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34 Externalities

34 Externalities - CHAPTER 3 4 EXTERNALITIES We say that an...

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Unformatted text preview: CHAPTER 3 4 EXTERNALITIES We say that an economic situation involves a consumption externality if one consumer cares directly about another agent’s production or consump- tion. For example, I have definite preferences about my neighbor playing loud music at 3 in the morning, or the person next to me in a restaurant smoking a cheap cigar, or the amount of pollution produced by local auto ””5515‘WP‘EPUE “'5 “up“ uuilunsufinwfiiefiwags‘mufimu extpflmlflgi‘e’shQn . “nun XIGNJddV sibilities of one firm are influenced by me cnoices or auumm nun w WA. sumer. A classic example is that of an apple orchard located next to a beekeeper, where there are mutual positive production externalities—each firm’s production positively affects the production possibilities of the other firm. Similarly, a fishery cares about the amount of pollutants dumped into its fishing area, since this will negatively influence its catch. The crucial feature of externalities is that there are goods people care about that are not sold on markets. There is no market for loud music at 3 in the morning, or drifting smoke from cheap cigars, or a neighbor who SMOKERS AND NONSMOKERS 627 keeps a beautiful flower garden. It is this lack of markets for externalities that causes problems. Up until now we have implicitly assumed that each agent could make consumption or production decisions without worrying about what other agents were doing. All interactions between consumers and producers took place via the market, so that all the economic agents needed to know were the market prices and their own consumption or production possibilities. In this chapter we will relax this assumption and examine the economic consequences of externalities. In earlier chapters we saw that the market mechanism was capable of achieving Pareto efficient allocations when externalities were not present. If externalities are present, the market will not necessarily result in a Pareto efficient provision of resources. However, there are other social institutions such as the legal system, or government intervention, that can “mimic” the market mechanism to some degree and thereby achieve Pareto efficiency. In this chapter we’ll see how these institutions work. 34.1 Smokers and Nonsmokers It is convenient to start with an example to illustrate some of the main considerations. We’ll imagine two roommates, A and B, who have prefer- ences over “money” and “smoke.” We suppose that both consumers like money, but that A likes to smoke and B likes clean air. We can depict the consumption possibilities for the two consumers in an Edgeworth box. The length of the horizontal axis will represent the total amount of money the two agents have, and the height of the vertical axis will represent the total amount of smoke that can be generated. The preferences of agent A are increasing in both money and smoke, while agent B’s preferences are increasing in money and clean air—the absence of smoke. We’ll measure smoke on a scale from 0 to 1, where 0 is no smoke at all, and 1 is the proverbial smoke-filled room. This setup gives us a diagram like that depicted in Figure 34.1. Note that the picture looks very much like the standard Edgeworth box, but the interpretation is quite different. The amount of smoke is a good for A and a bad for B, so that B is moved to a more preferred position as A consumes less smoke. Be sure to note the difference in the way things are measured on the horizontal and vertical axes. We measure A’s money horizontally from the lower left—hand corner of the box, and B’s money horizontally from the upper right-hand corner. But the total amount of smoke is measured vertically from the lower left—hand corner. The difference occurs because money can be divided between the two consumers, so there will always be two amounts of money to measure, but there is only one amount of smoke that they must both consume. 628 EXTERNALITIES (Ch. 34) In the ordinary Edgeworth box diagram B is made better off when A reduces his consumption of good 2wbut that is because B then gets to consume more of good 2. In the Edgeworth box in Figure 34.1 B is also better Oh? when A reduces his consumption of good 2 (smoke), but for a very different reason. In this example, B is better off when A reduces his consumption of smoke since both agents must consume the same amount of smoke and smoke is a bad for agent B. We’ve now illustrated the consumption possibilities of the two roommates and their preferences. What about their endowments? Let’s assume that they both have the same amount of money, say $100 apiece, so that their endowments will lie somewhere on the vertical line in Figure 34.1. In order to determine exactly where on this line the endowments lie, we must determine the initial “endowment” of smoke / clean air. Possible endowment E ' - .