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Rural Urban Migration: The Harris Todaro
Model
In many developing countries, the wage in the city, even adjusted for cost of
living, can greatly exceed wages in rural areas. However, workers who migrate
to the city are not employed for sure as there are fewer jobs than applicants for
them. Why then does the wage in the city not fall? The reason assumed is that
there is a labor union which sets wages at a higher than market clearing level.
What is the effect of such a distortion? We show that it puts the economy
inside its production possibility frontier (PPF) as people migrate to the city
but as not all get jobs, there is unemployment which put the economy inside its
PPF. We also look at the effects of various policies to deal with the distortion
as well as the optimal policy. Since the distortion is a factor market one, the
principle of targeting implies that the optimal policy will be one that deals
with the distortion at the source, i.e. a factor market policy that corrects the
distortion at the source.
In what follows, we use the speciÞc factor model. Let L̄ be the total number of workers available and LR and LM be the labor in the rural and manufacturing sectors respectively. The production function in the manufacturing
sector uses labor and capital, K, to make manufactures, and is given by X M =
F M (K, LM ) while the production function in the rural sector uses land and labor
to make food and is given by X R = F R (T, LR ). Let FLM (K, LM ) and FLR (T, LR )
denote the marginal physical product of labor, and let P M FLM (K, LM ) and
P R FLR (T, LR ) denote the marginal value product of labor in the manufacturing and rural sectors respectively. Setting the marginal value product of labor
(MVPL) equal to the wage deÞnes factor demand: for any given wage, the point
on the MVPL curve gives the labor demanded at that wage. The Þrm increases
proÞts by increasing its labor use till this point as MVPL exceeds the cost of the
labor, the wage, and decreases it beyond this point as the MVPL is less than
the cost of labor there. Thus, in the speciÞc factors box (depicted in Figure 1)
equilibrium in the absence of any distortions would be where the two MVPL’s
intersect at A and the wage in both industries be w∗ . There would be 0M LM
workers employed in manufacturing and 0R LM ≡ L̄ − LM workers employed in
the rural sector.
Let w̄ be the urban wage Þxed by the union. It is above the market clearing
wage so that at this wage in both sectors there would be excess supply of labor.
If we could restrict migration, then we could segment markets and maintain a
wage differential between sector. The wage in the rural sector would be w̄R , (at
C) at which point all remaining labor is absorbed into the rural sector, albeit
at a low wage.
Given that we cannot restrict migration, what can will happen? Once possibility, is that jobs are rationed in the high wage sector. All job seekers have an
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Figure 1: Labor Market Equilibrium
wage 6
wage
6
w̄
A
w∗
wR
B
w
¯
0M
C
L̄M
LR LM
0R
equal chance of getting a job. At w̄ there are L̄M jobs in manufacturing. That
is,
(1)
P M FLM (K, L̄M ) = w̄.
Also, in the rural sector, if the wage is wR ,them LR workers will be employed
there where
(2)
wR = P R FLR (K, LR ).
If LR workers are employed in the rural sector at a wage wR and the remainder,
L̄ − LR , are looking for a job in the manufacturing sector, then the chance
L̄M
. In the absence of a job, assume they get nothing. In
of getting a job is L̄−L
R
equilibrium, workers are indifferent between sectors, that is, between a low wage
of wR and a chance at the high wage w̄. That is,
µ
¶
L̄M
R
w =
w̄.
(3)
L̄ − LR
Thus, we have three unknowns, L̄M , LR , wR and three equations. Solving
them to get the unknowns is easy. Equation (1) gives L̄.Since we know L̄M ,
equation (3) and equation (2) are then two equations in two unknowns and can
be solved to give wR and LR .
The solution can also be depicted in Figure 1. Rewriting equation (3) as
¡
¢
wR L̄ − LR = L̄M w̄
reveals that with OM as the origin, the product of the X and Y coordinates
must be a constant and equal to L̄M w̄. Hence¡ equation
¢ (3) can be depicted
as a rectangular hyperbola through the point L̄M , w̄ . The intersection the
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Figure 2: The PPF
M
P
XR @
@
@
C @
@
•
@
@
@•
@ A
•
@
B@
@
@
@
@
@
@
@
@
@
@
@
@
@
0
XM
curve representing ¡the MVPL
¢ in the rural sector and the rectangular hyperbola
through the point L̄M , w̄ occurs at B which is therefore the equilibrium. In
equilibrium, LR people work in the rural sector at a wage wR and the remainder,
L̄ − LR ,look for work in manufacturing. Of these, only L̄M Þnd work and the
remainder, represented by the distance L̄M − LR , are unemployed.
What do the points A and B correspond to in terms of the PPF for the
economy depicted in Figure 2? The point A in Figure 1 corresponds to the
point A on the PPF where the value of output is maximized for the given price
ratio. The point B corresponds to the equilibrium output with a Þxed wage w̄
in manufacturing, resulting in migration and unemployment. At B, labor used
in manufacturing is lower and labor used in the rural sector is higher that at A
as depicted in Figure 1.Hence, output in manufacturing is lower and output in
the rural sector is higher at B that at A as depicted in Figure 2. Recall that
the point C corresponds to the equilibrium where migration is prohibited but
there is a union set wage at w̄ in manufacturing. At C, labor used and output
in manufacturing is the same as at B but as there is no unemployment we are
on the PPF so that output of the rural sector is higher at C than B as drawn
in Figure 2.
To verify that you understand these pictures, ask yourself if it is possible
for B to lie below A in both its coordinates. Show that if the MVPL curve in
manufactures is very inelastic so that it is steeper than the rectangular hyperbola
at the point (L̄M , w̄) then this is indeed the case.
Now we ask what the effects of various policies might be in such an economy,
and what optimal policy is. An optimum policy would move the economy from
B to C.
A Þrst cut might be to say that there is too little of XM made so that a
subsidy on the production of XM might be a good idea. This will shift out the
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Figure 3: Production Subsidy to Manufacturing
wage 6
wage
6
D
w̄
A
w∗
wR
B
w
¯
0M
C
L̄M
LR LM
0R
MV P L in manufactures. It is easy to verify that there is no way to get output
to be that at A. If the subsidy is such that the rectangular hyperbola through
the new employment level in manufacturing, L0M and w̄ goes through A then
there is unemployment so we remain inside the PPF. If the subsidy is so large
that the MVPL in manufacturing goes through the MVPL in the rural sector at
a wage of w̄ then there is no unemployment but we are making too much XM
relative to A.
Next consider a subsidy to labor in manufacturing alone. This will shift
out the MV P L in manufactures by the amount of the subsidy. It is easy to
verify again that there is no way to get output to be that at A. If the subsidy
is such that the rectangular hyperbola through the new employment level in
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manufacturing, LM and w̄ goes through A then there is unemployment so we
remain inside the PPF. If the subsidy is so large that the MVPL in manufacturing goes through the MVPL in the rural sector at a wage of w̄ then there is
no unemployment but we are making too much XM relative to A.
Finally consider the effect of a uniform subsidy to labor in both sectors of
the distance AD in Figure 3,or larger. Such subsidies are large enough to make
the equilibrium wage w̄ as depicted in Figure 3.
This illustrates the principle of targeting. The idea is to Þx things where
they are broken, Here the distortion is a labor market one so a labor market
subsidy was needed, not a product market one. Recall, no production subsidy
could do the trick. This is a very general idea which we will see again.
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