Environmental Regulation:
Supported by Polluting Firms,
but Opposed by Green Firms?
Félix Muñoz-Garcíay
Sherzod Akhundjanovz
School of Economic Sciences
Washington State University
Pullman, WA 99164
School of Economic Sciences
Washington State University
Pullman, WA 99164
January 21, 2013
Abstract
This paper investigates the production decisions of polluting and green …rms, and how their
pro…ts are a¤ected by environmental regulation. We demonstrate that emission fees entail
a negative e¤ect on …rms’ pro…ts, since they increase unit production costs. However, fees
can also produce a positive e¤ect for a relatively ine¢ cient …rm, given that environmental
regulation ameliorates its cost disadvantage. If such a disadvantage is su¢ ciently large, we
show that the positive e¤ect dominates, thus leading this …rm to actually favor the introduction
of environmental policy, while relatively e¢ cient …rms oppose regulation. Furthermore, we
show that such support can not only originate from green …rms but, more surprisingly, also
from polluting companies.
Keywords: Cost asymmetries; Cost disadvantage; Emission fees; Green …rms.
JEL classification: L13, D62, H23, Q20.
We thank Ana Espinola-Arredondo and Hayley Chouinard for helpful comments and suggestions.
Address: 103G Hulbert Hall, Washington State University. Pullman, WA 99164. E-mail: [email protected].
Phone: (509) 335 8402. Fax: (509) 335 1173.
z
Address: 313 Hulbert Hall, Washington State University.
Pullman, WA 99164.
E-mail:
[email protected].
y
1
1
Introduction
Firms with relatively clean production processes (“green” …rms) often support the introduction of
stringent environmental regulation. Examples include General Electric, the ABB Group, and the
German producer of electrical equipment AEG, among others.1 This practice is usually considered
a tool that green …rms use to increase the costs of their polluting rivals, ultimately helping their
own competitiveness. While green companies can indeed bene…t from the introduction of environmental regulation, this paper shows that polluting …rms can also favor emission fees under certain
conditions. In particular, we show that dirty …rms competing against a green rival can actually
obtain larger pro…ts when the regulator is present, thus leading the polluting …rm to support the
regulator’s task. Our results would, therefore, help to explain the recent lobbying e¤orts for stringent environmental regulation of relatively polluting …rms, such as the mining company Rio Tinto,
and the oil company BP.2
Our paper examines an oligopoly model in which …rms di¤er along two dimensions: their production costs, and the pollution that each unit of output generates, i.e., green and polluting (brown)
…rms, thus allowing for four types of …rms: e¢ cient or ine¢ cient brown …rms, and e¢ cient or ine¢ cient green companies. This setting helps us analyze green companies that are not necessarily
cost-e¢ cient, but also cost-ine¢ cient. In order to assess the e¤ect of emission fees on …rms’pro…ts,
and thereby determine …rms’preferences towards the regulatory context, we evaluate equilibrium
output levels and pro…ts when environmental regulation is present, and subsequently compare them
with those arising when regulation is absent.
We …rst demonstrate that, when the green …rm is extremely clean, the regulator imposes no
emission fees on this company, while the brown …rm is still subject to a fee. As a consequence, the
green …rm is unambiguously bene…ted by the introduction of environmental policy, while its brown
competitor is harmed. In this extreme setting, our results suggest that environmental regulation
is only favored by a “natural ally,”i.e., the green …rm. Such …nding, however, does not necessarily
hold under less extreme settings, such as when the green …rm generates a non-negligible level of
pollution. In this context, both the brown and green …rm become subject to emission fees, which
entails a negative e¤ect on both …rms’ pro…ts. However, emission fees can also yield a positive
e¤ect on the brown …rm’s pro…ts, which emerges when its green competitor is relatively e¢ cient.
Speci…cally, the regulator anticipates that, while the green …rm’s production process is cleaner
in relative terms, its cost-e¢ ciency would lead this …rm to produce a large output level, and an
1
Other examples are the German company Deutsche Telekom, the Swiss Bank Sarasin, the Japanese manufacturing
companies Ricoh and Kyocera, the German insurance company Gerling-Konzern, the chemical company DuPont, the
UK’s leading gas supplier CalorGas, the German insurance company Gerling-Konzern, the German railway company
Deutsche Bahn AG, and the Japanese multinational Shimano.
2
In particular, these …rms joined 46 companies participating in the Pew Center on Global Climate Change, which
lobbies in favor of “mandatory climate policy.” These lobbying e¤orts could also be rationalized using arguments
on corporate social responsibility and the …rms’ concerns for their public image among environmentally friendly
customers; see, for instance, Baron (2001, 2008) and Besley and Ghatak (2007). Nonetheless, our equilibrium
predictions suggest that, even if the corporate image arguments are absent, …rms would still have incentives to
promote a stricter environmental policy.
2
associated large pollution. In order to curb this socially excessive pollution, we show that, under
certain conditions, the regulator needs to impose a more stringent emission fee on the green than
on the brown …rm. As a consequence, environmental policy entails a larger increase in the marginal
costs of the former than the latter, which ultimately reduces the cost ine¢ ciency that the brown
…rm su¤ered when regulation was absent, hence yielding a positive e¤ect on its pro…ts.
Comparing the relative size of these positive and negative e¤ects, we demonstrate that the
overall pro…ts of the brown …rm are larger with than without regulation. This …rm is hence
induced to actually favor the introduction of emission fees when it experiences a substantial cost
disadvantage that regulation helps to ameliorate. As a consequence, the most polluting …rm in
the industry becomes the “unexpected ally” of the regulator. By contrast, the green …rm would
oppose environmental policy in this setting. Speci…cally, emission fees yield large negative e¤ects
for this …rm: not only do they increase its production costs but, in addition, they shrink the cost
advantage that the green …rm enjoyed prior to the imposition of emission fees. Such preferences
for emission fees are likely to arise, for instance, in industries where some …rms develop cleaner
technologies which, despite being relatively polluting, provide these companies with a substantial
cost advantage. In this context, …rms using polluting and ine¢ cient production processes would not
oppose regulation but, instead, favor it in order to alleviate their cost disadvantage. In contrast, if
green technologies are su¢ ciently clean, …rms adopting them would be exempt from emission fees,
thus leading them to support environmental policy.3
In summary, our …ndings suggest that, when a polluting industry is characterized by signi…cant cost asymmetries, the introduction of emission fees would be favored by ine¢ cient …rms but
opposed by their e¢ cient rivals. This goes against common belief, which predicts that stringent
environmental policy would be especially harmful for …rms with ine¢ cient production processes.
This argument, however, does not di¤erentiate …rms according to their production costs and environmental damages. Instead, it considers that cost-ine¢ cient …rms are also polluting while e¢ cient
companies are green, thus implying that emission fees on the former will be more stringent than on
the latter. Unlike this argument, our model allows for both forms of asymmetries, thus highlighting
the role of relative e¢ ciency in the design of optimal environmental regulation. Our …ndings show
that, when the green …rm is extremely clean, relative e¢ ciency can be overlooked, since only the
brown …rm is subject to emission fees, leading it to oppose regulation regardless of its e¢ ciency
level. By contrast, when the green company is not extremely clean, relative e¢ ciency becomes
relevant: when …rms are cost-asymmetric, only the most ine¢ cient …rm supports emission fees;
while, when companies are cost-symmetric, both …rms oppose regulation, since none of them would
experience a signi…cant positive e¤ect from regulation, i.e., emission fees produce only a small reduction in all …rm’s cost disadvantage. This …nding helps to evaluate di¤erent policies, such as
government programs that disseminate production technologies (not necessarily) among all industry participants, which reduce the cost asymmetries between …rms. In particular, these programs
3
Our equilibrium predictions also provide analogous results when the green …rm is the most ine¢ cient producer
in the industry, whereby this …rm favors regulation in order to ameliorate its signi…cant cost disadvantage.
3
can unintentionally build a political resistance against environmental regulation, as cost symmetry
induces …rms to oppose emission fees under large parameter conditions.
Related literature. Our paper relates to the literature analyzing the e¤ect of environmental
policy on …rm pro…ts. Speci…cally, Farzin (2003) examines how more stringent environmental
standards can promote a better product quality and, as a consequence, increase the demand for
the product. If demand is su¢ ciently responsive to product quality, …rm overall pro…ts increase
as a result of stricter environmental regulation.4 Similarly, Porter (1991) and Porter and van der
Linde (1995a,b) demonstrate that regulation can trigger innovation which can ultimately lead to an
increase in pro…ts.5 Unlike these studies, our paper shows that certain …rms might have incentives
to support the introduction of emission fees, even when such a regulation does not lead …rms to
improve product quality or to invest in innovation. Instead, in our model relatively ine¢ cient …rms
favor environmental policy in order to alleviate their cost disadvantage.6;7 Our results hence also
connect with studies on the pollution haven hypothesis, whereby …rms oppose the introduction of
environmental regulation and, in certain cases, relocate to jurisdictions with less stringent emission
fees.8 Similarly to these studies, our …ndings predict that some …rms would …ght environmental
policy. However, allowing for cost asymmetries between …rms helps to explain the incentives of
companies that have recently favored the introduction of emission fees.
Our …ndings also connect with the literature analyzing …rms’ interests in raising their rival’s
costs, i.e., Salop and Sche¤man (1983, 1987).9 In particular, these studies examine …rms’incentives
to strategically select a costly action, such as technology, advertising expenditures, or backward
integration, that would increase their rival’s costs (or reduce their revenues) in their subsequent
competition. Similarly, in our model the …rm favoring regulation, while it does not select emission
4
Ordover and Willig (1981) also analyze the role of regulation (not only environmental) as a form of market
predation where, in particular, very stringent policies would drive certain …rms out of the industry. In such a
setting, the …rm that remains (exits) in the market would favor (oppose, respectively) the introduction of regulation.
Our model, hence, provides more general results, since we demonstrate that …rms would obtain larger pro…ts when
emissions are implemented, even if regulation does not lead to the exit of any …rm.
5
Palmer et al (1995) have, nonetheless, criticized Porter and van der Linde (1995a,b) on the grounds that, while
they examine the incentives to innovate that environmental regulation provides, they overlook the optimal design of
environmental policy, i.e., explicitly analyzing the marginal costs and bene…ts of raising emission fees. Our paper, in
contrast, considers that the regulator sets socially optimal emission fees, thus avoiding such potential shortcoming.
