that even though there is a shift to the industrial sector, the agricultural sector will still be given enough attention to be able to produce food and raw materials for the industrial sector. The result therefore will be that both agricultural and industrial sectors will grow under ‘Balanced Growth’ pattern.

73. Ngwu Osita Enoch
2017/242022
Ositangwu95@gmail.com
Edu Economics
Enochonline.blogspot.com

Lewis-Fei-Ranis Model (Surplus labour theory)
INTRODUCTION
The Lewis (1954) theory of dualistic economic development provides the seminal contribution to theories of economic development particularly for labour-surplus and resource-poor developing countries. In the Lewis theory, the economy is assumed to comprise the agricultural and non-agricultural sectors. The agricultural sector is assumed to have vast amounts of surplus labour that result in an extremely low, close to zero, marginal productivity of labour. The agricultural wage rate is presumed to follow the sharing rule and be equal to average productivity, which is also known as the institutional wage. The non-agricultural sector has an abundance capital and resources relative to labour. It pursues profit and employs labour at a wage rate higher than the agricultural institutional wage by approximately 30 percent (Lewis, 1954, p.150).
The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output.
HISTORY OF SURPLUS LABOUR THEORY
The historical emergence of surplus labour is, according to Marx, also closely associated with the growth of trade (the economic exchange of goods and services) and with the emergence of a society divided into social classes. As soon as a permanent surplus product can be produced, the moral-political question arises as to how it should be distributed, and for whose benefit surplus-labour should be performed. The strong defeat the weak, and it becomes possible for a social elite to gain control over the surplus-labour and surplus product of the working population; they can live off the labour of others.
Labour which is sufficiently productive so that it can perform surplus labour is, in a cash economy, the material foundation for the appropriation of surplus-value from that labour. How exactly this appropriation will occur, is determined by the prevailing relations of production and the balance of power between social classes.
THE CONCEPT OF SURPLUS LABOUR
The concept of surplus labour is widely discussed among development economics but its specific meaning needs to be defined, especially in technical terms, as many neoclassical economists still doubt the existence of surplus labour in an economy. Defining the source and the extent of surplus labour is then a prerequisite for further study. This section considers the various definitions of surplus labour and clarifies them.
The simple definition of surplus labour implies the existence of a point at which the marginal product of labour becomes zero and labour can be transferred out of the traditional sector without reducing the quantity of output, as noted by Wellisz (1968: 22): The (disguised-unemployment or the Unlimited Supply of Labour) hypothesis claims that in poor, densely populated countries, more people are employed than needed to produce the prevailing output with the existing techniques and the existing supply of non-labour inputs. The ‘surplus’ labour constitutes ‘hidden’ or ‘disguised’ unemployment. Many of the proponents of the hypothesis make the further claim that agricultural output will not decrease, and industrial output will increase, if measures are taken to re-allocate labour from subsistence agriculture (where the surplus is supposed to exist) to industry (where there is no surplus labour).
ASSUMPTIONS OF THE LEWIS-FEI-RANIS MODEL
(A) Surplus Labour in the Subsistence Sectors:
The basic assumption of the model is that there exists surplus labour in the subsistence sectors. It includes labour whose marginal productivity is zero as well as that whose marginal productivity is positive but is less than the institutional wage. This labour comprises farmers, agricultural labourers, petty traders domestic servants and women.
The surplus labour in the agriculture sector acts as a source of unlimited supply of labour for the manufacturing sector. By unlimited supply of labour. Lewis means that the supply of labour is perfectly elastic at a particular wages. This particular wage is somewhat higher than the institutional wage which each worker in the agricultural sector gets.
(B) Importance of Saving:
Another important assumption that Lewis makes is about the savings generated in the capitalist sector and in the subsistence sector. The capitalist sector invests all its savings for its further expansion. Those in the subsistence sector, on the other hand squander away their savings, if any in purchase of jewellery & for construction of temples etc of those in the capitalist sector. Lewis in fact so much fascinated by the higher propensity to save of the capitalist sector that he even advocates a transfer of income from the subsistence sector to the capitalist sector. He feels that steps have to be taken to raise the rate of savings from 10% to 15% if the development of the economy has to be smooth.
COMPARISONS OF THE THEORY OF SURPLUS LABOUR
Surplus labor models are a class of models for analyzing developing countries as dual economies with a modern capitalist sector and a traditional precapitalist sector. The precapitalist sector is viewed as having a large pool (“unlimited supplies”) of labor from which the capitalist sector may draw at constant cost. While these models are often described as finding their inspiration in the old classical economists and Karl Marx, the 1954 model of W. Arthur Lewis and its extensions are technically more neoclassical than truly classical. The Lewis model was elaborated and formalized by many others, most notably John C. H. Fei and Gustav Ranis (1964), with important theoretical contributions from Amartya Sen (1966) and Stephen Marglin (1976). Questions have been raised as to the historical relevance of the neoclassical labor surplus models (Schultz 1964; Myint 1971; Arrighi 1973; Williamson 1985).
CRITICISM
Lewis-Fei-Ranis model of economic growth has been criticized on multiple grounds, although if the model is accepted, then it will have a significant theoretical and policy implications on the underdeveloped countries’ efforts towards development and on the persisting controversial statements regarding the balanced vs. unbalanced growth debate.
It has been asserted that the Lewis-Fei-Ranis model did not have a clear understanding of the sluggish economic situation prevailing in the developing countries. If they had thoroughly scrutinized the existing nature and causes of it, they would have found that the existing agricultural backwardness was due to the institutional structure, primarily the system of feudalism that prevailed.
