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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 pollution-

permit 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

JEL 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 pol-

lution-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 one-

sided markets attain a type of productive efficiency. However, one-sided markets

do not generally attain full social efficiency (minimization of the sum of abate-

ment costs and damages) because total emission of pollution is equal to the total

number of permits issued. Unless the permit-issuing agency has perfect informa-

tion about the costs and benefits of pollution, it is likely to issue a socially inef-

ficient number of permits.

   Many real pollution-permit markets are two sided in that they allow both pol-

luters and pollutees to purchase permits. For example, in the Environmental Pro-

tection 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 Lander University (e-mail:

scsmith@mail.lander.edu), and Andrew J. Yates is an associate professor of economics at the Uni-

versity of Richmond.

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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 pollu-

tion-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 con-

sumers 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 pollu-

tion, then two-sided markets attain efficiency. More likely, however, consumers

will free ride, and, in this case, efficiency occurs only when the number of per-

mits 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. Two-

sided 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 equi-

librium is not efficient. Thus, the regulatory agency should strive to issue permit

levels that price consumers completely out of the market.

A SIMPLE POLLUTION MODEL

   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 pol-

lution 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 dam-

ages, 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 simulta-

neously 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

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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 spe-

cial 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 pur-

chase 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 qf 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 differ-

ence between the MD curve and the fixed supply of permits represents the con-

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sumer’s demand for permits. For example, at a permit price of p , the consumer

will demand qc 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 equi-

librium 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 w1 > 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 w1 increases, the equilib-

rium price and level of pollution are unchanged, but wealth is transferred from

the consumer to the regulatory agency.

   Now suppose that the agency issues w2 < 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 w2. The equilibrium

price is determined by the intersection of a vertical line at w2 and the marginal-

abatement cost curve. We see that the equilibrium that results from an under-

issuance of permits is not efficient. The welfare loss is shown by area A in Fig-

ure 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 pay-

ing 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 effec-

tive 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-dam-

age curve. A graphical analysis of the market is shown in Figure 2. The aggre-

gate 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 per-

mits. Two possible results are shown in Figure 2. First, suppose that the agency

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FIGURE 2. Many firms, many consumers: permit market equilibria.

                                           

chooses a permit endowment level w1 > q . Then the equilibrium price is p , the

                                                     

corresponding equilibrium quantity of pollution is q , and consumers purchase w1

  

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 w2 < 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 w2. The welfare loss is equal to area A. The equi-

librium is efficient if, and only if w2 = 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. Further-

more, somewhat contrary to the intuition that consumer participation in the mar-

ket is a sign of increased welfare, we find that pricing consumers out of the mar-

ket 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 equiva-

lent to the single-consumer case discussed earlier. Efficiency requires only that

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the regulatory agency issue a quantity of permits greater than or equal to the effi-

cient 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 con-

sumers 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 marginal-

damage curve but has perfect information about the aggregate marginal-abate-

ment cost curve. Uncertainty about damages is quantified into two equally like-

ly states, high marginal damages or low marginal damages. These two possible

states are represented in Figure 3 by MDH and MDL, respectively. We denote the

efficient quantity of pollution in these two states by qH and qL. Clearly, if mar-

ginal damages are higher, the efficient level of pollution is lower, and so q* < q* .

                                                                              HL

   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 MDH, the con-L

sumer will retire exactly w q* permits, and the equilibrium is efficient. If the

                                  H

true state of the world is MDL, the consumer will retire exactly w q* permits,L

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 previ-

ous 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 RPH and RPL.

Loosely speaking, these curves lie some distance, åq, below the respective aggre-

gate marginal damage curves. We can think of å as a measure of the severity of

the free-riding problem. Now, knowing that consumers face a free-riding prob-

lem 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 q* . To see this, first supposeHL

that the severity of the free-riding problem, å, is small and suppose that the

agency selects w = q* . If the true state of marginal damages is low, then con-

                         L

sumers 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-

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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 å is larger. For some large enough å, the high state effective

inverse demand for retired permits, RPH, lies below the low state marginal-damage

curve, MDL. If the agency issues permit level, w = q* , consumers will not retire anyL

permits regardless of the true state. If the true state is MDH , the welfare loss asso-

ciated with w = q* (equal to the sum of areas A and B and C) is very large. If the

                   L

true state is MDL, then obviously w = qL 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

å, expected welfare is maximized by some permit level between q* and q* .HL

   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 sec-

ond period. For example, suppose that the agency issues q* permits and then

                                                                   L

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.

                                                                 L

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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 aggre-

gate 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 peri-

od 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 mini-

mize the welfare loss in the first period. As discussed earlier, this consideration

leads to a choice of w between q* and q* . The second consideration is to maxi-

                                    HL

mize the information value of the signal from the market. This consideration

leads to a choice of w between the intersections of the RPH and RPL curves with

the MAC curve. When w is in this range, the behavior of the consumers unam-

biguously 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 con-

sumers 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 compati-

ble. 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 per-

mits 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.

CONCLUSION

   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 con-

sumers actually purchase permits, it indicates that the market equilibrium is inef-

ficient. 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-

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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.

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