6
In a recent paper, Espinola-Arredondo and Munoz-Garcia (2012) consider …rms that are symmetric both in
their production costs and in their pollution levels, and study their incentives to support countries’participation in
international environmental agreements. Their paper shows that, under certain conditions, …rms’ pro…ts are larger
when countries join an international treaty than otherwise, i.e., when every country independently sets its own
environmental policy. Our model, however, allows …rms to di¤er not only in their production costs but also in the
environmental damage they generate.
7
Maloney and McCormick (1982) empirically analyze …rms supporting regulation in order to improve their competitiveness in di¤erent U.S. industries, such as textile mills and smelting plants for cooper, lead and zinc. Their
study shows that, while these …rms are subject to a costly regulation, their market share and prices increase. Unlike
our paper, however, their article does not di¤erentiate between brown and green …rms.
8
See, for instance, Brunnermeier and Levinson (2004) and Ederington et al (2004).
9
This line of research was then followed by Krattenmaker and Salop (1986) for the study of exclusionary rights
in the use of inputs, Hart and Tirole (1990) for the analysis of vertical integration, Ordover et al (1990) and Gaudet
and Long (1996) for vertical foreclosures, and Sartzetakis (1997) for the study of dominant …rms in emission permit
markets.
4
fees, it must nonetheless bear a cost of environmental regulation, measured by the negative e¤ect
of emission fees on its pro…ts, in order to capture a bene…t, i.e., the cost-amelioration e¤ect of such
policy.10
The following section presents the model, while section 3 discusses the equilibrium results,
when the environmental damages of the brown and green …rm are signi…cantly di¤erent. Section 4
analyzes equilibrium behavior when the environmental damages of each …rm become more similar,
providing discussions and policy implications, and section 5 concludes.
2
Model
Consider a duopoly industry, with a brown and a green …rm with marginal production costs cB and
cG , respectively. For generality, cB ; cG 2 (0; 1), thus allowing for the brown …rm to be more (less)
e¢ cient than the green …rm, i.e., cB < cG (cB > cG , respectively). The inverse demand function is
p(Q) = 1
Q, where Q = qB + qG denotes the aggregate output. We examine a two-stage complete
information game where, in the …rst stage, the regulator sets type-dependent emission fees (tB ; tG )
and, in the second stage, …rms respond to these fees by simultaneously and independently selecting
their output levels. In particular, the social planner maximizes the social welfare function
CS (Q) + P S (Q) + T
Env (Q) ;
which depends on consumer and producer surplus, the total tax revenue collected from emission
fees, and the environmental damage from aggregate production. Speci…cally, the environmental
damage associated with pollution is
Env (Q) = dB
(qB )2 + dG
(qG )2 ,
where every unit of output generates a more damaging pollution when it is produced by the brown
than the green …rm, i.e., dB
dG
0. Given the pair of emission fees (tB ; tG ) set by the regulator,
every …rm of type K = fB; Gg, competing against a rival of type J 6= K, chooses its output level
in order to maximize duopoly pro…ts, (1
qK
qJ )qK
(cK
tK )qK . In the following sections
we analyze …rms’equilibrium pro…ts with and without environmental regulation, and subsequently
compare them in order to evaluate how …rms are a¤ected by the introduction of environmental
policy.
10
Korber (1995, Ch. 4) studies the incentives of a green domestic …rm (dirty foreign competitor) to lobby in favor
of (against, respectively) more stringent environmental regulation. In particular, his paper considers a relatively
clean domestic producer and, as a consequence, such a …rm promotes stricter regulation in order to hinder the
competitiveness of its foreign rival. While our model examines this case, it also analyzes a more counterintuitive
setting, namely, that emerging when polluting …rms favor environmental regulation while their green competitors
oppose such a regulation.
5
3
Di¤erent environmental damages
In this section, we evaluate equilibrium pro…ts when the pollution that the green …rm generates
is relatively low, i.e., dB
1=2 > dG
0. In this context, the green …rm becomes clean and,
as Proposition 1 shows below, the regulator does not impose emission fees on this …rm, but on
the brown …rm alone.11 As the following proposition shows, this regulatory context is especially
harmful for the brown …rm, which obtains lower pro…ts when the regulator is present (denoted with
superscript R) than when he is absent (represented by N R).
Proposition 1. When environmental damages satisfy dB
1=2 > dG , the pro…ts of the brown
…rm are lower with than without environmental regulation, i.e.,
values; while those of the green …rm are larger, i.e.,
R
G
N R,
G
R
B
N R,
B
under all parameter
for all parameter values.
Pro…t comparisons in this setting are, therefore, unambiguous. In particular, as the proof of
Proposition 1 shows, …rms are only subject to positive emission fees when their environmental
damage is larger than 1=2. Hence, only the brown …rm is subject to emission fees, implying that
environmental policy increases the production costs of this …rm alone. This makes the brown (green)
…rm less (more, respectively) competitive. As a consequence, the green …rm favors environmental
regulation, while the brown …rm opposes emission fees, under all parameter conditions satisfying
dB
1=2 > dG . However, when both …rms generate similar environmental damages, i.e., dB
dG
1=2, both companies are subject to emission fees, and the unambiguous …nding of Proposition
1 does not necessarily hold; as the next section shows.
4
Similar environmental damages
This section analyzes equilibrium behavior where both …rms’ production is relatively damaging,
but the green …rm is still cleaner than the brown …rm, i.e., dB
dG
1=2. Before providing
pro…t comparisons, however, the following lemma describes under which parameter conditions
…rms produce positive amounts (or, instead, prefer to remain inactive, i.e., exit), with and without
environmental regulation.
11
As a consequence, the regulator relies on a single instrument, the fee on the brown …rm, tB , to induce the
production of the aggregate socially optimal output, QSO . The regulator, hence, uses a “second-best” environmental
policy. Speci…cally, while emission fee tB is designed to induce output QSO , the distribution of production among the
brown and green …rms is not necessarily socially optimal; as described in the proof of Proposition 1. Intuitively, with
two …rms exhibiting asymmetries in both production costs and in their environmental damages, a single instrument
SO
SO
generates ine¢ ciencies, since …rms cannot be induced to exactly produce the optimal output pair, qB
and qG
for
the brown and green …rms, respectively. Such output pair can only be achieved if the regulator has at least two
instruments at his disposal, such as tB and tG , a case that arises when the environmental damages of both …rms are
relatively large, as we discuss in the following section.
6
Lemma 1. The brown …rm produces positive amounts when the regulator is absent (present)
N R ( c < C R , respectively).
if and only if its production costs are su¢ ciently low, i.e., cB < CB
B
B
The green …rm’s output is positive when regulation is absent (present) if and only if the costs of its
N R ( c > C R , respectively). In particular, the
brown competitor are su¢ ciently high, i.e., cB > CG
B
G
NR
cuto¤ s under no regulation are CB
1+cG
2
NR
and CG
respectively; while under regulation they become
R
CB
NR
CB
but
R
CG
<
R
CB
2cG
2dG +cG
2dG +1
1 for the brown and green …rm,
R
and CG
cG (2dB + 1)
2dB , where
N R.
CG
Figure 1. Production regions when dB
dG
1=2.
R and C R when regulation is
Figure 1 depicts the (cB ; cG )-quadrant, superimposing cuto¤s CB
G
N R and C N R when it is absent, which divide this quadrant into …ve regions, A
present, and CB
G
through E, according to whether …rms produce positive amounts with or without regulation.12
Speci…cally, in the shaded region C, both …rms produce positive amounts, both when the regulator
is present and absent, given that their costs are relatively symmetric. The opposite happens in
region A (E), where the brown …rm (green …rm, respectively) su¤ers such a cost disadvantage that
it is induced to remain inactive, producing zero units (i.e., exit), with and without environmental
regulation. However, when …rms’ cost disadvantage is intermediate, e.g., region B, the brown
…rm, being relatively ine¢ cient, remains inactive in the absence of regulation, but becomes active
otherwise. In particular, while every unit of production from the green …rm is cleaner than that of
the brown …rm, the e¢ ciency of the green …rm induces this company to produce larger output levels
than its competitor when the regulator is absent. Since both …rms generate pollution, the regulator
must hence impose a more stringent emission fee on the green than on the brown …rm, tG > tB . As
a consequence, the marginal costs of the former, cG + tG , experience a larger increase than those of
12
R
NR
R
NR
The brown …rm’s cuto¤s CB
and CB
satisfy CB
CB
if and only if the environmental damage that the green
…rm generates is su¢ ciently high, i.e., dG
1=2, which holds by de…nition in this section of the paper; while the
NR
R
green …rm’s cuto¤s satisfy CG
> CG
for all admissible parameter values.
7
the latter, cB + tB , ultimately reducing the cost ine¢ ciency that the brown …rm su¤ered before the
introduction of emission fees, helping it produce positive amounts. An analogous argument applies
to region D, where the ine¢ cient green …rm is only active when the regulator is present.
Intuitively, the introduction of emission fees entails a negative e¤ect on all …rms’pro…ts, since
their costs become larger, but can also give rise to a positive e¤ect for the least e¢ cient …rm,
given that environmental regulation helps this …rm ameliorate its cost disadvantage. The following
lemma identi…es under which conditions such positive e¤ect emerges.
Lemma 2. The presence of environmental regulation reduces the brown (green) …rm’s cost
disadvantage (advantage, respectively) if and only if cB satis…es cB > CA , where
CA =
dB dG
dB (1 + 2dG )
1
+
dG (1 + 2dB )
dB (1 + 2dG )
1
cG
1
N R , and above the 450 -line, C > c . Otherwise, i.e.,
and cuto¤ CA lies in region C, i.e., CA < CB
A
G
if cB < CA , regulation reduces the green (brown) …rm’s cost disadvantage (advantage, respectively).
Hence, cost pairs above cuto¤ CA , as …gure 2 depicts, imply that tG > tB , thus implying that
the introduction of emission fees entail a larger cost increase for the green …rm than for its brown
rival. Intuitively, as suggested above, the green …rm’s pre-tax e¢ ciency, and its associated excessive
production and pollution, induces the regulator to set more stringent fees on this …rm than on its
competitor. In turn, these fees ameliorate the brown …rm’s cost disadvantage, which produces a
positive e¤ect on this company’s pro…t.