The Lewis-Fei-Ranis model say, “It has been argued that money is not a simple substitute for physical capital in an aggregate production function. There are reasons to believe that the relationship between money and physical capital could be complementary to one another at some stage of economic development, to the extent that credit policies could play an important part in easing bottlenecks on the growth of agriculture and industry.” This indicates that in the process of development they neglect the role of money and prices. They fail to differ between wage labor and household labor, which is a significant distinction for evaluating prices of dualistic development in an underdeveloped economy.
The Lewis-Fei-Ranis model assume that MPPL is zero during the early phases of economic development, which has been criticized by Harry T.Oshima and some others on the grounds that MPPL of labor is zero only if the agricultural population is very large, and if it is very large, some of that labor will shift to cities in search of jobs. In the short run, this section of labor that has shifted to the cities remains unemployed, but over the long run it is either absorbed by the informal sector, or it returns to the villages and attempts to bring more marginal land into cultivation.
CONCLUSIONS AND RECOMMENDATIONS
Lewis-Fei-Ranis model can be grouped under three instruments; labour force, capital accumulation and integration to the world economy. The main focus in Lewis-Fei-Ranis model was on the reallocation of labour until the turning point is reached, i.e., the time when labour reallocation has outstripped population growth long enough for dualism to atrophy and the economy to become fully commercialized. The model implicitly showed that the traditional sector do not produce any capital accumulation as they are very small and poor. Trade between agriculture and industry as the supply or marketed food falls or the demand for it rises, or both causing the value of marginal product of labour in agriculture to rise.
In sum up, there are several weaknesses of Lewis-Fei-Ranis model that are underlined by many economists. The first and most important is that if marginal productivity of labour in agricultural sector is negligible, zero. Schultz (1964), Sen (1967), Harris and Todaro (1970) and Fields (1975) proved with their empirical results that this cannot happen in agriculture sector. It is obvious that there is a disguised unemployment in agriculture. Particularly, agricultural sector should be considered in two ways: during harvest time and post harvest. If the agricultural surplus is solely considered for the regions where there can be seen harsh winter conditions, it could be accepted of the doctrine of Lewis, otherwise it is irrelevant to say there is a zero marginal productivity for agriculture labours. Also, there are positive opportunity costs, e.g. loss of crops in times of peak harvesting season, labour transfer will reduce agricultural output.
Second, the model employed mostly for the closed economies and gave relatively less information on open economies. Lewis-Fei-Ranis model was criticized as it neglects international trade. The model was to a certain extent supply-oriented, which does not foresee any trade between capital and other sectors. Also it was criticized advocating industrialization and ignores agriculture. If a section of the profit made by the capitalists is not devoted to agricultural development, the process of industrialization would be jeopardized.
Third, Lewis-Fei-Ranis model believed that the more the rate of labour transfer to urban employment, the more the economic grows and more jobs are created. But this is not a common applicable in practice if industrial development involves more intensive use of capital than labour, then the flow of labour from agriculture to industry will simply create more unemployment.
Fourth, the Lewis-Fei-Ranis model would imply that aggregate living standards should not rise as rapidly as productivity until surplus labour is eliminated. However, the evidence on living standards in Latin America during the twentieth century indicates that these have risen in line with productivity, and that the ‘indirect’ components of the real wage (health and education) have actually risen more rapidly that average incomes.
Fifth, the Lewis-Fei-Ranis model stated the wage in industrial sector does not increase before labour surplus is absorbed. But this does not happen in any way in reality as the development of the urban, or industrial, or formal sector can itself lead to the creation of pressure groups and swing the balance of power towards those in that sector, to the detriment of those remaining outside it. The wage in the industrial sector in reality outstandingly rises long before the labour surplus is absorbed.
Haven tested the Lewis-Ranis-Fei theory for developing economy over 1965-2002 we have found that the developing economic growth is mainly attributable to the development of the non-agricultural sector. This is driven by rapid capital accumulation as well as employment growth. The reallocation of labour away from agriculture has made a positive net contribution to rapid economic of the developing economy. The rise in the marginal productivity of agricultural labour indicates the absorption of redundant agricultural labour since the 1978 Economic Reform. However, the marginal productivity of agricultural labour is still lower than the initial low average productivity of agricultural labour. This implies the continued existence of disguised agricultural unemployment. This suggests that the these developing economy has entered the Lewis-Ranis-Fei phase two of development but has not yet achieved phase three. The continuing widening productivity gap between the two sectors calls for the removal of market restrictions and government interventions so as to allow the continued absorption of surplus labour. Several policy recommendations are tentatively suggested. First and foremost, more effort should be made in promoting employment to effectively absorb the remaining labour surplus and promote economic development. This can be achieved by further relaxing the Hukou restrictions on migration, increasing labour market flexibility and improving the allocative efficiency of labour. It can also be achieved by encouraging the development of private enterprise to create more employment opportunities. Second, Government of developing economy should continue implementing the Sunshine Policy, initiated in 2003, designed to provide rudimentary job training, recruitment information and information about conditions in the destination cities to rural migrants. This will not only help facilitate employment of rural migrants but also satisfy the increasing demand for skilled labour in the growing non-agricultural sector. Third, agriculture could be promoted by tax breaks, direct subsidies and most importantly, by removing price controls on agricultural products. Agriculture could thus be commercialised and the economy would enter phase three of economic development.

