Consider the Edison Electric Company with a production function Q = K.5L.5, where Q is output, K is capital, and Lis labor. The market rental rate of capital is $0.50 and the wage rate is $0.50 also. The utility commission has set the allowed rental rate at $0.80. (Rental rates of capital are in dollars per unit of capital per year. With zero depreciation they are related to percentage costs of capital in the following way. Suppose that the utility must invest in a generator at a cost of $5 per kilowatt of capacity, and 10 percent is its cost of capital; then the rental rate per year is 10 percent of the $5 per unit, or $0.50. Similarly, the percentage allowed rate of return would be 16 percent since 16 percent of $5 is $0.80. Rental rates are therefore comparable to wage rates and other factor costs in applying standard static production theory.)
Edison faces a demand curve with the constant elasticity of demand 2.857, or Q = P-2.857. If Edison were unregulated, it would produce efficiently at a constant average and marginal cost of $1. However, because of Averch-Johnson effects, it uses too much capital under regulation and produces at an average cost of $1.01. Edison charges a price of $1.35 and sells Q = 0.42.
a. Find the price and quantity if Edison were an unregulated monopoly. Hint: Marginal revenue is P(1 -1/2.857).
b. Find the sum of consumer and producer surplus for the case where Edison is regulated and where it is not. Hint: Using calculus, it can be shown that consumer surplus is (0.54)Q0.65. Does regulation, even though imperfect because of Averch-Johnson effects, nevertheless result in an improvement over an unregulated onopoly case?
c. Of course, the first-best case of price-equal marginal cost and efficient production is superior to regulation. Find the efficient solution. Draw a figure that shows the two types of losses that regulation causes as compared to the efficient solution.
d. Assume now that the utility commission decides to lower the allowed rental rate from $0.80 closer to the market rate of $0.50. Assume that it picks $0.58. It can be shown that Edison will now choose to sell 0.67 units at a price of $1.15. Its average cost of production rises to $1.04. Compare this Averch-Johnson equilibrium with the earlier one in terms of total economic surplus. This, in fact, is the socially optimal allowed rental rate. Lower rates actually reduce total surplus.