- Person SMOKE ' ‘ I ' ' Possibie Equilibrium X'. Possible _ ' : equilibrium x _ indifference curves Person A .. . .1 _' ' MONEY ' _ _ 1 \Possible . ' ' " ' ' endonemE Preferences for money and smoke. Smoke is a good for person A but a bad for person B. Which equilibrium We end up at depends on which endowment we start at The answer to this question depends on the legal rights of smokers and nonsmokers. It may be that A has a right to smoke as much as he wants, and B just has to put up with it. Or, it could be that B has a right to SMOKERS AND NONSMOKERS 629 clean air. Or the legal right to smoke and clean air could be somewhere between these two extremes. The initial endowment of smoke depends on the legal system. This is not so different from the initial endowment of ordinary sorts of goods. To say that A has an initial endowment of $100 means that A can decide to consume the $100 himself, or he can give it away or trade it to any other individual. There is a legal definition of property involved in saying that a person “owns” or “has a right to” $100. Similarly if a person has a property right to clean air, it means that he can consume clean air if he wants to, or he can give it away or sell that right to someone else. In this way, having a property right to clean air is no different from having a property right to $100. Let’s start by considering a legal situation where person B has a legal right to clean air. Then the initial endowment in Figure 34.1 is labeled E; it is where A has (100, 0) and B has (100,0). This means that both A and B have $100, and that the initial endowmentgwhat there would be in the absence of trade—is clean air. Just as before, in the case with no externalities, there is no reason why the initial endowment is Pareto efficient. One of the aspects of having a property right to clean air is having the right to trade some of it away for other desirable goodswin this case, for money. It can easily happen that B would prefer to trade some of his right to clean air for some more money. The point labeled X in Figure 34.1 is an example of such a case. As before, a Pareto efficient allocation is one where neither consumer can be made better off without the other being made worse off. Such an allocation will be characterized by the usual tangency condition that the marginal rates of substitution between smoke and money should be the same between the two agents, as illustrated in Figure 34.1. It is easy to imagine A and B trading to such a Pareto efficient point. In effect, B has the right to clean air, but he can allow himself to be “bribed” to consume some of A’s smoke. Of course, other assignments of property rights are possible. We could imagine a legal system where A had a right to smoke as much as he wanted, and B would have to bribe A to reduce his consumption of smoke. This would correspond to the endowment labeled E’ in Figure 34.1. Just as before, this would typically not be Pareto efficient, so we could imagine the agents trading to a mutually preferred point such as the one labeled X ’. Both X and X’ are Pareto efficient allocations; they just come from different initial endowments. Certainly the smoker, A, is better off at X ’ than at X, and the nonsmoker, B, is better off at X than at X ’ . The two points have different distributional consequences, but on grounds of efiiciency they are equally satisfactory. In fact, there is no reason to limit ourselves to just these two efficient points. As usual there will be a whole contract curve of Pareto efficient allocations of smoke and money. If agents are free to trade both of these 630 EXTERNALITIES (Ch. 34) goods, we know that they will end up somewhere on this contract curve. The exact position will depend on their property rights involving smoke and money and on the precise mechanism that they use to trade. One mechanism that they could use to trade is the price mechanism. Just as before we could imagine an auctioneer calling out prices and asking how much each agent would be willing to buy at those prices. If the initial endowment point gave A the property rights to smoke, he could consider selling some of his smoking rights to B in exchange for B’s money. Similarly, if the property rights for clean air were given to B, he could sell some of his clean air to A. When the auctioneer manages to find a set of prices where supply equals demand everything is fine: we have a nice Pareto efficient outcome. If there is a market for smoke, a competitive equilibrium will be Pareto effi— cient. Furthermore, the competitive prices will measure the marginal rate of substitution between the two goods, just as in the standard case. This is just like the usual Edgeworth box analysis, but described in a slightly different framework. As long as we have well-defined property rights in the good involving the externality~no matter who holds the prop— erty rightsmthe agents can trade from their initial endowment to a Pareto efficient allocation. If we want to set up a market in the externality to encourage trade, that will work as well. The only problem arises if the property rights