Question

Edison is a utility company. Edison uses both labors, L and capital, K to produce electricity. The production function of Edison’s is given by Q = L^0.25K^0.75 where Q is measured in millions of kilowatts per hour. The price of a unit of Lis $27per hour and the price of a unit of Kis $1 per hour. Edison’s has additional fixed costs of $544per hour. For parts (a)-(b) assume that Edisonmay chooses any amount of L and K.

a) What is Edison’s (compensated) demand curve for labor? What is the (compensated) demand for capital? What is the variable cost curve? What is the total cost curve?

b) What is Edison’s marginal cost curve? What is the average cost curve? For what values of Q, does Edison have scale economies?

For parts (c) –(d) below assume that the amount of K is fixed in the short run at K = 81This results in additional fixed costs in the short run of $81(ie in addition to the 544).

c) In the short run, what is Edison’s (compensated) demand curve for labor? What is the variable cost curve? What is the total cost curve?

d) In the short run, what is the marginal cost curve of Edison’s Inc? What is the average cost curve? What is the optimal size of the firm? Let’s compare the average cost curves in the short and long runs. You may assume that at every quantity the long-run average cost is less than or equal to the short-run average cost.

e) At what quantity is the demand for K equal to 81? What must be true about the short and long-run average costs at this quantity? Verify your answer using your average cost curves.f)Illustrate the long run and short-run average cost curves. Be sure to indicate where the curves meet and the optimal scale of the short-run average cost curve.

Answer 1

Part (A)

Part (B)

for output levels less than the minimum efficient scale (that is point where MC=AC), economies of scale exist

Part (C)

now capital is fixed at 81 units

Part (D)

Part (E)

we need to find level of output at which 81 units of capital is used

using cost minimizing condition, we know that