In their original paper from 1970 Harris and Todaro intend to prove that rural-to-urban migration in the face of urban unemployment is a rational choice for
2.2. THE BASIC HARRIS TODARO MODEL 41
rural workers. In its most basic form it is a two sector, three factor model. The two sectors are the rural or agricultural sector and the urban or manufacturing sector. The rural sector is labour intensive and uses labour, capital and land as factor inputs in production. The manufacturing sector is capital intensive and produces its output using labour and capital only. Capital is sector specific, but it is fully utilised in production. The overall capital stock is assumed to be fixed.
Labour is free to move between the sectors and is not fully utilised.
As stated above, the most important distinction between the Harris Todaro model and other models of migration is the assumption of an institutionally fixed minimum wage in the urban manufacturing sector. It distorts the urban labour market and is the source of persistently high urban unemployment levels.
Rural-to-urban migration is modelled to take place due to the resulting wage differential between the rural and the urban sector. Therefore, migration will continue until wages are equalised between the two sectors. Note however, that rural migrants do not compare the two money wages. Rather the rural wage is compared with the urban expected wage. This is modelled as the minimum wage multiplied by the probability of finding employment in the urban sector. This probability depends on the urban unemployment rate. Therefore, rural-to-urban migration will continue as long as the expected urban real income is greater than the wage rate in the rural sector that equals the marginal product of agricultural labour.
Harris and Todaro assume a closed economy, so that all transactions take place between the urban and the rural sector. This implies that the agricultural and the manufacturing goods are traded only for each other. Consumers are assumed to have homothetic preferences. The price of the agricultural good, which has been defined in terms of the manufactured good, is directly determined by the relative quantities of the two goods produced. Producers are assumed to behave perfectly competitively in both sectors. Further, periodic random job selection is assumed to take place in the urban sector. This means that migrants are as likely to find employment in the urban sector as the permanent urban residents are in each time period.
For the ease of understanding, a summary of the notations used in the basic Harris Todaro model will be given here. It also includes those variables that are used in the extensions to the model, which follow below.
Note that A, M, F, and I stand for agriculture, manufacturing, formal and informal respectively. In what follows, all variables displayed as xf refer to foreign values. Those taking the form of x∗ show equilibrium values.
Table 2.1: Summary of Notations
CL search cost of finding formal sector employment Di demand for goods, wherei=A, M, F
ER total number of firms in the rural sector EU total number of firms in the urban sector G¯ other government expenditure
IM manufacturing segment of informal sector IS services segment of informal sector
j number of informal sector firms
Ki capital input in production ofXi, where i=A, M, F K¯i fixed capital input, where i=A, M
L¯ fixed total labour supply
Li labour input in production ofXi, wherei=A, M, F, I L¯R initial endowment of rural labour
LU total amount of labour in the urban area L¯U initial endowment of urban labour
LU N total amount of urban unemployment lm total amount of rural manual labourers
λ ratio of unemployed to urban employed (LU N/LF) µ urban employment ration (LI/LF)
N¯ fixed amount of land PC consumer price index
Pi price of good, where i=A, M, F, I
pL probability of finding urban sector employment RH total amount of rural hirers
r capital rental
Si subsidy, where i=U, R
T lump sum taxes
t tariff rate
W¯C fixed direct costs of urban unemployed
Wi wage rate paid in each sector, wherei=A, M, F, I W¯M minimum wage
Wue expected urban wage
Xi output, where i=A, M, F, I
ζ ratio of unemployed to urban formal labour (LU N/LF)
2.2. THE BASIC HARRIS TODARO MODEL 43
The formulation of the model used here is based on the model developed by Harris and Todaro in their paper published in 1970.
The agricultural and manufacturing production functions take the following form:
XA = fA(LA,N ,¯ K¯A), fA0 >0, fA00 <0 (2.1) XM = fM(LM,K¯M), fM0 >0, fM00 <0. (2.2)
Thus, agricultural production relies on three inputs: labour, land and capital.
Manufacturing production on the other hand uses only labour and capital. Xi
is the level of output of production, Li and ¯Ki are the amounts of labour and capital respectively needed to produce Xi, where i=A, M. Note that A and M denote the agricultural and manufacturing sectors respectively. ¯N is the amount of land used in the production ofXA. Additionally, fA0 andfM0 are the derivatives of fM and fM with respect to Li, where again i = A, M. Also, fA0 and fM0 give the competitive wage rates for agricultural and manufacturing production respectively, which equal the marginal products of labour. Note that the amount of labour, Li, is the only variable factor in the two production functions.
The terms of trade are expressed as the price of the agricultural good in terms of the manufactured good. Due to the assumption of homothetic preferences, the terms of trade can be expressed as a function of the relative outputs of the agricultural and the manufactured good.
