Models of Surplus Labour | Economic Models | Economics

The following points highlight the two main models of surplus labour. The models are: 1. The Lewis Model 2. Harris-Todaro Model.

1. The Lewis Model:

The Lewis model presents a long run view of the development of a dual economy. It traces the path over time of a low-income, backward economy moving slowly but steadily towards a distinct but clearly visible goal—industrialisation, which is equated with economic development.

Lewis himself described his model as a ‘classical’ one, since, in the rural sector, there is an unlimited supply of labour at the subsistence wage. Due to the existence of surplus labour, at this wage, any rise in the demand for (unskilled) labour can be easily met without causing the wage rate to rise.

However, the modern (capitalist) sector cannot draw, even if it wishes, on this unlimited supply of labour at the subsistence wage. It has to pay a higher wage, W_u, which is due to the saver existence of a mark-up (m) on the rural subsistence wage, W_p (W_u = W_r + m, where m > 0 or, W_u > W_r). The wage gap exists largely due to higher cost of living in the urban sector.

Let L be the total amount of labour in the economy (if we ignore the important issue of population growth). Let the rural marginal product curve of labour be horizontal over a considerable stretch, with the marginal product of labour more or less equal to the subsistence level. This is shown in Fig. 1, in which O_R is the origin of the rural sector and O_M of the modern sector.

The wage rate in the urban sector, W_u, is much above the subsistence level. It is assumed to be rigid downward because it is exogenously determined. We also assume, unrealistically though, that both the sectors produce the same good. Initially, the MP_L curve in the urban sector is D₁D₁. We also assume that a typical urban employer is a wage-taker. In order to maximise profit, he employs O_ML₁ workers. The remaining workers, L- O_ML₁ = O_RL₁, stay in the rural sector, where the marginal worker earns W_r.

Absorption of Rural Labour:

In the Lewis model, the central theme of the dual economy is the dynamics of the system. Since the capitalists save their entire profit (surplus) in period 1, the capital stock with the urban employer in period 2 increases which is equal to D₁EW_U in Fig. 1.

With increase in the capital stock the MP_L rises since workers get more of the complementary factors to work with. Hence the MP_L curve in period 2 shifts to the right to D₂D₂. Then urban employment rises to O_ML₂and rural employment is O_RL₂. Now the urban sector profit is D₂FW_U. This is again invested, leading to a further rightward shift of the urban MP_L curve.

Here the rate of profit or surplus (s) is expressed as:

 

 

 

where π is profit, K is the capital stock, L is labour, k = K/L and Y/L is the AP_L. This unending cycle (Lewis virtuous cycle) of surplus, reinvestment, and growth continues, and the modern sector gradually absorbs all surplus labour of the rural sector. See Fig. 2.

The Turning Point:

The process of expansion of the modern capitalist sector continues so long as the urban wage remains constant—in this case up to the point where O_ML₃ units of labour is employed in the urban sector and where the character of the economy changes in an unpredictable way.

From this stage of capitalist development, the wage rate in both the sectors start to move upward and a competitive parity is established at point H. Furthermore, at this point, the rural MP_L is equated to the urban wage. This is indeed the turning point in the Lewis model. From here onward, the economy begins to look like a developed economy, and the classical assumption of unlimited supply of labour is no longer valid.

Criticisms:

1. Irrational:

If the capitalists behave rationally, the whole process of capitalist develop­ment, as described by Lewis, suddenly comes to a dead end. This, however, violates the very spirit of the model, which is inherently classical in nature. If we take into consideration the objectives or motivations of economic agents, as Lewis did, we find that the model is neo- classically inclined.

2. Lack of Dynamism:

Lewis assumed that, in each time period, the capitalist takes opti­mum decisions regarding optimum usage of labour by equating the MP_L with the wage rate. So, from the Lewis model it is not possible to say how much the capitalist invests because it is an inter-temporal decision. Thus, the objective of profit-maximisation is well defined in a static context, but is quite ambiguous in Lewis’ dynamic model.

3. Single Good:

A really serious problem arises if we relax the assumption of a single good. If we assume, as Lewis does, that the industrial sector produces a good that is distinct from the product of the agricultural sector. In such a situation, we find a serious obstacle to growth due to deteriorating of the terms of trade against agriculture.

