Should Consumers Be Priced Out of Pollution-Permit Markets?

Should Consumers Be Priced Out of Pollution-Permit Markets? Stefani C. Smith and Andrew J. Yates Abstract: The authors present a simple diagrammatic exposition of a pollutionpermit market in which both firms that generate pollution and consumers who are harmed by pollution are allowed to purchase permits at a single market price. They show that the market equilibrium is efficient if and only if the endowment of permits is equal to the efficient level of pollution. Furthermore, if consumers actually participate in the market, then the equilibrium is not efficient. Welfare can be improved by decreasing the endowment of permits and thereby pricing consumers out of the market. Key words: diagrammatic, efficiency, environmental policy, pollution permit markets, retired permits JE codes: H41, Q25 The analysis of pollution-permit markets has traditionally focused on markets in which polluting firms trade permits amongst themselves. Such markets are one sided in the sense that only those who generate pollution, not those who are harmed by it, participate in the market. The welfare properties of one-sided pollution-permit markets are well known. These markets generally enable firms to attain aggregate emission-reduction targets in the least-cost manner, that is, the manner that minimizes total abatement costs (Montgomery 1972). As discussed in the extant permit-market literature, Montgomery s result indicates that onesided markets attain a type of productive efficiency. However, one-sided markets do not generally attain full social efficiency (minimization of the sum of abatement costs and damages) because total emission of pollution is equal to the total number of permits issued. Unless the permit-issuing agency has perfect information about the costs and benefits of pollution, it is likely to issue a socially inefficient number of permits. Many real pollution-permit markets are two sided in that they allow both polluters and pollutees to purchase permits. For example, in the Environmental Protection Agency s (EPA) acid-rain program, some market participants buy, and then do not use, pollution permits. An unused permit is said to be retired. Because the total availability of permits is fixed by the EPA, retiring a permit reduces the aggregate level of emissions. The EPA s acid-rain Web page Stefani C. Smith is an assistant professor of economics at ander University (e-mail: scsmith@mail.lander.edu), and Andrew J. Yates is an associate professor of economics at the University of Richmond. Spring 2003 181

(www.epa.gov/airmarkets/arp/) contains links to several interest groups that accept donations to purchase and retire permits. Permits are also retired by other groups and individuals. We use simple diagrams to analyze the welfare properties of two-sided pollution-permit markets. 1 A retired permit is a classic example of a public good: it provides a nonexcludable and nonrival benefit for all consumers. Some consumers may be tempted to free ride on the purchases by other consumers. The welfare properties of two-sided markets depend on the degree of free riding and the initial permit endowment. If consumers do not free ride, and the initial endowment of permits is greater than or equal to the efficient quantity of pollution, then two-sided markets attain efficiency. More likely, however, consumers will free ride, and, in this case, efficiency occurs only when the number of permits issued is equal to the efficient quantity of pollution. Although the welfare result for two-sided markets (with free riding) is similar to the one obtained in one-sided markets, there is an important difference. Twosided markets offer an easily observable indicator of inefficiency even when the regulator has imperfect information about the costs and benefits of pollution. In particular, if any consumers are observed retiring permits, then the market equilibrium is not efficient. Thus, the regulatory agency should strive to issue permit levels that price consumers completely out of the market. A SIMPE POUTION MODE We consider a simple pollution model with firms that generate pollution and consumers that are harmed by pollution. The economic relationship between the firms and the consumers is represented in Figure 1. The horizontal axis indicates the level of pollution. The firms benefits from pollution are described by the aggregate marginal-abatement cost curve (MAC). As the level of allowable pollution decreases, the firms must either decrease output or increase spending on pollution control, or both. We assume that these actions become increasingly costly to the firms, so the MAC curve has a negative slope. The consumers costs from pollution are described by the aggregate marginal-damage curve (MD). We assume that increases in pollution lead to increasingly large increases in damages, so the MD curve has a positive slope. Although the MAC curve and the MD curve are both aggregate curves, they are constructed in fundamentally different ways. A pollution permit purchased by a firm is a private good. The aggregate abatement cost curve is thus the horizontal sum of the individual firm s abatement cost functions. Conversely, a pollution permit purchased by a consumer is a public good. Because pollution is simultaneously and nonrivally experienced by all consumers, the aggregate marginal damage curve is the vertical sum of the consumers individual marginal damage curves. This means that any individual consumer s marginal damage curve lies below the MD curve. One can find the efficient pollution level by equating the marginal benefits from pollution to the marginal costs from pollution. Graphically, this occurs at the intersection of the MAC and MD curves. The efficient solution is indicated in 182 JOURNA OF ECONOMIC EDUCATION

