The Harris-Todaro model
This note is intended as a note to give a brief review of the Harris-Todaro model and present graphs that are easier to read than those presented at the blackboard.
The basic ingredients are two sectors, Modern and Agricultural, where there is declining marginal productivity in both sectors. Hence the higher the wage is, the lower is the demand for workers in both sectors.
Total labour force is L, and it does not depend on the wage. There are LA workers in agriculture, LM workers in the modern sector, and the remaining LU are unemployed.
Consider first the case where wages are flexible in both sectors. Then we get equal wages in agriculture and the modern sector and no unemployment. The situation can be depicted in the bath tub diagram below, where AA is demand for labour in agriculture and MM demand for labour in the modern sector:
In the Harrris-Todaro model, the wage in the modern sector is for some reason stuck at a level W, which is above the level that would clear the labour market. If we say that unemployed have a wage of zero, the expected income in the city is (LM/LM+LU)*W. As LM is determined from W, the only thing that can vary here is LU, and we see that the expected income in the city is declining in LU. This can be shown in the following graph, where qq is the expected income in the city:
A new equilibrium is reached when the expected income in the city is equal to the income in the countryside, which in the graph is where the qq curve and the AA curve cross. From these two curves, we get the wage in agriculture wA and the employment level in agriculture LA. As we know LM and LA, we can also find the number of unemployed as the remaining workers.
The next step is to try to study the effect of different policies. Here I will only look at a policy that is intended to raise employment in the city by shifting the MM-curve up so the modern sector hires more people at any wage. The wage is still stuck at W.
Here labour demand shifts from MM to M’M’ and expected income changes from qq to q’q’. This will always increase employment in the modern sector LM and reduce employment in the agricultural sector LA. The effect on unemployment is uncertain, the way the figure is drawn, the number of unemployed increases.
However, the share of the urban population that is unemployed must decrease. To see this, notice that agricultural employment decreases, so agricultural wages increase. Then the expected income in the city must also increase. As W is fixed, the only way this can happen is if LM/LM+LU increases, which means that a smaller fraction of city residents are unemployed.
Exercises:
1. Redraw the figure above so unemployment LU declines
2. What will the qq curve look like if instead of being unemployed, those who cannot get a job in the modern sector gets a wage wU<wM in the urban informal sector?