Output for a simple production process is given by Q = KL, where K denotes capital and L denotes labor. The price of labor is $10 per unit and the price of capital is $2 per unit. Suppose at the current level of production the firm is minimizing costs and the marginal product of labor is 10. Given this you know that the marginal product of capital must be

Question

Quizplus · Accepted Answer

Since the firm is minimizing costs at the current level of production, it must be maximizing the productivity of each input, i.e. labor and capital. Marginal product (MP) of labor is given as 10, so the cost of the last unit of labor hired is equal to its marginal product, i.e. $10. For capital, the cost of the last unit of capital used is also equal to its marginal product. We know that the price of capital is $2 per unit, so its marginal product must be $2 per unit as well.

Using the production function Q = KL, we can also find the relationship between MP of labor and MP of capital:
MP of L / MP of K = w/r
where w denotes the price of labor and r denotes the price of capital. Plugging in the given values, we get:
10 / MP of K = 10/2
Simplifying, we get:
MP of K = 2

Therefore, the marginal product of capital must be 2, and the answer is B.

Output for a Simple Production Process Is Given by Q