regulation of a natural monopoly

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Econ 6370 HW 9. Regulation - part 1

1. Assume a natural monopoly with total costs C = 500+20Q. Market demand is Q = 100 −P.

(a) If a price is set at marginal cost, what is the monopolist’s output and profit? Compute

consumer surplus.

(b) Suppose the monopolist is a public enterprise who doesn’t seek profit maximization but

adopts average cost pricing to stay break-even. Find price, output, and the deadweight

loss.

(c) Consider two-part tariff. Each consumer must pay a fixed fee regardless of consumption

level plus a price per unit. Assume that the market consists of ten consumers with

identical demand curves for the product. If the price is set equal to marginal cost, what

is the largest fixed fee that a consumer would pay for the right to buy at that price?

What fixed fee would permit the monopolist to break even? What is the deadweight

loss in this case?

2. Assume the same facts as in question 1, but assume that there are six “rich” consumers with

each having inverse demands: p = 100 − 6.3q; also, there are four “pour” consumers, each with demands: p = 100 − 80q.

(a) What is the largest fixed fee that a poor consumer would pay for the right to buy at

marginal cost?

(b) Because the poor consumers would not be willing to pay the uniform fixed fee of $50

necessary for the monopolist to break even, the rich consumers would have to pay a fixed

fee of $83.33. What is the deadweight loss in this case?

(c) Third-degree price discrimination could be a solution. That is, if it is legal, resales are

not feasible, and consumers could be identified by the monopolist as being rich or poor,

the monopolist could charge different fixed fees to the two consumer types. If the price

per unit is still equal to marginal cost, what are two fixed fees that are feasible? In this

case, what is the deadweight loss?