Figure 2. Cuto¤ CA .
While such a positive e¤ect of regulation emerges for all cB > CA , the brown …rm is only
in favor of the introduction of emission fees if this positive e¤ect o¤sets the negative e¤ect that
regulation produces on pro…ts. The next proposition compares the relative size of these two e¤ects,
8
and thus identi…es in which cases …rms’equilibrium pro…ts are actually larger with than without
environmental regulation, leading …rms to support emission fees.
Proposition 2. When environmental damages satisfy dB
1. The brown …rm is una¤ ected by regulation in region A,
bene…ted by regulation in region B,
R
B
N R.
B
dG
R
B
=
1=2:
NR
B
= 0, but is unambiguously
In contrast, in region C regulation is bene…cial
for the brown …rm if and only if its cost disadvantage is su¢ ciently large, i.e., cB > C B , where
cuto¤ C B lies in region C, and
CB
2 [dB 2(1
dB (4 + 8dG )
dB )dG ]
dB (2 + 4dG ) + 2dG
+
2dG 3 dB (4 + 8dG ) 2dG
3
cG .
3
Finally, in regions D and E, the brown …rm is harmed by regulation, under all parameter
conditions.
2. The green …rm is una¤ ected by regulation in region E,
bene…ted by regulation in region D,
R
G
N R.
G
R
G
=
NR
G
= 0, but is unambiguously
However, in region C regulation is bene…cial
for the green …rm if and only if its cost disadvantage is su¢ ciently large, i.e., cB < C G , where
cuto¤ C G lies in region C, satis…es C G < C B , and
CG
4dB (1 dG ) 2dG
4dG dB (2 8dG )
+
dB (2 + 4dG ) + 2dG 3 dB (2 + 4dG ) + 2dG
3
cG ,
3
In regions B and A, the green …rm is harmed by regulation, for all parameter conditions.
Figure 3 below illustrates our results by superimposing on …gure 2 the cuto¤s identi…ed in
Proposition 1, namely, C B and C G .13 In particular, cost pairs (cB ; cG ) above cuto¤ CA identify
settings in which regulation entails a positive e¤ect on the pro…ts of the brown …rm, as described
in Lemma 2. Such a positive e¤ect, however, does not imply that the brown …rm favors regulation
for all cB > CA . In particular, it only supports emission fees for cost pairs above C B , where
C B > CA . Intuitively, in the region between cuto¤s C B and CA , while the brown …rm bene…ts
from a positive e¤ect of regulation, i.e., emission fees reduce its costs disadvantage since cB > CA ,
the negative e¤ect of regulation outweighs its positive e¤ect, thereby entailing a net loss since
cB > C B . Speci…cally, the cost asymmetry in this region is small and, hence, regulation does not
produce a signi…cant reduction in the cost di¤erential, thus implying that the brown …rm opposes
regulation. In contrast, cost pairs above C B describe contexts in which the cost disadvantage of
13
For compactness, …gure 3 does not include the vertical and horizontal intercepts of each cuto¤. Nonetheless,
the proof of Proposition 2 analyzes and compares these intercepts in detail. In addition, …gure 3 considers that
2dB
2dB
dG > 1+2d
, so cuto¤ C G originates in the negative quadrant. Otherwise, if dG is su¢ ciently low, i.e., dG
,
1+2dB
B
cuto¤ C G originates in the positive quadrant, thus shrinking region C II. The following subsection explores these
comparative statics results in more detail. In contrast, the vertical intercept of the brown …rm’s cuto¤, C B , is positive
for all admissible environmental damages, i.e., dB dG 1=2.
9
the brown …rm is su¢ ciently strong, which yield a large bene…t from regulation, i.e., the positive
e¤ect dominates, ultimately leading this …rm to support regulation.
Figure 3. Pro…t comparison.
For presentation purposes, let us next examine …rms’preferences for environmental regulation
in each of the regions. First, in region A, the brown …rm remains inactive, both with and without
regulation, obtaining zero pro…ts in both cases. Therefore, the …rm is una¤ected by emission fees.
In contrast, the green …rm opposes regulation: being the only active …rm in the industry under both
regulatory contexts, its monopoly pro…ts are larger when emission fees are absent than otherwise.
In region B, the brown …rm is inactive under no regulation, obtaining zero pro…ts, but produces
positive output levels when regulation is present, i.e., emission fees ameliorate the signi…cant cost
disadvantage it experiences. As a result, the brown …rm favors the introduction of emission fees
when its costs lie in this region. By contrast, the green …rm opposes regulation: emission fees not
only increase its production costs but, in addition, they “reactivate” the brown …rm, forcing the
green …rm to share the industry with a competitor (which does not occur when regulation is absent,
whereby the green …rm enjoys monopoly rents).
When …rms’costs become more symmetric, however, as in region C, the brown …rm produces
positive output levels with and without regulation. Therefore, the presence of the regulator becomes
bene…cial for the brown …rm only when its cost disadvantage is su¢ ciently large, i.e., cB > C B .
This suggests that cuto¤ C B divides region C into two subareas, as depicted in …gure 3: subarea
C I, whereby the brown …rm still obtains a larger pro…t with than without regulation,
R
B
N R,
B
providing the same pro…t ranking as in region B; and subareas C II and C III, where the pro…ts
of the brown …rm become lower with regulation, i.e.,
R
B
<
N R.
B
The green …rm, however, is
unambiguously harmed by regulation: not only does regulation increase the …rm’s costs by the
10
amount of the emission fee, but also reduces the cost advantage that the green …rm enjoys relative
to its brown competitor in these areas. As a consequence, the interests of the brown and green
…rms are misaligned regarding environmental regulation in regions B and C I, where the brown
…rm favors the introduction of regulation while the green …rm opposes it, but aligned in region
C II, whereby both …rms dislike emission fees.
A similar argument applies to cost pairs below the 450 degree line, where now it is the green
…rm who experiences a cost disadvantage. When this …rm is relatively ine¢ cient (region C III), the
positive e¤ect of regulation on pro…ts, i.e., reducing its cost disadvantage, dominates its negative
e¤ect. As a consequence, the green …rm favors the introduction of environmental regulation, while
its brown competitor opposes emission fees. In region D, the green …rm supports emission fees,
since such regulation allows it to produce positive amounts, while otherwise it would have to remain
inactive given its substantial cost disadvantage. Finally, in region E, the green …rm becomes so
ine¢ cient that it remains inactive under both regulatory settings, thus obtaining zero pro…ts in
both cases.
4.1
Comparative statics
The following corollary examines the comparative statics of our above results. Since Proposition 2
already identi…ed how …rms’preferences for regulation are a¤ected by changes in production costs,
as depicted in regions A through E in the (cB ; cG ) quadrant, we next focus on how these preferences
are in‡uenced by di¤erent environmental damages.
Corollary 1. When the pollution generated by the green …rm entails larger environmental
damages, i.e., dG approaches dB , the region in which only the brown (green) …rm favors regulation
expands (shrinks, respectively), and the area in which both …rms oppose regulation expands. In
contrast, an increase in dB produces opposite e¤ ects on the size of these three regions.
Figure 4 summarizes our results about …rms’preferences for environmental regulation, by identifying three di¤erent areas: (1) in regions B and C I, only the ine¢ cient brown …rm favors emission
fees; (2) in region C II, since …rms are relatively symmetric, both of them oppose regulation; and
(3) in regions C III and D, only the ine¢ cient green …rm supports emission fees. In addition,
…gure 4a depicts the case in which the environmental damage of the green …rm is relatively high,
dG >
2dB
1+2dB ,
while …gure 4b represents the case in which dG
2dB
1+2dB .
Intuitively, as the pollution
associated with the production of the green …rm becomes less damaging, this …rm is subject to lower
emission fees. As a consequence, the positive e¤ect of emission fees on its pro…ts (ameliorating its
cost disadvantage) dominates the negative e¤ect under larger parameter conditions, and the area
in which it supports environmental regulation (regions C III and D) expands. In contrast, the
region in which the brown …rm favors regulation (areas B and C I) shrinks.
11
Fig. 4a. Preferences when dG >
2dB
1+2dB .
Fig. 4b. Preferences when dG
2dB
1+2dB .
The above results embody two extreme situations as special cases: (1) that in which …rms are
symmetric in the environmental damage of their production, i.e., dB = dG
1=2; and (2) that where
…rms are highly asymmetric in their damages and dG reaches its lower bound, i.e., dB > dG = 1=2.
Corollary 2 (Extreme cases). When both …rms’environmental damages coincide, i.e., dB =
dG
1=2, the brown and green …rm support regulation under symmetric conditions. If, instead,
…rms’environmental damages satisfy dB > dG = 1=2, the green (brown) …rm is bene…ted (harmed,
respectively) by regulation under all parameter conditions.
When …rms’production entails the same environmental pollution, our results still predict that
…rms favor regulation under a large set of parameter values. Figure 5a below shows how the cuto¤s
depicted in …gure 4a are modi…ed when environmental damages become symmetric. In particular,
…rms favor regulation under similar conditions, i.e., the region in which only the brown …rm favors
regulation in …gure 5a (above the 450 -line) is a mirror image of the area where only the green …rm
supports regulation (below the 450 -line). Interestingly, our results also embody the special case in
which …rms are symmetric in their environmental damages, dB = dG
costs, cB = cG ; as depicted in the points along the
oppose regulation.
12
450
1=2, and in their production
line of …gure 5a, which leads both …rms to
Fig. 5b. dB > dG = 1=2.
Fig. 5a. Symmetric damages, dB = dG .
Let us now examine the second result of Corollary 2, which analyzes how …rms’ preference
for regulation are a¤ected by a decrease in dG . In this setting, region C III, in which only the
green …rm favors regulation expands ; as described in Corollary 1. In the limit, when dG is further
NR
R , C , and C
decreased to its lower bound, dG = 1=2, cuto¤s CB
B
G coincide with CB , becoming
1+cG
2 ;
as depicted in …gure 5b. In this case, only the region in which the green …rm favors regulation
can be sustained, since this …rm is unambiguously bene…ted by emission fees.14 Interestingly, since
the emission fee imposed on the green …rm is exactly zero when dG = 1=2, this case yields the same
equilibrium results as Proposition 1, whereby dB
1=2 > dG , and the green …rm supports emission
fees under all parameter values given that it is not subject to emission fees.
