Market Entry

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

optimal result in part (b). The competitive market price, including tax, becomes: 60 10 $70. d.At an added cost of $12, low-impact studded tires are not cost effective. At a market price of $70 as in part (b) or (c), they cannot compete profitably and should not be produced. 7.a.The firms’ costs are C1 2Q1 .1Q1 2 and C2 .15Q2 2. It follows that MC1 2 .2Q1; MC2 .3Q2. In turn, MB 9 .4Q 9 .4(Q1 Q2). b.Setting MB MC1 MC2, we find Q1 5 and Q2 10, and the common marginal value is $3. It is economically efficient for firm 2 to clean up more pollution than firm 1 since its marginal cost of cleanup is lower. c.Each firm cleans up to the point where MC $4; Using the MC expressions in part (a), we find Q1 10 and Q2 13.33. d.The optimal tax is $3.00 (equal to the common value of MB MC1 MC2). Facing this tax, the firms choose Q1 5 and Q2 10, as in part (b). 9.a.To maximize net benefit (i.e. benefit minus cost), RWE should compare MB and MC, where MC $150,000 per facility. The optimal number of facilities is: N 4. Adopting the program at the fourth facility implies MB $225,000 (greater than MC) but adopting at the fifth facility has MB $100,000 (less than MC). RWE’s maximum net benefit at N 4 is: 1,600,000 (4)(150,000) $1,000,000. b.The additional benefit to society means that MB increases by $75,000. Now the optimal number of facilities is N 6. Adopting the program at the sixth facility has MB $100,000 $75,000 (greater than MC) but adopting at the seventh facility has MB $50,000 $75,000 (less than MC). c.Requiring N 8 reduces total net benefit relative to N 6 in part (b). The marginal benefits of adopting the program at the seventh and eighth facilities are not worth the marginal costs. d.Without any regulatory intervention, RWE would enroll only 4 facilities in the health and safety program (as in part a). An OSHA subsidy per facility would encourage RWE to expand the safety program. The optimal subsidy is exactly equal to the marginal social benefit generated by the program. Thus, the appropriate subsidy is exactly $75,000 per facility. In response, RWE will extend the program to 6 facilities as recommended in part (b). 11.a.Sketching the demand curve, we find the price intercept to be $3.00 and the quantity intercept to be 900 cars. At a rate of $1.50, 450 cars will park each hour, implying revenue of $675 per hour. In turn,