Problem Set 6 Answer Key 16 July 2013

Transcription

1 Eco 333 Name Problem Set 6 nswer Key 16 July Railway engines create sparks, which sometimes set fire to crops planted near the tracks. large number of farmers are affected, and transactions costs prevent the farmers and the railroad from negotiating bribes or side payments. The price of railway service is $250 per train, and each train causes $50 of crop damage. The accompanying diagram shows the relevant market for railway service. a. Suppose a Pigovian tax of $50 per train is imposed on the railroad and given to farmers. By how much will social gain increase? With No Tax With Pigou Tax Net Gain to Railroad $8,000 $4,500 Damage Suffered by Farmers 4,000 3,000 3,000 = 0 Social Gains 4,000 4,500 b. Suppose that the farmers can move their crops away from the tracks at a cost of $2,400 per month. If the goal is to achieve economic efficiency, which party should be made liable for the crop damage? What will be the resulting social gain? Farmers should be liable for the damage. Railroad Liable Farmers Liable Net Gain to Railroad $4,500 $8,000 Cost to Farmers 3,000-3,000 2,400 Social Gains 4,500 5,600

2 c. Suppose that farmers still have the option of moving their crops as described in part b. lso suppose that the railroad can install safety equipment that will prevent the engine sparks at a cost of $25 per train. If the goal is to achieve economic efficiency, which party should be made liable for the crop damage? What will be the resulting social gain? The Railroad company should be liable since it is the lower cost avoider of the harm. Railroad Liable Railroads Not Liable Net Gain to Railroad $6,125 $8,000 Cost to Farmers 2,400 Social Gains $6,125 5,600 dding spark arresters raises the marginal cost of railway services by $25 per train. The new marginal cost schedule crosses the marginal revenue schedule at 70 trains per month. The net benefit is equal to the area beneath the marginal revenue schedule and above the new private marginal cost schedule. The net benefit is ½($250 $75)(70) = $6,125.

3 2. paper mill locates along the banks of a river. The mill sells paper at $10 per unit in a perfectly competitive market. Thus the mill faces a perfectly elastic demand curve, labeled MR, in the figure below. Its marginal costs of production, labeled MCp, rise with output by $0.10 for each extra unit produced. The mill uses the water for waste disposal, making it unfit for swimming and fishing for some distance downstream. The external costs on swimmers and fishers are constant at $4 per unit of paper produced. a. Suppose a Pigovian tax of $4 per unit of paper is imposed on the mill and given to swimmers and fishers. By how much will social gain increase? Net Gain to Mill Costs to Downstream Users Tax Revenue Social Gains With No Tax + C + D =$500 B + C + D $ = $400 B 80 = $100 With Pigou Tax C $240 C $240

4 b. ssume a world with no transactions costs. Would it matter whether the legislature granted to the mill owner the right to use the river to dispose of chemical wastes or the downstream swimmers and fishers the right to a clean river? Explain. In a Coasian world, the allocation of resources is not changed, but the distribution of wealth does change. If the mill were not liable for damages to people downstream, the swimmers could offer D + ½B (or anything more than $80) to the mill to cut its output from 100 to 60 tons of paper. If the mill were liable for damages to people downstream, the mill would cut output to 60 tons of paper and pay C in damages, netting () in producer surplus. c. Suppose that transaction costs are high and that swimmers and fishers have decided to bring a trespass action against the mill. Suppose in the course of the trial the lawyer for the mill points out (and the plaintiffs attorney does not deny) that abundant pollution free swimming and fishing opportunities are available upstream from the mill. ll the plaintiffs have to do is build a road to this alternative recreation area, which can be done at a cost of $300. If the goal is to achieve economic efficiency, which party should be made liable for the pollution damage? What will be the resulting social gain? Swimmers and fishers should be liable. Mill Liable Mill Not Liable Net Gain to Mill +C+D $500 Cost of Road $300 Social Gains $200 d. Suppose that swimmers and fishers still have the option of building a road as described in part c. lso suppose that the mill can install pollution control equipment that will prevent the pollution at a cost of $280. If the goal is to achieve economic efficiency, which party should be made liable for the pollution damage? What will be the resulting social gain? Mill should be liable for the damages. Mill Liable Mill Not Liable Net Gain to Mill +C+D 280 $500 $220 Cost of Road $300 Social Gains $220 $200