are not well defined. If A believes that he has the right to smoke and B believes that he has the right to clean air, we have difficulties. The practical problems with ertemaltties generally arise because of poorly defined property rights. My neighbor may believe that he has the right to play his trumpet at 3 in the morning, and I may believe that I have the right to silence. A firm may believe that it has the right to dump pollutants into the atmosphere that I breathe, while I may believe that it doesn’t. Cases where property rights are poorly defined can lead to an inefficient production of externalities-which means that there would be ways to make both parties involved better off by changing the production of externalities. If property rights are well defined, and mechanisms are in place to allow for negotiation between people, then people can trade their rights to produce externalities in the same way that they trade rights to produce and consume ordinary goods. 34.2 Quasilinear Preferences and the Coase Theorem We argued above that as long as property rights were well defined, trade between agents would result in an efficient allocation of the externality. In general, the amount of the externality that will be generated in the efficient solution will depend on the assignment of property rights. In the case of the two roommates, the amount of smoke generated will depend on whether the smoker has the property rights or the nonsmoker has them. QUASILINEAR PREFERENCES AND THE COASE THEOREM 631 But there is a special case Where the outcome of the externality is inde- pendent of the assignment of property rights. If the agents’ preferences are quasilinear, then every efficient solution must have the same amount of the externality. This case is illustrated in Figure 34.2 for the Edgeworth box case of the smoker versus the nonsmoker. Since the indifference curves are all horizontal translates of each other, the locus of mutual tangencie5*the set of Pareto efficient allocationsiwill be a horizontal line. This means that the amount of smoke is the same in every Pareto efficient allocation; only the dollar amounts held by the agents differ across the efficient allocations. SMOKE Person _' A’s indifference curves Pareto efficient allocations ' - - B‘s indifference Curves Person - . A _ _ . MONEY Quasilinear preferences and the Coase theorem. If each consumer’s preferences ”are quasilinear, so that they are all hor- izontal translates of each other, the set of Pareto efiicient allo~ cations will be a. horizontal line. Thus there will be a unique amount of the externality, in this case smoke, at each Pareto efficient allocation. The result that under certain conditions the efficient amount of the good 1nvolved in the externality is independent of the distribution of property rights is sometimes known as the Coase Theorem. However, it should be emphasized just how special these conditions are. The quasilinear prefer— ence assumption implies that the demands for the good causing the exter- 632 EXTERNALlTlES (Ch. 34) nality doesn’t depend on the distribution of income. Therefore a realloca« tion of endowments doesn’t affect the efficient amount of the externalities. This is sometimes expressed by saying that the Cease theorem is valid if there are no “income effects.”1 In this case, the Pareto efficient allocations will involve a unique amount of the externality being generated. The different Pareto efficient allocations will involve different amounts of money being held by the consumers; but the amount of the externalityflthe amount of smoke—will be independent of the distribution of wealth. 34.3 Production Externalities Let us now Consider a situation involving production externalities. Firm S produces some amount of steel, 3, and also produces a certain amount of pollution, m, which it dumps into a river. Firm F, a fishery, is located downstream and is adversely affected by S’s pollution. Suppose that firm S’s cost function is given by cs(s,m), where s is the amount of steel produced and a: is the amount of pollution produced. Firm F’s cost function is given by cf(f,2:), where f indicates the production of fish and a: is the amount of pollution. Note that F’s costs of producing a given amount of fish depend on the amount of pollution produced by the steel firm. We Will suppose that pollution increases the cost of providing fish Acf/Aa: > 0, and that pollution decreases the cost of steel production, Acs/Am S 0. This last assumption says that increasing the amount of pollution will decrease the cost of producing steel—that reducing pollution will increase the cost of steel production, at least over some range. The steel firm’s profit-maximization problem is max p33 — cs(s, ac) 5,37 and the fishery’s profit-maximization problem is mgx pff — Cf(f,:v)- Note that the steel mill gets to choose the amount of pollution that it generates, but the fishery must take the level of pollution as outside of its control. 