Prices vs. Quantities:Environmental Regulation and Imperfect Competition

Erin T. Mansur∗

March 13, 2013

Abstract

By exercising market power, a firm will distort the production, and therefore theemissions decisions, of all firms in the market. This paper examines how the welfareimplications of strategic behavior depend on how pollution is regulated. Under anemissions tax, aggregate emissions do not affect the marginal cost of polluting. Incontrast, the price of tradable permits is endogenous. I show when this feedback effectincreases strategic firms’output. Relative to a tax, tradable permits may improve wel-fare in a market with imperfect competition. As an application, I model strategic andcompetitive behavior of wholesalers in a Mid-Atlantic electricity market. Simulationssuggest that exercising market power decreased emissions locally, thereby substantiallyreducing the regional tradable permit price. Furthermore, I find that had regulatorsopted to use a tax instead of permits, the deadweight loss from imperfect competitionwould have been even greater.JEL Classification: H23, L11, L94Key Words: Environmental Regulation, Market Based Instruments, Imperfect Com-

petition, Electricity Restructuring

∗Dartmouth College and NBER, 6106 Rockefeller Hall, Hanover, NH 03755, Tel: (603) 646-2531,erin.mansur@dartmouth.edu. I would like to thank Severin Borenstein, Jim Bushnell, Stephen Holland,Nat Keohane, Barry Nalebuff, Sheila Olmstead, Ben Polak, Chris Timmins, Frank Wolak, Catherine Wol-fram and seminar participants at Berkeley, Yale, and NBER.

1 Introduction

This paper examines the welfare implications of strategic behavior in a market subject to

environmental regulation. Market-based policies, including some tradable permit systems,

appear to be implemented without the consideration of whether or not the polluting markets

are competitive. This omission is important because, if firms have market power, they alter

the output and emissions of all firms relative to a competitive market. This paper studies

the interaction of environmental regulation and imperfectly competitive markets by asking:

how does the choice of environmental policy instrument affect the welfare implications of

imperfect competition?

This paper develops a theoretical model of environmental regulation, focusing on the

comparison between emissions taxes (i.e., a price instrument) and tradable permits (a quan-

tity instrument). In a classic analysis, Weitzman (1974) examines the welfare consequences

of price and quantity regulations when abatement costs are uncertain. In contrast to mod-

eling uncertainty, this paper examines the welfare consequences of policy 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

of polluting. However, under a tradable permit system, polluters’decisions can affect the

permit price. I show how this feedback effect can increase the output of strategic firms and

improve welfare. Consider the case of a dominant firm competing with a fringe that has

lower emissions rates that it does. By the dominant firm exercising market power in the

product market, this paper shows that demand for pollution permits falls in comparison to

what would have occurred in a competitive market. As the permit price falls, firms’marginal

costs decrease as well, particularly for the relatively “dirty”dominant firm. Thus, the firm

produces more when regulated by a permit system relative to a price mechanism without

this feedback effect. The theory is developed for a dominant firm and competitive fringe

setting and then extended to the case of multiple strategic firms.

In the context of a restructured electricity market, this paper measures the magnitude

of these welfare consequences. Restructuring has enabled wholesalers to exercise market

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power (for example, see Borenstein et al., 2002; Joskow and Kahn, 2002; and Wolfram,

1999). The Pennsylvania, New Jersey, and Maryland (PJM) market was restructured in

April 1999. During the previous summer, wholesale prices were consistent with those of a

competitive market, while after restructuring actual prices were substantially higher than

simulated competitive prices (Mansur, 2007b). Exercising market power lead to production

ineffi ciencies (Mansur, 2008) and lower emissions from PJM firms.1

At the same time, the Ozone Transport Commission (OTC) established a tradable permit

system to regulate nitrogen oxides (NOx) emissions by power plants throughout the North-

east, including those in the PJM market. I simulate the interaction of the PJM and OTC

markets to determine the impact of policy instrument choice on welfare. Results imply that

the market power introduced by restructuring reduced emissions in PJM by approximately

9%. Given that the regional tradable permits market caps aggregate pollution, this resulted

in greater emissions elsewhere. Relative to a competitive market, I find that the permit price

was almost 50% lower because of imperfect competition in the electricity market. Had an

emissions tax been set at the permit price that would have occurred under a competitive

regime, welfare loss would have increased by 7%.

The theory of environmental regulation in imperfectly competitive markets has been well

studied. Due to an additional distortion in the output market, the second-best tax for a

monopolist is less than the marginal external cost (e.g., Buchanan (1969)). For oligopolies,

the pollution implications of market power depend on demand elasticity, the costs and emis-

sions associated with various technology types, the distribution of technologies among firms,

and the exact strategic game. Determining the optimal environmental regulation in this

second-best setting becomes more complicated.2

This literature discusses optimal taxation policy assuming regulators observe market

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

2For 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).

