J Regul Econ (2013) 44:80–102DOI 10.1007/s11149-013-9219-6

ORIGINAL ARTICLE

Prices versus quantities: environmental regulationand imperfect competition

Erin T. Mansur

Published online: 28 March 2013© Springer Science+Business Media New York 2013

Abstract By exercising market power, a firm will distort the production, and there-fore the emissions decisions, of all firms in the market. This paper examines howthe welfare implications of strategic behavior depend on how pollution is regulated.Under an emissions tax, aggregate emissions do not affect the marginal cost of pollut-ing. In contrast, the price of tradable permits is endogenous. I show when this feedbackeffect increases strategic firms’ output. Relative to a tax, tradable permits may improvewelfare in a market with imperfect competition. As an application, I model strategicand competitive behavior of wholesalers in a Mid-Atlantic electricity market. Sim-ulations suggest that exercising market power decreased emissions locally, therebysubstantially reducing the regional tradable permit price. Furthermore, I find that hadregulators opted to use a tax instead of permits, the deadweight loss from imperfectcompetition would have been even greater.

Keywords Environmental regulation · Market based instruments ·Imperfect competition · Electricity restructuring

JEL Classification H23 · L11 · L94

1 Introduction

This paper examines the welfare implications of strategic behavior in a market subjectto environmental regulation. Market-based policies, including some tradable permitsystems, appear to be implemented without the consideration of whether or not thepolluting markets are competitive. This omission is important because, if firms have

E. T. Mansur (B)Dartmouth College and NBER, 6106 Rockefeller Hall, Hanover, NH 03755, USAe-mail: erin.mansur@dartmouth.edu

123

Prices versus quantities 81

market power, they alter the output and emissions of all firms relative to a competitivemarket. This paper studies the interaction of environmental regulation and imper-fectly competitive markets by asking: how does the choice of environmental policyinstrument affect the welfare implications of imperfect competition?

This paper develops a theoretical model of environmental regulation, focusing onthe comparison between emissions taxes (i.e., a price instrument) and tradable permits(a quantity instrument). In a classic analysis, Weitzman (1974) examines the welfareconsequences of price and quantity regulations when abatement costs are uncertain.In contrast to modeling uncertainty, this paper examines the welfare consequences ofpolicy instrument choice when firms have market power in selling a polluting good.

If firms are regulated by a tax, changing emissions will not affect the marginal cost ofpolluting. However, under a tradable permit system, polluters’ decisions can affect thepermit price. I show how this feedback effect can increase the output of strategic firmsand improve welfare. Consider the case of a dominant firm competing with a fringethat has lower emissions rates that it does. By the dominant firm exercising marketpower in the product market, this paper shows that demand for pollution permits falls incomparison to what would have occurred in a competitive market. As the permit pricefalls, firms’ marginal costs decrease as well, particularly for the relatively “dirty”dominant firm. Thus, the firm produces more when regulated by a permit systemrelative to a price mechanism without this feedback effect. The theory is developedfor a dominant firm and competitive fringe setting and then extended to the case ofmultiple strategic firms.

In the context of a restructured electricity market, this paper measures the magnitudeof these welfare consequences. Restructuring has enabled wholesalers to exercise mar-ket power (for example, see Borenstein et al. 2002; Joskow and Kahn 2002; Wolfram1999). The Pennsylvania, New Jersey, and Maryland (PJM) market was restructuredin April 1999. During the previous summer, wholesale prices were consistent withthose of a competitive market, while after restructuring actual prices were substan-tially higher than simulated competitive prices (Mansur 2007b). Exercising marketpower lead to production inefficiencies (Mansur 2008) and lower emissions from PJMfirms.1

At the same time, the Ozone Transport Commission (OTC) established a tradablepermit system to regulate nitrogen oxides (NOx ) emissions by power plants through-out the Northeast, including those in the PJM market. I simulate the interaction of thePJM and OTC markets to determine the impact of policy instrument choice on welfare.Results imply that the market power introduced by restructuring reduced emissionsin PJM by approximately 9 %. Given that the regional tradable permits market capsaggregate pollution, this resulted in greater emissions elsewhere. Relative to a compet-itive market, I find that the permit price was almost 50 % lower because of imperfectcompetition in the electricity market. Had an emissions tax been set at the permitprice that would have occurred under a competitive regime, welfare loss would haveincreased by 7 %.

1 Mansur (2007a) finds emissions measured using a model of competitive behavior exceeded the actualemissions of firms in PJM by 8 %.

123

82 E. T. Mansur

The theory of environmental regulation in imperfectly competitive markets has beenwell studied. Due to an additional distortion in the output market, the second-best taxfor a monopolist is less than the marginal external cost (e.g., Buchanan 1969). Foroligopolies, the pollution implications of market power depend on demand elasticity,the costs and emissions associated with various technology types, the distributionof technologies among firms, and the exact strategic game. Determining the optimalenvironmental regulation in this second-best setting becomes more complicated.2

This literature discusses optimal taxation policy assuming regulators observe mar-ket structure. However, regulators may be slow to adjust to the introduction of strategicbehavior (for example, deregulation, restructuring, or a merger). As with uncertainty(Weitzman 1974) and technological change (Jaffe et al. 2002), important differencesarise between policy instrument choices when regulators are slow to react. Further-more, environmental policy may ignore strategic behavior in polluting markets becauseof the separation of regulatory obligations in the government. The Environmental Pro-tection Agency and Department of Justice have different mandates. For example, theEPA’s Integrated Planning Model assumes a competitive electricity industry.3 Thisis not to say regulators do not know whether markets are competitive, but rather, Iexamine the consequences of not accounting for strategic behavior. In contrast to theexisting literature, this paper asks whether ignoring imperfect competition in settingenvironmental policy has welfare consequences. In particular I ask, if environmentalregulators assume markets are competitive when they are not, what type of policyinstrument will maximize social welfare, prices or quantities?

The paper proceeds as follows. Section 2 describes a model of optimal environ-mental regulation for the case of perfectly competitive markets. Section 3 examinesenvironmental regulation under imperfect competition. In particular, using a dominantfirm-competitive fringe model, I explore how exercising market power affects firms’emissions decisions and how this, in turn, affects the welfare implications of policychoice. Section 4 extends this model to the case when regulators realize whether firmshave market power and the case when there are multiple strategic firms. In Sect. 5, Isimulate how NOx permit prices respond to market power in the PJM electricity mar-ket and quantify the welfare impacts of the policy instrument choice of taxes versustradable permits. Section 6 offers concluding remarks.

2 Model setup

Suppose that N firms emit pollution into a common airshed. For each firm i, emissions(ei ) equal the firm’s output (qi ) times its emissions rate (ri ): ei = ri qi , i ∈ {1, . . . , N }.Pollution results in environmental damages, D = f (e1, . . . , eN ). I assume:

2 For example, even when proportional to emissions rates, an emissions tax may increase pollution fromoligopolists with asymmetric cost functions (Levin 1985). Since market structure leads to production ineffi-ciencies and distorts the total quantity produced, the second-best tax may exceed the marginal environmentalcost (e.g., Shaffer 1995). A related literature has examined the importance of strategic behavior in settingenvironmental policy with international trade (e.g., Barrett 1994).3 See Sect. 2 of the description of the Integrated Planning Model, written by ICF, on the electricity market(http://www.epa.gov/airmarkets/epa-ipm/).

123

Prices versus quantities 83

• (A1) Firms emissions rates, ri , are fixed (firms cannot change technology).• (A2) The number of firms, N , is fixed (firms cannot enter or exit).• (A3) Production costs, ci (qi ), are convex.• (A4) Pollution is uniformly mixed (D = f (

∑Ni=1 ei )).

• (A5) The damage function, D(·), is convex.