= < 1 @ A B C E G 2 6 $ H H ; : < = 1 > : 9 J 1? 7 I 1 9 7 8 2 3 5 FIGURE 1. Many firms, single consumer: permit market equilibrium. Figure 1, by (q *, p * ), where p * is the value of aggregate marginal abatement cost (and aggregate marginal damage) at the efficient number of permits q *. A Two-Sided Permit Market with One Consumer The elements of the pollution-permit market are also illustrated in Figure 1. Although most pollution problems affect many consumers simultaneously, to understand how the market functions, we found it useful to first consider a special case in which only one consumer is harmed by the pollution. In this case, the aggregate marginal damage curve is equal to the single consumer s marginal damage curve. A government agency issues an initial endowment of permits, w, and sells them in a competitive market open to both the firms and the consumer. Thus, the supply of permits is perfectly inelastic at w. Because firms must purchase a permit for each unit of pollution generated, firms will buy permits as long as the marginal abatement cost from pollution exceeds the permit price. Hence, the inverse MAC curve indicates the firms demand for permits. For example, at a permit price of p, firms will demand q f permits. The consumer will buy and retire permits as long as the marginal damage from pollution exceeds the permit price. The first permit bought by the consumer reduces pollution from w to w 1, for a given price of permits; thus, the difference between the MD curve and the fixed supply of permits represents the con- Spring 2003 183

sumer s demand for permits. For example, at a permit price of p, the consumer will demand q c permits. We can now describe equilibrium in the market for pollution permits. For a given supply of permits, w, the permit price and quantity pair (p, q) is an equilibrium if (1) given p, the quantity of permits demanded by firms is q, and (2) given p, the quantity of permits demanded by the consumer is w q. Notice that the equilibrium level of pollution is equal to q, the quantity of permits held by firms. The market equilibrium is efficient if q = q *. Suppose, as shown in Figure 1, that the government issues w 1 > q * permits. Consider a price p > p *. The sum of the quantity demanded by the consumer and the firms is less than the supply at this price (Figure 1). On the other hand, a price below p * leads to excess demand. Clearly p * is the equilibrium price, and q * is the equilibrium quantity of pollution, and hence, the equilibrium that results from an overissuance of permits is efficient. Notice that, as w 1 increases, the equilibrium price and level of pollution are unchanged, but wealth is transferred from the consumer to the regulatory agency. Now suppose that the agency issues w 2 < q * permits. In this case, each permit is more highly valued by the firms than by the consumer. The consumer is priced out of the market, and the equilibrium level of pollution is w 2. The equilibrium price is determined by the intersection of a vertical line at w 2 and the marginalabatement cost curve. We see that the equilibrium that results from an underissuance of permits is not efficient. The welfare loss is shown by area A in Figure 1. Firms could potentially compensate the consumer for an increase in the allowable level of pollution. Many Consumers: A Free-Riding Problem Now consider the general case in which there are many consumers harmed by the pollution. Some consumers may attempt to free ride on the permit purchases of other consumers and thereby enjoy the benefits of reduced pollution without paying the costs of permit purchases. To illustrate a particularly severe example of free riding, we suppose that the consumer who is hurt the most by pollution purchases permits and the rest free ride. In this example, the effective demand curve for retired permits would be equal to the single consumer s marginal-damage curve. When the magnitude of the free-riding problem is more moderate, the effective demand curve for retired permits will be some complicated function of the individual marginal-damage curves. As long as there is any degree of free riding, however, the effective demand curve will lie below the aggregate marginal-damage curve. A graphical analysis of the market is shown in Figure 2. The aggregate marginal-damage curve, the aggregate marginal-abatement cost curve, and the efficient level of pollution are all defined as before. A new curve, denoted by RP, indicates the effective inverse demand for retired permits. The analysis of the market proceeds as before, except that we use the effective inverse demand for retired permits rather than the aggregate marginal-damage curve. The market equilibrium depends critically on the initial endowment of permits. Two possible results are shown in Figure 2. First, suppose that the agency 184 JOURNA OF ECONOMIC EDUCATION