P = PA
PM
=ρ
XM
XA
, ρ0 >0 (2.3)
P represents the terms of trade, and PA and PM are the price of the agricultural and the manufactured goods respectively.
The agricultural wage is at its market clearing level and equals the value of the marginal product of rural labour.
WA = P fA0 (2.4)
Urban producers are assumed to be profit maximisers in a perfectly competitive economy. Therefore, the manufacturing wage must equal the marginal product of labour in the urban sector. However, it is constrained to be at least as great
or greater than the institutionally fixed minimum wage. The latter is fixed in terms of the manufacturing good at the level ¯WM.19
WM = fM0 ≥W¯M
For simplicity it will be assumed that the marginal product of urban labour always exactly equals the fixed minimum wage, so that there is never excess demand for labour in the urban economy.
fM0 = W¯M (2.5)
It can be seen that the inequality in the previous equation simply has been turned into an equality.
The rural migrants, however, do not take the going urban wage rate, the mini-mum wage ¯WM, as the benchmark in their migration decision. They take account of the possibility of not finding urban employment and employ the concept of an expected wage. For this, potential migrants weigh ¯WM by the unemployment rate persisting in the urban area. Thus, the migration decision depends on the mini-mum wage multiplied by the probability of finding employment in the urban area.
This probability is represented byLM/LU, whereLU is the total amount of urban labour and equals NM plus the number of unemployed, LU N. This ratio gives the proportion of workers out of the total urban labour force actually employed in the urban area and is naturally less than one, if there is unemployment. Therefore the expected urban wage used by migrants in their decision making process equals
Wue = W¯MLM
LU
, LM
LU
≤1. (2.6)
Note that if there is no unemployment LM = LU and the expected wage equals the minimum wage, that is Wue = ¯WM.
Also note that Equation (2.6) is sometimes represented as follows:
Wue = ¯WM(1−λ). (2.6a)
Hereλrepresents the urban unemployment rate,LU N/LU, and (1−λ) =LM/LU.
19Note that fixing the minimum wage in terms of the agricultural good instead does not affect the principal conclusions of the analysis and only complicates the calculations.
2.2. THE BASIC HARRIS TODARO MODEL 45
The labour constraint ensures that the number of labourers employed in the agricultural sector, LA, plus the total number of urban inhabitants, LU, is equal to the initial endowment of labour that is assumed to be fixed.
LA+LU = ¯LR+ ¯LU = ¯L (2.7) L¯R and ¯LU are the initial endowments of labour in the rural and urban areas respectively, while ¯L represents the fixed total labour supply in the economy.
In equilibrium the agricultural wage and the urban expected wage are equalised, and rural-to-urban migration ceases.
WA = W¯M(1−λ) = Wue (2.8)
The above formulation gives eight equations and eight unknowns. Equation (2.1) to (2.8) can be used to solve for the agricultural output, XA, the manufacturing output,XM, the amount of labour employed in the production of the agricultural good, LA, the amount of labour needed to produce the manufactured good, LM, the agricultural wage, WA, the expected urban wage,Wue, the total urban labour force, LU, and the terms of trade, P. The amount of urban unemployment can be calculated by subtracting LM from LU, and its rate can then be established by dividing LU N byLU.
The mechanisms behind the model can be clarified by a diagram. Figure 2.1 shows the full employment and the Harris Todaro equilibria as developed by Corden and Findlay (1975, p.61). OA is the origin for labour employed in agriculture and the left-hand side vertical axis measures the agricultural wage, WA. Equivalently, OM is the origin of labour working in manufacturing, with the right-hand side vertical axis determining the wage rate in manufacturing.
The M M curve represents the value of the marginal product of labour in the manufacturing sector. AAis the equivalent locus for the agricultural production.
The two curves meet at at Z, the full employment equilibrium. All workers receive a uniform wage of WZ. The share OALZ works in agriculture, while the rest, OMLZ, are employed in manufacturing.
Remember that the wage rate in the manufacturing sector is institutionally set at WM. To find the equilibrium, the concept of the Harris Todaro curve is introduced. It is derived from the equilibrium condition, equation (2.8).
WALU = ¯WMLM (2.8a)
A A
WA
WM
WZ
W¯M
H
LZ LA LM
M
M
OA OM
q
q
R
x y
Z
Figure 2.1: Full Employment and Harris Todaro Equilibria Source: Corden and Findlay (1975), Figure 1, p.61
It is assumed that the wage rates in the two sectors equal the marginal product of labour in that sector. Together with the above condition, the rectangular hyperbola or Harris Todaro curve qq can be drawn with an elasticity of one. It gives the two points H and R that constitute the equilibrium. The wage rate in agriculture is lower than at the full employment equilibrium, so that WA < Wf. The shares of OMLM and OALA workers are employed in manufacturing and agriculture respectively. The share LALM of the labour force is unemployed.
