Prices vs. Quantities:
Environmental Regulation and Imperfect Competition
Erin T. Mansur
March 13, 2013
Abstract
By exercising market power, a …rm will distort the production, and therefore the
emissions decisions, of all …rms in the market. This paper examines how the welfare
implications of strategic behavior depend on how pollution is regulated. Under an
emissions tax, aggregate emissions do not a¤ect the marginal cost of polluting. In
contrast, the price of tradable permits is endogenous. I show when this feedback e¤ect
increases strategic …rms’output. Relative to a tax, tradable permits may improve welfare in a market with imperfect competition. As an application, I model strategic and
competitive behavior of wholesalers in a Mid-Atlantic electricity market. Simulations
suggest that exercising market power decreased emissions locally, thereby substantially
reducing the regional tradable permit price. Furthermore, I …nd that had regulators
opted to use a tax instead of permits, the deadweight loss from imperfect competition
would have been even greater.
JEL Classi…cation: H23, L11, L94
Key Words: Environmental Regulation, Market Based Instruments, Imperfect Competition, Electricity Restructuring
Dartmouth College and NBER, 6106 Rockefeller Hall, Hanover, NH 03755, Tel: (603) 646-2531,
[email protected]. I would like to thank Severin Borenstein, Jim Bushnell, Stephen Holland,
Nat Keohane, Barry Nalebu¤, Sheila Olmstead, Ben Polak, Chris Timmins, Frank Wolak, Catherine Wolfram 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 …rms have market power, they alter
the output and emissions of all …rms 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 a¤ect 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 quantity instrument). In a classic analysis, Weitzman (1974) examines the welfare consequences
of price and quantity regulations when abatement costs are uncertain. In contrast to modeling uncertainty, this paper examines the welfare consequences of policy instrument choice
when …rms have market power in selling a polluting good.
If …rms are regulated by a tax, changing emissions will not a¤ect the marginal cost
of polluting. However, under a tradable permit system, polluters’ decisions can a¤ect the
permit price. I show how this feedback e¤ect can increase the output of strategic …rms and
improve welfare. Consider the case of a dominant …rm competing with a fringe that has
lower emissions rates that it does. By the dominant …rm 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, …rms’marginal
costs decrease as well, particularly for the relatively “dirty” dominant …rm. Thus, the …rm
produces more when regulated by a permit system relative to a price mechanism without
this feedback e¤ect. The theory is developed for a dominant …rm and competitive fringe
setting and then extended to the case of multiple strategic …rms.
In the context of a restructured electricity market, this paper measures the magnitude
of these welfare consequences. Restructuring has enabled wholesalers to exercise market
1
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
ine¢ ciencies (Mansur, 2008) and lower emissions from PJM …rms.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 Northeast, 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 …nd 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 emissions associated with various technology types, the distribution of technologies among …rms,
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
1
Mansur (2007a) …nds emissions measured using a model of competitive behavior exceeded the actual
emissions of …rms in PJM by 8%.
2
For example, even when proportional to emissions rates, an emissions tax may increase pollution from
oligopolists with asymmetric cost functions (Levin, 1985). Since market structure leads to production ine¢ ciencies and distorts the total quantity produced, the second-best tax may exceed the marginal environmental
cost (e.g., Sha¤er, 1995). A related literature has examined the importance of strategic behavior in setting
environmental policy with international trade (e.g., Barrett, 1994).
2
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 (Ja¤e et al., 2002), important di¤erences 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 di¤erent 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 …rm-competitive
fringe model, I explore how exercising market power a¤ects …rms’ emissions decisions and
how this, in turn, a¤ects the welfare implications of policy choice. Section 4 extends this
model to the case when regulators realize whether …rms have market power and the case
when there are multiple strategic …rms. 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 o¤ers concluding
remarks.
3
See section 2 of the description of the Integrated Planning Model, written by ICF, on the electricity
market (http://www.epa.gov/airmarkets/epa-ipm/).
3
2
Model Setup
Suppose that N …rms emit pollution into a common airshed. For each …rm i, emissions (ei )
equal the …rm’s output (qi ) times its emissions rate (ri ): ei = ri qi ; i 2 f1; :::; N g. Pollution
results in environmental damages, D = f (e1 ; :::; eN ). I assume:
(A1) Firms emissions rates, ri , are …xed (…rms cannot change technology);
(A2) The number of …rms, N , is …xed (…rms cannot enter or exit);
(A3) Production costs, ci (qi ), are convex;
P
(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 …rms 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 (D0 ( )) 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 commandand-control regulation or non-linear taxes, are not modeled.4 Also, I only examine interior
solutions (qi > 0). In practice, …rms may choose to shut down if environmental regulations
become costly enough.
Emissions Tax
Pj q i
ci (qi )
When facing a tax (t), price-taking …rm i earns pro…ts in market j:
tri qi , where Pj is the price of the good sold in market j. The …rst-order
condition can be stated as:
Pj
c0i (qi )
= t:
ri
4
(1)
By tracing the marginal damages function, nonlinear taxes can achieve the …rst best even in the presence
of cost uncertainty (Ireland, 1977; Weisbach, 2011).
4
Hence, the marginal cost of reducing pollution is the forgone pro…ts. The regulator levies
P
P c0 (q )
the tax such that t = j rii i = D0 ( N
i=1 ri qi ); for all i 2 f1; ::; N g, where fq1 ; :::; qN g are
the socially optimal levels of production.