Furthermore, I assume that regulators act as if all firms take prices as given. Theregulator will set environmental policy, either an emissions tax or a tradable permitscap, in order to maximize social welfare under this assumption. Namely, regulatorsset policy where they expect marginal damages (D′(·)) to equal the marginal cost ofreducing emissions:

• (A6) Environmental policies are set assuming perfectly competitive behavior.

I restrict the analysis in several ways. I examine only tradable permit systems andlinear taxes with a constant marginal tax rate. Other regulatory forms, like prescriptivecommand-and-control regulation or non-linear taxes, are not modeled.4 Also, I onlyexamine interior solutions (qi > 0). In practice, firms may choose to shut down ifenvironmental regulations become costly enough.

2.1 Emissions tax

When facing a tax (t), price-taking firm i earns profits in market j : Pj qi −ci (qi )−tri qi ,

where Pj is the price of the good sold in market j. The first-order condition can bestated as:

Pj − c′i (qi )

ri= t. (1)

Hence, the marginal cost of reducing pollution is the forgone profits. The regulator

levies the tax such that t = Pj −c′i (q

∗i )

ri= D′(

∑Ni=1 ri q∗

i ), for all i ∈ {1, . . . , N }, where{q∗

1 , . . . , q∗N } are the socially optimal levels of production.

2.2 Permit system

Under a (grandfathered) permit system, firms are allocated permits (ei ) and, in equi-librium, trade at permit price τ. For a given firm i, neither its allocation nor the permitprice depend on qi . Firm i earns profits in market j : Pj qi − ci (qi )− τri qi + τei . Thefirst-order condition is similar to (1):

Pj − c′i (qi )

ri= τ. (2)

4 By tracing the marginal damages function, nonlinear taxes can achieve the first best even in the presenceof cost uncertainty (Ireland 1977; Weisbach 2011).

123

84 E. T. Mansur

The firm sets its marginal cost of abatement equal to the permit price. Here, regulatorsallocate permits equal, in aggregate, to the optimal level of emissions:

∑Ni=1 ei =

∑Ni=1 ri q∗

i . Both taxes and permits achieve the first best. Next, I examine the welfareimplications of introducing market power under these alternative policy choices.

3 Dominant firm and competitive fringe

Suppose that the N firms in the airshed consist of three groups, i ∈ {m, f, o}, thatsell to one of two markets, j ∈ {m, o}. First, a dominant firm produces qm, has anemissions rate rm, and sells as price Pm . Second, a competitive fringe competes in thesame output market as the dominant firm (earning the price Pm): the fringe producesq f and pollutes at rate r f . Third, other price-taking firms face the same environmentalregulation but do not compete in the dominant firm’s output market. In aggregate,these firms produce qo, emit at rate ro, and earn price Po. Under a permit system,these “other” firms trade permits in accordance with (2). For the dominant firm andthe competitive fringe, I assume the following5:

• (A7) The demand function is perfectly inelastic (q).

In equilibrium, qm +q f = q. To measure the relative welfare effects of environmentalpolicies, the paper first examines firms’ incentives under each policy type.

3.1 Firm incentives

3.1.1 Emissions tax

The competitive fringe produces where price equals marginal cost. Under a tax, from(1): Pm = c′

f (q f ) + tr f . By substituting in the equilibrium condition, qm + q f = q,

and simplifying notation, P ≡ Pm, I define P as the inverse residual demand for thedominant firm: P(qm) = c′

f (q − qm) + tr f . By choosing qm , the dominant firm setsP(qm) and earns profits π = P(qm)qm − cm(qm) − trmqm . Let qm solve:

dπ(qm)

dqm= P(qm) + P ′(qm)qm − c′

m(qm) − trm = 0. (3)

Note that assuming demand is perfectly inelastic does not imply that P ′(qm) = −∞:the dominant firm recognizes that the fringe’s output depends on its own behavior.Thus, (3) can be written as:

dπ(qm)

dqm= c′

f (q − qm) + tr f − c′′f (q − qm)qm − c′

m(qm) − trm = 0. (4)

5 This is an assumption common to the literature on wholesale electricity markets: retail consumers payregulated rates that do not depend on the current wholesale price so the derived demand for wholesaleelectricity is completely inelastic.

123

Prices versus quantities 85

The dominant firm produces less that it would have in a competitive market: qm < q∗m .6

Note that qm depends only on exogenous factors: cost functions cm and c f , emissionsrates rm and r f , inelastic demand q, and the tax t.

3.1.2 Permit system

Under a permit system, the fringe will produce where Pm = c′f (q f ) + τr f , see (2).

Here, I denote the residual demand for the dominant firm as P(qm) = c′f (q − qm) +

τ(qm)r f : In choosing qm, the dominant firm sets both P(qm) and τ(qm) and earnsprofits π = P(qm)qm − cm(qm) − τ(qm) (rmqm − em) . Substituting in the residualdemand, let qm solve7:

dπ(qm)

dqm= c′

f (q − qm) + τ(qm)r f − c′′f (q − qm)qm + τ ′(qm)r f qm

−c′m(qm) − τ(qm)rm − τ ′(qm) (rmqm − em) = 0. (5)

Under a permit system, the dominant firm will produce less than the competitive level,qm < q∗

m, assuming a downward sloping residual demand curve.8

Note that the sign of τ ′(qm) depends on whether, relative to the fringe, the dominantfirm is “dirty” (rm > r f ) or “clean” (rm < r f ). In the output comparison below, I willuse the following lemma:

Lemma 1 The permit price is increasing (decreasing) in the dominant firm’s outputif the dominant firm is relatively dirty (clean) in comparison to the fringe, given (A1)–(A7).

Proof By (A7), any equilibrium level of production qm +q f = q∗m+q∗

f = q. When thedominant firm exercises market power, qm < q∗

m, we see that q f −q∗f = q∗

m −qm > 0.

The sign of rm − r f equals the sign of rm(q∗m −qm)− r f (q f −q∗

f ) = rmq∗m + r f q∗

f −(rmqm + r f q f

). Thus, if the dominant firm is relatively dirty then, by exercising

market power, aggregate emissions from the dominant firm’s market will be less thanthe competitive level. For the permit cap to bind, the “other” firms outside this marketwill abate less than the competitive equilibrium, and the permit price will be relativelylow: τ ′(qm) > 0. When the dominant firm is relatively clean, the opposite occurs:the aggregate emissions from the dominant firm’s market exceed the competitive leveland now τ ′(qm) < 0. ��

6 This follows immediately from comparing (1) and (3). As production costs are convex, P ′(qm )qm =−c′′

f (q − qm )qm < 0.

7 Note that if there are only two agents (a single dominant firm and the competitive fringe) that are in boththe product and permit markets, then there is only one (qm , q f ) pair that will solve the two constraints ofperfectly inelastic demand for the product and a fixed supply of permits. However, in this model, there arefirms in other product markets that are also regulated by the permit market. This relaxes the constraint andallows even a single strategic firm to exercise market power without violating the two constraints.8 This holds if τ ′(q∗

m ) < c′′f (q − q∗

m )/r f .

123

86 E. T. Mansur

3.2 Output effect of policy choice

Recall that regulators set environmental policies as if all firms take prices as given,(A6): t = τ(q∗

m). In other words, there is no externality if qm = q∗m . Here, the question

asked is: If competition is imperfect, will welfare be greater under a permit systemor under a tax? A dominant firm, facing either a tax or permit, produces less thatit would in a competitive market. As discussed below, the welfare effects of policychoice depend on the relative magnitudes of qm and qm .

