Answers to Text Questions and Problems Chapter 10 Answers to Review Questions 1. When a motorist enters an already congested highway, the highway becomes marginally more congested, which increases the travel time of thousands of other motorists. Excessive congestion results because individual motorists have no incentive to take these external costs into account when deciding whether to drive on the highway. 2. The socially optimal amount of highway capacity is the amount for which the marginal cost of expanding highway capacity exactly equals its marginal benefit (as measured by the value to motorists of reduced travel time). To reduce highway congestion to zero would mean building that quantity of highway for which the marginal benefit of extra capacity would be zero. But that solution cannot be socially optimal, because the marginal cost of additional highway capacity is always positive. 3. An activity that generates external costs tends to be pursued excessively. But the optimal quantity of such an activity is not zero; rather, it is that amount for which the marginal benefit of the activity equals the marginal cost, both private and external. Outlawing activities that generate external costs would thus move society from a situation in which those activities were pursued too extensively to one in which they were pursued too little. If the total cost of the unregulated activity were less than its benefit, outlawing the activity would make matters worse. 4. Because many different governments border Lake Erie, enacting legislation that curbs pollution is harder than curbing pollution of the Great Salt Lake, which is regulated by only a single government. 5. If there is a social advantage to being relatively tall, then individuals who wear high-heeled shoes will do better than others who don t. But when everyone wears them, the relative height distribution remains unchanged. Answers to Problems 1a. True. Consider that if the marginal cost of the pollution curbed in plant A were higher than that in plant B, pollution emissions could be transferred from plant B to plant A, lowering the total cost. b. True. An example is the excessive use of pesticides on crops. This activity reduces the amount of insect damage to crops, and thus lowers the farmer s production cost. However, the pesticide runoff pollutes waterways, imposing an external cost on recreational users of those waters. 2. (all parts) The socially optimal number of beehives could be greater or less than the privately optimal number, depending on the magnitude of the social marginal cost relative to the private marginal cost, as well as the magnitude of the social marginal benefit relative to the private marginal benefit. If the external cost is negligible and the external benefit is large, the result is shown in the right panel of the diagram, in which the socially optimal number of beehives, X s, exceeds the privately optimal number, X p. However, if the external cost is large relative to the external benefit, the result is shown in the left panel, in which the socially optimal number, X s, is smaller than the privately optimal number, X p. Phoebe should not be banned from keeping the killer bees, but rather should be either taxed or subsidized so that the social optimal number of beehives is the same as the privately optimal number.
$/hive Social MC $/hive Social MC Private MC Private MC Social MB Private MB Social MB Private MB X S X P X P X S Number of beehives Number of beehives 3. The equilibrium quantity of boom box rentals is found by solving 5 + 0.1Q = 20 0.2Q for Q private = 50 units per day. To find the socially optimal number of rentals we first find the social MC curve by adding the $3 per unit noise cost to the private MC curve to get social MC = 8 + 0.1Q. Equating social MC to demand, we have 8 + 0.1Q = 20 0.2Q, which solves for Q social = 40 units per day, or 10 less than the privately optimal number. 4. Imposition of this tax would shift the private MC curve upward by $3 per unit, making it identical to the social MC curve. The socially optimal number of boom boxes would be rented, resulting in an overall increase in efficiency in this market. 5. The most efficient outcome is for Jones to emit smoke, because the total daily surplus in that case will be $600, compared to only $580 when Jones does not emit smoke. Since Smith has the right to insist that Jones emit no smoke, Jones will have to compensate Smith for not exercising that right. If Jones pays Smith $30, each will be $10 better off than if Smith had forced Jones not to emit smoke 6. John and Karl stand to save $200 per month in rental payments by living together. The lowestcost accommodation to the dirty dish problem is for John to leave his dirty dishes in the sink. Under that arrangement, the maximum monthly rent Karl would be willing to pay to share an apartment with John is $350 $175 = $175 per month. That amount would leave John with a remaining monthly rent bill of $325, which generates a social surplus of $25 per month. If John splits this surplus evenly with Karl, John ends up paying $337.50 per month and Karl pays $162.50. Thus both will be better off sharing. 7. Adding an additional $30 per month to the cost of the shared living arrangement makes the total cost of sharing $205 per month. Because that amount exceeds the $200 per month saved by joint living, the two should live separately. 8a. Since Barton s monthly payoff without soundproofing is $50 more than with it, his natural inclination is not to install soundproofing. Statler would have to pay Barton at least $50 to induce Barton to install it, but since soundproofing is worth only $40 per month to Statler, Statler will not do so. Since the joint payoff is $230 without soundproofing and $220 with it, their choice is socially efficient. b. Barton will not install soundproofing. Instead, he will pay Statler $40 per month to compensate for the noise damage. As in part (a), this solution is socially efficient. c. No; the same result was obtained in both (a) and (b).