4.2
Discussion
Opponents of environmental policy. Our results suggest that the introduction of environmental
regulation can be especially opposed by existing …rms when their production costs are relatively
symmetric, cB = cG . Such opposition against emission fees also arises when, despite …rms being
cost asymmetric, the environmental damage of the green and brown …rms are relatively similar.
Essentially, in this setting, the introduction of environmental policy produces a similar increase
in the production costs of both …rms, implying that cost asymmetries remain almost una¤ected.
As a consequence, regulators planning to introduce emission fees on this type of industries should
anticipate a strong political opposition, e.g., lobbying and advertising campaigns against the policy.
14
Recall that, from our above analysis, in region A the green …rm strictly opposes regulation, but it is una¤ected
by the introduction of emission fees in region E. Therefore, the shaded region in …gure 5b depicts (cB ; cG ) pairs for
R
R
which the green …rm strictly favors regulation, i.e., CB
> cB > CG
.
13
Unexpected supporters of environmental policy. While the regulator’s task is usually supported
by a “natural ally”of environmental policy, the green …rms, our results also demonstrate that regulatory agencies can often …nd an “unexpected ally.”In particular, …rms with a polluting production
process, despite being ine¢ cient relative to their green rivals, support the introduction of emission
fees, in order to ameliorate their cost disadvantage. In other words, the brown …rm sees environmental regulation as its only chance to remain active in the industry when its cost disadvantage is
su¢ ciently large.
Policy implications. Our results indicate that …rms’support for emission fees can be facilitated
or hindered by other environmental policies. Speci…cally, policies that promote the dissemination of
new technologies, allowing …rms to become more symmetric in their production costs, i.e., cB = cG ,
would actually lead to settings in which both …rms oppose emission fees. A similar argument
applies to government programs that help all companies to acquire cleaner technologies, allowing
for similar environmental damages across …rms, i.e., dB = dG , which would facilitate the emergence
of settings in which both …rms oppose emission fees; as discussed in the …rst part of Corollary 2. In
contrast, policies targeted to relatively green …rms, which provide technological and …nancial help
to make their production process even cleaner, would move industry incentives towards contexts in
which the green company favors regulation under large parameter conditions (as identi…ed in the
second part of Corollary 2 and …gure 5b).
5
Conclusions
We analyze a duopoly model with and without environmental policy, examining under which conditions the green or, perhaps more surprisingly, the brown …rm supports the introduction of emission
fees. Intuitively, a …rm (either brown or green) supports regulation in order to reduce the cost
disadvantage it su¤ers relative to its more e¢ cient competitor. In addition, we demonstrate that a
…rm is more likely to support regulation as the environmental damage generated by its own production (the production of its rival) decreases (increases, respectively). In the extreme case in which
the production of the green …rm becomes very clean, only this …rm favors environmental regulation
under all parameter conditions. These equilibrium predictions allow regulatory agencies, such as
the EPA in the United States, to anticipate in which contexts emission fees will be opposed by
more …rms in the industry.
Our paper considers that …rms simultaneously select their production decisions. However, in
certain industries, …rms might act sequentially, thus allowing the industry leader to strategically
produce a su¢ ciently high output level that forces the follower to remain inactive. In such a setting,
the regions of parameter values (production costs and environmental damages) for which either type
of …rm supports regulation would di¤er from those identi…ed in this paper. Furthermore, our model
does not allow for the goods sold by the green and brown …rm to be di¤erentiated, whereas certain
consumers might exhibit di¤erent preferences for similar goods because of the amount of pollution
generated during their production processes. Finally, we assume that …rms’ technology is given,
14
while companies often choose to strategically invest in clean technologies in order to alter their
costs and/or environmental damages.
6
Appendix
6.1
Proof of Proposition 1
Before analyzing the equilibrium pro…ts of each …rm, and for completeness, we examine each …rm’s
production decision with and without regulation, identifying for which set of parameter values their
production is positive.
Lemma A. The brown …rm produces positive amounts when the regulator is absent (present) if
b R , respectively); while
and only if its production costs are su¢ ciently low, i.e., cB < C N R ( cB < C
B
B
the green …rm’s output is positive when regulation is absent (present) if and only if the costs of its
N R ( c > C R , respectively), where
brown competitor are su¢ ciently high, i.e., cB > CG
B
G
R
bB
C
2dB (1 dG ) dG
4dB dG dB dG
+
cG .
dB 2dG (1 dB ) dB 2dG (1 dB )
b R < C N R and C R < C N R . In addition, the brown (green) …rm’s cost disadvantage
Cuto¤ s satisfy C
B
B
G
G
(advantage, respectively) is larger when the regulator is present than absent under all parameter
b R coincides with C N R when dG ! 0.
values. Finally, cuto¤ C
G
B
Proof of Lemma A. No regulation. When the regulator is absent, …rms compete a la Cournot,
maximizing pro…ts
max (1
qB
qG ) qB
cB qB
max (1
qB
qG ) qG
cG qG
qB
qG
to obtain equilibrium output levels qB =
only if cB <
1+cG
2
NR
CB
and cB > 2cG
1 2cB +cG
and qG = 1 2c3G +cB ,
3
N R , respectively.
1 CG
which are positive if and
Environmental regulation. When the regulator is present, the brown and green …rms compete a la Cournot, solving:
max (1
qB
qG ) qB
cB + tB qB
max (1
qB
qG ) qG
cG + tG qG
qB
qG
G
B
1 2cB +cG 2tB +tG
and qG (tG ; tB ) = 1 2cG +cB3 2t +t ,
3
qB (tB ; tG ) + qG (tG ; tB ). The regulator maximizes the
where we obtain output functions qB (tB ; tG ) =
entailing an aggregate output of Q(tB ; tG ) =
15
social welfare
CS Q(tB ; tG ) + P S Q(tB ; tG ) + T tB ; tG
Env Q(tB ; tG )
1
B G 2
B G
2 (Q(t ; t )) denotes consumer surplus, P S(Q(t ; t )) is the producer
surplus, T (tB ; tG ) = tB qB (tB ; tG ) + tG qG (tG ; tB ) is tax revenue arising from emission fees, and
Env Q(tB ; tG ) = dB (qB (tB ; tG ))2 + dG (qG (tB ; tG ))2 is the environmental damage from the
where CS(Q(tB ; tG )) =
production of the brown and green …rms, with dB > dG
0. The social planner can maximize
the above social welfare by taking …rst-order conditions with respect to qB and qG , obtaining the
SO =
socially optimal output levels of qB
2dG +cG
R
CB
2dG +1
tG that induce
positive if and only if cB <
the emission fees
tB
and
2dG (1 cB ) cB +cG
2(dB +dG +2dB dG )
levels can be recovered by setting qB
2dB (1 cG )+cB cG
2(dB +dG +2dB dG ) , which are
R , respectively. Then,
2dB CG
SO =
and qG
and cB > cG (2dB + 1)
the duopolists to produce the socially optimal output
(tB ; tG )
SO and q (tB ; tG ) = q SO , i.e.,
= qB
G
G
1 2cB +cG 2tB +tG
3
2dG (1 cB ) cB +cG
1 2cG +cB 2tG +tB
B (1 cG )+cB cG
= 2d
3
2(dB +dG +2dB dG ) and
2(dB +dG +2dB dG ) . Simultaneously solving for emission
1)[2dG (1 cB ) cB +cG ]
1)[2dB (1 cG )+cB cG ]
tB and tG yields tB = (2dB 2(d
and tG = (2dG 2(d
. However, tG
B +dG +2dB dG )
B +dG +2dB dG )
cannot be supported for dG < 1=2. Hence, in the current setting where dB
that
qG
tG
(tB )
= 0, implying that output becomes a function of
=
1 2cG +cB +tB
.
3
tB
alone, i.e., qB
=
fees
>0
1=2 > dG , we have
(tB )
=
1 2cB +cG 2tB
3
and
Let us now analyze the regulator’s task in this setting. If the regulator
2dG (1 cB ) cB +cG
2(dB +dG +2dB dG )
dB (1 cG )+dG (1 cB )
. The
dB +dG +2dB dG
SO =
could choose socially optimal output levels for each …rm, he would select qB
SO =
and qG
2dB (1 cG )+cB cG
2(dB +dG +2dB dG ) ,
entailing an aggregate production of QSO =
regulator can now use only a single policy instrument, which is tB . As a result, he sets the level of
such emission fee, tB , in order to guarantee that the aggregate output still coincides with QSO , i.e.,
qB (tB ) + qG (tB ) = QSO . In particular, the emission fee tB that solves qB (tB ) + qG (tB ) = QSO is
tB =
2dB dG (2
cB
cG )
dG (1 2cB + cG )
dB + dG + 2dB dG
inducing the brown …rm to produce qB (tB ) =
produce qG
(tB )
=
[cB cG +2dB (1 cG )]dG
.
dB +dG +2dB dG
dB (1 + cB
dG (1 2cB +cG )+dB (1 cG )(1 2dG )
dB +dG +2dB dG
2cG )
,
and the green …rm to
Therefore, the use of a single emission fee, tB , creates ine¢ -
SO
ciencies, as the regulator cannot guarantee that each …rm produces its socially optimal amount, qK
for each type of …rm K = fB; Gg. Nonetheless, this regulation ensures that aggregate production
is still equal to QSO .
The emission fee tB is positive if and only if cB < C10 , where
C10
4dB dG dB dG
2dB (1 dG ) dG
+
cG .
dB 2dG (1 dB ) dB 2dG (1 dB )
4dB dG dB dG
dB
1
dB 2dG (1 dB ) , which is negative for all dG < 4dB 1 < 2 , but becomes
positive when dG exceeds 4ddBB 1 , i.e., for all 4ddBB 1 < dG < 12 . Such cuto¤ C10 crosses the horizontal
G dB dG
axis at cG = d4dGB d2d
; as illustrated in …gure A1. In addition, such horizontal intercept is
B (1 dG )
1
N R.
smaller than 2 , implying that cuto¤ C10 lies above CG
Cuto¤ C10 originates at
16
Fig. A1. Production decisions when dB
1=2 > dG .