In order to determine whether a dominant firm will produce more under a permitsystem or under a tax, I compare the firm’s marginal profits at a specific point. Namely,I examine dπ(qm)

dqmand dπ(qm)

dqmat output qm where the dominant firm maximizes profits

under a tax. From the first-order condition (3), dπ(qm )dqm

|qm = 0.Hence, if dπ (qm )dqm

|qm > 0,

then the firm produces more under a permit system (otherwise it produces more underthe tax). From (4) and (5), we see:

dπ(qm)

dqm|qm = dπ(qm)

dqm|qm − dπ(qm)

dqm|qm

= [τ (qm)r f + τ ′(qm)r f qm − tr f

] − [τ (qm)rm + τ ′(qm) (rmqm − em) − trm

],

(6)

where the first part in brackets is the difference in marginal revenue between a permitand a tax, and the second is the difference in marginal costs. Equation (6) can bewritten as:

dπ(qm)

dqm|qm = (t − τ(qm))

(rm − r f

) + τ ′(qm)r f qm + τ ′(qm) (em − rmqm) , (7)

(i) (i i) (i i i)

which I decompose into three parts.The first two components of (7) are direct effects of firm’s incentives to exercise

market power in the polluting market. Component (i), (t − τ(qm))(rm − r f

), is the

relative differences in marginal costs. Note that this is always positive. If the dominantfirm is relatively dirty, rm > r f , then exercising market power will drive down thepermit price (see Lemma 1). When the dominant firm is relatively clean, the permitprice will exceed the tax. Component (ii), τ ′(qm)r f qm, is related to the incentive toraise rivals’ costs, which other theoretical and empirical papers examine.9 The sign ofthis component depends on the relative emissions rates (see Lemma 1). The net effectsof these components are discussed below.

The last component of (7), τ ′(qm) (em − rmqm) , shows how firms may have incen-tive to exercise market power in the permit market, as well. This literature began withthe theoretical contribution of Hahn (1984), and has been studied in the context of

9 Misiolek and Elder (1989) and Sartzetakis (1997) provide theoretical analysis of this issue. Kolstad andWolak (2003) find that Californian electricity producers’ behavior in the RECLAIM permit market wasconsistent with this incentive.

123

Prices versus quantities 87

electricity markets.10 In a more general setting, Hahn shows that firms with marketpower in permit markets will have either oligopoly or oligopsony power dependingon whether they have net selling or buying positions. In his setting, a firm minimizestotal compliance costs κ(em) + τ(em)(em − em), where κ(em) are abatement costsand the permit price depends on the strategic firm’s emissions, em . On the margin,the firm sets −κ ′(em) = τ + τ ′(em)(em − em), or marginal abatement costs equal tomarginal permit expenditure costs. If the permit allocation differs from the least costsolution, em = e∗

m, then the firm will exert market power. Interestingly, the type ofmarket power (oligopoly versus oligopsony), depends on the sign of the net position,em − em . For example, a firm long in permits will under abate (by polluting more) inorder to drive up the permit price.

This analysis also holds for component (iii) of (7) with two notable caveats. First,I only model the short run effect where abatement technology is fixed so the onlyabatement cost is the forgone profits of production. Relaxing this assumption addsmore realism to the model, but with substantial additional notation and small changesto the underlying intuition.11 Second, I model how the dominant firm’s productionaffects its market’s aggregate emissions in the equilibrium so τ ′(qm) may be negativeor positive. For this reason, a relatively clean dominant firm that is long in permitswill actually produce less (which increases emissions in its market) in order to driveup the permit price.

Therefore, the sign of (7) depends on whether the dominant firm is relatively cleanor dirty and how many permits are allocated. In practice, firms trade substantially incap-and-trade systems suggesting that they have large net positions, some positive andsome negative. Firms with market power in permit markets may profit by distortingabatement decisions. While this ‘Hahn’ effect, or component (iii), is important inpractice I will abstract away from it for the moment in order to focus on the mainpoint of this paper. Namely, what are the consequences of firms direct incentive toexercise market power in polluting markets? To make this tractable, I make a strongassumption about the initial allocation of permits:

• (A8) The dominant firm is allocated permits equal to its equilibrium emissionsunder (3): em = rmqm .

The implication of this assumption is the dominant firm will not have an incentive trade,at the margin, when starting at qm . Thus, the sign of (7) only depends on components(i) and (ii), or the “feedback effect.” We can now show the following two cases.

3.2.1 Relatively dirty dominant firm

Lemma 2 If the dominant firm is relatively dirty, then it will produce more under apermit system than under a tax (qm > qm), given assumptions (A1)–(A8).

10 Chen and Hobbs (2005) and Chen et al. (2006) examine the interaction of market power in the PJMand NOx markets. They note that firms may exercise market power in the permit market, depending on theinitial allocation of permits. They find that exercising market power in the electricity market will lower theprice of permits.11 Mansur (2006) sketches out a note with a more complex model.

123

88 E. T. Mansur

Proof As discussed above, component (i) of (7) is always positive. By Lemma 1,component (ii) is positive. By (A8), component (iii) is zero. ��

To reiterate, when a dominant firm exercises market power, it will reduce output andthe fringe will increase output by the exact same amount because demand is perfectlyinelastic. However, because the dominant firm is relatively dirty, the net effect is areduction in emissions in the dominant firm’s market. Under a permit system, thisreduction in demand for permits results in other polluters who are not competingdirectly with the dominant firm to emit more, roqo. The new equilibrium in the permitmarket will be at a lower price but with the same aggregate emissions.12 Relativeto a tax, the drop in the permit price has a feedback effect on the dominant firm. Itwill produce more because its marginal costs have fallen. Even though the marginalrevenue may have decreased, the effect on costs dominates.

Note that it is possible that this feedback effect could dominate even if the firm has alarge net purchasing position in the permit market, em rmqm . In other words, permitsare preferable to a tax if components (i) and (ii) overcome a negative component (iii).The bottom line is that the sign of (7) depends on the allocation of permits: the morepermits to the dominant firm, the more likely that a permit market will result in greateroutput than a tax.

3.2.2 Relatively clean dominant firm

Lemma 3 If the dominant firm is relatively clean, then it will produce more (less)under a permit system than under a tax if (t − τ(qm))

(rm − r f

)is greater (less) than

|τ ′(qm)r f qm |, given assumptions (A1)–(A8).

Proof By Lemma 1, component (ii) is negative for the relatively clean dominant firm.(A8) assumes the third component is zero. Thus, (7) is positive only if component (i)offsets component (ii). ��

Here, when the dominant firm produces less than the competitive level, its emissionsreductions (rmq∗

m − rmqm) are more than offset by the dirty fringe. The increase indemand for permits drives up the permit price. The other firms in the permit marketabate more so that in equilibrium the cap is still met. When the permit price rises,it increases the dominant firm’s marginal costs but, as the fringe is relatively dirty,the residual demand curve shifts up by even more. However, this does not imply thatthe dominant firm’s marginal revenue has increased more than its marginal costs.The dominant firm will produce more under a permit system than under a tax only ifcomponent (i) is greater than component (ii).

As with the relatively dirty dominant firm case, a substantial net position can alsooverturn this result. Here, the effect of the permit allocation is the opposite sinceτ ′(qm) < 0. If the dominant firm receives too many permits, then the Hahn effect candominate the feedback effect.

In summary, a strategic firm’s production decision depends on the type of environ-mental regulation. For some cases, like a relatively dirty dominant firm with a small

12 If the pollutant is not uniformly mixed, the new distribution of emissions could have further welfareimplications.

123

Prices versus quantities 89

net permit position, it is easy to sign the effect. In other cases, it is ambiguous. In prac-tice, electricity firms have a mix of technologies. In general, coal plants have higheremissions and lower marginal costs than natural gas plants. In this case, even if allfirms have the same mix of technologies, there will be cases when coal will be on themargin in a competitive equilibrium. Here, strategic behavior will result in less pro-duction from the dominant firm’s coal plants, and more production from the fringe’snatural gas plants. Historically, this is likely the case for PJM (Mansur 2007a). Duringthe late 1990s, emissions rates tended to be negatively correlated with aggregate load(see Holland and Mansur 2008) in most of the U.S., suggesting that the dirty dominantfirm case was more prevalent. Today, as we see entry of low-emissions, low-cost tech-nologies, the opposite case may be more appropriate. For example, combined cyclegas plants have lower costs and emissions rates than gas peaker plants. In the end, thisbecomes an empirical question which I explore with a simulation below.