4. Reverse Migration:

If the two sectors produce the same good, there is no need to transfer workers to urban areas ‘by paying extra wages. It is more judicious to set up produc­tion units in rural areas and produce the commodity using cheap rural labour.

In this case, workers from urban areas may move to rural areas in search of jobs and that may depress rural wage further and make relocation of urban production units in rural areas more profit­able. This is the main idea behind setting up growth centres in backward areas of both devel­oped and developing countries.

Even the Harris-Todaro model did not consider this type of reverse migration:

Comments:

The Lewis type of dual economy model was at the centre of Early Development Econom­ics. It has considerable appeal because of its essentially optimistic vision of the develop­ment process. Earlier, many advanced countries had proceeded through such a process, and the latecomers to development might now begin to do the same.

The model would run its course to a happy end—provided no components were missing (such as a capitalist class or a market for the product of the capitalist sector), and no obstacles arose (such as premature rise in wages that cut into profits).

The employment or capital accumulation could also fit aptly with other elements of economic thinking about development, and with the practice of development planning. Moreover, promotion of the capitalist sector could be readily identified with the objective of industrialisation via import substitution. As a model of what might be, it was able to synthesise the most significant elements of develop­ment throughout the 1950s.

2. Harris-Todaro Model:

From the middle of the 1970s development was increasingly taking on the form of govern-mentality, with the international organisations and development states identifying absolute poverty as the target of interventions. In the same time a shift was observed also in the conceptualization of the dual economy.

John Harris and Michel. P. Todaro offered a description of the underdeveloped economy in the American Economic Review (1970) which was different from the dual economy of the Lewis model.

In addressing the question of rural-urban migration in Africa, they discovered a “curious economic phenomenon”- “despite the existence of positive marginal product in agriculture and significant levels of urban unemployment, rural-urban migration not only continues to exist, but indeed, appears to be accelerating”.

The Harris-Todaro Hypothesis:

To provide an analytical explanation of “curious eco­nomic phenomenon”, they considered rural-urban divide in which the “modern urban sec­tor” offers a politically determined wage that is substantially higher than what an indi­vidual would earn in the agricultural sector. The rural-urban wage differentials lure rural workers to migrate to the urban centres.

The urban job is limited. So most of the migrated workers fail to get an urban job and become unemployed. But they do not return to their native villages because they expect that they will get an urban job in the near future.

Their expected income is equal to higher urban wage times the probability of getting a modern sector job (which is less than unity). As long as this expected income is higher than the certain income in the rural sector, the rural-urban migration continue. Thus labour power remains un-utilised, causing a loss, in the sense of non_–realisation of potential output, to the economy as a whole.

Alternative Derivation of Harris-Todaro Model:

According to Harris-Todaro hypothesis, the answer to the curious phenomenon lies in the migrant leaving a secure rural wage w_r for a higher expected urban wage w^e_u even though the latter carried with it the possibility of urban unemployment. The expected wage is computed by using the rate of urban employment as an index for the probability of finding a job.

 

 

 

 

 

 

where w_u = urban wage,

L_u = Number of urban employed,

U = Number of urban unemployed,

λ. = The rate of urban unemployment. Thus Harris-Todaro hypothesis is precisely by the equilibrium condition

Once the Harris-Todaro equilibrium condition is embedded in a two-sector so called gen­eral equilibrium model, we obtain the Harris-Todaro Model.

The Observations of Harris-Todaro Model:

(i) Migration is stimulated primarily by rational economic considerations of relative benefits and costs, largely financial and partly psychological.

(ii) The decision to migrate depends on expected rather than the actual urban-rural real wage differentials where the expected differential is determined by the interaction of two vari­ables

(a) The actual urban rural wage differential; and

(b) The probability of successfully obtaining employment in the urban sector.

(iii) The probability of obtaining an urban job is directly related to the urban employment rate and is, thus, inversely related to the urban unemployment rate.

(iv) The rate of migration may exceed the rate of growth of urban job opportunities.

Kaushik Basu’s Formalization of the Harris-Todaro Model:

The Harris-Todaro model of rural-urban migration can be formalized in the following way:

Let us suppose the economy is divided into two sectors: rural and urban. Suppose there are N number of employable persons in the economy of which N_r are employed in the rural sector and N_u are employed in the urban sector.

