Suppose a firm is producing 2,475 units of output by hiring 50 workers (W = $20 per hour) and 25 units of capital (R = $10 per hour). The marginal product of labor and marginal product of capital are 40 and 25, respectively. Is the firm minimizing the cost of producing 2,475 units of output?
A) Yes, the ratio of the number of workers to the wage equals the ratio of the number of units of capital to the rental rate.
B) No, the firm should use more labor and less capital.
C) No, the firm should use more capital and less labor.
D) No, the firm should use more of both labor and capital.

Question

Quizplus · Accepted Answer

To minimize costs while producing a certain output, a firm should equate the ratio of the marginal product of labor (MPL) to the wage (W) with the ratio of the marginal product of capital (MPK) to the rental rate of capital (R). Here, MPL/W = 40/20 = 2 and MPK/R = 25/10 = 2.5. Since the MPK/R is higher, the firm should use more capital and less labor to minimize costs, as it gets more output per dollar spent on capital than on labor.

Suppose a Firm Is Producing 2,475 Units of Output by Hiring