3.3 Welfare effect of policy choice

Before simulating the effects, however, it is important to consider the welfare impli-cations of dominant firms producing more. If (7) is positive, does this imply greatersocial welfare? To examine this question, I write welfare, W, as:

W = Bm(q)+Bo(qo) − cm(qm) − c f (q f )−co(qo) − D(rmqm + r f q f + roqo), (8)

where B j is the total willingness to pay of market j consumers. The focus of this paperis to ask, if regulators do not account for imperfect competition, then which policyinstrument will result in less welfare loss: an emissions tax or a permit system? Therelationship between the quantity ranking, qm < qm < q∗

m, and welfare can be seen bytaking the derivative of (8) with respect to qm . Note that, in equilibrium, Po = B ′

o(qo).

dW

dqm= Po

dqo

dqm− c′

m(qm) − c′f (q f )

dq f

dqm− c′

o(qo)dqo

dqm

−D′(q)

(

rm + r fdq f

dqm+ ro

dqo

dqm

)

, (9)

where D′(q) ≡ D′(rmqm + r f q f + roqo).

Under a tax, the dominant firm does not interact with the other firms in the airshedin any market: dqo/dqm = 0. From (A7), dq f /dqm = −1. Marginal welfare is:

dW

dqm= c′

f (q f ) − c′m(qm) + D′(q)(r f − rm). (10)

Welfare is maximized when firms have the same marginal social costs: c′m(qm) +

D′(q∗)rm = c′f (q f ) + D′(q∗)r f , which occurs at q∗ = {q∗

m, q∗f , q∗

o }.Under a permit system, the welfare effects are slightly different. If a permit cap is

binding, then there are no environmental effects: rmdqm +r f dq f +rodqo = 0. Given(A7), we can write this as dqo/dqm = (r f − rm)/ro. So the marginal welfare effect is

123

90 E. T. Mansur

−c′m(qm)+c′

f (q f )+ Po−c′o(qo)

ro

(r f − rm

). By substituting in the first-order condition

of the other firms in the airshed, (2), we can rewrite the marginal welfare as:

dW

dqm= c′

f (q f ) − c′m(qm) + τ(qm)(r f − rm). (11)

Again, welfare is maximized at q∗ where the firms equate marginal private costs thatinclude the permit price. Both W and W are increasing in qm up to q∗

m .

The marginal welfare effects, (10) and (11), will be the same only at q∗m, q∗

f , q∗o .

When the dominant firm is relatively dirty, there will be fewer emissions under a tax.As D(q) is convex by (A5), the marginal damages will be less than the tax. Under apermit system, the permit price would also be less than the tax. When the dominantfirm is relatively clean, both marginal damages and the permit price are greater thanthe tax.

Lemmas 2 and 3 show conditions under which the dominant firm will produce moreunder a permit system than under a tax: qm > qm . However, if dW

dqm> dW

dqmfor all qm <

q∗m then total welfare could be less under a permit system even though the dominant

firm is producing more than under a tax. At qm, the difference in the marginal welfareeffects dW

dqm− dW

dqm= (D′(q)−τ(qm))(rm −r f ). In other words, a change the dominant

firm’s production will have differential welfare effects: under a tax, this change willhave environmental costs, D′(q)(rm −r f ); whereas under a permit system, this changewill result in more abatement costs, τ(rm −r f ), incurred by other firms in the airshed.The policy implications are akin to Weitzman’s (1974) finding regarding uncertainty.He showed that if marginal damages are relatively flat then a tax will be preferred,otherwise a permit system will improve welfare under uncertainty. In this analysis,reducing production distortions in the dominant firm’s market, c′

f (q f )− c′m(qm), will

improve welfare. However, there are other considerations that arise due to differencesin environmental regulations.13

The welfare implications are unambiguous only if the difference between environ-mental damages and abatement costs are weakly concave in qm :

d2 D(q)/dq2m − τ ′(qm) ≥ 0,∀qm < q∗

m . (12)

Equation (12) is likely to hold in cases where there are either ecosystem or healththresholds that cause marginal damages change quickly. A good example would be alocal air pollutant like smog where there are short run effects and health thresholds. Incontrast, the welfare consequences would be ambiguous for greenhouse gases, wheremarginal damages are flat in the near term. Also note that local air markets like theNortheast OTC, or even smaller markets like in Los Angeles and Houston, are alsomore likely to have firms with the ability to move permit prices.

13 For example, for a relatively dirty dominant firm, τ(qm ) < τ(q∗m ) and if marginal damages are perfectly

elastic, then D′(q) > τ(qm ) and rm > r f , implying dWdqm

> dWdqm

. The welfare signs are ambiguous as

they depend on the slope of τ ′(qm ) and the equilibrium quantities qm and qm .

123

Prices versus quantities 91

Proposition 1 If a permit system increases production from the dominant firm relativeto a tax (i.e., (7) is positive), then social welfare will be unambiguously greater only ifthe marginal damages are increasing in the dominant firm’s production (d2 D(q)/dq2

m)faster than the marginal cost of abatement (τ ′(qm)). Otherwise, the social welfareeffects will depend on market characteristics.

Proof First consider the case of a relatively dirty dominant firm. From Lemma 2,qm < q∗

m leads to either lower emissions (in the case of a tax) or a lower permitprice (under a permit system). If (12) holds, then the lower emissions under a taxwill result in marginal damages falling faster than the permit price will fall under thepermit system: For a given qm, D′(q) < τ(qm). For the relatively clean dominantfirm, qm < q∗

m results in more emissions (under a tax) or a higher permit price (seeLemma 3). If (12) is positive, then marginal damages increase faster than the permitprice. Thus, when (12) is positive, dW

dqmis greater than dW

dqmfor all qm < q∗

m and, fromLemmas 2 and 3, qm > qm so greater welfare will result under a tradable permitsystem than under a tax. If (12) does not hold, a tax may result in more or less welfarethan a permit system depending on the parameters of the model. ��

Intuitively, if environmental damages have been internalized and the dominant firmminimizes private costs, then the more that it produces the greater the welfare effects.These welfare effects could be quite large.14 I provide a real world example in thesimulation below. First, however, I examine a few extensions of the theory.

4 Extensions

4.1 Can environmental regulators achieve the first best?

By relaxing (A6), we can ask: what would a regulator—who could choose any tax, t, orand permit system, ei —do in order to maximize welfare given imperfect competition?In the dominant firm-competitive fringe setting described above, welfare is maximizedat q∗

m and q∗o (q∗

f is implied by (A7)). Under a permit system, there are effectivelytwo instruments,

∑i �=mei and em, so the first best can be achieved. If qm = q∗

m, then

by allocating∑N

i=1 ri q∗i permits, in aggregate, the equilibrium permit price will equal

marginal damages. Therefore, the second instrument, the share of permits grandfa-thered to the dominant firm, is set such that its marginal revenue equals its marginalcost where qm = q∗

m . Let:

14 For example, suppose the dominant firm has production costs of cm = 30qm and rm = 20. The fringehas c f = 1

2 q2f and r f = 0. For q = 100, the dominant firm’s residual demand is P(qm) = 100 − qm .

