A firm employs 100 workers at a wage rate of $10 per hour, and 50 units of capital at a rate of $21 per hour. The marginal product of labor is 3, and the marginal product of capital is 5. The firm:
A) is producing its current output level at the minimum cost.
B) could reduce the cost of producing its current output level by employing more capital and less labor.
C) could reduce the cost of producing its current output level by employing more labor and less capital.
D) could increase its output at no extra cost by employing more capital and less labor.
E) Both B and D are true.

Question

Quizplus · Accepted Answer

To minimize cost, the firm should use the inputs in a way that the marginal product per dollar spent on each input is equal. In this case,

MPL = 3 and wage rate = $10 per hour
MPPK = 5 and capital rate = $21 per hour

So, for labor, the marginal product per dollar spent is 3/10 = 0.3 and for capital, the marginal product per dollar spent is 5/21 = 0.24.

Since the marginal product per dollar spent on labor is higher than that of capital, the firm should use more labor and less capital to minimize its cost of producing the given output level. Therefore, the correct answer is C.

A Firm Employs 100 Workers at a Wage Rate of $10