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Answers to Odd-Numbered Problems
b. With multiple rounds, the buyer could vary its purchases to encourage lower prices (for instance, by purchasing 6 units at P $6, 2 units otherwise). If this succeeds, the resulting payoff is (12, 18). c. Maximum total profits (32) are achieved at Q 8 units. A negotiated price of P $6 (an equal profit split) appears to be equitable.
Chapter 11 1. Although there could be some cost economies from such a merger, the main effect on consumers likely would be higher soft-drink prices. Aggressive price competition to claim market share would be a thing of the past. Because the merged entity would account for over 80 percent of total soft-drink sales, the United States Justice Department would be likely to fight such a merger on the grounds that it would create a monopoly. 3. a. Setting MR MC, we have: 500 20Q 150, or QM 17.5 thousand units and PM $325. b. Under perfect competition, PC LAC $150 and QC 35 thousand. c. With a $100 tax, the monopolist’s MC is 250. Setting MR MC, we find QM 12.5 thousand and PM $375. d. The efficient solution calls for a double dose of regulation: promote perfect competition while taxing the externality. The efficient price is: PC LMC MEC 150 100 $250. The corresponding (efficient) level of output is 25 thousand units. This is the optimal solution. All of the analysts’ recommended outcomes are inefficient. (Of the three, the part (a) outcome, Q 17.5 thousand is the best. It comes closest to the efficient outcome, implying the smallest deadweight loss). 5. a. The competitive price of studded tires is PC AC $60. The price equation P 170 5Q can be rearranged as Q 34 .2P. Thus, one finds the competitive quantity to be QC 34 (.2)(60) 22 thousand tires. b. The full MC of an extra tire is 60 .5Q. Equating industry demand to marginal cost, we find P 170 5Q 60 .5Q. Therefore, the optimal quantity is Q* 20 thousand tires. The optimal price is 170 (5)(20) $70. Net social benefit is the sum of consumer surplus and producer profit, net of external costs. Consumer surplus is (.5)(170 70)(20,000) $1,000,000. Producer profit is (70 60)(20,000) $200,000. External costs are C .25Q2 (.25)(20)2 $100 thousand. Thus, net social benefit is $1,100,000. c. At Q* 20 thousand tires, the marginal external cost is .5Q* $10 per studded tire. Set a tax of $10 per studded tire to obtain the
