尼克尔森中级微观经济学第九版答案ch13

CHAPTER 13

MONOPOLY

The problems in this chapter deal primarily with marginal revenue-marginal cost calculations in different contexts. For such problems, students’ primary difficulty is to remember that the marginal revenue concept requires differentiation with respect to quantity. Often students choose to differentiate total revenue with respect to price and then get very confused on how to set this equal to marginal cost. Of course, it is possible to phrase the monopolist’s problem as one of choosing a profit-maximizing price, but then the inverse demand function must be used to derive a marginal cost expression. The other principal focus of some of the problems in this chapter is consumer’s surplus. Because the computations usually involve linear deman d curves, they are quite straightforward.

Comments on Problems

13.1 A simple marginal revenue–marginal cost and consumer surplus computation.

13.2 An example of the MR = MC calculation with three different types of cost curves.

13.3 An example of the MR = MC calculation with three different demand and marginal

revenue curves. Illustrates the “inverse elasticity” rule.

13.4 Examines graphically the various possible ways in which shift in demand may affect the

market equilibrium in a monopoly.

13.5 Introduces advertising expenditures as a choice variable for a monopoly. The problem

also asks the student to view market price as the decision variable for the monopoly. 13.6 This problem examines taxation of monopoly output. It shows that some results from

competitive tax-incidence theory do not carry over.

13.7 A price discrimination example in which markets are separated by transport costs. The

problem shows how the price differential is constrained by the extent of those costs. Part

d asks students to consider a simpl

e two-part tariff.

13.8 A marginal revenue-marginal cost computation for the case in which monopolist’s costs

exceed those of a perfect competitor. The problem suggests that the social losses from

such increased costs may be of the same order of magnitude as the deadweight loss from monopolization.

13.9 This problem examines some issues in the design of subsidies for a monopoly.

13.10 A problem involving quality choice. Shows that in this case, monopolist’s and

competitive choices are the same (though output levels differ).

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Chapter 13/Monopoly 65

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Solutions

13.1 a. P = 53 – Q PQ = 53Q –Q 2 MR = 53 – 2Q = MC = 5

Q = 24, P = 29, π = (P – AC) ⋅ Q = 576

b. MC = P = 5 P = 5, Q = 48

c. Competitive Consumers' Surplus = 2(48)2 = 1152.

Under monopoly:

Notice that the sum of consumer surplus, profits, and deadweight loss under monopoly equals competitive consumer surplus.

13.2 Market demand Q = 70 –P , MR = 70 –2Q . a. AC = MC = 6. To maximize profits set MC = MR. 6 = 70 – 2Q Q = 32 P = 38

π = (P – AC) ⋅ Q = (38 –6) 32 = 1024

b. C = .25Q 2 – 5Q + 300, MC = .5Q – 5. Set MC = MR .5Q – 5 = 70 – 2Q Q = 30 P = 40 π = TR – TC = (30)(40) – [.25(30)2 –5 (30) + 300] = 825.

c. C = .0133Q 3 – 5Q + 250. MC = .04Q 2 – 5

MC = MR

Therefore: 04Q 2 – 5 = 70 –2Q or .04Q 2 + 2Q – 75=0.

Quadratic formula gives Q = 25. If Q = 25, P = 45 R = 1125

C = 332.8 (MC = 20) π = 792.2