9a. Barton will now install and maintain soundproofing, because doing so is cheaper than compensating Statler at a rate of $60 per month for the noise nuisance. This outcome is socially efficient. b. Barton will not install soundproofing. The noise costs Statler $60 per month, so in the absence of transaction costs, Statler would be willing to pay up to that amount to induce Barton to install soundproofing. However, if he must also pay a $15 fee for this transaction, it is not worthwhile. Thus, no soundproofing will be installed, and the outcome will be socially inefficient. c. If Statler has the legal right to peace, then installing and maintaining the soundproofing than will be cheaper for Barton than to pay Statler $60 compensation for noise damage. So this time, the outcome is socially efficient. d. The difference is due to the presence of the negotiation costs, which in part (b) outweigh the gains from adopting the most efficient accommodation to the noise problem. No agreement was necessary in part (c), because the law placed the burden of accommodation on Barton. 10. The following table shows the total village income from grazing llamas, together with the marginal village income from the activity. Number of llamas on the commons Price per 2- year-old llama ($) Income per llama ($ per year) 1 122 22 22 2 118 18 36 3 116 16 48 4 114 14 56 5 112 12 60 6 109 9 54 Total village income ($ per year) Marginal income ($ per year) 22 14 12 8 4 6 a. Three llamas will be sent onto the commons. The resulting net village income will be $48 from the llamas plus $45 from government bonds, or $93. b. The socially optimal number is only one llama. Villagers send three instead, because in deciding whether or not to send a llama, each villager ignores the impact of his or her llama s presence on the other llamas fleece quality. The total village income at the socially optimal number of one llama is $22 from the llama and $75 from government bonds, or $97. c. If a single villager could control access to the commons, she would send only a single llama, which she could sell after one year for $22 more than she paid for it. If the land were free, the owner would thus earn $22 per year by raising one llama per year on it, or $7 more than she would have earned had she used her $100 to buy a bond. The price of the land will be bid up until it owning the land is no better than putting the same amount in the bank at 15 percent interest. That price is the amount of money that would yield $7 per year if deposited at 15 percent interest: 0.15X = $7, or X = $46.67. The new owner will graze one llama. Total village income will be the same as in part (b).
Sample Homework Assignment 1. Suppose the supply curve for cans of pop in your residence is given by P = 0.20 + 0.001Q, where P is the price and Q is the number of cans sold per day. The demand curve for cans of pop in the residence is given by P = 0.80 0.002Q. a. Find the equilibrium price and quantity of pop cans per day sold in the residence. b. If each pop can imposes $0.05 in costs on society (because they become litter or must be thrown away or recycled), what is the socially optimal number of pop cans for the residence? c. How could a tax on pop cans be used to assure the socially optimal number of cans is sold? 2. You own an apple orchard and sell apples at your own fruit stand. The neighbour next door to your orchard is a beekeeper. She keeps bees to make and sell honey. This year, the neighbour is considering getting rid of her bees because her honey business loses money. If she doesn t raise her bees, your apple production will fail without the bees to pollinate the trees. The following payoff matrix shows the returns to you and your neighbour with and without the bees. No bees You $1000 Bees $1300 Neighbour $0 -$100 a. If your neighbour makes her decision without considering your orchard, will she keep the bees? Why or why not? b. Is it socially optimal for your neighbour to keep the bees? Explain. c. If your neighbour consults with you, will she decide to keep the bees? What would you suggest to your neighbour if she consults you? 3. Your neighbours have decided to raise hogs in their backyard. They are economists who use marginal analysis to determine the optimal number of hogs to raise. a. Draw a diagram of your neighbours marginal cost and marginal benefit curves, assuming they are normally shaped, and show their privately optimal number of hogs. b. If the smell of the hog operation is very unpleasant to you (and most other people) so that your neighbours hog farming reduces the value of your house, show how the graph from part (a) is affected. c. Indicate the socially optimal number of hogs on your diagram. How does it compare to the privately optimal number from part (a)?