REFERENCE
Sadik-Zada, Elkhan Richard (2020). “Natural resources, technological progress, and economic modernization”. Review of Development Economics. doi:10.1111/rode.12716.
“Economnics4Development Website”. Surplus Labor Model of Economic Development. Archived from the original on 16 October 2011. Retrieved 12 October 2011.
Thirlwall, A.P (2006). Growth and Development: With Special Reference to Developing Economies. Palgrave Macmillan. ISBN 1-4039-9600-8.
Subrata, Ghatak (2003). Introduction to Developmental Economics. London: Routledge. ISBN 0-415-09722-3.
“Ranis-Fei model vs. Lewis Model” (PDF). Developmentafrique.com. Archived from the original (PDF) on 30 May 2012. Retrieved 14 October 2011.
“American Economic Review”. The Ranis-Fei Model of Economic Development: Comment. 53: 448–452. JSTOR 1809172.
Ranis, Gustav. “Paper on Labor Surplus Economies” (PDF). Retrieved 4 October 2011.
J. Choo, Hakchung. “American Economic Review”. On the Empirical Relevancy of the Rans-Fei Model of Economic Development: Comment. 61: 695–703. JSTOR 1811863.
Misra, Puri, S.K, V.K (2010). Economics of Development and Planning. Mumbai, India: Himalaya Publishing House. pp. 270–279. ISBN 978-81-8488-829-4.