Permit System
Under a (grandfathered) permit system, …rms are allocated permits (ei )
and, in equilibrium, trade at permit price . For a given …rm i, neither its allocation nor the
permit price depend on qi . Firm i earns pro…ts in market j: Pj qi
ci (qi )
ri qi + ei . The
…rst-order condition is similar to (1):
Pj
c0i (qi )
= :
ri
(2)
The …rm sets its marginal cost of abatement equal to the permit price. Here, regulators
P
PN
allocate permits equal, in aggregate, to the optimal level of emissions: N
i=1 ei =
i=1 ri qi .
Both taxes and permits achieve the …rst 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 …rms in the airshed consist of three groups, i 2 fm; f; og, that sell to
one of two markets, j 2 fm; og. First, a dominant …rm 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 …rm (earning the price Pm ): the fringe produces qf and pollutes at rate rf .
Third, other price-taking …rms face the same environmental regulation but do not compete
in the dominant …rm’s output market. In aggregate, these …rms produce qo , emit at rate ro ,
and earn price Po . Under a permit system, these “other”…rms trade permits in accordance
with (2). For the dominant …rm and the competitive fringe, I assume the following:5
(A7) The demand function is perfectly inelastic (q).
5
This 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 wholesale
electricity is completely inelastic.
5
In equilibrium, qm +qf = q. To measure the relative welfare e¤ects of environmental policies,
the paper …rst examines …rms’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 = c0f (qf )+trf . By substituting in the equilibrium condition, qm +qf = q,
and simplifying notation, P
…rm: P (qm ) = c0f (q
pro…ts
Pm , I de…ne P as the inverse residual demand for the dominant
qm ) + trf . By choosing qm , the dominant …rm sets P (qm ) and earns
= P (qm )qm
cm (qm )
trm qm . Let qbm solve:
d (qm )
= P (qm ) + P 0 (qm )qm
dqm
c0m (qm )
trm = 0:
Note that assuming demand is perfectly inelastic does not imply that P 0 (qm ) =
(3)
1: the
dominant …rm recognizes that the fringe’s output depends on its own behavior. Thus, (3)
can be written as:
d (qm )
= c0f (q
dqm
qm ) + trf
c00f (q
qm )qm
c0m (qm )
trm = 0:
(4)
The dominant …rm produces less that it would have in a competitive market: qbm < qm .6
Note that qbm 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 = c0f (qf ) + rf ,
see (2). Here, I denote the residual demand for the dominant …rm as Pe(qm ) = c0f (q
qm ) +
(qm )rf : In choosing qm , the dominant …rm sets both Pe(qm ) and (qm ) and earns pro…ts
e = Pe(qm )qm
cm (qm )
(qm ) (rm qm
em ). Substituting in the residual demand, let qem
6
This follows immediately from comparing (1) and (3). As production costs are convex, P 0 (qm )qm =
c00f (q qm )qm < 0.
6
solve:7
de(qm )
= c0f (q qm ) + (qm )rf c00f (q qm )qm + 0 (qm )rf qm
dqm
0
c0m (qm )
(qm )rm
(qm ) (rm qm em ) = 0.
(5)
Under a permit system, the dominant …rm will produce less than the competitive level,
qem < qm , assuming a downward sloping residual demand curve.8
Note that the sign of
0
(qm ) depends on whether, relative to the fringe, the dominant
…rm 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 …rm’s output if the
dominant …rm is relatively dirty (clean) in comparison to the fringe, given (A1)-(A7).
Proof. By (A7), any equilibrium level of production qm + qf = qm + qf = q. When the
dominant …rm exercises market power, qm < qm , we see that qf
sign of rm
rf equals the sign of rm (qm
qm )
rf (qf
qf = qm
qf ) = rm qm + rf qf
qm > 0. The
(rm qm + rf qf ).
Thus, if the dominant …rm is relatively dirty then, by exercising market power, aggregate
emissions from the dominant …rm’s market will be less than the competitive level. For the
permit cap to bind, the “other”…rms outside this market will abate less than the competitive
equilibrium, and the permit price will be relatively low:
0
(qm ) > 0. When the dominant …rm
is relatively clean, the opposite occurs: the aggregate emissions from the dominant …rm’s
0
market exceed the competitive level and now
3.2
(qm ) < 0.
Output E¤ect of Policy Choice
Recall that regulators set environmental policies as if all …rms take prices as given, (A6):
t = (qm ). In other words, there is no externality if qm = qm . Here, the question asked is:
7
Note that if there are only two agents (a single dominant …rm and the competitive fringe) that are in
both the product and permit markets, then there is only one (qm ; qf ) pair that will solve the two constraints
of perfectly inelastic demand for the product and a …xed supply of permits. However, in this model, there
are …rms in other product markets that are also regulated by the permit market. This relaxes the constraint
and allows even a single strategic …rm to exercise market power without violating the two constraints.
8
This holds if 0 (qm ) < c00f (q qm )=rf .
7
If competition is imperfect, will welfare be greater under a permit system or under a tax?
A dominant …rm, facing either a tax or permit, produces less that it would in a competitive
market. As discussed below, the welfare e¤ects of policy choice depend on the relative
magnitudes of qbm and qem .