N-N_r = Unemployed work force in the urban sector. Urban unemployment (u) = N-N_r-N_u

where N_u = employed work force in the urban sector.

Let w_r = wage rate in the rural sector.

w_u = wage rate in the urban sector.

From the assumption of the Harris-Todaro hypothesis, w_u > w_r. The motivational objective underlying the decision to migrate from rural to urban sector is the expectation of earning larger incomes in the urban sector compared to rural sector. The expected earnings in the rural sector = w_r x Probability of getting a job in the rural sector = w_r x 1. [because rural sector is in a state of full employment]

The expected earnings in the ueban sector = w. P_u

[P_u = probability of getting a job in the urban sector]

The probability of getting a job in urban sector may be represented by the rate of employment in the urban sector, i.e., N_u/(N -N_u).

The expected earning in the urban sector = w {N_u/(N-N_u)}.

As long as w {N_u/(N-N_u)} > w_r, the people will migrate from rural sector to urban sector. The process will continue until w {N_u/(N-N_u)} = w_r.

This is the equilibrium condition in the Harris-Todaro Model.

This condition can be written in the following way:

Hence, du/dN_u > 0 which means that an increase in urban employment will increase urban unemployment.

The Development of Harris-Todaro Model:

Harris-Todaro model introduces a further unknown, namely the equilibrium rate of unemploy­ment, and thus, in contrast to the standard two sector model, this model must be buttressed by a theory of urban wage determination.

The simplest selling is the one originally adopted by Harris-Todaro and subsequently by Bhagwati, Srinivasan (1973, 1974, 1977) and others. This work assumes the urban wage to be an endogenously given constant and typically rationalises it as a consequence of government fiat.

In the 1970s, several theories were proposed, foremost among these is the work of Joseph Stiglitz who provides a micro-foundation for the urban wage in terms of labour-turnover or in terms of biological efficiency considerations. One may also mention in this context the work of ealvo, who sees the equilibrium urban wage as an outcome of trade union behaviour.

Generalised Harris-Todaro Model:

In Khan (1980a), the elementary observation is made that all these variants of Harris-Todaro model could be studied under one riubric if the determination of urban wages is summed in a somewhat more abstract way i.e. w_α = Ω. (w_r, λ, R, π); where R is the rental on capital and x a shift parameter. This led to the so-called generalized Harris-Todaro Model (GHT).

Let the i-th sector produce a commodity i in amount x_i in accordance with a production function

X_i = F_i (L_i-, K_i) i = u, r … (4)

which is assumed to exhibit CRS and is twice continuously differentiate and concave The allocation of labour and capital, L, and K, is determined through marginal productivity pricing Thus, we have

The country is considered too small to influence the positive international prices of the two commodities P_u and P_r.

We rewrite the equilibrium condition (2) in a slightly more general form w_u = p w_r (1 + λ)… (7)

where p = shift parameter. Now equality (4), (5), (6) and (7), along with two material balance equations presented below, complete the specification of the model

K_r + K_U = K and L_r + L_u(l + λ) = L … (8)

The first point to be noticed about this model is a “decomposability property” whereby the factor prices, w_u, w_r and R and λ are independent of the endowments of labour and capital and depend solely on P_u, P_r and the shift parameters τ and p. This can be seen most easily if we subsume the marginal productivity conditions (5) and (6) into price equal unit cost equations

Pi = C_i (w_i, R); i = u, r … (9)

This allows one to decompose the model into a subsystem comprising equations (7) (9) and

w_u = w_r .

Conclusion:

We have confined our attention to the version with intersect orally mobile capital. In many ways, the case for sector-specific capital is more difficult and also more interesting. In addition even for the version that we have discussed, several substantive questions of interest have not been touched on.

These relate to gains from trade which now depend on the asymmetric nature of the model and as to whether the rural or urban commodity is being exported; to the possibility of educated unemployment as to the consequence of a distorted capital market; to the interaction of ethnic groups to the introduction of an informal sector to cost-benefit analysis. However, what we have hoped to show is that GHT model is a versatile and useful analyti­cal tool for a variety of questions arising in international and development economics.