Harris-Todaro Model of Migration
INTRODUCTION
Harris and Todaro work, is considered one of the starting points of the classic rural-urban migration theory. The hypothesis and predictions of Harris-Todaro model have been subjected to econometric evaluation and have been corroborated by several studies. The key hypothesis of Harris and Todaro are that migrants react mainly to economic incentives, earnings differentials, and the probability of getting a job at the destination have influence on the migraton decision. In other words, these authors posit that rural-urban migration will occur while the urban expected wage exceed the rural wage. From this crucial assumption, as denominated by Harris-Todaro, is deduced that the migratory dynamics leads the economic system toward an equilibrium with urban concentration and high urban unemployment.
THE HARRIS-TODARO MODEL
Assumptions
Harris and Todaro studied the migration of workers in a two-sector economic system, namely, rural sector and urban sector. The difference between these sectors are the type of goods produced, the technology of production and the process of wage determination. The rural sector is specialized in the production of agricultural goods. The productive process of this sector can be described by a Cobb-Douglas production function: where Ya is the production level of the agricultural good, Na is the amount of workers used in the agricultural production, Aa > 0 and 0 < f 0 and 0 < a < 1 are parametric constants. Both goods and labor markets are perfectly competitive. Nevertheless, there is segmentation in the labor market due to a high minimum urban wage politically determined. In the rural sector, the real wage, perfectly flexible, is equal to the marginal productivity of labor in this sectors where wa is the real wage and p is the price of the agricultural good, both expressed in units of manufactured good.
HARRIS-TODARO AGENT-BASED MODEL
Computational Implementation

Initially, workers are randomly placed in a square lattice with linear dimension L = 500. The reference values of the parameters used for these simulations are the same done to evaluate the equilibrium of the Harris-Todaro model, namely, Aa = 1.0, Am = 1.0, f = 0.3, a = 0.7, r = 1.0 and g = 1.0. The value of the minimum wage used is wm = 0.8 and the initial urban fraction of the total population is nu = 0.2, where nu = Nu/N is the normalized urban population also called urban share. The initial value nu = 0.2 is in agreement with historical data of developing economies. Given these parameters, one can calculate the vector which characterizes temporary equilibrium of the system by using eqs. (7 – 12). By using eq. (7), the employment level of the urban sector, Nm, is obtained. If nu Nm/N there will be a fraction of Nm/Nu workers employed, which earn the minimum wage, wi = wm, and (1-Nm/Nu) workers unemployed, which earn a wage wi = 0. Each worker can be selected to review his sectorial location with probability a, called activity. Therefore, in each time step only a fraction of workers becomes potential migrants, going through the sectorial location reviewing process. Potential migrants will determine their satisfaction level of being in the current sector by comparing their earnings, wi, among nearest neighbors. The potential migrant starts the comparison process with a initial satisfaction level si = 0. When wi > wneighbor the satisfaction level si is added in one unit; if wi < wneighbor, si is diminished in one unit; if wi = wneighbor, si does not change. After the worker has passed through the reviewing process his/her satisfaction level is checked. The migration will occur only if si < 0, what means that the worker's i earnings is less than the most of his/her nearest neighbors. After all the potential migrants complete the reviewing process and have decided migrate or not, a new configuration of the system is set. Therefore, once again a new temporary equilibrium of the system is calculated by using eqs. (8 – 12). The whole procedure is repeated until a pre-set number of steps is reached. It is important to emphasize that Nm is kept constant throughout the simulation. Its given by eq. (7) which depends on the technological parameters, a,Am, and the minimum wage, wm, which are constants too.
In this case, the differential of expected wages is negative. In an economy mainly rural (nu < 0:5), the transitional dynamics characterized by a continuous growth of population of the urban sector with a differential of expected wages relatively high is followed by the stabilization of rural-urban differential of expected wages. In other words, the generalized Harris-Todaro condition, eq. (15), arises as a long run equilibrium result of the agent-based migratory dynamics.
CONCLUSION
In this paper we developed and agent-based computational model which formalizes the rural-urban allocation of workers as a process of social learning by imitation. We analyze a two-sectorial economy composed by adaptative agents, i.e., individuals that grope over time for best sectorial location in terms of earnings. This search is a process of imitation of successful neighbor agents. The dispersed and non-coordinated individual migration decisions, made based on local information, generate aggregate regularities.
Firstly, the crucial assumption of Harris and Todaro, the principle that rural-urban migration will occur while the urban expected wage exceed the rural wage, comes out as spontaneous upshot of interaction among adaptative agents.
Secondly, the migratory dynamics generated by agents that seek to adaptate to the economic environment that they co-create leads the economy toward a long run equilibrium characterized by urban concentration with urban unemployment. When this long run equilibrium is reached, the generalized Harris-Todaro condition is satisfied, i.e., there is a stabilization of the rural-urban expected wage differential.
Thirdly, the impact of the minimum wage and elasticity of terms of trade in a long run equilibrium obtained by simulations are in agreement with the predictions of the original Harris-Todaro model with Cobb-Douglas technology.
Finally, the simulations showed an aggregated pattern not found in the original Harris-Todaro model. There is the possibility of small fluctuations of the urban share around an average value. This phenomenon is known as reverse migration.

