DP2010-28

Envir onmental a nd Tr ade Policies for
Oligopolistic I ndustr y in th e Presence ofConsum ption Exter nalities
Jota ISHIK AWA
Toshihiro OKUBO
October 20, 2010

Environmental and Trade Policies for Oligopolistic Industry
in the Presence of Consumption Externalities∗
Jota Ishikawa†Toshihiro Okubo

Hitotsubashi University

Kobe University

and RIETI

and University of Manchester
October 20, 2010

Abstract
We explore the eﬀects of environmental and trade policies with negative consumption externalities when a domestic firm and a foreign rival produce imperfect
substitutes and compete in the domestic market. Consumption of the foreign product generates more emissions than that of the domestic product. Emission taxes
reduce emissions, harm the foreign firm, but may benefit the domestic firm. Tariﬀs
could mitigate externalities more “eﬀectively” than emission taxes. Consumption
subsidies provided to the domestic product may raise emissions and worsen domestic welfare. Stringent environmental policies may induce the foreign firm to produce
an environmentally friendly good, though environmental damages may increase.
Key words: environmental policies, trade policies, consumption externalities,
international oligopoly, diﬀerentiated products
JEL classification numbers: F13, F18∗

This paper is partly based on Ishikawa and Okubo (2010). We thank a referee, Naoto Jinji, Monika

Mrázová, seminar participants at Hitotsubashi University and Okayama University, and attendees at
the Otago Workshop 2009 for helpful comments. Any remaining errors are our own responsibility. We
acknowledge financial support from the Ministry of Education, Culture, Sports, Science and Technologyof Japan under the Global Center of Excellence Project.
†
Corresponding author : Faculty of Economics, Hitotsubashi University, Kunitachi, Tokyo 186-8601,
Japan; Fax: +81-42-580-8882; E-mail: jota@econ.hit-u.ac.jp1

1

Introduction

Environmental deterioration is now worldwide concerns. To cope with the concerns,
various environmental policies have been employed all over the world. Some economists
including Professor Kojima argue that a certain supranational regime is necessary to deal
with global environmental problems.1 However, such a regime has not been establishedexcept for the Kyoto Protocol. Basically, each country tackles various problems noncooperatively.
Some countries (mainly, developed countries) are concerned about environmental
damages more seriously than some others (mainly, developing countries).2 The former
tend to actively adopt environmental policies resulting in production and consumption of
more environmentally friendly products. For instance, purchases of hybrid cars and/or
electric cars are subsidized or are subject to tax reductions in a number of developed
countries. Exhaust emission and fuel consumption regulations are more stringent indeveloped countries than in developing countries.
Not only environmental policies but also trade policies are used to protect environment. For instance, trade restrictions are authorized under multilateral environmental
agreements (MEAs) such as the Montreal Protocol on Substances that Deplete the Ozone
Layer to protect environment and to encourage non-signatories of the MEAs to change
their environmental policies. However, trade policies are sometimes used to protect domestic producers under a pretext for environmental protection, which is called “disguised
protection”.3 Examples include the US ban on imports of yellowfin tuna and their related
processed products from Mexico based on the Marine Mammal Protection Act.
The purpose of this paper is to explore the eﬀects of environmental and trade policies on the economy in the framework of international oligopoly. We are particularly
concerned with the eﬀects of policies aimed to protect environment on environment andproducers. Economic activities could damage environment at various stages: production,transportation, and consumption stages. Since production externalities have been paid
considerable attention in the literature, we focus on negative externalities associated with
consumption (including disposal) such as emissions of carbon dioxide, sulfur oxide and12

For example, see Kojima (2000).
A typical argument is the environmental Kuznets Curve. See Grossman and Krueger (1993), forexample.
3
Environmental policies could also create trade barriers. In particular, this is the case if it is diﬃcult
for foreign firms to comply with domestic environmental regulations, standards, rules, etc.

