the amount of entry or exit a given industry experiences?
23.5. The pro?ts or losses of the ?rms that are currently operating in the industry.
6. The model of entry presented in this chapter implies that the more ?rms in a given industry, the (steeper, ?atter) is the long-run industry supply curve. 23.6. Flatter.
7. A New York City cab operator appears to be making positive pro?ts in the long run after carefully accounting for the operating and labor costs. Does this violate the competitive model? Why or why not? 23.7. No, it does not violate the model. In accounting for the costs we failed to value the rent on the license.
24 Monopoly
1. The market demand curve for heroin is said to be highly inelastic. Heroin supply is also said to be monopolized by the Ma?a, which we assume to be interested in maximizing pro?ts. Are these two statements consistent?
24.1. No. A pro?t-maximizing monopolist would never operate where the demand for its product was inelastic.
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2. The monopolist faces a demand curve given by D(p) = 100?2p. Its cost function is c(y)=2 y. What is its optimal level of output and price? 24.2. First solve for the inverse demand curve to get p(y) = 50? y/2. Thus the marginal revenue is given by MR(y) = 50? y. Set this equal to marginal cost of 2, and solve to get y = 48. To determine the price, substitute into the inverse demand function, p(48) = 50?48/2 = 26.
3. The monopolist faces a demand curve given by D(p) = 10 p?3. Its cost function is c(y)=2 y. What is its optimal level of output and price? 24.3. The demand curve has a constant elasticity of ?3. Using the formula p[1 + 1/ +=MC, we substitute to get p*1 ? 1/3] = 2. Solving, we get p = 3. Substitute back into the demand function to get the quantity produced: D(3) = 10×3?3.
4. If D(p) = 100/p and c(y)=????, what is the optimal level of output of the monopolist? (Be careful.)
24.4. The demand curve has a constant elasticity of ?1. Thus marginal revenue is zero for all levels of output. Hence it can never be equal to marginal cost.
5. A monopolist is operating at an output level where |ε| = 3. The government imposes a quantity tax of $6 per unit of output. If the
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demand curve facing the monopolist is linear, how much does the price rise?
24.5. For a linear demand curve the price rises by half the change in cost. In this case, the answer is $3.
6. What is the answer to the above question if the demand curve facing the monopolist has constant elasticity?
24.6. In this case p = k MC, where k =1 /(1?1/3) = 3/2. Thus the pricerises by $9.
7. If the demand curve facing the monopolist has a constant elasticity of 2, then what will be the monopolist’s markup on marginal cost? 24.7. Price will be two times marginal cost.
8. The government is considering subsidizing the marginal costs of the monopolist described in the question above. What level of subsidy should the government choose if it wants the monopolist to produce the socially optimal amount of output?
24.8. A subsidy of 50 percent, so the marginal costs facing the monopo- list are half the actual marginal costs. This will ensure that price equals marginal cost at the monopolist’s choice of output.
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9. Show mathematically that a monopolist always sets its price above marginal cost.
24.9. A monopolist operates where p(y)+yΔp/Δy = MC(y). Rearranging, we have p(y)=MC(y)?yΔp/Δy. Since demand curves have a negative slope, we know that Δp/Δy<0, which proves that p(y) >MC (y).
10. True or false? Imposing a quantity tax on a monopolist will always cause the market price to increase by the amount of the tax.
24.10. False. Imposing a tax on a monopolist may cause the market price to rise more than, the same as, or less than the amount of the tax.
11. What problems face a regulatory agency attempting to force a monopolist to charge the perfectly competitive price?
24.11. A number of problems arise, including: determining the true marginal costs for the ?rm, making sure that all customers will be served, and ensuring that the monopolist will not make a loss at the new price and output level.
12. What kinds of economic and technological conditions are conducive to the formation of monopolies?
24.12. Some appropriate conditions are: large ?xed costs and small marginal costs, large minimum e?cient scale relative to the market, ease
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of collusion, etc.
25 Monopoly Behavior
1. Will a monopoly ever provide a Pareto e?cient level of output on its own?
25.1. Yes, if it can perfectly price discriminate.
2. Suppose that a monopolist sells to two groups that have constant elasticity demand curves, with elasticity ε1 and ε2. The marginal cost of production is constant at c. What price is charged to each group? 25.2. pi =εic/(1 +εi) for i =1 ,2.
3. Suppose that the amusement park owner can practice perfect ?rst-degree price discrimination by charging a di?erent price for each ride. Assume that all rides have zero marginal cost and all consumers have the same tastes. Will the monopolist do better charging for rides and setting a zero price for admission, or better by charging for admission and setting a zero price for rides?
25.3. If he can perfectly price discriminate, he can extract the entire consumers’ surplus; if he can charge for admission, he can do the same. Hence, the monopolist does equally well under either pricing policy. (In practice, it is much easier to charge for admission than to charge a di?erent price for every ride.)
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