Multiple Choice Quiz 1. A cost or benefit that falls on people other than those pursuing an activity is called a(n) a. positive externality. b. negative externality. c. externality. d. external cost. e. external benefit. 2. Which of the following is an example of an external cost? a. Your neighbours enjoying the loud music you play. b. A firm dumping waste into a stream. c. Bees pollinating flowers on adjacent property. d. Whales swimming in international waters. e. None of the above. 3. An external cost will result in an equilibrium quantity of an activity that is the socially optimal quantity. a. above b. below c. above or below d. equal to e. unrelated to 4. People can purchase and sell the right to perform activities that cause externalities to arrive at efficient solutions. This describes a. the tragedy of the commons. b. a positional externality. c. an external benefit. d. the Coase Theorem. e. the problem of unpriced resources. 5. The optimal amount of an external cost is a. zero. b. where marginal benefit is zero. c. where marginal cost is zero. d. where marginal benefit equals marginal cost. e. where price equals zero. 6. The efficient way to reduce pollution is to make sure that a. the marginal benefit of abatement is the same for all polluters. b. the marginal cost of abatement is the same for all polluters. c. all polluters reduce pollution by the same amount. d. all polluters use the same technology. e. none of the above.
7. That people will use a resource that has no price until marginal benefit equals zero is a description of a. the tragedy of the commons. b. an external benefit. c. an external cost. d. the Coase Theorem. e. property rights. 8. A positional externality occurs when a. rewards depend on relative performance. b. returns depend on your starting position. c. transaction costs do not equal zero. d. there are arms control agreements. e. none of the above. 9. Which of the following is an example of a positional arms control agreement? a. Campaign spending limits. b. Arbitration agreements. c. Mandatory kindergarten starting dates. d. Baseball roster limits. e. All of the above. 10. Which of the following is an example of the tragedy of the commons that is not easily solved by private ownership? a. Sharing a milkshake. b. Berries in a public park. c. Timber on remote public land. d. Harvesting whales in international water. e. All of the above.
Problems/Short Answer 1. Suppose you are selling t-shirts at your own t-shirt stand. The supply and demand curves for t-shirts are given below. P = 5 + 0.15Q P = 30 0.1Q a. What are the equilibrium price and quantity for t-shirts? b. If the process of making your t-shirts results in chemical waste that you dump in a nearby stream, creating $5 worth of damage to the environment per shirt, what is the socially optimal number of t- shirts for you to sell, and what is the socially optimal price? c. What tax policy could the government use to assure that you sell the socially optimal number of t- shirts? 2. Refer to the graph provided below. You are deciding the optimal number of flower bulbs to plant in your front yard. Your house is by a well-travelled road and people enjoy seeing the flowers in your yard as they pass by. The relevant marginal cost and benefit curves are given below. a. $ Private MC 10 8 6 5 Social MB Private MB 700 800 Quantity a. What is the optimal number of bulbs for you to plant if you do not consider the people passing by your house? b. What is the socially optimal number of bulbs for you to plant? c. By how much would the government need to subsidize you per bulb to assure that you will plant the optimal number of flower bulbs?
Answer Key to Extra Questions in Instructor s Manual Sample Homework Assignment 1a. Equilibrium P = $0.40 and Q = 200. b. With a $0.05 external cost per can, the new supply curve is P = 0.25 + 0.001Q, so the equilibrium quantity is now 183. c. A tax (or can deposit) of $0.05 can be placed on each can so that the cost reflects the social as well as private cost. 2a. No, because she earns a loss of $100. b. Yes, because net gains are $300 $100 = $200 with the bees. c. Yes. You can pay her anywhere between $101 and $299 and both be better off. 3. $ Social MC Private MC Private MB Q S Q P Number of hogs a. Q P is the number of hogs produced. b. The new MC is higher (MC shifts to the left). c. Q S is the socially optimal number of hogs produced. Multiple Choice 1. c 2. b 3. a 4. d 5. d 6. b 7. a 8. a 9. e 10. e
Problems/Short Answer 1a. P = $20 and Q = 100. b. P = $22 and Q = 80. c. Place a tax on t-shirts equal to $5 each. 2a. 700. b. 800. c. $8 $5 = $3.