In order to determine whether a dominant …rm will produce more under a permit system
or under a tax, I compare the …rm’s marginal pro…ts at a speci…c point. Namely, I examine
de(qm )
dqm
and
d (qm )
dqm
at output qbm where the dominant …rm maximizes pro…ts under a tax. From
the …rst-order condition (3),
d (qm )
j
dqm qbm
= 0. Hence, if
de(qm )
j
dqm qbm
> 0, then the …rm produces
more under a permit system (otherwise it produces more under the tax). From (5) and (4),
we see:
de(qm )
de(qm )
d (qm )
jqbm =
jqbm
jqb
dqm
dqm
dqm m
= [ (b
qm )rf + 0 (b
qm )rf qbm trf ]
(6)
[ (b
qm )rm + 0 (b
qm ) (rm qbm
em )
trm ];
where the …rst part in brackets is the di¤erence in marginal revenue between a permit and
a tax, and the second is the di¤erence in marginal costs. Equation (6) can be written as:
de(qm )
jqb = (t
dqm m
(b
qm )) (rm
(i)
rf ) + 0 (b
qm )rf qbm + 0 (b
qm ) (em
(ii)
(iii)
rm qbm ) ;
(7)
which I decompose into three parts.
The …rst two components of (7) are direct e¤ects of …rm’s incentives to exercise market
power in the polluting market. Component (i), (t
(b
qm )) (rm
rf ), is the relative di¤er-
ences in marginal costs. Note that this is always positive. If the dominant …rm is relatively
dirty, rm > rf , then exercising market power will drive down the permit price (see Lemma 1).
When the dominant …rm is relatively clean, the permit price will exceed the tax. Component
(ii),
0
(b
qm )rf qbm , 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 e¤ects of these components are discussed below.
9
Misiolek and Elder (1989) and Sartzetakis (1997) provide theoretical analysis of this issue. Kolstad
and Wolak (2003) …nd that Californian electricity producers’behavior in the RECLAIM permit market was
consistent with this incentive.
8
The last component of (7),
0
(b
qm ) (em
rm qbm ), shows how …rms 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 …rms 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 …rm minimizes total compliance costs
(em )+ (em )(em em ), where (em ) are abatement costs and the permit price depends on the
strategic …rm’s emissions, em . On the margin, the …rm sets
0
(em ) =
+ 0 (em )(em
em ),
or marginal abatement costs equal to marginal permit expenditure costs. If the permit
allocation di¤ers from the least cost solution, em = em , then the …rm 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 …rm 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 e¤ect where abatement technology is …xed so the only abatement cost is
the forgone pro…ts 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 …rm’s production a¤ects its market’s aggregate emissions
in the equilibrium so
0
(qm ) may be negative or positive. For this reason, a relatively clean
dominant …rm 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 …rm is relatively clean or
dirty and how many permits are allocated. In practice, …rms trade substantially in cap-andtrade systems suggesting that they have large net positions, some positive and some negative.
Firms with market power in permit markets may pro…t by distorting abatement decisions.
10
Chen and Hobbs (2005) and Chen et al. (2006) examine the interaction of market power in the PJM
and NOx markets. They note that …rms may exercise market power in the permit market, depending on the
initial allocation of permits. They …nd that exercising market power in the electricity market will lower the
price of permits.
11
Mansur (2006) sketches out a note with a more complex model.
9
While this ‘Hahn’ e¤ect, 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 …rms 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 …rm is allocated permits equal to its equilibrium emissions under (3): em = rm qbm .
The implication of this assumption is the dominant …rm will not have an incentive trade, at
the margin, when starting at qbm . Thus, the sign of (7) only depends on components (i) and
(ii), or the “feedback e¤ect.”We can now show the following two cases.
Relatively Dirty Dominant Firm
Lemma 2 If the dominant …rm is relatively dirty, then it will produce more under a permit
system than under a tax (e
qm > qbm ), 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 …rm 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 …rm is relatively dirty, the net e¤ect is a reduction in emissions in the dominant …rm’s market. Under a permit system, this reduction in demand for
permits results in other polluters who are not competing directly with the dominant …rm
to emit more, ro qo . 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 e¤ect on the dominant …rm. It will produce more because its marginal costs have
fallen. Even though the marginal revenue may have decreased, the e¤ect on costs dominates.
Note that it is possible that this feedback e¤ect could dominate even if the …rm has a
large net purchasing position in the permit market, em << rm qbm . In other words, permits
12
If the pollutant is not uniformly mixed, the new distribution of emissions could have further welfare
implications.
10
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 …rm, the more likely that a permit market will result in greater output than
a tax.
Relatively Clean Dominant Firm
Lemma 3 If the dominant …rm is relatively clean, then it will produce more (less) under a
permit system than under a tax if (t
(b
qm )) (rm
given assumptions (A1)-(A8).
rf ) is greater (less) than j 0 (b
qm )rf qbm j,
Proof. By Lemma 1, component (ii) is negative for the relatively clean dominant …rm.
(A8) assumes the third component is zero. Thus, (7) is positive only if component (i) o¤sets
component (ii).
Here, when the dominant …rm produces less than the competitive level, its emissions
reductions (rm qm
rm qm ) are more than o¤set by the dirty fringe. The increase in demand
for permits drives up the permit price. The other …rms in the permit market abate more so
that in equilibrium the cap is still met. When the permit price rises, it increases the dominant
…rm’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 …rm’s marginal revenue
has increased more than its marginal costs. The dominant …rm 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 …rm case, a substantial net position can also overturn this result. Here, the e¤ect of the permit allocation is the opposite since
0
(qm ) < 0.
If the dominant …rm receives too many permits, then the Hahn e¤ect can dominate the
feedback e¤ect.