Under an emissions tax t = 1, the competitive equilibrium is P∗ = 50, q∗m = 50, and e∗ = 1,000. The

dominant firm would opt to produce qm = 25, P = 75, and e = 500. The welfare loss under a tax wouldbe the increase in production costs (813) less the environmental damages abated (suppose D′(e) = 0.001e,then 375), or 438. Under a permit system, suppose that τ(qm ) = 0.001e = 0.02qm and em = 1,000. Thenthe dominant firm will produce where: 100 − 2qm = 30 + 0.4qm + 0.02(20qm − 1000), or qm = 32.1;P = 67.9 and e = 642. The welfare loss is now composed of increased production costs (518) less the

avoided abatement costs for the other firms in the airshed of∫ 50

32.1 τ(e)de, or 294, for a total deadweightloss of 224. In this example, a tax would approximately double the deadweight loss relative to a permitsystem.

123

92 E. T. Mansur

e∗m ≡ (rm − r f )q

∗m + c′′

f

(q − q∗

m

)q∗

m/τ ′ (q∗m

). (13)

Substituting e∗m into (5), the first-order condition becomes

c′m(qm) + τ(qm)rm − c′

f (q − qm) − τ(qm)r f

=[−c′′

f (q − qm) − τ ′(qm)(rm − r f

)] (qm − q∗

m

), (14)

for which qm = q∗m is the solution.

In contrast, the first best will not be achieved under a tax: there is only one instrumentand two market failures. To see this, note that if there were an emissions tax for eachmarket, to and tm, then the first best could be achieved. As in Sect. 2, to = D′(q∗).The tax (subsidy) in the dominant firm’s market would be tm = D′(q∗) − c′′

f (q −q∗

m)q∗m/(rm − r f ). By substituting tm into (4):

c′m(qm) + D′(q∗)rm − c′

f

(q − q∗

m

) − D′ (q∗) r f = c′′f

(q − q∗

m

) (qm − q∗

m

), (15)

for which qm = q∗m is the solution. However, to �= tm . If the dominant firm is relatively

dirty (clean), then its optimal tax would be less (greater) than to. If a regulator can setonly one tax, t, the regulator will trade off the welfare loss from the environmentalexternality with that from market power, choosing a tax between to and tm . This resultis well known in the literature discussed in Sect. 1.

4.2 Multiple strategic firms

Next, I extend the results of Sect. 3 to the case of multiple strategic firms. Supposethere are several, quantity-setting strategic firms rather than a single dominant firm.The fringe and “other” firms are as before. As above, assume (A1)–(A7), a competitivefringe, and other price-taking firms under the same environmental regulation but notcompeting directly with the strategic firms. Suppose there are M symmetric, Cournotplayers facing a tax. Strategic firm s produces qs and emits at rate rs . It earns profitsP(qs)qs −cs(qs)− trsqs, where residual demand equals P(qs) = c′

f (q −q−s −qs)+tr f and q−s is the output of the other strategic firms. Let qs solve:

dπ(t)

dqs= c′

f (q − q−s − qs) + tr f − c′′f (q − q−s − qs)qs − c′

s(qs) − trs = 0. (16)

In equilibrium, because the M strategic firms are symmetric, they each produce qs :

c′f (q − Mqs) + tr f − c′′

f (q − Mqs)qs = c′s(qs) + trs .

Similarly, under a permit system, let qs solve:

dπ (qs)

dqs= c′

f (q − q−s − qs) + τ(qs)r f − c′′f (q − q−s − qs)qs + τ ′(qs)r f qs

−c′s(qs) − τ(qs)rs − τ ′(qs) (rsqs − es) = 0. (17)

123

Prices versus quantities 93

In equilibrium, because the M strategic firms are symmetric, they each produce qs :

c′f (q − Mqs) + τ(qs)r f − c′′

f (q − Mqs)qs + τ ′(qs)r f qs

= c′s(qs) + τ(qs)rs + τ ′(qs) (rs qs − es) .

Again, the welfare effects can be measured by examining the marginal profits undera permit system at the optimal output under a tax, dπ(qs )

dqs|qs :

dπ(qs)

dqs|qs = dπ(qs)

dqs|qs − dπ(qs)

dqs|qs

= τ(qs)r f + τ ′(qs)r f qs − tr f − τ(qs)rs − τ ′(qs) (rs qs − es) + trs .

(18)

Proposition 2 Proposition 1 holds for M symmetric strategic firms.

Proof When all strategic firms are the same, the difference between the permit systemand tax depends on the permit price function, which depends on the actions of the otherfirms not competing in the market with strategic firms, and exogenous characteristics(r f , rs, es) that do not vary across strategic firms. If the best response function of onefirm shifts by δ, then all best response functions shift by δ. In equilibrium, qs is thesame for all firms and the marginal profits will be the same for all M strategic firms.Therefore, the difference between the permit system and tax is composed of the samecomponents as in Lemmas 2 and 3 and, given the same assumptions, the same resultsfollow. ��

While these results are clear for the case of symmetric Cournot oligopolists, they donot hold in all cases. In particular, when the oligopolists are sufficiently asymmetric,changes in input prices (like tradable permits) can increase production inefficiencies(Fevrier and Linnemer 2004). The welfare loss associated with distorting productioncan be substantial enough to counter the above findings. For example, suppose thatwhen strategic firms produce less than they would have in a competitive market, thisreduces emissions from all firms in their market (the dirty dominant firms analog),which in turn lowers the permit price. The appendix provides a duopoly with fringeexample where one strategic firm has both higher marginal production costs and higheremissions rates than the other one. When the firms reduce pollution in their marketrelative to the competitive equilibrium, the marginal cost of the inefficient strategicfirm falls under a permit system relative to a tax. As a result, it produces more (whichincreases the production inefficiencies) so, for this example, welfare is greater under atax than under a permit system: Lemma 2 does not hold. In order to determine whether apermit system increases welfare in actuality, I simulate the welfare outcomes of policyinstrument choice for the PJM electricity market and the OTC NOx regulation.

5 Simulation of policy instrument choice

This section asks whether these welfare effects are of economic significance. Specif-ically, the question I ask is: what would be the additional deadweight loss in the PJM

123

94 E. T. Mansur

electricity market had a tax been implemented instead of a permit system? Through-out this paper, I assume the tax would have been set optimally assuming competitivebehavior (A6). Since strategic firms in PJM are dirtier—on average—than those in thefringe, exercising market power reduces emissions from PJM firms (Mansur 2007a).If the OTC permit price is endogenous, the decreased demand for permits will resultin a permit price below the tax.

To determine what tax regulators would have chosen, I develop a model of permitsupply. From May to September, the OTC NOx permit market regulates firms in PJM,New England, and New York. During 1999, OTC did not apply to firms in Maine,Maryland, Vermont, Virginia, and Washington, D.C. The number of permits are fixed:If PJM firms pollute more, then the other firms (in New England and New York) mustabate an equal amount.15

This simulation develops a model of firm behavior in the PJM electricity market.The strategy is first to determine what the permit price would have been had the firmsin PJM behaved competitively. In equilibrium, the increase in emissions in PJM as themarket changes from a strategic “regime” to a competitive one must equal the increasein abatement by firms outside of PJM. Given the equilibrium price, I assume thatregulators would have set the tax at this intended level and then simulate how strategicfirms would have produced. As demand is assumed to be perfectly inelastic, the welfareeffects of a tax are the extra production costs. These costs include the environmentalexternality that is valued at the tax level. This assumes optimal regulation wherebythe tax equals the marginal external cost.

The section begins by describing the model of abatement supply outside of PJM.Then I model firm behavior in the PJM electricity market for both the competitiveand strategic regimes. Finally, the simulation method is discussed and the results arepresented.