l x z l m h k t u g n o p q r s w x v w { g y v g h i j FIGURE 2. Many firms, many consumers: permit market equilibria. chooses a permit endowment level w 1 > q. Then the equilibrium price is p,the corresponding equilibrium quantity of pollution is q, and consumers purchase w 1 q permits. This inefficient outcome results from the free-riding problem. The welfare loss is shown in Figure 2 as the sum of areas A and B. Now suppose that the agency issues w 2 < q. In this case, consumers are priced out of the market because every permit is valued more highly by firms. The equilibrium price is p 2, and the equilibrium quantity is w 2. The welfare loss is equal to area A. The equilibrium is efficient if, and only if w 2 = q *. Because of free riding, equilibria in two-sided but single-price pollution-permit markets with many consumers are efficient if, and only if, the regulatory agency selects the permit endowment equal to the efficient quantity of pollution. Furthermore, somewhat contrary to the intuition that consumer participation in the market is a sign of increased welfare, we find that pricing consumers out of the market is a necessary condition for efficiency. In other words, if we observe consumers participating in the market, then the market equilibrium is not efficient. At this point, it is useful to summarize the welfare properties of the various types of markets. Efficiency in one-sided pollution-permit markets requires that the regulatory agency issue the efficient number of permits. Two-sided markets in which the consumers are able to eliminate the free-riding problem are equivalent to the single-consumer case discussed earlier. Efficiency requires only that Spring 2003 185

the regulatory agency issue a quantity of permits greater than or equal to the efficient number of permits. We would normally expect, however, that consumers are not able to eliminate free riding. Efficiency then requires that the regulatory agency issue the efficient number of permits. The market, however, sometimes offers a signal (consumer purchase of permits) to the agency that the number of permits issued was indeed inefficient. As we shall see, this signal can be used to improve welfare. IMPERFECT INFORMATION If the regulatory agency has perfect information about the marginal benefits and marginal damages from pollution, then the obvious policy prescription in light of the above results is to issue the efficient level of permits and price consumers out of the market. Of course, the agency does not have this information. In this section, we consider a simple model of imperfect information. We assume that the agency s objective is to minimize expected welfare loss. Suppose initially that the agency is uncertain about the aggregate marginaldamage curve but has perfect information about the aggregate marginal-abatement cost curve. Uncertainty about damages is quantified into two equally likely states, high marginal damages or low marginal damages. These two possible states are represented in Figure 3 by MD H and MD, respectively. We denote the efficient quantity of pollution in these two states by q H and q. Clearly, if marginal damages are higher, the efficient level of pollution is lower, and so q * < H q*. In the special case in which the pollution harms only one consumer, the agency should select any w so that w q *. If the true state of the world is MD, the consumer will retire exactly w q * permits, and the equilibrium is efficient. If the H H true state of the world is MD, the consumer will retire exactly w q * permits, and the equilibrium is efficient. When more than one consumer is harmed by pollution, irrespective of which state is true, consumers again face the free-riding problem. Just as in the previous analysis, the effective inverse demand for retired permits will be less than the actual aggregate marginal-damage curve. In the two possible states of the world, the effective inverse demand for retired permits is denoted by RP H and RP. oosely speaking, these curves lie some distance, εq, below the respective aggregate marginal damage curves. We can think of ε as a measure of the severity of the free-riding problem. Now, knowing that consumers face a free-riding problem and not knowing the true state of the world, the regulatory agency must determine how many permits to issue. In this case, we claim that the agency will minimize expected welfare loss by issuing some number of permits satisfying q * w H q*. To see this, first suppose that the severity of the free-riding problem, ε, is small and suppose that the agency selects w = q *. If the true state of marginal damages is low, then consumers are exactly priced out of the market, and the equilibrium is efficient. If the true state is high, then, because of free riding, consumers do not retire enough permits, and the equilibrium is inefficient. The welfare loss (equal to area A in Figure 3) is small, however, because the effective inverse demand for retired per- 186 JOURNA OF ECONOMIC EDUCATION

