Question

Suppose the hourly wage is $20 and the price of each unit of capital is $50. The price of output is constant $80 per unit. The production function is f(E,K)= 1/2K1/2 so that the marginal product of labor is MPE=(1/2)(K/E)1/2. The current capital stock is fixed at 10 units. How much labor should the firm employ in the short run? a. b. How much profit will the firm earn?

Answer 1

The value of the marginal product (VMP) can be calculated by multiplying the marginal product of labor (MPL) by the price of output. We can find the profit-maximizing level of employment by comparing the market wage with the MPE.

Step-by-step explanation:

The value of the marginal product (VMP) is calculated by multiplying the marginal product of labor (MPL) by the price of output. In this case, the production function is given as f(E,K)= 1/2K1/2. So, the MPL can be calculated as MPE=(1/2)(K/E)1/2.

To find the value of the marginal product at each level of labor, we can substitute the given values. For example, if the current capital stock is fixed at 10 units, we can calculate MPE for different levels of labor, such as 50 units, 20 units, and 10 units.

To find the profit-maximizing level of employment, we need to compare the market wage with the MPE. If the going market wage is $12, the firm will hire workers up to the point where the market wage equals the MPE. So, the profit-maximizing level of employment can be determined by finding the level of labor where the MPE is equal to $12.