5.1 Model of permit supply

The degree to which the price rises depends, in part, on the elasticity of the non-PJMfirms’ supply of abatement. NOx pollution can be abated by installing technologiessuch as selective catalytic reduction (SCR), by reducing the burning efficiency of apower plant, and by improving the monitoring of the production process. Some of thistechnology was installed in preparation for this regulation. I assume that these capitalinvestments are fixed in the short run and that firms could not change these investmentdecisions during the first summer of the regulation. In the short run, firms can abatepollution by not operating. The firm forgoes profits but no longer needs to purchase orto hold on to a pollution permit. It is this trade-off of profits for permits that determinesmy abatement supply curve.16

15 This market allows firms to bank permits for future summers but is not modeled here. Given the highprice in the first summer, banking was minimal.16 In the long run, the permit supply function becomes much more elastic. This will dampen the respon-siveness of the permit price to the actions of the dominant firm (i.e., τ ′(qm ) is smaller). This will reduceany differences between the welfare effects of taxes and permits.

123

Prices versus quantities 95

In order to construct this curve, I model the permit market and the New Englandand New York electricity markets as competitive. Recall from (2), the marginal costof abatement (MCA) of a firm taking prices as given is equal to the rents (P − c′(q))divided by the emissions rate (r ). For the period of May to September, I construct anabatement supply curve by measuring the hourly MCA for each power plant regulatedby OTC but not in PJM. To measure the market price (P), I use the hourly system-wideprice from ISO New England for the New England firms. New York did not restructureuntil the following winter. Therefore, I use the New England price as a proxy for theNew York electricity price. The price is assumed to be exogenous to individual costshocks. Further, I do not model the New England electricity price as a function of thepermit price. Note that if electricity prices are endogenous, then more abatement willmean higher permit prices and higher electricity prices. This will increase the slope ofthe abatement supply curve. Ignoring this endogeneity results in a less elastic supplyof permits, which in turn results in a smaller difference between the welfare effects oftaxes and permits.

The EPA’s Egrid database includes information on a power plant’s heat input, elec-tricity output, capacity, emissions, primary fuel source, and regulations. The datasources of the New York city gate natural gas spot market and New York oil spotmarket are discussed in Mansur (2007b), while the EIA’s form 767 spot coal pricesby power plant are discussed in Keohane (2007). The daily marginal costs (c′(q)) aredefined as the sum of fuel costs, variable operating and maintenance costs, and SO2pollution costs.17 These costs do not include the costs of the NOx regulation.

From these data, I construct the abatement supply curve. If the hourly price equalsor exceeds a plant’s marginal cost, then that plant can abate up to its capacity timesits emissions rate that hour. I sort the quantity of abatement by the plant-hour’s MCA.Then I calculate a cumulative abatement function, assuming a linear fit of abatementfor observations with MCA below $5,000/ton. An OLS regression implies that forevery additional ton abated by firms outside of PJM, the permit price will increase by$0.1053/ton.18

5.2 Model of competitive and strategic behavior

This section adapts a model of competition and Cournot behavior from Bushnell et al.(2008, henceforth BMS). As noted above, some firms in PJM had incentives to increaseprices as they sold a substantial amount of energy, q, in the wholesale market. Otherfirms had obligations to serve large amounts of electricity, or native load, (qc) to retailcustomers at fixed rates. These firms may have benefited from lower wholesale prices.The difference between a firm’s production of q and retail obligations of qc, or “netpositions,” affect firms’ incentives. The first-order condition is:

17 Data on variable O&M costs are not readily available so I assume them to be $2/MWh for all powerplants. The SO2 pollution costs apply to power plants regulated by Phase I of the 1990 Clean Air ActAmendment’s Title IV.18 The independent variable is the emissions rate times the plant’s capacity. In the long run, firms will installabatement technology, changing its emissions rate. This may be correlated with the dependent variable(foregone profits). However, in the short run, this is not likely to be the case as abatement technology andcapacity are fixed. For this reason, I assume the independent variable to be exogenous.

123

96 E. T. Mansur

P(q) + P ′(q) · (q − qc) = c′(q) + τ(q) · r + τ ′(q) · (rq − e), (19)

where now firms profit from higher prices only on the amount sold in the market netof the contracts. BMS discuss and account for these net positions. That paper’s modeluses a firm’s first-order condition of profit maximization to solve for equilibrium inthe PJM electricity market.

Note that firms may have incentives to exercise market power in permit marketsdirectly (Hahn 1984). If the allocation of permits, e, is similar to the amount emittedby a strategic firm (rq e), then the term last term of (19), τ ′(q) · (rq − e), willbe small. The two firms likely to set prices in the wholesale electricity market arethe Philadelphia Electric Company (PECO) and Pennsylvania Power & Light (PPL)(Mansur 2007b). These firms emitted 120 and 74 % as much NOx as they were allocatedin permits, respectively.19 In order to focus on the impact of policy instrument choiceon welfare in the electricity market, I assume that firms did not behave strategically inthe permit market: rq e. For a given permit price, I simulate how much each firmin PJM would have produced under both the competitive and Cournot regimes.

Regardless of whether firms take prices as given or act strategically, they willproduce a given amount using their least costly generating units. The BMS modelincludes data on marginal costs, capacity, and emissions rates for all polluting units.Thus, a firm can respond to changes in permit prices by substituting across its unitsusing different fuels or abatement technologies (i.e., fuel switching). For a given permitprice, I recalculate the merit order (least costly set of generating units a firm owns). Iuse these data to determine each firms’ hourly emissions. This allows me to compareaggregate emissions across regimes and permit prices.

5.3 Simulation results

5.3.1 Market power and permit prices

The simulation is solved in several steps. I begin by modeling the permit price assumingfirms actually behave as Cournot firms in the PJM electricity market (see BMS). Theactual permit price was volatile during the summer of 1999; the price started near$5,000/ton and eventually settled around $1,000/ton. In comparison, a tax would havebeen constant throughout this period. It would be difficult to interpret the effects of avolatile permit price relative to a tax. Therefore, I model the permit price as a constantequal to the price that permits were trading at in late September. This is when firmshad to demonstrate compliance. I model the permit price as equal to $1,000/ton.

Second, I use the BMS model to estimate firm behavior in PJM for each hour inthe summer of 1999 when OTC was in effect.20 From May 1 to September 30, 1999,the Cournot model simulation predicts that the PJM firms regulated by OTC emit

19 Using CEMS data, I calculate that during the period of OTC regulation, PECO emitted 3,554 tons ofNOx . In contrast, the firm was allocated permits for 2,939 tons of NOx (see http://www.pacode.com/secure/data/025/chapter123/s123.121.html). PPL emitted 14,785 tons and was allocated permits for 20,027 tons.20 For greater discussion of the assumptions of this model, see BMS.

123

Prices versus quantities 97

Table 1 Simulation of policy choice effects on emissions and welfare

Permit system Tax Difference Percent difference

Marginal private cost of a ton of NOx pollution $1,000 $1,934 $934 93

NOx emissions (tons)

Cournot 88,222 85,923 2,300 2.7

Competitivea 100,936 97,096 3,839 4.0

Difference 12,713 11,174

Percent difference 11 12

Additional permitsb 8,874 10.1

Variable costs ($ millions)

Cournot 1,565 1,573 8.3

Competitive 1,452 1,452 0

Welfare loss

Emissions component –4.4

Firm cost component 11.7

PJM total 113 121 8.3 7.4

Percent loss 7.8 8.3

Change in imports 3.0

Total percent loss 11.3 10.0a Under a permit system, the competitive regime’s permit price would equal $1,934/ton. The first columnholds the price at $1,000/ton (the Cournot regime’s permit price) for comparison purposes onlyb “Additional permits” compares the Cournot regime’s emissions at a $1,000/ton permit price with thecompetitive regime’s emissions at a $1,934/ton permit price or tax

88,222 tons of NOx (see Table 1). In contrast, these same firms would have emitted100,936 tons, an increase of 11 %, if they had taken prices as given. Therefore, PJMfirms in a competitive regime would have demanded 12,713 more permits than thosein a Cournot regime. This increase in demand for permits would have resulted in ahigher permit price. If the firms in PJM behaved the same regardless of the permitprice, then based on the permit supply estimates above, the price would have been$2,338/ton.21 However, the PJM firms do change their production decisions as thepermit price increases.

