# Additional Questions. Externalities and Public Goods.

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1 Additional Questions. Externalities and Public Goods. Problem 1. The purpose of this problem is to help you understand the difference in market demand for purely private and purely public good. For each of the following situations suppose that private marginal benefits are given by MP B = 10 Q, where Q is the quantity of a good, keep in mind that MP B measures the maximum price a person will be willing to pay for an additional unit of the good. a) Suppose the good is purely private, for example, apples. On a diagram plot individual demand for apples and construct market demand for apples if there are two consumers in the market. Market demand for private good is obtained by adding quantities demanded at each price. You can construct market demand by points: at price P = 10 none of the consumers is willing to purchase any quantity, then total quantity demanded is Q = 0, this is the first point on your diagram (0,10); at P = 9 each person will demand 1 apple and the total quantity demanded in the market is 2 1 = 2, the second point is (2; 9) and so on. You can also use algebra: from the MPB you can find individual quantity demanded as a function of price Q 1 = 10 P is demand by the first person and Q 2 = 10 P is quantity purchased by the second person at each price; market demand is the sum of individual quantities Q M = Q 1 +Q 2, substitute the expressions for the individual demands (plug 10-P for Q 1 and Q 2 ) which will give you Q M = 10 P + 10 P, simplify to Q M = 20 2P and single out price as a function of Q M. Both methods give you exactly the came market demand curve: P = 10.5Q M where Q M is the total quantity demanded at each price. Notice that the market demand curve has the same vertical intercept as individual demands, has half of the slope and twice the horizontal intercept. b) Suppose the good is purely public, for example a street lights installed in the neighborhood. On a diagram plot private marginal benefits and construct market demand for the public good if there are two consumers. Pure public good is nonexcludable and nonrival in consumption. Nonexcludable means that if one of the consumers purchases one unit of the good, the other consumer will be able to consume that unit as well and there is no way to preclude the second consumer from enjoying the benefits. Nonrival means that the fact that the second person is consuming the good does not diminish the benefits to the first person. When you construct the market demand for public good use the notion of maximum amount all consumers will be willing to pay in order to purchase an additional unit. You can construct the market demand curve by points: for example, for the first unit Q = 1 of the good each of the consumers is willing to pay P=9 dollars, it means that the maximum that both will be willing to pay in order to install the first unit of the public good is 18, so one of the points on the market demand for the public good is (1, 18); for the second unit one person will pay up to 8 dollars, max. that two will pay is 16, the second point is (2, 16) etc. You can also notice that when you construct market demand for public good 1

