Question

Suppose a firm is producing 3,000 units of output by hiring 25 workers ( w = $20/hour) and 10 units of capital ( r = $50/hour). It'sMP_L is 50 and MP_K is 30.

Is the firm minimizing the cost of producing 3,000 units of output?

	A.	No, the firm should use more of both labor and capital.
	B.	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.
	C.	No, the firm should use more capital and less labor.
	D.	No, the firm should use more labor and less capital.

Answer 1

According to cost minimizing condition a firm hires that amount of L and K such that :

MP_K/r = MP_L/w

where MP_K = Marginal product of capital, r = rent = MP_L= Marginal product of Labor and w = wage rate

So, When L(Labor) = 25 and K(Capital) = 10 units, then using above information we have :

MP_K/r = 30/50 = 0.6 and MP_L/w = 50/20 = 2.5

Thus we have MP_K/r < MP_L/w

So, currently he is not minimizing his cost.

According to diminishing marginal productivity, Marginal product of an input decreases as we hire more of an input.

So, In order to equalize, MP_K/r and MP_L/w, we have to increase MP_K and decrease MP_L.

As discussed above, MP_K will increase when K decreases and MP_L will decrease when L increases. So, in order to minimize cost he should use more Labor and Less capital.

Hence, the correct answer is (D) No, the firm should use more labor and less capital.