5 3. The following table shows the effects that varying numbers of flights will have on the net revenues of airlines using an airport and on the value of real estate in the neighborhood of the airport. Flights per Week irlines' Net Revenue per Week Rental Value of Real Estate per Week Joint Value 300 $ 30,000 $22, ,900 21, ,700 20, ,400 20,200 52, ,000 19, ,500 18, ,900 17, ,200 16, ,400 15, ,500 13, ,500 12,500 47, ,400 11, ,200 9,400 a. How many flights will be scheduled each week if the airlines do not take into account the effects of their actions on the value of the surrounding real estate? irline will offer 350 flights per week. b. What are the marginal potential gains from trade (or marginal cost of the externality) at the solution point in part (a)? The last five flights reduce the value of the rental property by $1,400. The additional damage exceeds the additional benefit to the airline by $1,400. c. What are the total potential gains from trade, starting at the number of flights determined in part (a)? The joint value of airline profits and the value of the rental property is maximized at $52,600 when the airline offers 315 flights per week. This compares with a joint value of $47,000 when the airline offers 350 flights per week. The net gain from reducing weekly flights from 350 to 315 is the difference in joint values or $5,600. d. If the airlines could purchase the real estate and if the owners of the real estate could buy the airlines at negligible transaction costs and with no loss of operational efficiency to either group, would one of them have a stronger incentive than the other to do so? It is not obvious that one or the other would have a comparative advantage in simultaneously operating an airline and managing rental property. Donald Trump did both.

6 Flights Net irline Rev Marg Net Rev Rental Value Marginal Damage Joint Value MD-MNR Cumulative per week per week per week per week per week per week per week per week 300 $30,000 $22,000 $52, ,900 $900 21,500 $500 $52,400 ($400) ,700 $800 20,900 $600 $52,600 ($200) ,400 $700 20,200 $700 $52,600 $0 $5, ,000 $600 19,400 $800 $52,400 $200 $5, ,500 $500 18,500 $900 $52,000 $400 $5, ,900 $400 17,500 $1,000 $51,400 $600 $5, ,200 $300 16,400 $1,100 $50,600 $800 $4, ,400 $200 15,200 $1,200 $49,600 $1,000 $3, ,500 $100 13,900 $1,300 $48,400 $1,200 $2, ,500 $0 12,500 $1,400 $47,000 $1,400 $1, ,400 ($100) 11,000 $1,500 $45,400 $1, ,200 ($200) 9,400 $1,600 $43,600 $1,800 $1,800 $1,600 $1,400 $1,200 $1,000 $800 $600 MNR MD $400 $200 $0 ($200) ($400) Flights per week

7 4. Consider the following information when answering the questions below: It is the factory's choice whether to install a filter; it is the choice of the nearby fishermen whether to install a treatment plant. Dollar figures show profit. The factory and the fishermen can negotiate costlessly, and no one else is affected by the result. Factory Fishermen Joint Profit : No filter or treatment plant $10,000 $ 2,000 $12,000 B: Filter; no treatment plant 6,000 10,000 16,000 C: No filter; treatment plant 10,000 4,000 14,000 D: Filter; treatment plant 6,000 6,000 12, What should the Fishermen do if they know the Factory will maximize profits and no negotiation is possible? a. Install a treatment plant. b. Do not install a treatment plant. c. It makes no difference if the Fishermen do or do not install a treatment plant. d. Install a filter. 2. It would be an acceptable bargain -- to both parties -- to have the fishermen pay the factory a. $500 to install a filter. b. $4,000 to install a filter. c. $6,000 to install a filter. d. any amount greater than $4,000 and less than 6,000 would make both parties better-off. 3. If the fishermen are given the right to clean water, a. the outcome will be more efficient than if the factory is given the right to use the water as it sees fit. b. the outcome will be less efficient than if the factory is given the right to use the water as it sees fit. c. the efficient outcome will occur no matter who is given which property right, and the individual gains will be the same in each case. d. the factory will be forced to shut down. e. the efficient outcome will occur no matter who is given which property right, but how that maximum gain is split will be determined during bargaining. 4. In the above case, the Coase theorem specifies that a. the result will be different if the fishermen are given the right to clean water than it will be if the factory is given the right to use the water as it sees fit, but the result will be inefficient in either case. b. the efficient result will occur whether the fishermen are given the right to clean water or the factory is given the right to use the water as it sees fit. c. economic efficiency requires that the fishermen be given the right to clean water. d. economic efficiency requires that no one may contaminate the water. e. economic efficiency requires that the fishermen be given the right to clean water and that the factory be given the right to use the water as it sees fit.