In summary, a strategic …rm’s production decision depends on the type of environmental
regulation. For some cases, like a relatively dirty dominant …rm with a small net permit
position, it is easy to sign the e¤ect. In other cases, it is ambiguous. In practice, electricity
…rms have a mix of technologies. In general, coal plants have higher emissions and lower
11
marginal costs than natural gas plants. In this case, even if all …rms 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 …rm’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 and Mansur, 2008) in most of the U.S., suggesting
that the dirty dominant …rm case was more prevalent. Today, as we see entry of lowemissions, 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 E¤ect of Policy Choice
Before simulating the e¤ects, however, it is important to consider the welfare implications
of dominant …rms 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(rm qm + rf qf + ro qo );
(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, qbm < qem < qm , and welfare can be seen by taking the derivative of (8)
with respect to qm . Note that, in equilibrium, Po = Bo0 (qo ).
dqo
dW
= Po
dqm
dqm
where D0 (q)
c0m (qm )
c0f (qf )
dqf
dqm
c0o (qo )
dqo
dqm
D0 (q)(rm + rf
dqf
dqo
+ ro
);
dqm
dqm
(9)
D0 (rm qm + rf qf + ro qo ).
Under a tax, the dominant …rm does not interact with the other …rms in the airshed in
any market: dqo =dqm = 0. From (A7), dqf =dqm =
c
dW
= c0f (qf )
dqm
1. Marginal welfare is:
c0m (qm ) + D0 (q)(rf
12
rm ):
(10)
Welfare is maximized when …rms have the same marginal social costs: c0m (qm ) + D0 (q )rm =
c0f (qf ) + D0 (q )rf , which occurs at q = fqm ; qf ; qo g.
Under a permit system, the welfare e¤ects are slightly di¤erent. If a permit cap is
binding, then there are no environmental e¤ects: rm dqm + rf dqf + ro dqo = 0. Given (A7),
we can write this as dqo =dqm = (rf
c0f (qf ) + Po
c0o (qo )
ro
(rf
rm )=ro . So the marginal welfare e¤ect is
c0m (qm ) +
rm ). By substituting in the …rst-order condition of the other …rms in
the airshed, (2), we can rewrite the marginal welfare as:
f
dW
= c0f (qf )
dqm
c0m (qm ) + (qm )(rf
(11)
rm ):
Again, welfare is maximized at q where the …rms equate marginal private costs that include
c and W
f are increasing in qm up to qm .
the permit price. Both W
The marginal welfare e¤ects, (10) and (11), will be the same only at qm ; qf ; qo . When
the dominant …rm 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 …rm 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 …rm will produce more
under a permit system than under a tax: qem > qbm . However, if
f
dW
dqm
>
c
dW
dqm
for all qm < qm
then total welfare could be less under a permit system even though the dominant …rm
is producing more than under a tax. At qm , the di¤erence in the marginal welfare e¤ects
f
dW
dqm
c
dW
dqm
= (D0 (q)
(qm ))(rm rf ). In other words, a change the dominant …rm’s production
will have di¤erential welfare e¤ects: under a tax, this change will have environmental costs,
D0 (q)(rm
costs, (rm
rf ); whereas under a permit system, this change will result in more abatement
rf ), incurred by other …rms in the airshed. The policy implications are akin to
Weitzman’s (1974) …nding regarding uncertainty. He showed that if marginal damages are
relatively ‡at then a tax will be preferred, otherwise a permit system will improve welfare
under uncertainty. In this analysis, reducing production distortions in the dominant …rm’s
market, c0f (qf )
c0m (qm ), will improve welfare. However, there are other considerations that
13
arise due to di¤erences in environmental regulations.13
The welfare implications are unambiguous only if the di¤erence between environmental
damages and abatement costs are weakly concave in qm :
2
d2 D(q)=dqm
0
(qm )
0; 8qm < qm :
(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 e¤ects and health thresholds. In contrast, the welfare
consequences would be ambiguous for greenhouse gases, where marginal damages are ‡at 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 …rms with the ability
to move permit prices.
Proposition 1 If a permit system increases production from the dominant …rm relative
to a tax (i.e., (7) is positive), then social welfare will be unambiguously greater only if the
2
marginal damages are increasing in the dominant …rm’s production (d2 D(q)=dqm
) faster than
the marginal cost of abatement ( 0 (qm )). Otherwise, the social welfare e¤ects will depend on
market characteristics.
Proof. First consider the case of a relatively dirty dominant …rm. From Lemma 2, qm < qm
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 ,
D0 (q) < (qm ). For the relatively clean dominant …rm, qm < qm 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,
than
13
c
dW
dqm
f
dW
dqm
is greater
for all qm < qm and, from Lemmas 2 and 3, qem > qbm so greater welfare will result
For example, for a relatively dirty dominant …rm, (qm ) < (qm ) and if marginal damages are perfectly
f
c
dW
dW
> dq
. The welfare signs are ambiguous as they
elastic, then D0 (q) > (qm ) and rm > rf , implying dq
m
m
0
depend on the slope of (qm ) and the equilibrium quantities qem and qbm .
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 …rm minimizes private costs, then the more that it produces the greater the welfare e¤ects. These
welfare e¤ects 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
4.1
Extensions
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 …rm-competitive fringe setting described above, welfare is maximized at qm and
qo (qf is implied by (A7)). Under a permit system, there are e¤ectively two instruments,
X
P
ei and em , so the …rst best can be achieved. If qm = qm , then by allocating N
i=1 ri qi
i6=m
permits, in aggregate, the equilibrium permit price will equal marginal damages. Therefore,
the second instrument, the share of permits grandfathered to the dominant …rm, is set such
that its marginal revenue equals its marginal cost where qm = qm . Let:
em
(rm
rf )qm + c00f (q
qm )qm = 0 (qm ).