The brown …rm produces positive amounts if and only if cB < C20 , where
C20
Cuto¤ C20 originates at cB =
dB + dG 2dB dG dG
+
2dG
dB +dG 2dB dG
,
2dG
dB (1
2dG
which lies above
1
2
2dG )
cG .
for all admissible parameter values;
as depicted in …gure A1. In addition, the vertical intercept of cuto¤ C20 lies above 1 if and only
if dG <
dB
1+2dB .
(Notice that, for dB > 1=2, cuto¤
i.e., dG < 1=2.) Finally, cuto¤
C20
dB
1+2dB
lies within the admissible values of dG ,
reaches cB = 1 when cG = 1. Hence, condition cB < C10 is
more restrictive than cB < C20 , since C10 < C20 . Therefore, for all the region in which emission fee
tB is positive, i.e., cB < C10 , the brown …rm produces positive amounts, i.e., cB satis…es cB < C20 .
b R . Notice that the limit
For presentation purposes, we next denote the binding cuto¤ C10 as C
B
R
N
R
b
lim C = 2cG 1, which coincides with C . Finally, the green …rm produces a positive output
dG !0
B
if and only if cB > cG (2dB + 1)
G
2dB
R , which coincides with the cuto¤ identi…ed in Lemma
CG
A.
N R , the brown …rm is inactive, both with and without
Summarizing, in region A0 , i.e., cB > CB
regulator, while its competitor is active regardless of the regulatory context. In region B 0 , i.e.,
N R > c > C 0 , the brown …rm is only active when regulation is absent, while the green …rm is
CB
B
1
N R , both …rms are active,
active under both regulatory settings. In region C 0 , i.e., C10 > cB > CG
N R > c > C R , the green …rm is only
regardless of the regulatory context. In region D0 , i.e., CG
B
G
active under regulation, while the brown …rm is active both with and without regulation. Finally, in
R > c , the green …rm (brown …rm) is inactive (active) regardless of the regulatory
region E 0 , i.e., CG
B
setting.
Let us now analyze whether the cost di¤erential between …rms when the regulator is absent, cB
17
cG , is ameliorated or emphasized when regulation is present, (cB + tB ) (cG + 0). Firms produce the
socially optimal output when the emission fee is tB =
2dB dG (2 cB cG ) dG (1 2cB +cG ) dB (1+cB 2cG )
.
dB +dG +2dB dG
In consequence, the regulation ameliorates the existing cost asymmetry if (cB + tB )
(cG + 0) <
R , or
< 0. However, such emission fee is positive for all cB < C^B
cG ), which reduces to tB
R ), but is never negative by de…nition. Hence, the presence of environmental
zero (for all cB
C^B
(cB
regulation does not ameliorate the brown …rm’s cost disadvantage under any parameter conditions.
Instead, it emphasizes the brown …rm’s cost disadvantage under all parameters for which tB > 0,
i.e., for all cB < C^ R .
B
Pro…t comparison. After analyzing the parameter values under which production is positive
with and without regulation, let us now examine equilibrium pro…ts in each of these parameter
regions, A0 through E 0 .
Region A’. In region A0 , the brown …rm stays inactive both with and without regulation
because the …rm experiences substantial cost disadvantage, i.e., cB > C N R > C^ R , compared to
B
B
more e¢ cient green …rm (see the proof of Lemma A for details). Thus, the …rm makes zero pro…ts,
i.e.,
R
B
=
NR
B
= 0. Given inactive brown …rm and tax-exempt status of the green …rm, i.e., tG = 0,
the green …rm will reap monopoly pro…ts of
G
(1 cG )2
4
=
in region A0 with and without regulation,
which are positive for all cG < 1.
Region B’. Brown …rm. In region B 0 , the brown …rm is still subject to a signi…cant cost
NR > c > C
^ R , and thus remains inactive in the
disadvantage relative to the green …rm, i.e., CB
B
B
presence of regulation (as shown in Lemma A above), i.e.,
R
B
= 0. However, in the absence of
NR =
environmental regulation, the brown …rm produces a positive output level, qB
)2
R = (1 2cB +cG , which satisfy
corresponding pro…ts of N
B
9
R
^
cB > CB , which holds in all (cB ; cG )-pairs within region B 0 .
Green …rm. The green …rm makes pro…ts of
>
R
B
= 0 for all
(1 cG )2
with environmental regulation, since
4
2
N
R
and G = (1 2cG9+cB ) without, given that the
R
G
it operates as the single producer in the industry,
NR
B
1 2cB +cG
, with
3
N R and
cB < CB
=
brown …rm is only active when regulation is absent. Comparing the equilibrium pro…ts of the green
…rm, we obtain that
R
G
>
NR
G
N R > c > C 0 , where C 0
if and only if cB satis…es CB
B
3
3
straightforward to show that cuto¤ C30 originates at
5
2
and crosses the horizontal axis
2dB
is greater than 1+2d
. Since, in addition, cuto¤ C30 reaches cB = 1
B
R ; as depicted in …gure A2 below. Thus, the
hand side of cuto¤ CG
under all (cB ; cG )-pairs within region B 0 , which implies that R
G
values in this region.
18
7cG 5
2 . It is
at 57 , which
when cG = 1, it lies to the rightN R > c > C 0 holds
condition CB
B
3
>
NR
G
holds for all parameter
Fig A2. Region B 0 and cuto¤ C30 .
Region C’. Brown …rm. As demonstrated in Lemma A, the brown …rm becomes active,
both with and without regulator, when (cB ; cG )-pairs lie within region C 0 . Speci…cally, this …rm’s
2
R = [(1 2cB +cG )dG +dB (1 cG )(1 2dG )] under environmental regulation, while they are
B
(dB +dG +2dB dG )2
2
N R = (1 2cB +cG ) in the absence of regulation. Thus, pro…ts satisfy N R < R if and only if
B
B
B
9
R
0
b
C4 > cB > CB , where
pro…ts are
C40
Cuto¤ C40 originates at
dG > 0 given that
cB =
2(dB +dG dB dG )
dB +2dG (2+dB ) ,
2(dB + dG dB dG ) 2dG dB (1 4dG )
+
cG
dB + 2dG (2 + dB )
dB + 2dG (2 + dB )
2(dB +dG dB dG )
dB +2dG (2+dB ) ,
dB
1 dB
which is positive for all dG >
dB
1 dB ,
which holds for all
< 0, and reaches cB = 1 when cG = 1. Moreover, its vertical intercept,
dB +dG 2dB dG
for all dG < 21 and dB > 0, which
2dG
N R and C 0 . However,
> dG . Therefore, cuto¤ C40 lies between CB
2
R is incompatible with region
C 0 since the condition C40 > cB > C^B
is greater than
hold by de…nition since dB
1=2
1
2
and less than
N R < R does not hold in region
B
B
0
C , i.e., there are no (cB ; cG ) pairs for which both areas
R
in region C 0 , the pro…ts of the brown …rm satisfy N
B >
19
overlap in …gure A3a. As a consequence,
R,
B
thus opposing regulation.
Fig A3a. Region C 0 and cuto¤ C40 .
Fig A3b. Region C 0 and cuto¤ C50 .
Green …rm. The green …rm, on the other hand, obtains
R =
regulation and N
G
b R > cB > C 0 , where
C
5
B
(1 2cG +cB )2
9
R
G
=
without regulation, where pro…ts
[cB cG +2dB (1 cG )]2 d2G
with
(dB +dG +2dB dG )2
N R for all
satisfy R
G >
G
dB + dG + 8dB dG
5dG + 2dB (1 + 5dG )
+
cG
dB + 2dG (2 + dB )
dB + 2dG (2 + dB )
C50
dB +dG +8dB dG
dB +2dG (2+dB ) , which lies in the negative quadrant for all dB and dG ,
+dG +8dB dG
and crosses the cG -axis at 2ddBB+5d
, and reaches cB = 1 when cG = 1. Furthermore, the
G +10dB dG
dB +dG +8dB dG
2dB
horizontal intercept cG = 2dB +5dG +10dB dG is larger than 12 and less than 1+2d
for all dG > 0 and
B
1
0
N
R
R
dB > 2 . Thus, cuto¤ C5 lies between CG and CG ; as depicted in …gure A3b above. Therefore,
b R > cB > C 0 holds under all (cB ; cG )-pairs within region C 0 , which means that the
the condition C
5
B
NR
pro…ts of the green …rm satisfy R
G > G .
Cuto¤ C50 originates at
Region D’. Brown …rm. As shown in Lemma A, the brown …rm produces positive amounts,
both with and without regulation, when costs lie in region D0 . Speci…cally, the …rm earns
[(1 2cB +cG )dG +dB (1 cG )(1 2dG
(dB +dG +2dB dG )2
)]2
when regulation is present and
NR
B
=
(1 cB
4
)2
R
B
=
when it is absent.
Comparing the pro…ts of the brown …rm, we obtain the following two roots for cB that solve the
equality
NR
B
=
R,
B
C60
C70
3(dB + dG ) 2dB dG 2[dG dB (1 2dG )]
+
cG
dB + dG (5 + 2dB )
dB + dG (5 + 2dB )
dB + dG 6dB dG
2[dG dB (1 2dG )]
cG
dB dG (3 2dB )
dB dG (3 2dB )
20
3(dB +dG ) 2dB dG
dB +dG (5+2dB ) and reaches cB = 1 when cG =
1
B +dG ) 2dB dG
1. In addition, its vertical intercept, cB = 3(d
dB +dG (5+2dB ) , lies above 2 under all admissible
N R . Furthermore, cuto¤
parameters, dB
1=2 > dG . As a consequence, cuto¤ C60 lies above CB
dB
, but between 1 and 1/2 otherwise. On the other hand,
C60 originates above cB = 1 if dG < 1+2d
B
dB +dG 6dB dG
0
cuto¤ C7 originates at dB dG (3 2dB ) , and reaches cB = 1 when cG = 1. Its vertical intercept,
dB +dG 6dB dG
dB
dB dG (3 2dB ) , is positive if and only if dG is su¢ ciently high, i.e., dG > 6dB 1 . Moreover, when
3dB
dG is further increased, it becomes larger than 12 , which occurs for all dG > 1+10d
, and exceeds
B
dB
dB
3dB
dB
cB = 1 for all dG > 1+2dB ; where 1+2dB > 1+10dB > 6dB 1 for all admissible values, i.e., dB > 1=2,
as depicted in …gure A4 below. Therefore, in region I of …gure A4, cuto¤ C60 (C70 ) originates below
one (above one, respectively). In region II, the origin of cuto¤ C60 becomes larger than 1, while that
of cuto¤ C70 lies above 1=2 but below 1. When dG is further decreased, cuto¤ C60 is still originating
below 1, while cuto¤ C70 origin lies between 0 and 1=2 in region III, and becomes negative in region
On the one hand, the cuto¤ C60 originates at
IV .