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structure. However, regulators may be slow to adjust to the introduction of strategic behavior

(for example, deregulation, restructuring, or a merger). As with uncertainty (Weitzman,

1974) and technological change (Jaffe et al., 2002), important differences arise between policy

instrument choices when regulators are slow to react. Furthermore, environmental policy

may ignore strategic behavior in polluting markets because of the separation of regulatory

obligations in the government. The Environmental Protection Agency and Department of

Justice have different mandates. For example, the EPA’s Integrated Planning Model assumes

a competitive electricity industry.3 This is not to say regulators do not know whether markets

are competitive, but rather, I examine the consequences of not accounting for strategic

behavior. In contrast to the existing literature, this paper asks whether ignoring imperfect

competition in setting environmental policy has welfare consequences. In particular I ask, if

environmental regulators assume markets are competitive when they are not, what type of

policy instrument will maximize social welfare, prices or quantities?

The paper proceeds as follows. Section 2 describes a model of optimal environmental

regulation for the case of perfectly competitive markets. Section 3 examines environmental

regulation under imperfect competition. In particular, using a dominant firm-competitive

fringe model, I explore how exercising market power affects firms’emissions decisions and

how this, in turn, affects the welfare implications of policy choice. Section 4 extends this

model to the case when regulators realize whether firms have market power and the case

when there are multiple strategic firms. In section 5, I simulate how NOx permit prices

respond to market power in the PJM electricity market and quantify the welfare impacts of

the policy instrument choice of taxes versus tradable permits. Section 6 offers concluding

remarks.3See section 2 of the description of the Integrated Planning Model, written by ICF, on the electricity

market (http://www.epa.gov/airmarkets/epa-ipm/).

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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 = riqi, i ∈ {1, ..., N}. Pollution

results in environmental damages, D = f(e1, ..., eN). I assume:

· (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(∑N

i=1 ei)); and

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

Furthermore, I assume that regulators act as if all firms take prices as given. The regulator

will set environmental policy, either an emissions tax or a tradable permits cap, in order to

maximize social welfare under this assumption. Namely, regulators set policy where they

expect marginal damages (D′(·)) to equal the marginal cost of reducing emissions:

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

I restrict the analysis in several ways. I examine only tradable permit systems and linear

taxes with a constant marginal tax rate. Other regulatory forms, like prescriptive command-

and-control regulation or non-linear taxes, are not modeled.4 Also, I only examine interior

solutions (qi > 0). In practice, firms may choose to shut down if environmental regulations

become costly enough.

Emissions Tax When facing a tax (t), price-taking firm i earns profits in market j:

Pjqi − ci(qi) − triqi, where Pj is the price of the good sold in market j. The first-order

condition can be stated as:Pj − c′i(qi)

ri= t. (1)

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

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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′(∑N

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

the socially optimal levels of production.

Permit System Under a (grandfathered) permit system, firms are allocated permits (ei)

and, in equilibrium, trade at permit price τ . For a given firm i, neither its allocation nor the

permit price depend on qi. Firm i earns profits in market j: Pjqi − ci(qi)− τriqi + τei. The

first-order condition is similar to (1):

Pj − c′i(qi)ri

= τ. (2)

The firm sets its marginal cost of abatement equal to the permit price. Here, regulators

allocate permits equal, in aggregate, to the optimal level of emissions:∑N

i=1 ei =∑N

i=1 riq∗i .

Both taxes and permits achieve the first best. Next, I examine the welfare implications 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}, that sell to

one of two markets, j ∈ {m, o}. First, a dominant firm produces qm, has an emissions rate

rm, and sells as price Pm. Second, a competitive fringe competes in the same output market

as the dominant firm (earning the price Pm): the fringe produces qf and pollutes at rate rf .

Third, other price-taking firms face the same environmental regulation 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 and the competitive fringe, I assume the following:5

· (A7) The demand function is perfectly inelastic (q).5This is an assumption common to the literature on wholesale electricity markets: retail consumers pay

regulated rates that do not depend on the current wholesale price so the derived demand for wholesaleelectricity is completely inelastic.

5

In equilibrium, qm+qf = q. To measure the relative welfare effects of environmental policies,

the paper first examines firms’incentives under each policy type.

3.1 Firm Incentives

Emissions Tax The competitive fringe produces where price equals marginal cost. Under

a tax, from (1): Pm = c′f (qf )+trf . By substituting in the equilibrium condition, qm+qf = q,

and simplifying notation, P ≡ Pm, I define P as the inverse residual demand for the dominant

firm: P (qm) = c′f (q − qm) + trf . By choosing qm , the dominant firm sets P (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) + trf − c′′f (q − qm)qm − c′m(qm)− trm = 0. (4)

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 cf , emissions rates

rm and rf , inelastic demand q, and the tax t.

Permit System Under a permit system, the fringe will produce where Pm = c′f (qf )+ τrf ,

see (2). Here, I denote the residual demand for the dominant firm as P (qm) = c′f (q − qm) +

τ(qm)rf : In choosing qm, the dominant firm sets both P (qm) and τ(qm) and earns profits

π = P (qm)qm − cm(qm) − τ(qm) (rmqm − em). Substituting in the residual demand, let qm6This follows immediately from comparing (1) and (3). As production costs are convex, P ′(qm)qm =

−c′′f (q − qm)qm < 0.

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solve:7

dπ(qm)

dqm= c′f (q − qm) + τ(qm)rf − c′′f (q − qm)qm + τ ′(qm)rfqm (5)

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

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 dominant

firm is “dirty”(rm > rf) or “clean”(rm < rf). In the output comparison below, I will use

the following lemma:

Lemma 1 The permit price is increasing (decreasing) in the dominant firm’s output if the

dominant firm is relatively dirty (clean) in comparison to the fringe, given (A1)-(A7).