2

nitrogen oxide through driving cars.4 Thus, environmental and trade policies are directly
related to consumption. In the case of environmental tax, for example, we consider taxes
on consumption.
In our model, a domestic firm and a foreign rival produce slightly diﬀerentiatedproducts and compete in the domestic market. Both domestic and foreign products
generate negative externalities during consumption. We consider a situation in which
the foreign product results in more externalities than the domestic product. For example,
foreign cars (say, gasoline cars) emit more carbon dioxide than domestic cars (say, hybridcars).
We explore two kinds of policies: taxes/subsidies and standards. Specifically, we consider discriminative policies, because the degrees of externalities are diﬀerent between
the two goods. In the case of environmental taxes, the tax is heavier for the consumption of the foreign good than the domestic good. We also examine tariﬀs and comparethem with environmental taxes. It is shown that tariﬀs could reduce externalities more
“eﬀectively” than environmental taxes. With respect to subsidies, we consider consumption subsidies provided to the domestic good, i.e., the product generating less negative
externalities. We show that such a subsidy may worsen environment.
In the analysis of standards, we focus on a specific case in which the foreign good does
not meet domestic standards. It is often observed that governments prohibit firms fromselling those products that do not achieve certain standards.5 When domestic standards
are prohibitive for foreign firms, however, they may have an incentive to circumvent them.
Foreign producers may engage in R&D to develop products meeting the standards.6 Weshow that although the foreign firm may be led to produce an environmentally friendly
good, prohibitive standards do not guarantee an improvement in environment.
In the framework of international oligopoly, many studies have focused on strategicinteractions between governments with production externalities.7 However, relatively
4

For those studies that analyze various policies with production externalities in the context of inter-national trade, see Furusawa et al. (2004), Ishikawa and Kiyono (2006), Ishikawa and Kuroda (2007),
Ishikawa and Okubo (2008), and Ishikawa et al. (2010), among others. See also footnote 7.
5
In addition to the above-mentioned US bans on imports of yellowfin tuna and their related processed
products, Venezuelan-refined gas was forced to meet the same reformulation standards as U.S. in 1994.
The EU prohibited the use of chrysotile asbestos products and banned their imports from Canada in
1998. In 2002, China introduced the China Compulsory Certification, under which foreign firms cannot
export to China without implementing certain standards.
6
Ishikawa and Okubo (2010) examines licensing from the domestic firm to the foreign firm as well as
R&D.
7
See Barret (1994), Kennedy (1994), Conrad (1996,2001), Ulph (1996), Tanguay (2001), and Kiyono

3little attention has been paid to environmental and trade policies with consumption
externalities.8 By using a simple international duopoly model, Lai (2004) considers theeﬀects of trade liberalization on an environmental tax when externalities are associatedwith consumption.9

Kayalica and Kayalica (2005) and Kayalica and Yilmaz (2006)

analyze reciprocal dumping in the presence of consumption externalities. Fischer andSerra (2000) explore minimum standards on a good produced by a domestic firm and aforeign competitor when the consumption causes local damage. They consider optimal
standards and examine whether they are protectionist. Abe et al. (2001) investigate ecolabelling programs under consumption externalities as well as production externalities.
They analyze the eﬀects on the domestic economy of the introduction of eco-labelling
and the domestic recognition of foreign eco-labels. Tian (2003) also studies eco-labelling
schemes in an international duopoly model.
The above studies (except for Tian, 2003) basically consider homogeneous products
under Cournot competition.10 In contrast, we deal with diﬀerentiated products andexamine both Cournot and Bertrand competition. In the case of a homogeneous product,environmental policies aﬀect both domestic and foreign producers symmetrically. For
example, both producers face the identical environmental tax. However, this is notnecessarily the case when the goods are diﬀerentiated. Some of our analyses and results
crucially depend on product diﬀerentiation. For instance, an environmental tax could
benefit the domestic firm even if it must pay the tax.
The rest of the paper is organized as follow. In section 2, we present a basic model
which is an international Cournot duopoly model. As consumption externalities, weconsider a situation under which consumption generates “emissions” that deteriorate
environment. Then we examine emission taxes, tariﬀs, and consumption subsidies in
section 3 and emission standards in section 4. Section 5 concludes. In the appendix, weshow that the main results obtained with Cournot competition would not change with
Bertrand competition.
and Ishikawa (2004), among others.
8
For those studies which consider consumption externalities in open economies under perfect competition, see Krutilla (1991) and Copeland and Taylor (1995), among others. For studies under monopolisticcompetition, see Haupt (2000) and Ishikawa and Okubo (2009), for example.
9
Ohori (2006) and Wang et al. (2007) have extended Lai’s (2004) analysis.
10
Tian (2003) considers Bertrand competition with diﬀerentiated products. However, his focus is on
eco-labelling scheme and hence diﬀers from ours.