Fig. A4. Origin of cuto¤s C60 and C70 .
Let us next examine the equilibrium pro…ts of the brown …rm in each of the possible (dB ; dG ) pairs
considered above, i.e., regions I through IV in …gure A4. In region I, cuto¤ C70 originates above
cB = 1, and thus becomes inconsequential, since it does not belong to the admissible set of production costs (cB ; cG ) 2 [0; 1]2 . Cuto¤ C60 , however, originates below 1, but above 1=2. Therefore, for
all cB < C60 , we obtain that the pro…ts of the brown …rm satisfy
D0 ,
which lies below
cuto¤ C60 ,
R
B
<
N R,
B
implying that in region
the brown …rm opposes regulation. Similarly, in region II, cuto¤ C60
becomes now inconsequential, since it originates above cB = 1, while cuto¤ C70 originates between
b R . Thus, for all cB < C 0 , we …nd that the pro…ts of the brown …rm
1=2 and 1, thus lying above C
7
B
satisfy
R
B
<
N R,
B
also entailing that in region D0 the brown …rm opposes regulation. A similar
argument applies in region III, since cuto¤ C60 still originates above 1, but now the origin of cuto¤
b R , but still lying on the positive quadrant. Hence, for all
C 0 decreases below 1=2, thus crossing C
7
B
21
R
B
cB < C70 , the pro…ts of the brown …rm also satisfy
D0 ,
regulation in region
N R , entailing that this
B
cuto¤ C70 . Finally, in region
since such region lies below
<
…rm also opposes
IV cuto¤ C60 still
lies above 1, but C70 now originates in the negative quadrant. However, its horizontal intercept,
dB +dG 6dB dG
2(dB dG 2dB dG ) , is
cuto¤ C70 does not
smaller than
1
2
cross the upper bound of region
N R.
i.e., cuto¤ CG
NR
satisfy R
B < B ,
D0 ,
we …nd that the equilibrium pro…ts of the brown …rm
opposes regulation in region
dB
6dB 1 .
for all (dB ; dG ) pairs in region IV , i.e., dG <
Hence,
Thus, for all cB < C70 ,
implying that this …rm
D0 .
Green …rm. The green …rm is active when the regulation is present, with pro…ts of
[cB cG +2dB (1
(dB +dG +2dB
cG )]2 d2G
dG )2
, and inactive otherwise, i.e.,
NR
G
R
G
=
= 0. As shown in the proof of Lemma A,
the environmental regulation alleviates the cost disadvantage faced by the green …rm, so it can
produce positive amounts. Therefore, its pro…ts satisfy
R , which holds for all (c ; c )-pairs within region
cB < CG
B G
R
G
D0 .
>
NR
G
R and
for all costs cB > CG
Region E’. In this region, the green …rm experiences such a cost disadvantage relative to
the brown …rm, that it produces zero output regardless of the regulatory setting, yielding pro…ts
R
G
of
=
NR
G
= 0. The brown …rm, on the other hand, operates like a monopolist under both
regulatory contexts, earning pro…ts of
regulation. Thus, pro…ts satisfy
6.2
NR
B
>
2
R = (1 cB ) with regulation and N R
B
B
(1+2dB )2
R for all admissible parameter values.
B
=
(1 cB )2
4
without
Proof of Lemma 1
No regulation. When environmental regulation is absent, …rms’equilibrium output levels coincide
1 2cB +cG
3
G
cB < 1+c
2
with those in the proof of Proposition 1, i.e., qB =
and green …rms, which are positive if and only if
and qG =
NR
CB
1 2cG +cB
3
for the brown
and cB > 2cG
1
N R,
CG
respectively.
Environmental regulation. When the regulator is present, the brown and green …rms compete a la Cournot, solving:
max (1
qB
qG ) qB
cB + tB qB
max (1
qB
qG ) qG
cG + tG qG
qB
qG
G
B
1 2cB +cG 2tB +tG
and qG (tG ; tB ) = 1 2cG +cB3 2t +t ,
3
qB (tB ; tG ) + qG (tG ; tB ). The regulator maximizes the
where we obtain output functions qB (tB ; tG ) =
entailing an aggregate output of Q(tB ; tG ) =
social welfare
CS Q(tB ; tG ) + P S Q(tB ; tG ) + T tB ; tG
Env Q(tB ; tG )
1
B G 2
B G
2 (Q(t ; t )) denotes consumer surplus, P S(Q(t ; t )) is the producer
surplus, T (tB ; tG ) = tB qB (tB ; tG ) + tG qG (tG ; tB ) is tax revenue arising from emission fees, and
Env Q(tB ; tG ) = dB (qB (tB ; tG ))2 + dG (qG (tB ; tG ))2 is the environmental damage from the
where CS(Q(tB ; tG )) =
production of the brown and green …rms, with dB > dG
22
0. The social planner can maximize
the above social welfare by taking …rst-order conditions with respect to qB and qG , obtaining the
SO =
socially optimal output levels of qB
2dG +cG
R
CB
2dG +1
tG that induce
positive if and only if cB <
the emission fees tB and
2dG (1 cB ) cB +cG
2(dB +dG +2dB dG )
levels can be recovered by setting qB
2dB (1 cG )+cB cG
2(dB +dG +2dB dG ) , which are
R , respectively. Then,
2dB CG
SO =
and qG
and cB > cG (2dB + 1)
the duopolists to produce the socially optimal output
(tB ; tG )
SO and q (tB ; tG ) = q SO , i.e.,
= qB
G
G
1 2cB +cG 2tB +tG
3
=
2dG (1 cB ) cB +cG
1 2cG +cB 2tG +tB
B (1 cG )+cB cG
= 2d
3
2(dB +dG +2dB dG ) and
2(dB +dG +2dB dG ) . Simultaneously solving for emission
1)[2dB (1 cG )+cB cG ]
1)[2dG (1 cB ) cB +cG ]
and tG = (2dG 2(d
, which are
fees tB and tG yields tB = (2dB 2(d
B +dG +2dB dG )
B +dG +2dB dG )
R
R
positive if and only if cB < CB and cB > CG , respectively, and in addition, dB dG > 1=2.
Figure A5 summarizes the cuto¤ regions identi…ed in our above analysis with and without
regulation. In particular, …gure A5 identi…es …ve di¤erent regions: (1) in region A, the brown
(green) …rm is inactive (active, respectively), both with and without regulator; (2) in region B,
the brown …rm is active only with regulation, while the green …rm is active both with and without
regulation; (3) in the shaded region C, both …rms are active, both when the regulator is present
and absent; (4) in region D, the green …rm is active only with regulation, while the brown …rm
is active both with and without regulation; and (5) in region E, the brown (green) …rm is active
(inactive, respectively) regardless of the regulatory context.
Fig. A5. Production regions when dG
1=2.
Finally, note that for region B to exist in …gure A5, it must be that the brown …rm’s cuto¤s
R > C N R , i.e., their vertical intercepts satisfy
satisfy CB
B
2dG
1+2dG
>
1
2,
which holds if and only if
N R > C R,
dG > 1=2. On the other hand, for region D to exist, the green …rm’s cuto¤s must satisfy CG
G
i.e. 2cG
1 > cG (2dB + 1)
2dB , which holds for all dB > 1=2, which is true by de…nition.
23
Proof of Lemma 2
6.3
The cost asymmetry when regulation is absent is measured by cB cG , while that when regulation is
present is represented by (cB + tB )
(cG + tG ). Hence, regulation ameliorates the cost asymmetry
between the two …rms if and only if (cB + tB )
(cG + tG ) < (cB
cG ), which reduces to tB < tG .
Using the equilibrium emission fees for the brown and green …rms obtained in Lemma 1, i.e.,
(2dB 1)[2dG (1 cB ) cB +cG ]
2(dB +dG +2dB dG )
tB =
and tG =
(2dG 1)[2dB (1 cG )+cB cG ]
,
2(dB +dG +2dB dG )
respectively, we …nd that tB < tG
for all cB > CA , where
CA =
Cuto¤ CA originates at
1
2
>
1 dB
2dB
for all dB >
1
2,
dB dG
dB (1 + 2dG )
1
+
dG (1 + 2dB )
dB (1 + 2dG )
dB dG
dB (1+2dG ) 1 , which is positive if
and dB > 12 by de…nition, then
1
cG
1
and only if dG >
dG >
1
2
>
1 dB
2dB ,
1 dB
2dB .
However, since
implying that cuto¤
CA originates in the positive quadrant for all admissible parameter values. In addition, cuto¤ CA
R and c > C R ,
reaches cB = 1 when cG = 1. Therefore, since tB > 0 and tG > 0 when cB < CB
B
G
R identi…es the set of
respectively, our results imply that the area in which cB satis…es CA < cB < CB
parameter values for which the brown (green) …rm experiences a reduction in its cost disadvantage
R , the green
(advantage, respectively). In contrast, for cost pairs in the region CA > cB > CG
(brown) …rm experiences a reduction in its cost disadvantage (advantage, respectively).
Proof of Proposition 2
6.4
When environmental damages satisfy dB > dG > 1=2, as depicted in Figure 1, we obtain …ve
possible production regions depending on the symmetry of the …rms’ marginal costs. Below we
discuss …rms’pro…t levels corresponding to each of these regions.
Region A. In region A, the brown …rm experiences a substantial cost disadvantage, i.e., cB >
R
CB
N R , and thus withholds production both with and without regulation, with zero pro…ts.