(13)
Substituting em into (5), the …rst-order condition becomes
c0m (qm ) + (qm )rm
c0f (q
qm )
(qm )rf = [ c00f (q
14
qm )
0
(qm )(rm
rf )](qm
qm ); (14)
For example, suppose the dominant …rm has production costs of cm = 30qm and rm = 20. The fringe
has cf = 12 qf2 and rf = 0. For q = 100, the dominant …rm’s residual demand is P (qm ) = 100 qm : Under an
emissions tax t = 1, the competitive equilibrium is P = 50, qm = 50, and e = 1000. The dominant …rm
would opt to produce qbm = 25, Pb = 75, and eb = 500. The welfare loss under a tax would be the increase in
production costs (813) less the environmental damages abated (suppose D0 (e) = 0:001e, then 375), or 438.
Under a permit system, suppose that (qm ) = 0:001e = 0:02qm and em = 1000. Then the dominant …rm
will produce where: 100 2qm = 30 + 0:4qm + 0:02(20qm 1000), or qem = 32:1; Pe = 67:9 and ee = 642. The
welfare loss is now composed of increased production costs (518) less the avoided abatement costs for the
R 50
other …rms in the airshed of 32:1 (e)de, or 294, for a total deadweight loss of 224. In this example, a tax
would approximately double the deadweight loss relative to a permit system.
15
for which qm = qm is the solution.
In contrast, the …rst 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 …rst best could be achieved. As in Section 2, to = D0 (q ). The
_
tax (subsidy) in the dominant …rm’s market would be tm = D0 (q ) c00 (q q )q =(rm rf ).
f
m
m
By substituting tm into (4):
c0m (qm ) + D0 (q )rm
c0f (q
D0 (q )rf = c00f (q
qm )
qm )(qm
qm );
(15)
for which qm = qm is the solution. However, to 6= tm . If the dominant …rm 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 o¤ 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 …rms. Suppose there
are several, quantity-setting strategic …rms rather than a single dominant …rm. The fringe
and “other”…rms are as before. As above, assume (A1)-(A7), a competitive fringe, and other
price-taking …rms under the same environmental regulation but not competing directly with
the strategic …rms. Suppose there are M symmetric, Cournot players facing a tax. Strategic
…rm s produces qs and emits at rate rs . It earns pro…ts Pb(qs )qs cs (qs ) trs qs , where residual
demand equals Pb(qs ) = c0f (q
…rms. Let qbs solve:
d (t)
= c0f (q
dqs
q
q
s
s
qs ) + trf and q
qs ) + trf
c00f (q
q
s
s
is the output of the other strategic
qs )qs
c0s (qs )
trs = 0:
In equilibrium, because the M strategic …rms are symmetric, they each produce qbs :
c0f (q
M qbs ) + trf
c00f (q
16
M qbs )b
qs = c0s (b
qs ) + trs
(16)
Similarly, under a permit system, let qes solve:
de(qs )
= c0f (q q s qs ) + (qs )rf c00f (q q s
dqs
0
(qs )rs
(qs ) (rs qs es ) = 0.
c0s (qs )
qs )qs + 0 (qs )rf qs
In equilibrium, because the M strategic …rms are symmetric, they each produce qes :
c0f (q
M qes ) + (e
qs )rf
c00f (q
qs ) + (e
qs )rs + 0 (e
qs ) (rs qes
M qes )e
qs + 0 (e
qs )rf qes = c0s (e
(17)
es )
Again, the welfare e¤ects can be measured by examining the marginal pro…ts under a
permit system at the optimal output under a tax,
de(qs )
d (qs )
de(qs )
jqbs =
jqbs
jqb
dqs
dqs
dqs s
= (b
qs )rf + 0 (b
qs )rf qbs trf
de(qs )
j :
dqs qbs
(b
qs )rs
(18)
0
(b
qs ) (rs qbs
es ) + trs :
Proposition 2 Proposition 1 holds for M symmetric strategic …rms.
Proof. When all strategic …rms are the same, the di¤erence between the permit system and
tax depends on the permit price function, which depends on the actions of the other …rms
not competing in the market with strategic …rms, and exogenous characteristics (rf ; rs ; es )
that do not vary across strategic …rms. If the best response function of one …rm shifts by
, then all best response functions shift by . In equilibrium, qbs is the same for all …rms
and the marginal pro…ts will be the same for all M strategic …rms. Therefore, the di¤erence
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 su¢ ciently asymmetric, changes
in input prices (like tradable permits) can increase production ine¢ ciencies (Fevrier and
Linnemer, 2004). The welfare loss associated with distorting production can be substantial
enough to counter the above …ndings. For example, suppose that when strategic …rms
produce less than they would have in a competitive market, this reduces emissions from all
…rms in their market (the dirty dominant …rms analog), which in turn lowers the permit price.
17
The appendix provides a duopoly with fringe example where one strategic …rm has both
higher marginal production costs and higher emissions rates than the other one. When the
…rms reduce pollution in their market relative to the competitive equilibrium, the marginal
cost of the ine¢ cient strategic …rm falls under a permit system relative to a tax. As a
result, it produces more (which increases the production ine¢ 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 e¤ects are of economic signi…cance. Speci…cally,
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 …rms in PJM are dirtier–on average–than those in the fringe, exercising market
power reduces emissions from PJM …rms (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.
