Consider the Edison Electric Company with a production function Q = K.5, where Q is output, K is capital, and Lis labor. The market rental rate of...

3. 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 hasset the allowed rental rate at $0.80. (Rental rates of capital are in dollars per unit of capital per year. With zerodepreciation they are related to percentage costs of capital in the following way. Suppose that the utility mustinvest in a generator at a cost of $5 per kilowatt of capacity, and 10 percent is its cost of capital; then the rentalrate per year is 10 percent of the $5 per unit, or $0.50. Similarly, the percentage allowed rate of return would be 16percent since 16 percent of $5 is $0.80. Rental rates are therefore comparable to wage rates and other factor costsin 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 wereunregulated, it would produce efficiently at a constant average and marginal cost of $1. However, because ofAverch-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 thoughimperfect because of Averch-Johnson effects, nevertheless result in an improvement over an unregulatedmonopoly 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 comparedto the efficient solution.d. Assume now that the utility commission decides to lower the allowed rental rate from $0.80 closer to themarket rate of $0.50. Assume that it picks $0.58. It can be shown that Edison will now choose to sell 0.67 unitsat a price of $1.15. Its average cost of production rises to $1.04. Compare this Averch-Johnson equilibrium withthe earlier one in terms of total economic surplus. This, in fact, is the socially optimal allowed rental rate. Lowerrates actually reduce total surplus. For further details, see A. Klevorick, "The Optimal Fair Rate of Return," BellJournal of Economics and Management Science, Spring 1971.