Problem - Consider a firm that employs only capital (K) and labor (L). Output (Q) is determined by the following production function: Q = K^(1/2) L^(1/2)

Suppose the wage (W) for each worker is $8, the rental price (R) for each unit of capital is $2.

(a) With K = 4 fixed in the short run, derive the marginal product of labor (function). Is the marginal product of labor diminishing?

(b) With K = 4 fixed in the short run, derive the average product of labor (function). Is this an increasing or decreasing function?

(c) With K = 4 fixed in the short run, how much labor would this firm need to employ to produce Q = 200? How much will it cost to produce Q = 200 in the short run?

(d) What are the returns to scale for this production function? Suppose both K and L are flexible in the long run.

(e) In the long run, if the firm wishes to produce Q = 200, how many units of labor and capital should the firm employ to minimize its costs? How much will it cost to produce Q = 200?