4. The very small economy of Cantabrigia has a total labor force of 20 workers. These workers can produce two goods, manufactures and food. In production of manufactures, the marginal product of labor depends on employment as follows:

Number of workers 1

2 3

4 5

6 7

8 9

10 Marginal product of last worker 20 18 16 14 12 11 10 9

8 7

In the food sector the marginal product of labor is independent of employment, and is 9. The world price of a unit of manufactures is $10, so is the world price of a unit of food.

a. Suppose there were no distortion in the labor market; find the wage rate, the allocation of labor between manufactures and food, and the output of each good.

b. Now suppose that for some reason the minimum wage in the manufactures sector is $ 150. Full employment, however, is maintained. Find the output of the economy in this case. How large is the cost of the distortion?

c. Finally, suppose that workers migrate from the country to the city until the wage of city workers multiplied by the probability of being employed equals the rural wage. Find the level of output and unemployment.