Regulation

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Econ 6370 HW 9. Regulation - part 3

1. Assume a natural monopoly with total cost 500 + 20Q facing a demand of Q = 100 − P.

(a) Find the price that enables the monopolist to break even. Call this price P ∗.

(b) Loeb and Magat show that if the monopolist is allowed to choose its own price and to

have the regulatory agency subsidize the firm by an amount equal to consumer surplus

at the selected price, the monopoly will select price equal to marginal cost. What is the

price and amount of government subsidy?

(c) Loeb and Magat also note that a bidding process for the monopoly franchise would

enable the government to recover some of the subsidy. What is the amount recovered

and what is the net subsidy after bidding?

(d) An alternative proposal would make use of two-part tariffs. For example, assume that

the current regulated price is P ∗. Now assume that the regulatory agency offers the firm

the right to select any two-part tariff that it wishes as long as the consumer continues

to have the option of buying at P ∗. (For simplicity, assume a single consumer.) What is

the two-part tariff that the monopolist will choose, and what is its profit? What is the

deadweight loss?

(e) Assume that the government uses a bidding process to eliminate the monopoly profit in

part (d). The bid is in the form of a single price, like P ∗, that the consumer will always

have as an option to the two-part tariff. That is, the same rules are in effect as in part

d except that now the bidding is for the right to offer a two-part tariff optional to some

P ∗ that the bidding will determine. What is the low bid?

(f) Compare the Loeb and Magat proposal in part (c) with the proposal in part (e). Do

both proposals give efficient prices? Are there any substantive differences?

2. Consider the Edison Electric Company with a production function Q = K0.5L0.5, where Q is

output, K is capital, and L is 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

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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 monopoly 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.

3. In a certain city where all parking is controlled by the city, it is possible to provide parking

facilities in the downtown area at a constant marginal capital investment of $10,000 per space.

Costs of operation can be neglected. There are three equal periods during the day of eight

hours each, and spaces are rented only for complete eight-hour periods. During the peak

period of each of 250 days per year, the demand for parking is given by P = a − bQ, where P is the price per period for a parking space. During the other two off-peak periods of those

250 days, the spaces demanded are half that in the peak period, for each possible price. On

other days demand is zero. Assume that the interest rate is 10 percent and the facilities do

not depreciate.

(a) If a =$16, b =0.08, and existing spaces are 120, what would be the socially optimal

prices during the three periods?

(b) What is the optimal number of spaces, and what are the corresponding prices?

(c) This case is a so-called firm-peak case, with peak demanders paying all capital costs.

Now suppose that a =$5 and b =0.08. If peak demanders pay all capital costs, what

quantity is demanded by peak demanders? If off-peak demanders pay zero, what is their

quantity demanded? (Fractions of spaces are legitimate.)

(d) This is the shifting-peak case. For the demand curves in part (c), find the optimal

number of spaces and the corresponding prices.