A mutual monopoly faces the following demand curve: P = 100 - 3Q The natural mon

Question

A mutual monopoly faces the following demand curve: P = 100 - 3Q
The natural monopolist has a constant marginal cost of $4 and a fixed cost of $621. 3. A natural monopoly faces the following demand curve: P=100-3Q The natural monopolist has a constant marginal cost of $4 and a fixed cost of $621. (a) Find the market equilibrium price, quantity and profits. (b) Now the Public Utilities Commission (PUC) decides to regulate the natural mo- nopolist. The PUCs initial objective is to maximize the market quantity without considering the natural monopolist's profits. What price does the PUC set for the market, and what is the corresponding quantity and firm profit? (c) Now the PUC wants to maximize the market quantity and considers the natural monopolist's profits when making regulatory decisions. What rate should the PUC set for the market, and what is the market quantity and firm profit corresponding to this rate?

Explanation / Answer

(a) P = 100 - 3Q

MR = 100 - 6Q

MR = MC

100 - 6Q = 4

or, Q = 16

P = 52

Profit = Q(100 - 3Q) - (621 + 4Q) = 147

(b) P = MC = 4

Q = 32

Profit = Q(100 - 3Q) - (621 + 4Q) = - 621 (loss)

(c) P = ATC

or, 100 - 3Q = (621 - 4Q)/Q

or, Q = 23, 9

As PUC wants to maximise quantity, we take Q = 23

P = 31

Profit = Q(100 - 3Q) - (621 + 4Q) = 0

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