Suppose a firm that uses labor and capital as the only inputs in production is currently on the long-run expansion path.The marginal product of labor and capital at this least cost combination are 60 units and 80 units respectively and the wage rate of labor is $6.Calculate the rental cost of capital borne by the firm.
A)$10
B)$8
C)$5
D)$12

Question

Quizplus · Accepted Answer

The firm is on the long-run expansion path, which means it is producing at the minimum cost for a given level of output. The firm's least-cost combination of inputs occurs where the marginal product of labor divided by the wage rate equals the marginal product of capital divided by the rental rate.

In this case, the marginal product of labor is 60 and the wage rate is $6, so the marginal product of labor per dollar is 10 (60/6). The marginal product of capital is 80, but we don't know the rental rate, denoted by r.

Therefore, we have:

10 = 80/r

Solving for r, we get r = $8. Therefore, the rental cost of capital that the firm is bearing is $8.

Hence, the answer is B) $8.

Suppose a Firm That Uses Labor and Capital as the Only