ž ž š Ÿ œ Ÿ œ œ FIGURE 3. Imperfect information. mits is just below the aggregate marginal damage curve, and hence consumers buy nearly enough permits to reach the efficient quantity of pollution. Now suppose that ε is larger. For some large enough ε, the high state effective inverse demand for retired permits, RP H, lies below the low state marginal-damage curve, MD. If the agency issues permit level, w = q *, consumers will not retire any permits regardless of the true state. If the true state is MD H, the welfare loss associated with w = q * (equal to the sum of areas A and B and C) is very large. If the true state is MD, then obviously w = q is efficient. Therefore, the issuing agency can increase expected welfare by decreasing w slightly. A slight decrease in w would greatly decrease the welfare loss associated with the high state and introduce only a slight welfare loss associated with the low state. In fact, for any very large ε, expected welfare is maximized by some permit level between q * and H q*. As a further extension, we briefly consider a two-period model. The behavior of consumers in the first period sends an information signal to the regulatory agency. The agency can use this signal to improve expected welfare in the second period. For example, suppose that the agency issues q * permits and then observes that consumers purchase permits in equilibrium. This implies that the true state must be high. If the state was low, then the effective inverse demand for retired permits would lie below the low state aggregate marginal damage curve and consumers would be priced out of the market when q * permits are issued. Spring 2003 187

Because the agency observes consumers in the market, it must be the case that the effective inverse demand for retired permits lies above the low state aggregate marginal damage curve, and thus the true state of external costs cannot be low. It follows that the agency can obtain an efficient equilibrium in the next period by issuing q * permits. H Analyzing the optimal first-period permit endowment is beyond the scope of this article. 2 Our analysis suggests, however, that this choice will be influenced by two, possibly conflicting, considerations. The first consideration is to minimize the welfare loss in the first period. As discussed earlier, this consideration leads to a choice of w between q * and H q*. The second consideration is to maximize the information value of the signal from the market. This consideration leads to a choice of w between the intersections of the RP H and RP curves with the MAC curve. When w is in this range, the behavior of the consumers unambiguously indicates whether the damages are high or low. (If consumers make purchases then the damages are high, otherwise damages are low.) Therefore the signal in the first period enables the agency to identify the efficient allocation of permits for the second period. In practice, of course, the issuing agency is likely to be uncertain about both aggregate marginal damages and aggregate marginal-abatement costs, as well as the magnitude of the free-riding problem. Even in this case, the fact that consumers participate in the market indicates that the equilibrium is not efficient and that welfare can be improved in the second period by decreasing the number of permits. The difficulty now, however, is that the information revealed in the first period is not sufficient for the agency to identify precisely the efficient quantity of pollution. The problem of choosing the optimal permit endowment has the same structure, however, as in the simple model of uncertainty discussed earlier. The regulatory agency should take into consideration the expected welfare loss as well as the expected signal from the market when selecting the permit endowment. Finally, we note that these policy suggestions may not be incentive compatible. In other words, consumers may have an incentive to overstate their actual demand for permits in the first period if they realize that their actions influence the endowment of permits in the second period. By retiring an extra permit, the consumers send a false signal to the agency that the marginal damage curve is higher than it really is. This leads the agency to issue a smaller number of permits in the second period, to the benefit of the consumers but to the detriment of overall welfare. The ability of consumers to coordinate this type of behavior, however, may itself be hindered by free-riding problems. CONCUSION This simple diagrammatic exposition provides interesting policy implications for pollution markets. When consumers are allowed to participate in the market, their behavior may create a signal about the efficiency of the market. If consumers actually purchase permits, it indicates that the market equilibrium is inefficient. Welfare can be improved in future years by reducing the endowment of permits and pricing the consumers out of the market. On the other hand, if con- 188 JOURNA OF ECONOMIC EDUCATION

sumers do not purchase permits, then no information is revealed. One cannot tell whether the permit endowment is too large or too small. NOTES 1. Two-sided markets have received little attention in the literature. Two exceptions are Boyd and Conley (1997) and Shrestha (1998). 2. See Smith and Yates (2002) for a rigorous analysis of this issue in a similar model. REFERENCES Boyd, J., and J. Conley. 1997. Fundamental nonconvexities in Arrovian markets and a Coasian solution to the problem of externalities. Journal of Economic Theory 72 (2): 388 407. Montgomery, D. 1972. Markets in licenses and efficient pollution control programs. Journal of Economic Theory 5 (3): 395 418. Shrestha, R. 1998. Uncertainty and the choice of policy instruments: A note on Baumol and Oates propositions. Environmental and Resource Economics 12 (4): 497 505. Smith, S., and A. Yates. 2002. Optimal pollution permit endowments in markets with endogenous emissions. Working paper. University of Richmond. Spring 2003 189