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

dominant firm exercises market power, qm < q∗m, we see that qf − q∗f = q∗m − qm > 0. The

sign of rm− rf equals the sign of rm(q∗m− qm)− rf (qf − q∗f ) = rmq∗m + rfq

∗f − (rmqm + rfqf ).

Thus, if the dominant firm is relatively dirty then, by exercising market power, aggregate

emissions from the dominant firm’s market will be less than the competitive level. For the

permit cap to bind, the “other”firms outside this market will abate less than the competitive

equilibrium, and the permit price will be relatively low: 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 level and now τ ′(qm) < 0.

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:

7Note that if there are only two agents (a single dominant firm and the competitive fringe) that are inboth the product and permit markets, then there is only one (qm, qf ) pair that will solve the two constraintsof perfectly inelastic demand for the product and a fixed supply of permits. However, in this model, thereare firms in other product markets that are also regulated by the permit market. This relaxes the constraintand allows even a single strategic firm to exercise market power without violating the two constraints.

8This holds if τ ′(q∗m) < c′′f (q − q∗m)/rf .

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If competition is imperfect, will welfare be greater under a permit system or under a tax?

A dominant firm, facing either a tax or permit, produces less that it would in a competitive

market. As discussed below, the welfare effects of policy choice depend on the relative

magnitudes of qm and qm.

In order to determine whether a dominant firm will produce more under a permit system

or under a tax, I compare the firm’s marginal profits at a specific point. Namely, I examinedπ(qm)dqm

and dπ(qm)dqm

at 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 under the tax). From (5) and (4),

we see:

dπ(qm)

dqm|qm =

dπ(qm)

dqm|qm −

dπ(qm)

dqm|qm (6)

= [τ(qm)rf + τ ′(qm)rf qm − trf ]− [τ(qm)rm + τ ′(qm) (rmqm − em)− trm],

where the first part in brackets is the difference in marginal revenue between a permit and

a tax, and the second is the difference in marginal costs. Equation (6) can be written as:

dπ(qm)

dqm|qm = (t− τ(qm)) (rm − rf ) + τ ′(qm)rf qm + τ ′(qm) (em − rmqm) , (7)

(i) (ii) (iii)

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 − rf ), is the relative differ-

ences in marginal costs. Note that this is always positive. If the dominant firm is relatively

dirty, rm > rf , then exercising market power will drive down the permit price (see Lemma 1).

When the dominant firm is relatively clean, the permit price will exceed the tax. Component

(ii), τ ′(qm)rf qm, is related to the incentive to raise rivals’costs, which other theoretical and

empirical papers examine.9 The sign of this component depends on the relative emissions

rates (see Lemma 1). The net effects of these components are discussed below.

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

8

The last component of (7), τ ′(qm) (em − rmqm), shows how firms may have incentive

to exercise market power in the permit market, as well. This literature began with the

theoretical contribution of Hahn (1984), and has been studied in the context of electricity

markets.10 In a more general setting, Hahn shows that firms with market power in permit

markets will have either oligopoly or oligopsony power depending on whether they have

net selling or buying positions. In his setting, a firm minimizes total compliance costs

κ(em)+τ(em)(em−em), where κ(em) are abatement costs and 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 to marginal permit expenditure costs. If the permit

allocation differs from the least cost solution, em = e∗m, then the firm will exert market

power. Interestingly, the type of market 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) in order 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 only abatement cost is

the forgone profits of production. Relaxing this assumption adds more realism to the model,

but with substantial additional notation and small changes to the underlying intuition.11

Second, I model how the dominant firm’s production affects its market’s aggregate emissions

in the equilibrium so τ ′(qm) may be negative or positive. For this reason, a relatively clean

dominant firm that is long in permits will actually produce less (which increases emissions

in its market) in order to drive up the permit price.

Therefore, the sign of (7) depends on whether the dominant firm is relatively clean or

dirty and how many permits are allocated. In practice, firms trade substantially in cap-and-

trade systems suggesting that they have large net positions, some positive and some negative.

Firms with market power in permit markets may profit by distorting abatement decisions.

10Chen 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.11Mansur (2006) sketches out a note with a more complex model.

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While this ‘Hahn’effect, or component (iii), is important in practice I will abstract away

from it for the moment in order to focus on the main point of this paper. Namely, what are

the consequences of firms direct incentive to exercise market power in polluting markets? To

make this tractable, I make a strong assumption about the initial allocation of permits:

· (A8) The dominant firm is allocated permits equal to its equilibrium emis-

sions under (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.

Relatively Dirty Dominant Firm

Lemma 2 If the dominant firm is relatively dirty, then it will produce more under a permit

system than under a tax (qm > qm), given assumptions (A1)-(A8).

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 and the

fringe will increase output by the exact same amount because demand is perfectly inelastic.

However, because the dominant firm is relatively dirty, the net effect is a reduction in emis-

sions in the dominant firm’s market. Under a permit system, this reduction in demand for

permits results in other polluters who are not competing directly with the dominant firm

to emit more, roqo. The new equilibrium in the permit market will be at a lower price but

with the same aggregate emissions.12 Relative to a tax, the drop in the permit price has a

feedback effect on the dominant firm. It will produce more because its marginal costs have

fallen. Even though the marginal revenue may have decreased, the effect on costs dominates.

