Question

4. A company produces economic analysis reports using hours of labor (L) and computers (K). The production function is ? = 2?√? Initially, in the short run, they have just 1 computer (K = 1). The wage is $20 per hour, and the cost of capital is $10.

a. Derive short run total cost and short run average costs curves, with costs as a function of q. Do these costs curves exhibit economies or diseconomies of scale? Explain. (5)

b. The marginal cost curve is MC=10q. Assuming the market is perfectly competitive, and that the current price is $100 per report, what is the profit maximizing level of q for this firm, and how many hours of labor are used? (4)

c. Suppose that the wage falls to $10, but that we are still operating in the firm-level short run, so K is unchanged. What are the new total cost and average cost functions? (5)

d. After the wage falls, the new marginal cost function is MC=5q. If price is still $100, what are the new, profit maximizing levels of q and L? (4)

e. How do you expect the combination of K and L used to produce output might change in the (firm-level) long run, as the firm adjusts choices of inputs in response to the wage decline described in part (c)? (4)

Answer 1

q = 2KL^1/2

(a)

When K = 1,

q = 2L^1/2

L1/2 = q/2

L = q² / 4

Total cost (TC) = wL + rK

TC = 20 x (q² / 4) + 10 x 1

TC = 5q² + 10

AC = TC/q = 5q + (10/q)

Shape of LC curve implies that initially AC decreases with increase in q (exhibiting economies of scale) and then AC increases with increase in q (exhibiting diseconomies of scale).

(b)

Setting Price = MC,

10q = 100

q = 10

L = (10 x 10)/4 = 25

(c)

New TC = 10 x (q² / 4) + 10 x 1

TC = 2.5q² + 10

AC = TC/q = 5q + (10/q)

(d)

Setting P = new MC,

5q = 100

q = 20

L = (20 x 20)/4 = 100

NOTE: As HOMEWORKLIB's Answering Policy, 1st 4 parts have been answered.