I solve this simultaneity problem by iterating between the two models discussedin Sects. 5.1 and 5.2. I begin by picking a permit price. Then I measure the quantityof abatement, or number of permits, supplied by firms outside of PJM at that price.22

Next I determine the amount of permits demanded by competitive firms in PJM atthat price and compare that level with the amount demanded in the benchmark case:Cournot firms at the $1,000 price. I vary the permit price until one is found that equatessupply and demand. At the equilibrium price of $1,934/ton, the firms in the competitivemarket emit 97,096 tons, which is 8,874 more than the Cournot equilibrium emissions.

21 That is, the initial $1,000/ton plus the slope of $0.1053/ton times the change in emissions of 12,713 tons.22 Note that by changing the permit price for each iteration, this will change the merit order of each firm.For any given permit price, the firm will produce using the least costly generating units.

123

98 E. T. Mansur

This implies that introducing market power reduced local emissions by approximately9 %. To meet this extra demand for permits, the permit price rises by 93 %, a level wellwithin the range firms actually faced during that summer.

5.3.2 Welfare effects in PJM

As in Sect. 2, I assume that regulators would have set a tax equal to the marginal externalcost of NOx emissions. If they assumed a competitive PJM market, then (based on thecalculations of the permit price above) this tax would be $1,934/ton.23 As discussedin Sect. 3, deadweight loss may be greater under such a tax than under a permit systemwhen firms behave strategically. To test this, I measure the total variable social costin the PJM market including production costs and the environmental externalities ofNOx pollution. Note that consumer surplus does not change in the short run givenfixed retail prices.

Over the summer of 1999, the variable social costs for the competitive regime totaled$1,452 million. This is the case for both a permit system and a tax because, if PJM werea competitive market, then the permit price would equal the tax of $1,934/ton. TheCournot model predicts costs of $1,565 million given the permit price of $1,000/ton.This simulation predicts that firms exercising market power in PJM cause deadweightloss equal to $113 million, or 7.8 % of the variable social costs.

Next, the total variable social costs are estimated assuming a tax. As mentioned, thecompetitive model costs are the same as above since the tax and permit prices equate.With a tax, the strategic firms distort production even more. The variable social costs,including the externality, equal $1,573 million. The higher price of pollution resultedin 2,300 fewer tons, a reduction of 2.7 %. The value of this pollution reduction is$4.4 million. The benefit of these externalities have been taken into account in thesimulation’s measure of total cost. In other words, the costs to the firms are $12.7million greater under the tax in comparison to the permit system, but society alsovalues the cleaner air under a tax. Thus, relative to a permit system, social costs inPJM have increased by $8.3 million under a tax even though there is less pollution.

5.3.3 Welfare effects from imports

In addition, the equilibrium electricity price under the tax is greater than that underthe permit system. The higher prices imply greater imports of electricity, which arecostly. The area under the import supply curve between the electricity price with thepermit and that with the tax represents additional variable costs. Using the BMS importsupply function, I find that these costs total $3.0 million.

Therefore, a tax would have increased the deadweight loss in PJM by $11.3 millionin one summer. This is equal to 7.4 % of the total welfare loss associated with strategicbehavior in this market. In addition to these welfare effects, retail customers paymore for electricity under a tax. The simulated electricity price for the Cournot regimeaverages $52.85/MWh under a tax, slightly more than the $51.89/MWh average under

23 This first-best solution ignores any tax interaction effect (Goulder et al. 1997).

123

Prices versus quantities 99

a tradable permit system.24 If all electricity traded at these prices, then the procurementcosts of buyers in the wholesale market would have increased by $102.4 million under atax relative to a permit system. Recall these costs are for one market and one summeronly. If similar margins exist in other pollution regulations, the overall impacts onwelfare and transfers may be substantial.

6 Conclusions

Environmental policy choice has welfare consequences when output markets are notperfectly competitive. This paper assumes that environment policies are set as if firmstake prices as given. This may result from regulators being slow to adjust to theintroduction of strategic behavior or from regulatory jurisdiction.

Tradable permits may be preferable to taxes because of imperfect competition.When a dominant firm is dirtier than the competitive fringe, exercising market powerwill lower the permit price. This will result in more output from the strategic firm,increasing welfare. When the fringe is dirtier, strategic behavior increases the permitprice. If this increase the strategic firm’s marginal revenue more than its marginalcosts, then welfare will still be greater under a permit system. When there are multiplestrategic firms, the results are more complex. Production inefficiencies from asymmet-ric strategic firms may reverse these findings. As an application of the theory of thesecond best, when regulators initially determine optimal environmental policy assum-ing competitive product markets, the presence of strategic behavior in output marketsmay make tradable permits preferable to a tax.

This paper examines the magnitude of these welfare implications of environmentalpolicy instrument choice. I simulate the OTC permit market and firm behavior in thePJM electricity market. This simulation predicts that strategic behavior reduced localemissions by approximately 9 %. Had the market been competitive, the permit pricewould have been 93 % greater than the price given strategic behavior. I then estimateand compare the welfare effects of Cournot behavior at the observed permit priceand under a tax. I model regulators as setting the tax optimally given an assumptionof competitive behavior in all markets. The deadweight loss from strategic behaviorwould have increased by 7 % if regulators had chosen a tax rather than a tradablepermit system.

These theoretical and simulation results suggest that regulators may improve socialwelfare by considering the interactions between environmental regulation and firmbehavior in product markets. In particular, I find that more consideration should begiven to permit markets. However, there are many other factors that must be consideredin policy choice, most notably uncertainty (Weitzman 1974), transaction costs (Stavins1995) and tax-interaction effects (Goulder et al. 1997). The relative significance ofthese effects will be case specific.

24 These prices may seem small in an oligopoly market with perfectly inelastic demand. However, as BMSnote, this is because the vertically integrated PJM firms had large retail commitments and had less incentiveto set high prices.

123

100 E. T. Mansur

Acknowledgments I would like to thank Severin Borenstein, Jim Bushnell, Stephen Holland, Nat Keo-hane, Barry Nalebuff, Sheila Olmstead, Ben Polak, Chris Timmins, Frank Wolak, Catherine Wolfram andseminar participants at Berkeley, Yale, and NBER.

Appendix

This appendix provides an example of how Lemma 2 may fail if strategic firms areasymmetric. Suppose there are asymmetric Cournot duopolists (firms 1 and 2) and afringe with the following total production costs and emissions rates: c1 = 30qi , c2 =0, c f = 1

2 q2f , r1 = 20, r2 = 1, and r f = 0. Demand: q = 100, so the duopolists’

residual demand = P(q1 + q2) = 100 − q1 − q2. Marginal damages are D′ =0.7 exp(− ln(0.7)e/99). Under an emissions tax t = 1, the competitive equilibriumis: q∗

1 = 0; q∗2 = 99; P∗ = 1; e∗ = 20q∗

1 + q∗2 = 99. Under the tax, the duopolists’

best response functions are q1 = 25−0.5q2 and q2 = 49.5−0.5q1 so the equilibriumis q1 = 1

3 ; q2 = 49 13 ; P = 50 1

3 ; e = 56. The deadweight loss is the increase in

production costs,∫ 1/3

0 c′1(x)dx + ∫ 148/3

99 c′2(x)dx + ∫ 151/3

1 c′f (x)dx = 1276, less the

environmental benefits of less pollution,∫ 99

56 D′(e)de = 40, or 1236. Under a tradablepermit system, suppose τ(e) = 0.7 exp(− ln(0.7)e/99) = 0.7 exp(− ln(0.7)(20q1 +q2)/99) (note the permit price has the same function as marginal damages (assuming(12) holds),) and e2 = 99 (the others don’t pollute in the competitive case (A8)). Theduopoly equilibrium under the permit price is: q1 = 0.91; q2 = 49.18; P = 49.91;e = 67.3. The deadweight loss is the increased production costs, 1272, less the reducedabatement costs of other firms in the airshed,

∫ 9967.3 τ(x)dx = 30, or 1242. Welfare is

greater under the tax than under a permit system. In this example, the strategic firmsemit less pollution than in the competitive case but, because of large asymmetries incosts and emissions rates, welfare is greater under a tax than under a permit system.