From May to September, the OTC NOx permit market regulates …rms in PJM, New England,
and New York. During 1999, OTC did not apply to …rms in Maine, Maryland, Vermont,
Virginia, and Washington, D.C. The number of permits are …xed: If PJM …rms pollute more,
then the other …rms (in New England and New York) must abate an equal amount.15
This simulation develops a model of …rm behavior in the PJM electricity market. The
strategy is …rst to determine what the permit price would have been had the …rms in PJM
behaved competitively. In equilibrium, the increase in emissions in PJM as the market
15
This market allows …rms to bank permits for future summers but is not modeled here. Given the high
price in the …rst summer, banking was minimal.
18
changes from a strategic “regime”to a competitive one must equal the increase in abatement
by …rms 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 …rms would have produced.
As demand is assumed to be perfectly inelastic, the welfare e¤ects 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 …rm 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
…rms’supply of abatement. NOx pollution can be abated by installing technologies such as
Selective Catalytic Reduction (SCR), by reducing the burning e¢ 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 …xed
in the short run and that …rms could not change these investment decisions during the …rst
summer of the regulation. In the short run, …rms can abate pollution by not operating. The
…rm forgoes pro…ts but no longer needs to purchase or to hold on to a pollution permit. It
is this trade-o¤ of pro…ts 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 …rm taking prices as given is equal to the rents (P
c0 (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
16
In the long run, the permit supply function becomes much more elastic. This will dampen the responsiveness of the permit price to the actions of the dominant …rm (i.e., 0 (qm ) is smaller). This will reduce
any di¤erences between the welfare e¤ects of taxes and permits.
19
England for the New England …rms. 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 di¤erence between
the welfare e¤ects 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 (c0 (q)) are de…ned 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 …t of abatement for observations with MCA below $5000/ton. An OLS regression implies that for every additional ton
abated by …rms outside of PJM, the permit price will increase by $0.1053/ton.18
17
Data on variable O&M costs are not readily available so I assume them to be $2/MWh for all power
plants. The SO2 pollution costs apply to power plants regulated by Phase I of the 1990 Clean Air Act
Amendment’s Title IV.
18
The independent variable is the emissions rate times the plant’s capacity. In the long run, …rms will
install abatement technology, changing its emissions rate. This may be correlated with the dependent variable
(foregone pro…ts). However, in the short run, this is not likely to be the case as abatement technology and
capacity are …xed. 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 …rms in PJM had incentives to increase prices as
they sold a substantial amount of energy, q, in the wholesale market. Other …rms had
obligations to serve large amounts of electricity, or native load, (q c ) to retail customers at
…xed rates. These …rms may have bene…ted from lower wholesale prices. The di¤erence
between a …rm’s production of q and retail obligations of q c , or “net positions,”a¤ect …rms’
incentives. The …rst-order condition is:
P (q) + P 0 (q) (q
q c ) = c0 (q) + (q) r + 0 (q) (rq
e);
(19)
where now …rms pro…t 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 …rm’s
…rst-order condition of pro…t maximization to solve for equilibrium in the PJM electricity
market.
Note that …rms 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
…rm (rq ' e), then the term last term of (19),
0
(q) (rq
e), will be small. The two
…rms likely to set prices in the wholesale electricity market are the Philadelphia Electric
Company (PECO) and Pennsylvania Power & Light (PPL) (Mansur, 2007b). These …rms
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 …rms did not behave strategically in the permit market: rq ' e. For a given
permit price, I simulate how much each …rm in PJM would have produced under both the
competitive and Cournot regimes.
Regardless of whether …rms take prices as given or act strategically, they will produce
a given amount using their least costly generating units. The BMS model includes data on
19
Using CEMS data, I calculate that during the period of OTC regulation, PECO emitted
3554 tons of NOx .
In contrast, the …rm was allocated permits for 2939 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.
21
marginal costs, capacity, and emissions rates for all polluting units. Thus, a …rm can respond
to changes in permit prices by substituting across its units using di¤erent 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 …rm owns). I use these data to determine each …rms’
hourly emissions. This allows me to compare aggregate emissions across regimes and permit
prices.
5.3
5.3.1
Simulation Results
Market Power and Permit Prices
The simulation is solved in several steps. I begin by modeling the permit price assuming …rms
actually behave as Cournot …rms 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 di¢ cult to interpret the e¤ects 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 …rms had to demonstrate compliance. I model
the permit price as equal to $1000/ton.
Second, I use the BMS model to estimate …rm behavior in PJM for each hour in the
summer of 1999 when OTC was in e¤ect.20 From May 1 to September 30, 1999, the Cournot
model simulation predicts that the PJM …rms regulated by OTC emit 88,222 tons of NOx
(see Table 1). In contrast, these same …rms would have emitted 100,936 tons, an increase
of 11%, if they had taken prices as given. Therefore, PJM …rms 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 …rms 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 …rms do change their
production decisions as the permit price increases.
20
21
For greater discussion of the assumptions of this model, see BMS.
That 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 …rms outside of PJM at that price.22 Next I determine
the amount of permits demanded by competitive …rms in PJM at that price and compare
that level with the amount demanded in the benchmark case: Cournot …rms 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 …rms 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 …rms actually faced during that
summer.
5.3.2
Welfare E¤ects 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 …rms
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 …xed 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 …rms exercising market power in PJM cause deadweight loss equal to $113
million, or 7.8% of the variable social costs.
22
Note that by changing the permit price for each iteration, this will change the merit order of each …rm.
For any given permit price, the …rm will produce using the least costly generating units.
23
This …rst-best solution ignores any tax interaction e¤ect (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 …rms 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 bene…t
of these externalities have been taken into account in the simulation’s measure of total cost.
In other words, the costs to the …rms 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 E¤ects 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
…nd 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 e¤ects, 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.
