4. (8 points) Assume that a firm has the following production function: q = f(K,

Question

4. (8 points) Assume that a firm has the following production function: q = f(K,L). Further assume that the isoquants for this function are convex. The wage rate is $4/hour, and the rental rate is $6/hour. a. (4 pts) In the LR, the firm produces its output where the marginal product of labor is 8, and the marginal product of capital is 9. Is the firm producing its output in an economically efficient manner? Why or why not? b. (4 pts) Should the firm change its input mix? If so, should they use more L (and less K) or more K (and less L)?

Explanation / Answer

production function: q = f(K,L).

Wage W =$4/hour, and

The rental rate R= $6/hour.

MPL =8 , MPK =9

For an output to be efficient

W/MPL = R/MPK

W/MPL =4/8 =1/2 and R/MPK= 6/9 = 2/3

So, W/MPL < R/MPK

Hence  the firm producing its output in an economically efficient manner as it is not using and paying the labour and capital in the right ratio which minimizes the cost

2. Yes, the firm should change its input mix as the labour is cheaper relative o the capital , So they should use more L (and less K) .

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