Note that it is possible that this feedback effect could dominate even if the firm has a

large net purchasing position in the permit market, em << rmqm. In other words, permits12If the pollutant is not uniformly mixed, the new distribution of emissions could have further welfare

implications.

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are 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 more permits to

the dominant firm, the more likely that a permit market will result in greater output than

a tax.

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 − rf ) is greater (less) than |τ ′(qm)rf 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 emissions

reductions (rmq∗m − rmqm) are more than offset by the dirty fringe. The increase in demand

for permits drives up the permit price. The other firms in the permit market abate 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 that the 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 if component (i) is greater than component (ii).

As with the relatively dirty dominant firm case, a substantial net position can also over-

turn this result. Here, the effect of the permit allocation is the opposite since τ ′(qm) < 0.

If the dominant firm receives too many permits, then the Hahn effect can dominate the

feedback effect.

In summary, a strategic firm’s production decision depends on the type of environmental

regulation. For some cases, like a relatively dirty dominant firm with a small net permit

position, it is easy to sign the effect. In other cases, it is ambiguous. In practice, electricity

firms have a mix of technologies. In general, coal plants have higher emissions and lower

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marginal costs than natural gas plants. In this case, even if all firms have the same mix of

technologies, there will be cases when coal will be on the margin in a competitive equilibrium.

Here, strategic behavior will result in less production from the dominant firm’s coal plants,

and more production from the fringe’s natural gas plants. Historically, this is likely the case

for PJM (Mansur, 2007a). During the late 1990s, emissions rates tended to be negatively

correlated with aggregate load (see Holland andMansur, 2008) in most of the U.S., suggesting

that the dirty dominant firm case was more prevalent. Today, as we see entry of low-

emissions, low-cost technologies, the opposite case may be more appropriate. For example,

combined cycle gas plants have lower costs and emissions rates than gas peaker plants. In

the end, this becomes 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 implications

of dominant firms producing more. If (7) is positive, does this imply greater social welfare?

To examine this question, I write welfare, W , as:

W = Bm(q) +Bo(qo)− cm(qm)− cf (qf )− co(qo)−D(rmqm + rfqf + roqo), (8)

where Bj is the total willingness to pay of market j consumers. The focus of this paper is to

ask, if regulators do not account for imperfect competition, then which policy instrument will

result in less welfare loss: an emissions tax or a permit system? The relationship between

the quantity ranking, qm < qm < q∗m, and welfare can be seen by taking the derivative of (8)

with respect to qm. Note that, in equilibrium, Po = B′o(qo).

dW

dqm= Po

dqodqm− c′m(qm)− c′f (qf )

dqfdqm− c′o(qo)

dqodqm−D′(q)(rm + rf

dqfdqm

+ rodqodqm

), (9)

where D′(q) ≡ D′(rmqm + rfqf + roqo).

Under a tax, the dominant firm does not interact with the other firms in the airshed in

any market: dqo/dqm = 0. From (A7), dqf/dqm = −1. Marginal welfare is:

dW

dqm= c′f (qf )− c′m(qm) +D′(q)(rf − rm). (10)

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Welfare is maximized when firms have the same marginal social costs: c′m(qm) +D′(q∗)rm =

c′f (qf ) +D′(q∗)rf , 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 + rfdqf + rodqo = 0. Given (A7),

we can write this as dqo/dqm = (rf − rm)/ro. So the marginal welfare effect is −c′m(qm) +

c′f (qf ) +Po−c′o(qo)

ro(rf − 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 (qf )− c′m(qm) + τ(qm)(rf − rm). (11)

Again, welfare is maximized at q∗ where the firms equate marginal private costs that include

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 a permit system, the

permit price would also be less than the tax. When the dominant firm is relatively clean,

both marginal damages and the permit price are greater than the tax.

Lemmas 2 and 3 show conditions under which the dominant firm will produce more

under a permit system than under a tax: qm > qm. However, if dWdqm

> dWdqm

for 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 welfare effectsdWdqm− dWdqm

= (D′(q)−τ(qm))(rm−rf ). In other words, a change the dominant firm’s production

will have differential welfare effects: under a tax, this change will have environmental costs,

D′(q)(rm − rf ); whereas under a permit system, this change will result in more abatement

costs, τ(rm− rf ), 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 (qf )− c′m(qm), will improve welfare. However, there are other considerations that

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arise due to differences in environmental regulations.13

The welfare implications are unambiguous only if the difference between environmental

damages and abatement costs are weakly concave in qm:

d2D(q)/dq2m − τ ′(qm) ≥ 0,∀qm < q∗m. (12)

Equation (12) is likely to hold in cases where there are either ecosystem or health thresholds

that cause marginal damages change quickly. A good example would be a local air pollutant

like smog where there are short run effects and health thresholds. In contrast, the welfare

consequences would be ambiguous for greenhouse gases, where marginal damages are flat in

the near term. Also note that local air markets like the Northeast OTC, or even smaller

markets like in Los Angeles and Houston, are also more likely to have firms with the ability

to move permit prices.