> CB
Given that the brown …rm stays inactive, the green …rm operates like a monopolist with pro…t
levels of
R
G
=
(1 cG )2
(1+2dG )2
with regulation and
NR
G
=
(1 cG )2
4
without regulation, where R and N R
denote regulation and no regulation, respectively. The di¤erence in green …rm’s pro…ts is hence
R
G
NR
G
=
(1
cG )2 [3 4dG (1 + dG )]
,
4 (1 + 2dG )2
which is positive if and only if dG < 1=2. Otherwise, when dG > 1=2 (as in the case we consider in
this section), the pro…t di¤erence becomes negative and, hence,
R
G
<
N R.
G
Region B. Brown …rm. As shown in Lemma 1, the brown …rm does not produce positive
R > c > C N R , when the regulator is absent, thus implying
amounts in region B, i.e., CB
B
B
NR
B
= 0.
However, when the environmental policy is implemented, the (relatively ine¢ cient) brown …rm
produces positive output levels, entailing a pro…t of
R
B
>
NR
B
= 0 for all (cB ; cG ) pairs within region B.
24
R
B
=
1
4
cB (1+2dG ) 2dG cG
dB +dG +2dB dG
2
, which satis…es
Green …rm. It makes pro…ts of
cB +2dB cG (1+2dB )
dB +dG +2dB dG
1
4
2
NR
G
=
(1 cG )2
4
in the absence of the regulator, and
NR
G
in his presence. Comparing
and
only if cB lies in the interval C3 > cB > C4 , where C3
C4
cG
(1
R,
G
NR
G
we obtain that
cG + (1
>
cG )(2dB dG + dG
R
G
R
G
=
if and
dB ) and
cG )(2dB dG + dG + 3dB ). (For presentation purposes, …gure A6 below superimposes
R,
cuto¤s C3 and C4 on …gure A5.) It is straightforward to show that cuto¤ C3 satis…es C3 > CB
since it originates at 2dB dG + dG
R,
dB , which lies above the vertical intercept of cuto¤ CB
2dG
1+2dG ,
for all dG > 1=2, and cuto¤ C3 reaches cB = 1 when cG = 1. More speci…cally, the vertical
R,
intercept of cuto¤ C3 , while it lies above that of CB
all dG >
1+dB
1+2dB
>
1
2,
but lies below 1 (but still above
2dG
1+2dG , for all dG >
2dG
1+dB
1+2dG ) for all 1+2dB
N R , since it originates at
In addition, cuto¤ C4 satis…es C4 < CB
1=2, it also exceeds 1 for
> dG > 12 .
(2dB dG + dG + 3dB ), which
N R , 1 , for all
lies in the negative quadrant, which thus lies below the vertical intercept of cuto¤ CB
2
dB ; dG > 0. In addition, cuto¤ C4 reaches cB = 1 when cG = 1. (In particular, it is straightforward
to show that the horizontal intercept of cuto¤ C4 ,
R .)
CG
2dB dG +dB +3dB
1+2dB dG +dG +3dB ,
is larger than that of cuto¤
Therefore, condition C3 > cB > C4 holds under all (cB ; cG ) pairs within region B, i.e., the
R > c > C N R . Hence, the pro…ts of the
area satisfying C3 > cB > C4 is a subset of region B, CB
B
B
green …rm satisfy
NR
G
>
R.
G
Fig. A6. Region B and cuto¤s C3 and C4 .
Region C. Brown …rm. As Lemma 1 shows, the brown …rm produces positive amounts, both
with and without regulator when costs lie within region C. In particular, under environmental
regulation, the pro…ts of the brown …rm become
NR
B
=
(1 2cB +cG )2
9
R
B
=
1
4
cB (1+2dG ) 2dG cG
dB +dG +2dB dG
in the absence of regulation. Hence, pro…ts satisfy
25
R
B
>
2
, while they are
NR
B
for all costs in
the subregion C5 > cB > C6 , where
2 [dB + 2(2 + dB )dG ]
dB (2 + 4dG ) + 2dG + 3
+
cG , and
3 + 10dG + dB (4 + 8dG ) dB (4 + 8dG ) + 10dG + 3
C5
C6
2 [dB 2(1
dB (4 + 8dG )
On one hand, cuto¤ C5 originates at
dB )dG ]
dB (2 + 4dG ) + 2dG
+
2dG 3 dB (4 + 8dG ) 2dG
2[dB +2(2+dB )dG ]
3+10dG +dB (4+8dG ) ,
which lies above
3
cG .
3
1
2
for all dG > 1=2, and
reaches cB = 1 when cG = 1. (See …gure A7 below.) Hence, condition C5 > cB holds by de…nition
in region C if and only if dG > 1=2. On the other hand, cuto¤ C6 originates at
which is positive for all dG <
since 2(1dBdB ) > dB
that 2(1dBdB ) > dB
dB
2(1 dB ) .
This condition holds for all damages dB
2[dB 2(1 dB )dG ]
dB (4+8dG ) 2dG 3 ,
dG . In particular,
for all dB > 1=2, then the previous condition is satis…ed by de…nition, given
dG . Therefore, the vertical intercept of cuto¤ C6 lies in the positive quadrant
for all admissible parameters. In addition, such vertical intercept lies below
1
2
for all dG > 1=2.
Finally, cuto¤ C6 reaches cB = 1 when cG = 1. Hence, cuto¤ C6 divides region C into two subareas:
N R > c > C , the brown …rm’s cost asymmetry still implies that
for all CB
6
B
costs C6 > cB the pro…ts of the brown …rm satisfy
R
B
N R.
B
R
B
>
N R,
B
while for
(For presentation purposes, cuto¤
C6 is denoted as C B in the main text.)
Finally, comparing cuto¤ CA (obtained in Lemma 2), and C B , note that the vertical intercept of
cuto¤ CA ,
dB dG
dB (1+2dG ) 1 ,
is smaller than that of C B ,
2[dB 2(1 dB )]
dB (4+8dG ) 2dG 3 ,
for all dG > 21 , thus implying
that cuto¤ CA lies below C B for all parameter values.
Fig. A7. Region C and cuto¤s C5 and C6 .
Green …rm. In the case of the green …rm, it earns a pro…t of
regulation, and
NR
G
=
(1 2cG +cB
9
)2
R
G
=
1
4
cB +2dB cG (1+2dB )
dB +dG +2dB dG
without regulation. Therefore, pro…ts satisfy
26
R
G
>
NR
G
2
with
for all
costs in the subregion C7 > cB > C8 , where
C7
C8
4dB (1 dG ) 2dG
4dG dB (2 8dG )
+
dB (2 + 4dG ) + 2dG 3 dB (2 + 4dG ) + 2dG
3
cG , and
3
3 + 10dB + 4dG (1 + 2dB )
2 [dG + 2dB (2 + dG )]
+
cG .
3 + 2dG + dB (2 + 4dG )
3 + 2dG + dB (2 + 4dG )
On one hand, cuto¤ C7 originates at
4dB 4dB dG 2dG
dB (2+4dG )+2dG 3 ,
which is positive but lies below
1
2
for all
dG > 1=2, and reaches cB = 1 when cG = 1. (See …gure A8 below.) On the other hand, cuto¤
2[dG +2dB (2+dG )]
3+2dG +dB (2+4dG ) , which lies in the
2[dG +2dB (2+dG )]
axis at cG = 3+4d
(see the
G +2dB (5+4dG )
C8 originates at
negative quadrant for all values of dG , and
crosses the cG
horizontal intercept of cuto¤ C8 in …gure A8
below), and reaches cB = 1 when cG = 1. In addition, the horizontal cuto¤, cG =
is larger than
1
2,
and smaller than
2dB
1+2dB
for all dB > dG
2[dG +2dB (2+dG )]
3+4dG +2dB (5+4dG ) ,
1=2. Hence, cuto¤ C8 lies in region
D. Furthermore, cuto¤ C7 pivots downwards as dG increases, with center at (cG ; cB ) = (1; 1), and
its vertical intercept is positive for all dG <
2dB
1+2dB
< dB (as depicted in …gure A8a), but becomes
N R for all parameter values.
negative otherwise (see …gure A8b). Nonetheless, cuto¤ C7 lies above CG
In particular, when dG increases as much as possible, i.e., dG ! dB , cuto¤ C7 experiences a further
downward pivoting e¤ect, as depicted in …gure A8b, but its horizontal intercept,
becomes
2dB
3+4dB ,
which still lies to the left of
1
2
2[dG 2dB (1 dG )]
4dG dB (2 8dG ) 3 ,
for all values of dB > 1=2. As a consequence, cuto¤
C7 lies within region C for all admissible parameters. Thus, cuto¤ C7 divides region C into two
subareas: if C7 > cB , the pro…ts of the green …rm are larger with than without regulator,
R
G
>
N R,
G
while otherwise the green …rm obtains a lower pro…t when the regulator is present. Furthermore,
cuto¤ C7 lies below C6 , since the di¤erence between the vertical intercept of C6 and C7 is
6(1 2dB )(1 2dG ) (dB + dG + 2dB dG )
[2dG + dB (2 + 4dG ) 3] [dB (4 + 8dG ) 2dG
which is positive for all dB
3]
,
dG > 1=2. (For presentation purposes, cuto¤ C7 is denoted as C G in
the main text.)
27
Fig. A8(a). Cuto¤ C7 when dG <
2dB
1+2dB
Fig. A8(b). Cuto¤ C7 when dG
2dB
1+2dB
Region D. In this region, the green …rm is active when regulation is present, but inactive
otherwise. As a result, the green …rm obtains higher pro…ts with than without regulation (similar
to the brown …rm’s condition in region B), but the brown …rm is strictly worse o¤ with than without
regulation (also analogous to the green …rm’s interests in region B).
Region E. In this region, the green …rm is inactive, both when the regulator is present and
absent. As a consequence, the brown …rm obtains a larger pro…t without than with regulation, i.e.,
R
B
<
6.5
N R,
B
while the green …rm’s pro…ts are zero.