24
These prices may seem small in an oligopoly market with perfectly inelastic demand. However, as BMS
note, this is because the vertically integrated PJM …rms had large retail commitments and had less incentive
to 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 …rms 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 …rm is dirtier than the competitive fringe, exercising market power will lower
the permit price. This will result in more output from the strategic …rm, increasing welfare.
When the fringe is dirtier, strategic behavior increases the permit price. If this increase
the strategic …rm’s marginal revenue more than its marginal costs, then welfare will still
be greater under a permit system. When there are multiple strategic …rms, the results
are more complex. Production ine¢ ciencies from asymmetric strategic …rms may reverse
these …ndings. 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 policy instrument choice. I simulate the OTC permit market and …rm 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
e¤ects 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 welfare by considering the interactions between environmental regulation and …rm behavior in
product markets. In particular, I …nd that more consideration should be given to permit markets. 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
e¤ects (Goulder et al., 1997). The relative signi…cance of these e¤ects will be case speci…c.
26
Appendix
This appendix provides an example of how Lemma 2 may fail if strategic …rms are asymmetric. Suppose there are asymmetric Cournot duopolists (…rms 1 and 2) and a fringe
with the following total production costs and emissions rates: c1 = 30qi ; c2 = 0; cf =
1 2
q ;r
2 f 1
= 20; r2 = 1, and rf = 0. Demand: q = 100, so the duopolists’residual demand =
P (q1 +q2 ) = 100 q1 q2 : Marginal damages are D0 = 0:7 exp( ln(0:7)e=99). Under an emissions tax t = 1, the competitive equilibrium is: q1 = 0; q2 = 99; P = 1; e = 20q1 + q2 = 99:
Under the tax, the duopolists’best response functions are q1 = 25 0:5q2 and q2 = 49:5 0:5q1
so the equilibrium is qb1 = 31 ; qb2 = 49 13 ; Pb = 50 31 ; eb = 56. The deadweight loss is the increase
R 1=3
R 148=3
R 151=3 0
in production costs, 0 c01 (x)dx + 99 c02 (x)dx + 1
cf (x)dx = 1276, less the enviR 99 0
ronmental bene…ts of less pollution, 56 D (e)de = 40, or 1236. Under a tradable permit
system, suppose (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: qe1 = 0:91; qe2 = 49:18; Pe = 49:91; ee = 67:3. The deadweight loss is the
increased production costs, 1272, less the reduced abatement costs of other …rms in the
R 99
airshed, 67:3 (x)dx = 30, or 1242. Welfare is greater under the tax than under a permit
system. In this example, the strategic …rms 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 …rm or two symmetric
…rms. First, suppose that there is only on dominant …rm and a competitive fringe: c1 =
30qi ; cf = 12 qf2 ; r1 = 20, and rf = 0. Demand: q = 100, so the dominant …rm’s residual
demand = P (q1 ) = 100
q1 : Marginal damages are D0 = :7 exp( ln(:7)e=1000). Under an
emissions tax t = 1, the competitive equilibrium is: q1 = 50; P = 50; e = 20q1 = 1000:
Under the tax, the dominant …rm produces qb1 = 25; Pb = 75; eb = 500. The deadweight loss
R 25
R 75
is the increase in production costs, 50 c01 (x)dx + 50 c0f (x)dx = 813, less the environmental
R 1000
bene…ts of less pollution, 500 D0 (e)de = 458, or 355. Under a tradable permit system,
27
suppose (e) = 0:7 exp( ln(0:7)e=1000) and e1 = 1000. The equilibrium under the permit
price is: qe1 = 27:6; Pe = 72:4; ee = 552. The deadweight loss is the increased production
R 1000
costs, 699, less the reduced abatement costs of other …rms in the airshed, 552 (x)dx =
414, or 283. Lemma 2 holds.
For the symmetric duopolists, suppose c1 = 30qi ; c2 = 30q2 ; cf = 12 qf2 ; r1 = 20; r2 = 20,
and rf = 0. Demand: q = 100, so the strategic …rms’ residual demand = P (q1 + q2 ) =
100
q1
q2 : Marginal damages are D0 = :7 exp( ln(:7)e=1000). Under an emissions
tax t = 1, the competitive equilibrium is: q1 = q2 = 25; P = 50; e = 1000: Under the
tax, the …rms produce qb1 = qb2 = 16 23 ; Pb = 66 23 ; eb = 666 32 . The deadweight loss is the
R 16:7
R 16:7
R 66:7
increase in production costs, 25 c01 (x)dx + 25 c02 (x)dx + 50 c0f (x)dx = 472, less the
R 1000
environmental bene…ts of less pollution, 666:7 D0 (e)de = 314, or 158. Under a tradable
permit system, suppose (e) = 0:7 exp( ln(0:7)e=1000) and e1 = e2 = 500. The equilibrium
under the permit price is: qe1 = qe2 = 17:65; Pe = 64:71; ee = 705:8. The deadweight loss is
the increased production costs, 402, less the reduced abatement costs of other …rms in the
R 1000
airshed, 705:8 (x)dx = 279, or 123. Again, Lemma 2 holds.
28
References
[1] Barrett, Scott. 1994. “Strategic Environmental Policy and International Trade,”Journal
of Public Economics, 54: 325-338.
[2] Borenstein, Severin, James B. Bushnell, and Frank A. Wolak. 2002. “Measuring Market Ine¢ ciencies in California’s Restructured Wholesale Electricity Market,”American
Economic Review, 92: 1376-1405.
[3] Buchanan, James M. 1969. “External Diseconomies, Corrective Taxes, and Market
Structure,”American Economic Review, 59: 174-177.