Proposition 1 If a permit system increases production from the dominant firm relative

to a tax (i.e., (7) is positive), then social welfare will be unambiguously greater only if the

marginal damages are increasing in the dominant firm’s production (d2D(q)/dq2m) faster than

the marginal cost of abatement (τ ′(qm)). Otherwise, the social welfare effects 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 permit price (under a

permit system). If (12) holds, then the lower emissions under a tax will result in marginal

damages falling faster than the permit price will fall under the permit system: For a given qm,

D′(q) < τ(qm). For the relatively clean dominant firm, qm < q∗m results in more emissions

(under a tax) or a higher permit price (see Lemma 3). If (12) is positive, then marginal

damages increase faster than the permit price. Thus, when (12) is positive, dWdqm

is greater

than dWdqm

for all qm < q∗m and, from Lemmas 2 and 3, qm > qm so greater welfare will result

13For 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 > rf , implying dWdqm

> dWdqm

. The welfare signs are ambiguous as theydepend on the slope of τ ′(qm) and the equilibrium quantities qm and qm.

14

under a tradable permit system than under a tax. If (12) does not hold, a tax may result in

more or less welfare than a permit system depending on the parameters of the model.

Intuitively, if environmental damages have been internalized and the dominant firm min-

imizes 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 the simulation 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, or

and permit system, ei—do in order to maximize welfare given imperfect competition? In the

dominant firm-competitive fringe setting described above, welfare is maximized at q∗m and

q∗o (q∗f is implied by (A7)). Under a permit system, there are effectively two instruments,∑

i 6=m

ei and em, so the first best can be achieved. If qm = q∗m, then by allocating∑N

i=1 riq∗i

permits, in aggregate, the equilibrium permit price will equal marginal damages. Therefore,

the second instrument, the share of permits grandfathered to the dominant firm, is set such

that its marginal revenue equals its marginal cost where qm = q∗m. Let:

e∗m ≡ (rm − rf )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)rf = [−c′′f (q− qm)− τ ′(qm)(rm− rf )](qm− q∗m), (14)14For example, suppose the dominant firm has production costs of cm = 30qm and rm = 20. The fringe

has cf = 12q2f and rf = 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∗ = 1000. The dominant firmwould opt to produce qm = 25, P = 75, and e = 500. The welfare loss under a tax would be the increase inproduction 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 = 1000. Then the dominant firmwill produce where: 100− 2qm = 30+ 0.4qm + 0.02(20qm − 1000), or qm = 32.1; P = 67.9 and e = 642. Thewelfare loss is now composed of increased production costs (518) less the avoided abatement costs for theother firms in the airshed of

∫ 5032.1

τ(e)de, or 294, for a total deadweight loss of 224. In this example, a taxwould approximately double the deadweight loss relative to a permit system.

15

for which qm = q∗m is the solution.

In contrast, the first best will not be achieved under a tax: there is only one instrument

and two market failures. To see this, note that if there were an emissions tax for each

market, to and tm, then the first best could be achieved. As in Section 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−rf ).

By substituting tm into (4):

c′m(qm) +D′(q∗)rm − c′f (q − q∗m)−D′(q∗)rf = c′′f (q − q∗m)(qm − q∗m), (15)

for which qm = q∗m is the solution. However, to 6= tm. If the dominant firm is relatively dirty

(clean), then its optimal tax would be less (greater) than to. If a regulator can set only one

tax, t, the regulator will trade off the welfare loss from the environmental externality with

that from market power, choosing a tax between to and tm. This result is well known in the

literature discussed in Section 1.

4.2 Multiple Strategic Firms

Next, I extend the results of Section 3 to the case of multiple strategic firms. Suppose there

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 competitive fringe, and other

price-taking firms under the same environmental regulation but not competing directly with

the strategic firms. Suppose there areM symmetric, Cournot players facing a tax. Strategic

firm s produces qs and emits at rate rs. It earns profits P (qs)qs−cs(qs)−trsqs, where residual

demand equals P (qs) = c′f (q − q−s − qs) + trf and q−s is the output of the other strategic

firms. Let qs solve:

dπ(t)

dqs= c′f (q − q−s − qs) + trf − 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) + trf − c′′f (q −Mqs)qs = c′s(qs) + trs

16

Similarly, under a permit system, let qs solve:

dπ(qs)

dqs= c′f (q − q−s − qs) + τ(qs)rf − c′′f (q − q−s − qs)qs + τ ′(qs)rfqs (17)

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

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

c′f (q −Mqs) + τ(qs)rf − c′′f (q −Mqs)qs + τ ′(qs)rf qs = c′s(qs) + τ(qs)rs + τ ′(qs) (rsqs − es)

Again, the welfare effects can be measured by examining the marginal profits under a

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 (18)

= τ(qs)rf + τ ′(qs)rf qs − trf − τ(qs)rs − τ ′(qs) (rsqs − es) + trs.

Proposition 2 Proposition 1 holds for M symmetric strategic firms.

Proof. When all strategic firms are the same, the difference between the permit system and

tax depends on the permit price function, which depends on the actions of the other firms

not competing in the market with strategic firms, and exogenous characteristics (rf , rs, es)

that do not vary across strategic firms. If the best response function of one firm shifts by

δ, then all best response functions shift by δ. In equilibrium, qs is the same 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 same components as in Lemmas 2

and 3 and, given the same assumptions, the same results follow.