Lemma 2 holds for this example if there is either single dominant firm or twosymmetric firms. First, suppose that there is only on dominant firm and a competitivefringe: c1 = 30qi , c f = 1

2 q2f , r1 = 20, and r f = 0. Demand: q = 100, so the

dominant firm’s residual demand = P(q1) = 100 − q1. Marginal damages are D′ =.7 exp(− ln(.7)e/1000). Under an emissions tax t = 1, the competitive equilibriumis: q∗

1 = 50; P∗ = 50; e∗ = 20q∗1 = 1000. Under the tax, the dominant firm produces

q1 = 25; P = 75; e = 500. The deadweight loss is the increase in productioncosts,

∫ 2550 c′

1(x)dx + ∫ 7550 c′

f (x)dx = 813, less the environmental benefits of less

pollution,∫ 1000

500 D′(e)de = 458, or 355. Under a tradable permit system, supposeτ(e) = 0.7 exp(− ln(0.7)e/1000) and e1 = 1000. The equilibrium under the permitprice is: q1 = 27.6; P = 72.4; e = 552. The deadweight loss is the increasedproduction costs, 699, less the reduced abatement costs of other firms in the airshed,∫ 1000

552 τ(x)dx = 414, or 283. Lemma 2 holds.For the symmetric duopolists, suppose c1 = 30qi , c2 = 30q2; c f = 1

2 q2f , r1 =

20, r2 = 20, and r f = 0. Demand: q = 100, so the strategic firms’ resid-ual demand = P(q1 + q2) = 100 − q1 − q2. Marginal damages are D′ =.7 exp(− ln(.7)e/1000). Under an emissions tax t = 1, the competitive equilib-rium is: q∗

1 = q∗2 = 25; P∗ = 50; e∗ = 1000. Under the tax, the firms produce

123

Prices versus quantities 101

q1 = q2 = 16 23 ; P = 66 2

3 ; e = 666 23 . The deadweight loss is the increase in

production costs,∫ 16.7

25 c′1(x)dx + ∫ 16.7

25 c′2(x)dx + ∫ 66.7

50 c′f (x)dx = 472, less the

environmental benefits of less pollution,∫ 1000

666.7 D′(e)de = 314, or 158. Under a trad-able permit system, suppose τ(e) = 0.7 exp(− ln(0.7)e/1000) and e1 = e2 = 500.

The equilibrium under the permit price is: q1 = q2 = 17.65; P = 64.71; e = 705.8.

The deadweight loss is the increased production costs, 402, less the reduced abate-ment costs of other firms in the airshed,

∫ 1000705.8 τ(x)dx = 279, or 123. Again, Lemma

2 holds.

References

Barrett, S. (1994). Strategic environmental policy and international trade. Journal of Public Economics, 54,325–338.

Borenstein, S., Bushnell, J. B., & Wolak, F. A. (2002). Measuring market inefficiencies in California’srestructured wholesale electricity market. American Economic Review, 92, 1376–1405.

Buchanan, J. M. (1969). External diseconomies, corrective taxes, and market structure. American EconomicReview, 59, 174–177.

Bushnell, J. B., Mansur, E. T., & Saravia, C. (2008). Market structure and competition: A cross-marketanalysis of U.S. electricity deregulation. American Economic Review, 98, 237–266.

Chen, Y., & Hobbs, B. (2005). An oligopolistic power market model with tradable NOx permits. IEEETransactions on Power Systems, 20, 119–129.

Chen, Y., Hobbs, B., Leyffer, S., & Munson, T. (2006). Solution of large-scale leader-follower marketequilibria problems: Electric power and NOx permit markets. Computational Management Science, 3,307–330.

Fevrier, P., & Linnemer, L. (2004). Idiosyncratic shocks in an asymmetric Cournot oligopoly. InternationalJournal of Industrial Organization, 22, 835–848.

Goulder, L. H., Parry, I. W. H., Burtraw, D. (1997). Revenue-raising vs. other approaches to environmentalprotection: The critical significance of pre-existing tax distortions. RAND Journal of Economics, 28,708–731.

Hahn, R. W. (1984). Market power and transferable property rights. Quarterly Journal of Economics, 99,753–765.

Holland, S. P., & Mansur, E. T. (2008). Is real-time pricing green? The environmental impacts of electricitydemand variance. Review of Economics and Statistics, 90(3), 550–561.

Ireland, N. J. (1977). Ideal prices vs. prices vs. quantities. Review of Economic Studies, 44(1), 183–186.Jaffe, A. B., Newell, R. G., & Stavins, R. N. (2002). Environmental policy and technological change.

Environmental and Resource Economics, 22, 41–69.Joskow, P., & Kahn, E. (2002). A quantitative analysis of pricing behavior in California’s wholesale elec-

tricity market during summer 2000. Energy Journal, 23, 1–35.Keohane, N. (2007). Cost savings from allowance trading in the 1990 clean air act: Estimates from a choice-

based model. In J. Freeman & C. D. Kolstad (Eds.), Moving to markets in environmental regulation:Lessons from twenty years of experience (Chap. 8, pp. 194–229). Oxford: Oxford Press.

Kolstad, J., & Wolak, F. (2003). Using environmental emissions permit prices to raise electricity prices:Evidence from the California electricity market. Center for the Study of Energy Markets Working Paper113.

Levin, D. (1985). Taxation within Cournot oligopoly. Journal of Public Economics, 27, 281–290.Mansur, E. T. (2006). Note regarding endogenous emissions rates in prices vs. quantities. See http://www.

dartmouth.edu/~mansur/papers/mansur/papers/mansur_envreg_note.pdfMansur, E. T. (2007a). Do oligopolists pollute less? Evidence from a restructured electricity market. Journal

of Industrial Economics, 55, 661–689.Mansur, E. T. (2007b). Upstream competition and vertical integration in electricity markets. Journal of Law

and Economics, 50, 125–156.Mansur, E. T. (2008). Measuring welfare in restructured electricity markets. Review of Economics and

Statistics, 55, 369–386.

123

102 E. T. Mansur

Misiolek, W. S., & Elder, H. W. (1989). Exclusionary manipulation of markets for pollution rights. Journalof Environmental Economics and Management, 16, 156–166.

Sartzetakis, E. S. (1997). Raising rivals’ costs strategies via emission permits markets. Review of IndustrialOrganization, 12, 751–765.

Shaffer, S. (1995). Optimal linear taxation of polluting oligopolists. Journal of Regulatory Economics, 7,85–100.

Stavins, R. N. (1995). Transaction costs and tradable permits. Journal of Environmental Economics andManagement, 29, 133–147.

Weisbach, D. (2011). Instrument choice is instrument design. In G. E. Metcalf (Ed.), U.S. energy tax policy.Cambridge: Cambridge University Press.

Weitzman, M. L. (1974). Prices vs. quantities. Review of Economic Studies, 41, 477–491.Wolfram, C. (1999). Measuring duopoly power in the British electricity spot market. American Economic

Review, 89, 805–826.

123