REFERENCE

Aquino L. Espíndola thanks CAPES for the financial support. Jaylson J. Silveira acknowledges research grants from CNPq. T. J. P. Penna thanks CNPq for the fellowship.
J. R. Harris and M. P. Todaro, American Economic Review 60, 126 (1970).
M. P. Todaro, American Economic Review 59, 138 (1969).
D. Ray, Development Economics (Princeton: Princeton University Press, 1998).
L. Y. L. Yap, Journal of Development Economics 4, 239 (1977).
D. Mazumdar, Rural-urban Migration in Developing countries. In: Handbook of Regional and Urban Economics, Elsevier, Amsterdam, 1987.
L. Ghatak, P. Levine, and S. Price, Journal of Economics Surveys 10, 159 (1996).
J. G. Willianson, Migration and Urbanization. In: Chenery, H. and Srinivasan, T.N., Handbook of developments economics, Elsevier, Amsterdam, 1988.
J. J. Silveira, A. L. Espíndola, and T. J. P. Penna, physics/0506021, Physica A, to appear.

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LEWIS FEI-RANIS MODEL
INTRODUCTION
The Fei–Ranis model of economic growth is a dualism model developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.
ASSUMPTIONS OF THE MODEL
1. There is a dual economy divided into a traditional and stagnant agricultural sector and an active industrial sector.
2. The output of the agricultural sector is a function of land and labor alone.
3. There is no accumulation of capital in agriculture except in the form of land reclamation.
4. Land is fixed in supply.
5. Population growth is taken as an exogenous phenomenon.
The real wage in the industrial sector remains fixed and is equal to the initial level of real income in the agricultural sector. It is called an institutional wage.
6. Workers in either sector consume only agricultural products.
Given these assumptions, Fei and Ranis analyze the development of a labor surplus economy into three phases;
In the first phase, the disguised unemployed workers who are not adding to agricultural output are transferred to the industrial sector at a constant institutional wage.
In the second phase, agricultural workers add to agricultural output but produce less than the institutional wage they get. Such workers are shifted to the industrial sector. If the migration of the workers to the industrial sector continues, a point is eventually reached when farmworkers produce output equal to the institutional wage.
In the third phase, which makes the end of the take-of and the beginning of the self-sustained growth when farmworkers produce more than the institutional wage they get. In this phase, the surplus labor is exhausted and the agricultural sector becomes commercialized.
CRITICISMS OF FEI-RANIS MODEL
1. Commercialization of agriculture leads to inflation. According to the model, when the agricultural sector enters the third phase, it becomes commercialized, but the economy is not likely to move smoothly into a self-sustained growth because inflationary pressure will start.
2. Supply of land is not fixed. Fei-Ranis begins with the assumption that the supply of land is fixed during the development process. In the long run, the amount of land is not fixed, as the statistics of crop average in many Asian countries reveal.
3. Institutional wage not constant in the agricultural sector. The model assumes that the institutional wage remains constant in the first two phases even when agricultural productivity increases. This is unrealistic because with a general rise in agricultural productivity farm wages also tend to rise.
HOW IT RELATE TO NIGERIA ECONOMY
The Lewis theory of development to the Nigerian economy. Nigeria has both rural and urban sectors that provide for each forward and backward linkages and as such, the two sectors are not mutually exclusive in promoting the economic growth of the country and improving the standard of living of citizens. However, the Federal Government of Nigeria does not necessarily have to move surplus labour that exists in the rural areas to the urban areas but instead infrastructural facilities should be provided equally to both the rural and urban areas of the country.
CONCLUSION AND DRAW OPINIONS
Base on this model we can see that nation like Nigeria should invest in both sector to increase it productivity and ensure rapid development of the nation through stopping of transfer of labour from one sector to another , the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector.