While these results are clear for the case of symmetric Cournot oligopolists, they do not

hold in all cases. In particular, when the oligopolists are suffi ciently asymmetric, changes

in input prices (like tradable permits) can increase production ineffi ciencies (Fevrier and

Linnemer, 2004). The welfare loss associated with distorting production can be substantial

enough to counter the above findings. For example, suppose that when strategic firms

produce less than they would have in a competitive market, this reduces emissions from all

firms in their market (the dirty dominant firms analog), which in turn lowers the permit price.

17

The appendix provides a duopoly with fringe example where one strategic firm has both

higher marginal production costs and higher emissions rates than the other one. When the

firms reduce pollution in their market relative to the competitive equilibrium, the marginal

cost of the ineffi cient strategic firm falls under a permit system relative to a tax. As a

result, it produces more (which increases the production ineffi ciencies) so, for this example,

welfare is greater under a tax than under a permit system: Lemma 2 does not hold. In

order to determine whether a permit system increases welfare in actuality, I simulate the

welfare outcomes of policy instrument 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. Specifically,

the question I ask is: what would be the additional deadweight loss in the PJM electricity

market had a tax been implemented instead of a permit system? Throughout this paper, I

assume the tax would have been set optimally assuming competitive behavior (A6). Since

strategic firms in PJM are dirtier—on average—than those in the fringe, exercising market

power reduces emissions from PJM firms (Mansur, 2007a). If the OTC permit price is

endogenous, the decreased demand for permits will result in a permit price below the tax.

To determine what tax regulators would have chosen, I develop a model of permit supply.

FromMay 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) must abate 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 firms in PJM

behaved competitively. In equilibrium, the increase in emissions in PJM as the market

15This market allows firms to bank permits for future summers but is not modeled here. Given the highprice in the first summer, banking was minimal.

18

changes from a strategic “regime”to a competitive one must equal the increase in abatement

by firms outside of PJM. Given the equilibrium price, I assume that regulators would have

set the tax at this intended level and then simulate how strategic firms would have produced.

As demand is assumed to be perfectly inelastic, the welfare effects of a tax are the extra

production costs. These costs include the environmental externality that is valued at the tax

level. This assumes optimal regulation whereby the 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 competitive and strategic

regimes. Finally, the simulation method is discussed and the results are presented.

5.1 Model of Permit Supply

The degree to which the price rises depends, in part, on the elasticity of the non-PJM

firms’supply of abatement. NOx pollution can be abated by installing technologies such as

Selective Catalytic Reduction (SCR), by reducing the burning effi ciency of a power plant,

and by improving the monitoring of the production process. Some of this technology was

installed in preparation for this regulation. I assume that these capital investments are fixed

in the short run and that firms could not change these investment decisions during the first

summer of the regulation. In the short run, firms can abate pollution by not operating. The

firm forgoes profits but no longer needs to purchase or to hold on to a pollution permit. It

is this trade-off of profits for permits that determines my abatement supply curve.16

In order to construct this curve, I model the permit market and the New England and

New York electricity markets as competitive. Recall from (2), the marginal cost of 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 an abatement supply

curve by measuring the hourly MCA for each power plant regulated by OTC but not in

PJM. To measure the market price (P ), I use the hourly system-wide price from ISO New

16In 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.

19

England for the New England firms. New York did not restructure until the following winter.

Therefore, I use the New England price as a proxy for the New York electricity price. The

price is assumed to be exogenous to individual cost shocks. Further, I do not model the New

England electricity price as a function of the permit price. Note that if electricity prices

are endogenous, then more abatement will mean higher permit prices and higher electricity

prices. This will increase the slope of the abatement supply curve. Ignoring this endogeneity

results in a less elastic supply of permits, which in turn results in a smaller difference between

the welfare effects of taxes and permits.

The EPA’s Egrid database includes information on a power plant’s heat input, electricity

output, capacity, emissions, primary fuel source, and regulations. The data sources of the

New York city gate natural gas spot market and New York oil spot market are discussed

in Mansur (2007b), while the EIA’s form 767 spot coal prices by power plant are discussed

in Keohane (2007). The daily marginal costs (c′(q)) are defined as the sum of fuel costs,

variable operating and maintenance costs, and SO2 pollution 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 equals

or exceeds a plant’s marginal cost, then that plant can abate up to its capacity times its

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 abatement for observa-

tions with MCA below $5000/ton. An OLS regression implies that for every additional ton

abated by firms outside of PJM, the permit price will increase by $0.1053/ton.18

17Data 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.18The independent variable is the emissions rate times the plant’s capacity. In the long run, firms will

install abatement 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.

20

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 increase prices as

they sold a substantial amount of energy, q, in the wholesale market. Other firms had

obligations to serve large amounts of electricity, or native load, (qc) to retail customers 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 “net positions,”affect firms’

incentives. The first-order condition is:

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 net of the

contracts. BMS discuss and account for these net positions. That paper’s model uses a firm’s

first-order condition of profit maximization to solve for equilibrium in the PJM electricity

market.