Some policy suggestions to reduce urban unemployment have been made by Harris and Todaro. The consequences of wage subsidies can best be shown in graphical form. Figure 2.2 below is taken from Corden and Findlay (1975, Fig.7, p.71). First, the effects of a wage subsidy to the manufacturing sector will be looked at. A subsidy of the size H0Q increases employment in the manufacturing sector from LM to L0M. The manufacturing output is increased by the area L0MQHLM. This shifts the Harris Todaro curve from qq to q0q0. The AA-curve and the q0q0 now intersect at R0. Thus, employment in agriculture is reduced by LAL0A and the agricultural output is reduced by L0AR0RLA. To find out whether the overall output of the economy rises or falls, the loss in agricultural output, L0AR0RLA, and the gain in the manufacturing output, L0MQHLM, have to be compared. If the latter exceeds the former, the output across both sectors will increase. The level of unemployment may rise or fall, but the urban
2.2. THE BASIC HARRIS TODARO MODEL 47
Figure 2.2: Wage Subsidy to Manufacturing Source: Corden and Findlay (1975), Figure 7, p.71
unemployment ratio unambiguously falls.
A subsidy to the rural sector alone will always be welfare improving, as long as there is urban unemployment and as long as the minimum wage remains at its original level. If this is the case, the rural wage subsidy always lowers the wage differential between the sectors. There will be return migration to the countryside and urban unemployment will be reduced. Figure 2.2 can show that a subsidy of HN to all rural workers will bring the economy to full employment.
Rural employment rises to a level of OALM, while urban employment increases to OMLM,s and there is no unemployment.
However, neither of these policies will bring about the first best optimum, because marginal products are not equalised across the two sectors. This can only be achieved by a wage subsidy to the urban labour force coupled with migration restrictions on rural labour. Again, figure 2.2 can be used to show the effects of such a policy. To reach the full employment equilibrium Z, the wage subsidy must be equal to the difference between the minimum wage and the marginal productivity of labour, that isZ0Z. As the cost of labour to enterprises falls, the number of employment opportunities in the urban sector will increase.
Due to this and because the urban minimum wage will continue to exceed the real agricultural wage, rural-to-urban migration is still an attractive option for rural workers. In order to curb this flow of migrants, which exceeds the additional job opportunities available in the urban area, policy makers will have to restrict
migration. If such migrations restrictions can be implemented successfully, the economy will be in equilibrium at Z with full employment and equalised marginal products across sectors. However, this may prove an unpopular policy choice, especially in the rural sector, as it restricts the personal freedom of people.
Alternatively, policy makers could introduce a uniform wage subsidy to both sectors. Once the marginal product of labour has been equalised across sectors via rural-to-urban migration, the wage rates in the two sectors will be the same.
However, the minimum wage will be held at the level that the urban workers have been accustomed to. This equilibrium would also take place at point Z in figure 2.2. The urban and rural wage would be equalised at WM. Each employee in both industries would be subsidised at a rate of ZZ0. This policy choice may be politically preferable, because it does not reduce the income of the urban workers, while raising the income of rural labourers. However, subsidising the entire labour force is not an economically feasible option.20
If the minimum wage is institutionally set rather than the result of employment policies of individual companies, the government should consider lowering the minimum wage to make migration less attractive. Additionally, this would allow enterprises to run more efficiently. This again will have a positive effect on the welfare of the economy.21 However, this is only a feasible choice, if the institutionally fixed minimum wage can be lowered. If it is already at the lowest possible level, any reduction in the minimum wage could result in the exploitation of workers by their employers who will be paying them subsistence wages only. Also, potential social tension with a decrease in the minimum wage must be taken into consideration.
It now remains to evaluate the basic Harris Todaro model. Some of its shortcom-ings have already been mentioned in the literature review above. They include the simplifying assumptions. These must be relaxed in order to make the Harris Todaro model more realistic. However, there are additional disadvantages to the model that must be mentioned as well. First, the authors ignore all financial constraints when making their policy suggestions. Taxing workers and firms in order to finance subsidisation or other government policies distorts consumption and production patterns. This will have an effect on the efficiency of a wage subsidy to reduce unemployment and to confine rural-to-urban migration.
Second, transport costs and psychological costs related to moving are completely ignored in the basic model. Thus, migration is assumed to be costless. However, this is generally not the case. If the moving costs are too high, this can already act as a deterrent to migration. This implies that the policy suggestions of the basic Harris Todaro model only give an indication of how government policy packages should be designed.
20This will be proven in the next section with the help of a budget constraint.
21There will be a welfare analysis of policy options conducted in the next section.