HARRIS TODARO MODEL OF MIGRATION
John R. Harris and Michael P. Todaro presented the seminal ‘Two sector model’ in American Economic Association, 1970. This model is a pioneering study in the field encompassing rural-urban migration. The classical theory is used in development economics and is an economic illustration of migrants’ decision on expected income differentials between rural (agriculture) and urban (manufacturing) areas. The model of rural-urban migration is typically studied in the context of employment and unemployment situation in developing countries. The purpose of the model is to explain the critical urban unemployment problem in developing countries. The key hypothesis of Harris and Todaro’s model is that economic incentives, earnings differentials, and the probability of getting a job at the destination have influence on the migration decision. The distinctive concept in the model is that the rate of migration flow from rural (agricultural) areas to urban (industrial) areas is determined by the difference between expected urban wages and rural wages. The rural-urban two-sector model centrally holds the following futures: 1) Real wages (adjusted for cost-of-living differences) were higher in urban formal sector jobs than in rural traditional sector jobs. 2) To be hired for a formal sector job, it was necessary to be physically present in the urban areas where the formal sector jobs were located. 3) Consequently, from the first two features, more workers searched for formal sector jobs than were actually hired. Employers hired some of the searchers but not all of them. 4) To maintain equality between the expected wage associated with searching for an urban job and the expected wage associated with taking up a lower-paying rural job, the equilibrium arising in such a setting would be characterized by urban unemployment. 5) Any temporary difference in the expected wages between one sector and another would be eroded as workers migrate from the low expected wage labor market to the high expected wage one. Pelted wage exceeds the rural obtain wage.
1.2 COMPARISON OF THE MODEL TO OTHER MODEL
The Todaro (1969) and Harris-Todaro (1970) models also consider the role of internal migration in a dual economy in which the urban sector draws labor force from the rural sector. But the change of focus is radical. In the Lewis model, internal migration removed ‘disguised unemployment’ from rural areas and enabled the transition to a modern economy. In Todarian models, the focus is on explaining the existence of unemployment in urban areas and its link with internal migration.
1.3 Assumptions
Harris and Todaro studied the migration of workers in a two-sector economic system, namely, rural sector and urban sector. The difference between these sectors are the type of goods produced, the technology of production and the process of wage determination. The rural sector is specialized in the production of agricultural goods. The productive process of this sector can be described by a Cobb-Douglas production function:

Where Ya is the production level of the agricultural good, Na is the amount of workers used in the agricultural production, Aa > 0 and 0 < f 0 and 0 < a 0 and g > 0 are a parametric constants. g is the elasticity of p with respect to the ratio Ym/Ya.
The overall population of workers in the economy is N, which is kept constant during the whole period of analysis. By assumption there are only two sectors and rural prices are wholly flexible, which implies that there is full employment in the rural area, i.e., all workers living at the rural sector are employed at any period. Then at any period the following equality is verified:

B. Temporary Equilibrium
Given a parametric constant vector (Aa,Am,f,a,r,g), an initial urban population Nu, and a minimum wage wm one can calculate the temporary equilibrium of the economic system by using eqs. (1 – 6).
From eq. (4) one can find the employment level at the manufacturing sector

Replacing eq. (7) in eq. (2) we get the production level of the manufacturing sector

From eq. (6) one can obtain the relation

which is used with eq (1) to obtain the agricultural production

By using eqs (5), (8) and (10) the terms of trade are determined

Finally, by using eqs (3), (9) and (11), the rural wage in units of manufacturer good is obtained

In sum, the vector (Nm,Ym,Na,Ya,p,wa) configures a temporary equilibrium that might be altered whether occurs a migration of workers, induced by the differential of sectorial wages, which changes the sectorial distribution of overall population.
C. The Long Run Equilibrium
Harris and Todaro, in determining the long run equilibrium, i.e., the absence of a net rural-urban migratory flow, argue that the rural workers, in their decision on migrating to the urban area, estimate the expected urban wage, , defined as:

The ratio Nm/Nu, which is the employment rate, is an estimative of the probability that a worker living at urban sector gets a job in this sector.
As mentioned before, the key assumption of the model of Harris and Todaro is that there will be a migratory flow from the rural to the urban sector while the expected urban wage is higher than the rural wage. Thus, the long run equilibrium is attained when the urban worker population reaches a level such that the expected urban wage equates the rural wage:

This equality is known in the economic literature as the Harris-Todaro condition. Harris and Todaro argue that the differential of expected wages in eq. (14) can be a constant value d ¹ 0. When this differential reaches d, the net migration ceases. This generalized Harris-Todaro condition can be expressed as follows:

The level of the urban population that satisfies the eq. (15), i.e., the equilibrium urban share = /N, is determined from the solution of the equation resulting from substitution of equations (12), (13) in eq. (15):

The solution of eq. (16) is parameterized by the vector (Aa,Am,r,g,a,f,wm).
Harris and Todaro [1], in order to evaluate the stability of the long run equilibrium, postulate a mechanism of adjustment that is based on the following function of sign preservation:

The differential equation that governs the state transition in the model of Harris and Todaro is obtained by replacing equations (12), (13) in eq. (17). Based on this postulated adjustment process, Harris and Todaro show that the long run equilibrium is globally asymptotically stable. This means that the economy would tend to long run equilibrium with unemployment in the urban sector generated by the presence of a relatively high minimum wage for all possible initial conditions. From now on we will refer to the long run equilibrium simply as equilibrium.
Based on the numerical solutions of eq. (16) one can evaluate the impact that the variation of the minimum wage and the elasticity of the terms of trade on the equilibrium. In Fig. 1 we see that under the hypothesis of a Cobb-Douglas technology, the equilibrium urban share, , does not depend on the minimum wage wm. However, changes in the value of wm reduces the labor demand on the manufacturing sector what results in higher unemployment rates in the equilibrium.

In turn, as seen in Fig. 2, changes in the elasticity of the terms of trade alter slightly the equilibrium urban share and unemployment rate. A net migration toward urban sector shift the terms of trade to higher values. The greater g the greater this shift, what cause an increase in the rural wage in units of manufacturing good, becoming the urban sector less attractive.

HARRIS-TODARO AGENT-BASED MODEL
In this section we describe the implementation of the computational model we proposed, as well as the aggregate patterns obtained numerically and the comparison with the respective analytical results.
A. Computational Implementation
Initially, workers are randomly placed in a square lattice with linear dimension L = 500. The reference values of the parameters used for these simulations are the same done to evaluate the equilibrium of the Harris-Todaro model, namely, Aa = 1.0, Am = 1.0, f = 0.3, a = 0.7, r = 1.0 and g = 1.0. The value of the minimum wage used is wm = 0.8 and the initial urban fraction of the total population is nu = 0.2, where nu = Nu/N is the normalized urban population also called urban share. The initial value nu = 0.2 is in agreement with historical data of developing economies. Given these parameters, one can calculate the vector which characterizes temporary equilibrium of the system by using eqs. (7 – 12).
By using eq. (7), the employment level of the urban sector, Nm, is obtained. If nu Nm/N there will be a fraction of Nm/Nu workers employed, which earn the minimum wage, wi = wm, and (1-Nm/Nu) workers unemployed, which earn a wage wi = 0.
Each worker can be selected to review his sectorial location with probability a, called activity . Therefore, in each time step only a fraction of workers becomes potential migrants, going through the sectorial location reviewing process. Potential migrants will determine their satisfaction level of being in the current sector by comparing their earnings, wi, among nearest neighbors.
The potential migrant starts the comparison process with a initial satisfaction level si = 0. When wi > wneighbor the satisfaction level si is added in one unit; if wi < wneighbor, si is diminished in one unit; if wi = wneighbor, si does not change. After the worker has passed through the reviewing process his/her satisfaction level is checked. The migration will occur only if si < 0, what means that the worker's i earnings is less than the most of his/her nearest neighbors.
After all the potential migrants complete the reviewing process and have decided migrate or not, a new configuration of the system is set. Therefore, once again a new temporary equilibrium of the system is calculated by using eqs. (8 – 12). The whole procedure is repeated until a pre-set number of steps is reached. It is important to emphasize that Nm is kept constant throughout the simulation. Its given by eq. (7) which depends on the technological parameters, a,Am, and the minimum wage, wm, which are constants too.
CONCLUSION
Therefore, migration from rural areas to urban areas will increase in real world if:
Urban wages (wu) increase in the urban sector (le), increasing the expected urban income.
Agricultural productivity decreases, lowering marginal productivity and wages in the agricultural sector (wr), decreasing the expected rural income.
However, even though this migration creates unemployment and induces informal sector growth, this behavior is economically rational and utility-maximizing in the context of the Harris–Todaro model. As long as the migrating economic agents have complete and accurate information concerning rural and urban wage rates and probabilities of obtaining employment, they will make an expected income-maximizing decision.