[4] Bushnell, James B., Erin T. Mansur, and Celeste Saravia. 2008. “Market Structure and
Competition: A Cross-Market Analysis of U.S. Electricity Deregulation,” American
Economic Review, 98: 237-266.
[5] Chen, Yihsu and Benjamin Hobbs. 2005. “An Oligopolistic Power Market Model with
Tradable NOx Permits,”IEEE Transactions on Power Systems, 20: 119-129.
[6] Chen, Yihsu, Benjamin Hobbs, Sven Ley¤er, and Todd Munson. 2006. “Solution of
Large-Scale Leader-Follower Market Equilibria Problems: Electric Power and NOx Permit Markets,”Computational Management Science, 3: 307-330.
[7] Fevrier, Philippe and Laurent Linnemer. 2004. “Idiosyncratic Shocks in an Asymmetric
Cournot Oligopoly,”International Journal of Industrial Organization, 22: 835-848.
[8] Goulder, Lawrence H., Ian W.H. Parry, and Dallas Burtraw. 1997. “Revenue-Raising
vs. Other Approaches to Environmental Protection: The Critical Signi…cance of PreExisting Tax Distortions,”RAND Journal of Economics, 28: 708-731.
[9] Hahn, Robert W. 1984. “Market Power and Transferable Property Rights,” Quarterly
Journal of Economics, 99: 753-765.
[10] Holland, Stephen P. and Erin T. Mansur. 2008. “Is Real-Time Pricing Green? The
Environmental Impacts of Electricity Demand Variance,” Review of Economics and
Statistics, 90(3): 550-561.
[11] Ireland, N.J. 1977. “Ideal Prices vs. Prices vs. Quantities,”Review of Economic Studies,
44(1): 183-186.
[12] Ja¤e, Adam B., Richard G. Newell, and Robert N. Stavins. 2002. “Environmental Policy
and Technological Change,”Environmental and Resource Economics, 22: 41-69.
[13] Joskow, Paul and Edward Kahn. 2002. “A Quantitative Analysis of Pricing Behavior In
California’s Wholesale Electricity Market During Summer 2000,” Energy Journal, 23:
1-35.
29
[14] Keohane, Nathaniel. 2007. “Cost Savings from Allowance Trading in the 1990 Clean
Air Act: Estimates from a Choice-Based Model,” Chapter 8 in Moving to Markets in
Environmental Regulation: Lessons from Twenty Years of Experience, Jody Freeman
and Charles D. Kolstad, Ed. Oxford Press. 194-229.
[15] Kolstad, Jonathan and Frank Wolak. 2003. “Using Environmental Emissions Permit
Prices to Raise Electricity Prices: Evidence from the California Electricity Market,”
Center for the Study of Energy Markets Working Paper 113.
[16] Levin, Dan. 1985. “Taxation within Cournot Oligopoly,”Journal of Public Economics,
27: 281-290.
[17] Mansur, Erin T. 2006. “Note Regarding Endogenous Emissions Rates in Prices vs. Quantities,”see http://www.dartmouth.edu/~mansur/papers/mansur_envreg_note.pdf.
[18] ___. 2007a. “Do Oligopolists Pollute Less? Evidence from a Restructured Electricity
Market,”Journal of Industrial Economics, 55: 661-689.
[19] ___. 2007b. “Upstream Competition and Vertical Integration in Electricity Markets,”
Journal of Law and Economics, 50: 125-156.
[20] ___. 2008. “Measuring Welfare in Restructured Electricity Markets,” Review of Economics and Statistics, 55: 369-386.
[21] Misiolek, W.S. and H.W. Elder. 1989. “Exclusionary Manipulation of Markets for Pollution Rights,”Journal of Environmental Economics and Management, 16: 156-166.
[22] Sartzetakis, Eftichios S. 1997. “Raising Rivals’ Costs Strategies via Emission Permits
Markets,”Review of Industrial Organization, 12: 751-765.
[23] Sha¤er, Sherrill. 1995. “Optimal Linear Taxation of Polluting Oligopolists,”Journal of
Regulatory Economics, 7: 85-100.
[24] Stavins, Robert N. 1995. “Transaction Costs and Tradable Permits,” Journal of Environmental Economics and Management, 29: 133-147.
[25] Weisbach, David. 2011. “Instrument Choice Is Instrument Design.”In U.S. Energy Tax
Policy, Gilbert E. Metcalf, ed. Cambridge University Press.
[26] Weitzman, Martin L. 1974. “Prices vs. Quantities,” Review of Economic Studies, 41:
477-491.
[27] Wolfram, Catherine. 1999. “Measuring Duopoly Power in the British Electricity Spot
Market,”American Economic Review, 89: 805-826.
30
Table 1
Simulation of Policy Choice Effects on Emissions and Welfare
Marginal private cost of a
ton of NOx pollution
NOx emissions (tons)
Cournot
Competitivea
Difference
Percent difference
Additional permitsb
Variable costs ($ millions)
Cournot
Competitive
Welfare loss
Emissions component
Firm cost component
PJM total
Percent loss
Change in Imports
Total
Percent loss
Notes:
a)
b)
Permit
System
$1,000
Tax
$1,934
Difference
$934
Percent
Difference
93%
88,222
100,936
12,713
11%
85,923
97,096
11,174
12%
2,300
3,839
2.7%
4.0%
8,874
10.1%
1,565
1,452
113
7.8%
1,573
1,452
121
8.3%
8.3
0
-4.4
11.7
8.3
7.4%
3.0
11.3
10.0%
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.
“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.
31