Note that firms may have incentives to exercise market power in permit markets directly

(Hahn, 1984). If the allocation of permits, e, is similar to the amount emitted by a strategic

firm (rq ' e), then the term last term of (19), τ ′(q) · (rq − e), will be small. The two

firms likely to set prices in the wholesale electricity market are the Philadelphia Electric

Company (PECO) and Pennsylvania Power & Light (PPL) (Mansur, 2007b). These firms

emitted 120% and 74% as much NOx as they were allocated in permits, respectively.19 In

order to focus on the impact of policy instrument choice on welfare in the electricity market,

I assume that firms did not behave strategically in the permit market: rq ' e. For a given

permit price, I simulate how much each firm in PJM would have produced under both the

competitive and Cournot regimes.

Regardless of whether firms take prices as given or act strategically, they will produce

a given amount using their least costly generating units. The BMS model includes data on19Using CEMS data, I calculate that during the period of OTC regulation, PECO emitted

3554 tons of NOx. In contrast, the firm was allocated permits for 2939 tons of NOx (Seehttp://www.pacode.com/secure/data/025/chapter123/s123.121.html). PPL emitted 14,785 tons and wasallocated permits for 20,027 tons.

21

marginal costs, capacity, and emissions rates for all polluting units. Thus, a firm can respond

to changes in permit prices by substituting across its units using different fuels or abatement

technologies (i.e., fuel switching). For a given permit price, I recalculate the merit order

(least costly set of generating units a firm owns). I use these data to determine each firms’

hourly emissions. This allows me to compare aggregate 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 assuming firms

actually behave as Cournot firms in the PJM electricity market (see BMS). The actual permit

price was volatile during the summer of 1999; the price started near $5000/ton and eventually

settled around $1000/ton. In comparison, a tax would have been constant throughout this

period. It would be diffi cult to interpret the effects of a volatile permit price relative to a

tax. Therefore, I model the permit price as a constant equal to the price that permits were

trading at in late September. This is when firms had to demonstrate compliance. I model

the permit price as equal to $1000/ton.

Second, I use the BMS model to estimate firm behavior in PJM for each hour in the

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 88,222 tons of NOx

(see Table 1). In contrast, these same firms would have emitted 100,936 tons, an increase

of 11%, if they had taken prices as given. Therefore, PJM firms in a competitive regime

would have demanded 12,713 more permits than those in a Cournot regime. This increase

in demand for permits would have resulted in a higher permit price. If the firms in PJM

behaved the same regardless of the permit price, then based on the permit supply estimates

above, the price would have been $2338/ton.21 However, the PJM firms do change their

production decisions as the permit price increases.

20For greater discussion of the assumptions of this model, see BMS.21That is, the initial $1000/ton plus the slope of $0.1053/ton times the change in emissions of 12,713 tons.

22

I solve this simultaneity problem by iterating between the two models discussed in sections

5.1 and 5.2. I begin by picking a permit price. Then I measure the quantity of 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 at that price and compare

that level with the amount demanded in the benchmark case: Cournot firms at the $1000

price. I vary the permit price until one is found that equates supply and demand. At the

equilibrium price of $1934/ton, the firms in the competitive market emit 97,096 tons, which

is 8874 more than the Cournot equilibrium emissions. This implies that introducing market

power reduced local emissions by approximately 9%. To meet this extra demand for permits,

the permit price rises by 93%, a level well within the range firms actually faced during that

summer.

5.3.2 Welfare Effects in PJM

As in section 2, I assume that regulators would have set a tax equal to the marginal external

cost of NOx emissions. If they assumed a competitive PJM market, then (based on the

calculations of the permit price above) this tax would be $1934/ton.23 As discussed in section

3, deadweight loss may be greater under such a tax than under a permit system when firms

behave strategically. To test this, I measure the total variable social cost in the PJM market

including production costs and the environmental externalities of NOx pollution. Note that

consumer surplus does not change in the short run given fixed retail prices.

Over the summer of 1999, the variable social costs for the competitive regime totaled

$1452 million. This is the case for both a permit system and a tax because, if PJM were a

competitive market, then the permit price would equal the tax of $1934/ton. The Cournot

model predicts costs of $1565 million given the permit price of $1000/ton. This simulation

predicts that firms exercising market power in PJM cause deadweight loss equal to $113

million, or 7.8% of the variable social costs.

22Note 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.23This first-best solution ignores any tax interaction effect (Goulder et al., 1997).

23

Next, the total variable social costs are estimated assuming a tax. As mentioned, the

competitive 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 $1573 million. The higher price of pollution resulted in 2300 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 the simulation’s measure of total cost.

In other words, the costs to the firms are $12.7 million greater under the tax in comparison

to the permit system, but society also values the cleaner air under a tax. Thus, relative to a

permit system, social costs in PJM 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 under the

permit system. The higher prices imply greater imports of electricity, which are costly. The

area under the import supply curve between the electricity price with the permit and that

with the tax represents additional variable costs. Using the BMS import supply function, I

find that these costs total $3.0 million.

Therefore, a tax would have increased the deadweight loss in PJM by $11.3 million in one

summer. This is equal to 7.4% of the total welfare loss associated with strategic behavior

in this market. In addition to these welfare effects, retail customers pay more for electricity

under a tax. The simulated electricity price for the Cournot regime averages $52.85/MWh

under a tax, slightly more than the $51.89/MWh average under a tradable permit system.24

If all electricity traded at these prices, then the procurement costs of buyers in the wholesale

market would have increased by $102.4 million under a tax relative to a permit system.