Proof of Corollary 1
R
Increases in dG . Cuto¤ CB
2dG +cG
2dG +1
the size of region A. In contrast,
increases in dG since
NR
cuto¤ CB
R
@CB
@dG
=
2(1 cG )
,
(1+2dG )2
which, in turn, shrinks
is independent on dG , implying that region B expands
in dG since, graphically, its upper bound increases while its lower bound remains una¤ected. In
addition, cuto¤ C B decreases in dG , i.e., the derivative of the vertical intercept of cuto¤ C B ,
2[dB 2(1 dB )dG ]
dB (4+8dG ) 2dG 3 ,
with respect to dG yields
12 24dB
,
[3+2dG 4(dB +2dB dG )]2
which is negative for dB > 1=2.
As a consequence, given that the lower bound of region C I, cuto¤ C B , decreases in dG , but its
R , remains una¤ected, region C I ultimately expands in d . Let us now
upper bound, cuto¤ CB
G
analyze region C II. Since the vertical intercept of cuto¤ C B decreases in dG but C G decreases in
dG , the comparative statics of this region require a more detailed analysis. In particular, we …rst
28
measure the size of this region, where both …rms oppose regulation, as follows
Z1
CB
C G dcG =
0
3(1 2dB )(1 2dG ) (dB + dG + 2dB dG )
[2dG + dB (2 + 4dG ) 3] [dB (4 + 8dG ) 2dG
3]
and di¤erentiating with respect to dG , we obtain
[2dG
3(1
6(1 2dB )
4dB (1 + 2dG ) + 3]2
4d2B )
[2dG + dB (2 + 4dG )
which is positive for all admissible parameters, i.e., dB
3]2
dG > 1=2, thus implying that region
C II expands in dG . Let us now examine region C III. As shown above, cuto¤ C G decreases in
N R is independent on d . As a consequence, region C III shrinks. Cuto¤ C R
dG , while cuto¤ CG
G
G
is also una¤ected by variations in dG , thus implying that region D is unchanged in dG . A similar
argument is applicable to region E. Summarizing, the region in which only the brown (green) …rm
favor regulation expands (shrinks, respectively) in dG , while the area in which both …rms oppose
regulation expands in dG .
R is una¤ected in d , leaving region A unchanged as d varies. A
Increases in dB . Cuto¤ CB
B
B
N R is also independent on d . Region C I,
similar argument applies to region B, since cuto¤ CB
B
however, shrinks in dB , since its lower bound, cuto¤ C B , increases in dB , i.e., the derivative of the
vertical intercept of cuto¤ C B ,
2[dB 2(1 dB )dG ]
dB (4+8dG ) 2dG 3 ,
with respect to dB yields
6(4d2G 1)
,
[3+2dG 4(dB +2dB dG )]2
which is positive since dG > 1=2. Let us now analyze region C II. As shown above, its upper bound,
C B , increases in dB , while its lower bound, cuto¤ C G , also increases in dB , i.e., the derivative of
the vertical intercept of cuto¤ C G ,
4dB (1 dG ) 2dG
dB (2+4dG )+2dG 3 ,
12(2dG 1)
,
[2dG +dB (2+4dG ) 3]2
with respect to dB yields
which is positive since dG > 1=2. Thus, the comparative statics of region C II require a more
detailed analysis. As described above, the size of region C II is
Z1
CB
C G dcG =
0
3(1 2dB )(1 2dG ) (dB + dG + 2dB dG )
[2dG + dB (2 + 4dG ) 3] [dB (4 + 8dG ) 2dG
3]
and di¤erentiating with respect to dB , we obtain
3(2dG
1) 4(2dG
7)(dB + 2dB dG )2 + F + 2dG (2dG (2dG
[2dG + dB (2 + 4dG )
where F
2
3] [2dG
7)
9)
9
2
4dB (1 + 2dG ) + 3]
4dB (1 + 2dG ) [9 + 4dG (1 + 2dG )]. The above derivative is negative for all admissible
parameters, i.e., dB
dG > 1=2, thus implying that region C II shrinks in dB . Let us now examine
N R remains una¤ected
the comparative statics in region C III. Since cuto¤ C G increases in dB but CG
by variations in dB , region C III unambiguously expands in dB . Regarding region D, note that
N R , is constant in d , while its lower bound, C R
its upper bound, cuto¤ CG
B
G
is decreasing in dB , given that
R
@CG
@dB
=
2(1
cG (2dB + 1)
2dB ,
cG ) < 0. Therefore, the size of region D enlarges as
R decreases in d . In summary, we obtain
dB increases. Finally, region E shrinks, since cuto¤ CG
B
29
opposed comparative statics to those described above when dG increases. In particular, the region
in which only the brown (green) …rm favors regulation shrinks (expands, respectively) in dB , while
the area in which both …rms oppose regulation shrinks in dB .
6.6
Proof of Corollary 2
Symmetric damages, dB = dG . In this setting, the four relevant cuto¤s to identify whether …rms’
R =
equilibrium pro…ts increase as a result of regulation (depicted in …gure 4) become CB
R = c (2d + 1)
CG
G
B
originates at
2dB
3+2dB
2dB
3+4dB
2dB , C B =
<
1
2,
2dB
3+4dB
+
3+2dB
3+4dB cG ,
and C G =
2dB
3+2dB
+
3+4dB
3+2dB cG .
2dB +cG
1+2dB ,
Cuto¤ C B
as described in the proof of Proposition 2, while cuto¤ C G originates at
< 0, and crosses the horizontal axis at cG =
2dB
3+4dB ;
as depicted in …gure 5a in the main
text. As a consequence, when …rms generate the same environmental damage, the region in which
the brown …rm favors regulation (regions B and C I) is a mirror image of the area in which the
green …rm supports regulation (regions C III and D).
R , C , and
Cleanest green …rm, dG = 1=2. When dG is at its lower bound, dG = 1=2, cuto¤s CB
B
C G coincide with each other, becoming
1+cG
2 ,
NR
which is the expression of cuto¤ CB
1+cG
2 ;
as
N R and C N R
illustrated in …gure 5b in the main text. On the other hand, cuto¤s CB
2cG 1 are
G
R pivots downwards until
una¤ected by variations in dG . Hence, region A expands, since cuto¤ CB
N R . In contrast, region B collapses to zero since cuto¤ C R pivots downwards
coinciding with CB
B
N
R
until it coincides with CB . Similarly, region C I cannot be supported, since cuto¤ C B pivots
N R , and a similar argument applies to region C II, since cuto¤
upwards until coinciding with CB
N R . By contrast, region C III expands, given that its upper bound, C ,
C G also coincides with CB
G
N
R
pivots upwards, while its lower bound, CG , is una¤ected by dG . Finally, regions D and E are
N R and C R , are una¤ected
unchanged, provided that the cuto¤s describing their frontiers, cuto¤s CB
B
by variations in dG .
References
[1] Baron, D. (2001) “Private Politics, Corporate Social Responsibility and Integrated Strategy,”
Journal of Economics and Management Strategy, 10, pp. 7–45.
[2] Baron, D. (2008) “Managerial contracting and corporate social responsibility,” Journal of
Public Economics, 92, pp. 268–88.
[3] Besley, T. and M. Ghatak (2007) “Retailing public goods: The economics of corporate
social responsibility,”Journal of Public Economics, 91(9), pp. 1645–63.
[4] Brunnermeier, S. and A. Levinson (2004) “Examining the evidence on environmental
regulations and industry location.” Journal of Environment & Development 13, pp. 6–41.
30
[5] Ederington, J., A. Levinson, and J. Minier (2004) “Trade liberalization and pollution
havens.” Advances in Economic Analysis & Policy, 4(2) Article 6. Berkeley Electronic Press.
[6] Espinola-Arredondo, A. and F. Munoz-Garcia (2012) “When do Firms Support Environmental Agreements?” Journal of Regulatory Economics, 41(3), pp. 380-401.
[7] Farzin, Y. H. (2003) “The e¤ects of emission standards on industry.” Journal of Regulatory
Economics, 24, pp. 315–27.
[8] Gaudet, G. and N. V. Long (1996) “Vertical Integration, Foreclosure, and pro…ts in the
Presence of Double Marginalization,” Journal of Economics and Management Strategy, 5(3),
pp. 409-32
[9] Hart, O., and J. Tirole (1990) “Vertical Integration and Market Foreclosure,” Brookings
Papers on Economic Activity: Microeconomics, 4, pp. 205–86.
[10] Korber, A. (1995) The Political Economy of Environmental Protectionism, Edward Elgar
Publishing.
[11] Krattenmaker, T. G. and S. C. Salop (1986) “Anticompetitive Exclusion: Raising Rivals’
Costs to Achieve Power over Price," The Yale Law Journal, 96(2), pp. 209-293.
[12] Maloney, M. and R. McCormick (1982) “A Positive Theory of Environmental Quality
Regulation,” Journal of Law and Economics, 25(1), pp. 99-124.
[13] Ordover, J. A. and D. R. Willig (1981) “An Economic De…nition of Predation: Pricing
and Product Innovation,” The Yale Law Journal, 91(1), pp. 8-53.
[14] Ordover, J. A., G. Saloner, and S. C. Salop (1990) “Equilibrium Vertical Foreclosure,”
American Economic Review, 80, pp. 127–42.
[15] Palmer, K., W. E. Oates, and P. R. Portney (1995). “Tightening Environmental Standards: The Bene…t-Cost or the No-Cost Paradigm?” Journal of Economic Perspectives, 9(4),
pp. 119-132.
[16] Porter, M. E. (1991) “America’s green strategy.” Scienti…c American, 264, pp. 168.
[17] Porter, M. E. and C. van der Linde (1995a) “Green and competitive: Breaking the
stalemate.” Harvard Business Review, 73, pp. 120–34
[18] Porter, M. E. and C. van der Linde (1995b) “Toward a new conception of the
environment-competitiveness relationship.” Journal of Economic Perspectives, 9(4), pp. 97–
118.
[19] Salop, S. C., and D. T. Scheffman (1983) “Raising Rivals’Costs,” American Economic
Review, 73, pp. 267–71.
31
[20] Salop, S. C., and D. T. Scheffman (1987) “Cost-Raising Strategies,”Journal of Industrial
Economics, 26, pp. 19–34.
[21] Sartzetakis, E. S. (1997) “Raising Rivals’Costs Strategies via Emission Permits Markets,”
Review of Industrial Organization, 12, pp. 751–65.
32