1 Ronald Cease is an emeritus professor at the University of Chicago Law School. His famous paper, “The Problem of Social Costs,” The Journal of Law Ed Economics, 3 (October 1960), has been given a variety of interpretations. Some authors suggest that Coase only asserted that costless bargaining over externalities achieves a Pareto efficient outcome, not that the outcome will be independent of the assignment of property rights. Coase received the 1991 Nobel Prize in Economics for this work. PRODUCTION EXTERNALITIES 633 The conditions characterizing profit maximization will be Ac, (3*, 93*) ps — ———As 0 _ Acs(s*,x*) — A56 for the steel firm and _ Acf(f*, 20*) pf _ Af for the fishery. These conditions say that at the profit—maximizing point, the price of each good—steel and pollution—should equal its marginal cost. In the case of the steel firm, one of its products is pollution, which, by assumption, has a zero price. So the condition determining the profit- maximizing supply of pollution says to produce pollution until the cost of an extra unit is zero. It is not hard to see the externality here: the fishery cares about the production of pollution but has no control over it. The steel firm looks only at the cost of producing steel when it makes its profit—maximizing calculation; it doesn’t consider the cost it imposes on the fishery. The increase in the cost of fishing associated with an increase in pollution is part of the social cost of steel production, and it is being ignored by the steel firm. In general, we expect that the steel firm will produce too much pollution from a social point of View since it ignores the impact of that pollution on the fishery. What does a Pareto efficient production plan for steel and fish look like? There is an easy way to see what it should be. Suppose that the fishery and the steel firm merged and formed one firm that produced both fish and steel (and possibly pollution). Then there is no externality! For a production externality only arises When one firm’s actions affect another firm’s production possibilities. If there is only one firm, then it will take the interactions between its different “divisions” into account when it chooses the profit-maximizing production plan. We say that the externality has been internalized by this reassignment of property rights. Before the merger, each firm had the right to produce whatever amount of steel or fish or pollution that it wanted, regardless of What the other firm did. After the merger, the combined firm has the right to control the production of both the steel mill and the fishery. The merged firm’s profit—maximization problem is max £058 +pff — 03(8799) — Cf(f,:v), Sifts: 634 EXTERNALITIES (Ch. 34) which yields optimality conditions of _ [3643,50 p5 — A3 _ ACf(f,53) pf — T _ Amaze) Aegis?) 0 — T + T- The crucial term is the last one. This shows that the merged firm will take into account the effect of pollution on the marginal costs of both the steel firm and the fishery. When the steel division decides how much pollution to produce, it considers the effect of this action on the profits of the fish division; that is, it takes the social cost of its production plan into account. What does this imply about the amount of pollution produced? When the steel firm acted independently, the amount of pollution was determined by the condition Ac, (3* , m*) Am That is, the steel mill produced pollution until the marginal cost was zero: 3 0. (34.1) MCS(8*,33*) = 0. In the merged firm, the amount of pollution is determined by the condition Acsacic) + Aways) : M M 0. (34.2) That is, the merged firm produces pollution until the sum of the marginal cost to the steel mill and the marginal cost to the fishery is zero. This condition can also be written as _Acs(§,§:) _ Acme) Ax As; > 0 (34.3) 01‘ —MCS(§,§: = MCF(f,5:). In this latter expression M0136, i3) is positive, since more pollution in— creases the cost of producing a given amount of fish. Hence the merged firm will want to produce where PMCS(§,:E) is positive; that is, it will want to produce less pollution than the independent steel firm. When the true social cost of the externality involved in the steel production is taken into account, the optimal production of pollution will be reduced. When the steel firm considers minimizing its private costs of producing steel, it produces where the marginal cost of extra pollution equals zero; PRODUCTION EXTERNALITIES 635 but the Pareto efficient level of pollution requires minimizing the social costs of the pollution. At the Pareto efficient level of pollution, the sum of the two firm’s marginal costs of pollution must be equal to zero. This argument is illustrated in Figure 34.3. In this diagram —MCS measures the marginal cost to the steel firm from producing more pollution. The curve labeled M C p measures the marginal cost to the fishery of more pollution. The profit-maximizing steel firm produces pollution up to the point where its marginal cost from generating more pollution equals zero. PRICE —MC5 = MCF _ Privately ' _- optimal ' amount : ,3 xi: . .;: umrmros Social cost and ...
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