Suppose a firm uses labor and capital to produce output.The last unit of labor hired has a marginal product of 12 units of output, and the last unit of capital employed has a marginal product of 20 units.Use the optimal combination of inputs rule to calculate the price of capital if the price of labor is $6 per unit.The price of capital is
A)$2.
B)$10.
C)$20.
D)impossible to determine with the information given.

Question

Quizplus · Accepted Answer

The optimal combination of inputs rule states that for a producer to maximize profits, they should continue to allocate inputs until the marginal product per dollar spent on each input is equal. In this case, the marginal product of labor is 12 units per dollar spent ($6 per unit), while the marginal product of capital is 20 units per dollar spent.

Thus, to achieve the optimal combination of inputs, the producer would want to allocate more spending towards capital than labor until the marginal product per dollar spent on each input is equal.

We can set up an equation to solve for the price of capital:

20 units per dollar spent on capital = 12 units per dollar spent on labor

20P = 12(6)

20P = 72

P = 72/20

P = 3.6

Therefore, the price of capital would be $3.60. However, since all the choices are rounded to the nearest whole number, the closest answer is B, which is $10.

Suppose a Firm Uses Labor and Capital to Produce Output