4 proportionally: people with higher MB of trees should be paying more. This potentially creates a problem: if people know that their contributions will be proportional to their MBs, they have an incentive to lie and pretend they do not care about the trees at all so that they will not contribute, but will still enjoy the benefits. Problem 3. Externalities, Efficiency, and Property Rights. Alfred and Ben share an apartment. Alfred likes loud music and Ben does not. Suppose that music imposes an increasing marginal cost on Ben MEC = Q where MEC is dollars and Q is hours of loud music. Alfred s marginal value of each hour of loud music measured in dollars is MP B = 10 Q. (a) Represent this situation on diagram. Show efficient consumption of loud music and situation when Alfred listens to loud music as much as he wants. Since you are not given any info about private costs, assume MPC=0; On his own Alfred will consume where his MPB=MPC, Q=10. For efficiency we need MSC=MSB. MSC = MEC and MSB = MP B, efficient consumption of loud music is 5 hours, at Q=5 MSB=10-5=5=MSC. Welfare in unregulated outcome: DWL=25 Alfred s total benefits from the music=total value of 10 hours=50, denote U A = 50, Ben s total costs are summation of MEC from each hour=area under MEC, which is 50, denote U B = 50. (b) Suppose that there are no legal restrictions on volume of music and Alfred has a right to listen to music as loud as he wants and as much as he wants. Ben approaches Alfred with an offer to pay money for reducing the number of hours of the loud music. Will negotiations achieve efficient outcome? For simplicity suppose both guys know that if there is no agreement Alfred will listen to music for 10 hours. Negotiations will work as follows. For each hour when Alfred does not turn up the volume Ben will be willing to offer payment up to the amount of the marginal cost imposed on Ben. For example 10 th hour causes Ben MEC=10, meaning that it makes Ben so sick he will pay up to 10 dollars to avoid it. Alfred s marginal value of 10 th hour is MP B = = 0, meaning that he will accept any payment in order to give up the last hour of music. Clearly they can agree on some payment that will make both better off. They will continue negotiations until price that Ben is willing to pay is equal to price that Alfred is willing to accept, which happens at 5 hours of music, which is the efficient level of consumption. Suppose that Ben paid 5 dollars for each hour of music reduction. Let s calculate guys welfare in this case: U A = = 62.5, which is Alfred s total value of 5 hours consumed 2 + payment from Ben. Ben s utility U B = = 37.5, which is total damage from 5 hours of music and the payment. Notice what happened: both are better off compared to situation when Alfred listened to music for 10 hours, and sum of each guys increase in welfare = DWL, this means that during negotiations they managed to capture the efficiency loss brought about by the externality. Actual price for which the externality is traded does not have to be \$5/hour and is indeterminate - there are many prices that will be acceptable for both guys, but regardless of the price at least one of them will benefit from reducing level of music while the other one will not be hurt. 2 Total value = area under D curve for the quantity consumed. 4

5 Internalizing the externality in this case works as follows. although Alfred does not have to pay any price in order to listen to music, possibility of getting paid for not listening creates the opportunity cost, which as you remember is a part of economic costs: every time Alfred listens to 1 hour of music he loses an opportunity to get some money from Ben. (c) Suppose Ben has a right for quiet environment. This means that loud music is legal, but Ben has a right to prohibit Alfred from playing music loudly any time. Suppose Alfred approaches Ben with an offer to compensate Ben for each hour of loud music. Will negotiations reach efficient outcome? In order for Ben to accept an offer the compensation per hour should be at least as high as MEC, for example the minimum he will accept for the first hour is 1 dollar etc. Alfred will only pay up to his marginal value of the music, for the first hour he will pay about 9 dollars. Clearly it is possible for both to benefit from trading on the first hour. Alfred will purchase 5 hours of music in total: all gains are exploited when price that Alfred is willing to pay for one more hour is equal to price that Ben is willing to accept. Let s again calculate welfare assuming that Alfred paid 5 dollars per each hour. U A = 12.5, which is his consumer surplus = TV-payment, Ben s welfare U B = 12.5, which is the payment he received minus the cost of the music. (d) Compare parts (b) and (c) and make a conclusion. If you did everything correctly you already know that in both cases the level of music is the same and it is efficient. The difference is apparently in who pays. Notice that whoever has property rights is in advantageous position and will be able to gain from selling the rights. (e) Discussion. This problem is a demonstration of Coase theorem. Explain how does Coase theorem apply to the situation described in this problem. Can you think of any reasons why negotiations may fail between Ben and Alfred? Coase theorem: when there is small number of parties involved, transaction costs are zero, there is no hidden information and property rights are clearly defined, private parties will achieve efficient solution even if externality is present. More or less obvious reason for unsuccessful negotiations is asymmetric information: if guys do not know each other s costs and benefits they might not reach an agreement. Transaction costs/contract enforcement - what if Alfred takes money from Ben and then cheats and listens to music anyways? Notice that if guys lived in a residence building where half of people loved loud music and the other half did not, transaction costs would be extremely high and even if property rights were defined, it would be very hard to reach efficient solution. Discussion Questions 1. Summarize the main differences between pure private and pure public goods. Explain why in case of pure public goods private markets are likely to fail to achieve efficiency. 2. Is pollution abatement a public good? Explain your answer. 5

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