Answer to Question #88196 in Economics for BJ

Question

1. The Harris-Todaro Model.
Consider an economy with two sectors, manufacturing and agriculture, and 100 workers. The marginal product of labor in manufacturing is given by MPLM = 800 – 10M, and marginal product of labor in agriculture is given by MPLA = 400 – 2A, where M is the number of workers in manufacturing and A is the number of workers in agriculture.
The optimal allocation of labor between the two sectors is achieved when the marginal product of labor is equalized across sectors, which is also where the curves intersect.

a. What is the optimal number of workers in the manufacturing sector (M)? What is the optimal number of workers in the agricultural sector (A)?

b. Now suppose that the government sets a minimum wage of $400 in the manufacturing sector. How many workers will be employed in the manufacturing sector at the minimum wage? Assume that workers are paid their marginal product (WM = MPLM).

Answer 1

a. In equilibrium MPLM = MPLA, so:

800 - 10M = 400 - 2A,

A = 5M - 200,

M + A = 100, then M + 5M - 200 = 100,

M = 50, A = 100 - 50 = 50.

b. If WM = MPLM = 400, then:

800 - 10M = 400,

M = 40.