Question

Consider the production function: Y = AK^1/3L^2/3 . Y is output, K is capital, and L is labor.

The marginal product of labor is: 2/3A(K/L)1/3 The marginal product of capital is: 1/3A(L/K)2/3

a) Explain how a tax cut on capital promoting capital accumulation can benefit workers.

b) Labor unions have often opposed immigration. Using the above equations, explain why.

c) Why is productivity growth so important in raising living standards across the population?

Answer 1

We have the following information

Marginal product of labor = 2/3(A(K/L)^1/3)

Marginal product of capital = 1/3(A(L/K)^2/3)

Part a) Tax cut on capital will make capital relatively cheaper, and thus firms can use greater amount of capital with labor. As the marginal product of labor shows, increase in the amount of capital results in increase in the marginal product of labor. Since, the wage that is paid to the labor depends on its marginal product, so increase in capital will raise the marginal product of labor.

Part b) The reason why labor unions oppose immigration is that it causes the supply of labor to increase. As can be seen from the marginal product function of labor, as the amount of labor increases, the marginal product declines. ince, the wage that is paid to the labor depends on its marginal product, so increase in immigration will result in lower wages.

Part c) Reason why productivity growth is important in raising living standards across the population, is that productivity increase raises the marginal product of both labor and capital for a given amount of labor and capital. The productivity factor is A in the marginal product functions.