Recall these costs are for one market and one summer only. If similar margins exist in other

pollution regulations, the overall impacts on welfare and transfers may be substantial.

24These 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.

24

6 Conclusions

Environmental policy choice has welfare consequences when output markets are not perfectly

competitive. This paper assumes that environment policies are set as if firms take prices as

given. This may result from regulators being slow to adjust to the introduction 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 power will 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 permit price. If this increase

the strategic firm’s marginal revenue more than its marginal costs, then welfare will still

be greater under a permit system. When there are multiple strategic firms, the results

are more complex. Production ineffi ciencies from asymmetric strategic firms may reverse

these findings. As an application of the theory of the second best, when regulators initially

determine optimal environmental policy assuming competitive product markets, the presence

of strategic behavior in output markets may make tradable permits preferable to a tax.

This paper examines the magnitude of these welfare implications of environmental pol-

icy instrument choice. I simulate the OTC permit market and firm behavior in the PJM

electricity market. This simulation predicts that strategic behavior reduced local emissions

by approximately 9%. Had the market been competitive, the permit price would have been

93% greater than the price given strategic behavior. I then estimate and compare the welfare

effects of Cournot behavior at the observed permit price and under a tax. I model regulators

as setting the tax optimally given an assumption of competitive behavior in all markets. The

deadweight loss from strategic behavior would have increased by 7% if regulators had chosen

a tax rather than a tradable permit system.

These theoretical and simulation results suggest that regulators may improve social wel-

fare by considering the interactions between environmental regulation and firm behavior in

product markets. In particular, I find that more consideration should be given to permit mar-

kets. However, there are many other factors that must be considered in policy choice, most

25

notably uncertainty (Weitzman, 1974), transaction costs (Stavins, 1995) and tax-interaction

effects (Goulder et al., 1997). The relative significance of these effects will be case specific.

26

Appendix

This appendix provides an example of how Lemma 2 may fail if strategic firms are asym-

metric. Suppose there are asymmetric Cournot duopolists (firms 1 and 2) and a fringe

with the following total production costs and emissions rates: c1 = 30qi, c2 = 0, cf =

12q2f , r1 = 20, r2 = 1, and rf = 0. Demand: q = 100, so the duopolists’residual demand =

P (q1+q2) = 100−q1−q2.Marginal damages areD′ = 0.7 exp(− ln(0.7)e/99). Under an emis-

sions tax t = 1, the competitive equilibrium is: 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 = 49.5−0.5q1so the equilibrium is q1 = 1

3; q2 = 49

13; P = 501

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

in production costs,∫ 1/30

c′1(x)dx +∫ 148/399

c′2(x)dx +∫ 151/31

c′f (x)dx = 1276, less the envi-

ronmental benefits of less pollution,∫ 9956D′(e)de = 40, or 1236. Under a tradable permit

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)). The duopoly 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 reduced abatement 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 firms emit less pollution than in the competitive case

but, because of large asymmetries in costs 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 two symmetric

firms. First, suppose that there is only on dominant firm and a competitive fringe: c1 =

30qi, cf =12q2f , r1 = 20, and rf = 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 equilibrium is: 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 production costs,∫ 2550c′1(x)dx +

∫ 7550c′f (x)dx = 813, less the environmental

benefits of less pollution,∫ 1000500

D′(e)de = 458, or 355. Under a tradable permit system,

27

suppose τ(e) = 0.7 exp(− ln(0.7)e/1000) and e1 = 1000. The equilibrium under the permit

price is: q1 = 27.6; P = 72.4; e = 552. The deadweight loss is the increased production

costs, 699, less the reduced abatement costs of other firms in the airshed,∫ 1000552

τ(x)dx =

414, or 283. Lemma 2 holds.

For the symmetric duopolists, suppose c1 = 30qi, c2 = 30q2; cf =12q2f , r1 = 20, r2 = 20,

and rf = 0. Demand: q = 100, so the strategic firms’residual 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 equilibrium is: q∗1 = q∗2 = 25;P ∗ = 50; e∗ = 1000. Under the

tax, the firms produce q1 = q2 = 1623; P = 662

3; e = 6662

3. The deadweight loss is the

increase in production costs,∫ 16.725

c′1(x)dx +∫ 16.725

c′2(x)dx +∫ 66.750

c′f (x)dx = 472, less the

environmental benefits of less pollution,∫ 1000666.7

D′(e)de = 314, or 158. Under a tradable

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 abatement costs of other firms in the

airshed,∫ 1000705.8

τ(x)dx = 279, or 123. Again, Lemma 2 holds.

28

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31

Table 1

Simulation of Policy Choice Effects on Emissions and Welfare Permit Percent System Tax Difference 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 11.3 10.0% Percent loss

Notes:

a) Under a permit system, the competitive regime’s permit price would equal $1934/ton. The first column holds the price at $1000/ton (the Cournot regime’s permit price) for comparison purposes only.

b) “Additional permits” compares the Cournot regime’s emissions at a $1000/ton permit price with the competitive regime’s emissions at a $1934/ton permit price or tax.