42

Basic Model

We consider two goods X and Y , which are imperfect substitutes. Good X is produced
by a foreign firm (firm f ), that exports the good to the domestic country. In the domestic
country, a domestic firm (firm d) produces good Y . The two firms engage in Cournot
competition in the domestic market. We assume that emissions are generated throughconsumption of the products. By an appropriate choice of units, one unit of consumptionof good X generates one unit of emissions and that of good Y results in 0 < k < 1 unitsof emissions. The emissions cause negative externalities.
Demands are characterized by a representative consumer that consumes goods X
and Y as well as a numéraire good. The numéraire good is competitively produced andfreely traded between countries, and generates no externalities. We assume the following
utility function:(x)2 + (y)2
− φxy + m − V,2
where x, y and m are, respectively, the consumption of goods X and Y and the numéraire
U = αx + βy −good, V (> 0) is externalities, α and β are parameters, and 0 < φ < 1 is a parameter
indicating the degree of substitutability between goods X and Y . Following Fischer andSerra (2000) and Lai (2004), we assume that the representative consumer ignores thenegative externalities when making the consumption decisions.11
Then the inverse demands for the imperfectly substitutable goods X and Y are,respectively, given bypx = α − x − φy,(1a)py = β − y − φx,(1b)where px and py are the consumer prices of goods X and Y . Consumer surplus (CS) is
given by
CS = αx + βy −(x)2 + (y)2(x)2 + (y)2
− φxy − (px x + py y) =
+ φxy
2
2

(2)

The domestic government may impose an emission tax, τ , per unit of emission; may
impose a specific tariﬀ, t, on good X; or may provide a consumption subsidy, ς, to perunit of consumption of good Y .12 The profits of firms f and d can be written respectively
11

There is another modelling in which consumers care about environmental damage when making theconsumption decisions. For example, in Moraga-Gonzalez and Padron-Fumero (2002), consumers diﬀer
in their willingness-to-pay for goods due to diﬀerent environmental awareness.
12
In our model, consumption subsidies to good Y are equivalent to production subsidies to good Y .

5

as
πf

= (px − cx − τ − t)x,

π d = (py − cy − kτ + ς)y,where cj (j = x, y) is the constant marginal cost (MC) to produce good j. Then the firstorder conditions (FOCs) for profit maximization are:
dπ f
dx
dπ d
dy

= −x + px − cx − τ − t = 0,
= −y + py − cy − kτ + ς = 0.

In the laissez-faire equilibrium denoted by subscript 0, we havex0 =2A − φB
2B − φA,
2 , y0 =4−φ
4 − φ2where A ≡ α − cx and B ≡ β − cy . We focus on interior solutions (except for section 4).
Thus, we assume

2B − φA > 0, 2A − φB > 0.

(3)

The total emissions are
e0 = x0 + ky0 =A(2 − kφ) + B(2k − φ)
4 − φ2

By using the FOCs, the profits of firms f and d are
π f0 = (x0 )2 , π d0 = (y0 )2 .

(4)

Thus, the following lemma is immediate. It should be noted that the lemma is valid even
if taxes/subsidies exist.
Lemma 1 The profits increase if and only if the output rises.
In the laissez-faire equilibrium, domestic welfare W is measured by the sum of CS,
the profits of firm d, and the value of environmental damage. The total emissions cause
environmental damage, V (e), with V 0 (e) > 0. From Lemma 1 and (2), we have
W0 = CS0 + π d0 − V (e0 )(x0 )2 + 3(y0 )2+ φx0 y0 − V (e0 ).
=
2

6

3

Eﬀects of Taxes and Subsidies

In this section, we consider the eﬀects of emission taxes, tariﬀs, and consumption subsidies to good Y . We also compare emission taxes against tariﬀs.

3.1

Emission Taxes

Suppose that an emission tax, τ , per unit of emission is imposed. Since k > 0, both
goods are subject to the tax. The outputs arexτ =2(A − τ ) − φ(B − kτ )2(B − kτ ) − φ(A − τ ), yτ =,
24−φ
4 − φ2where subscript τ denotes the equilibrium with an emission tax. The eﬀects of a change
in the emission tax on the outputs of firms f and d are given bydxτ
φk − 2
φ − 2kdy=< 0, τ =.
dτdτ
4 − φ24 − φ2The output of firm f necessarily decreases, but that of firm d decreases if and only if
φ < 2k. Since Lemma 1 is still valid here, the eﬀects on the profits are straightforward.
Interestingly, although the consumption of both goods is subject to the tax, firm d could
benefit from the tax. This result stems from the diﬀerence in the tax rate per unitof consumption. An emission tax generates two opposing eﬀects on the outputs. An
emission tax decreases the output of each firm, which in turn increases the output of its
rival with strategic substitutes. Since the former eﬀect is stronger for firm f than firmd, the latter eﬀect is stronger for firm d than firm f . If k is relatively small, that is, if
the tax rate of consuming good X is relatively small, the latter eﬀect could dominate
the former for firm d.
The total emissions, e(≡ x + ky), areeτ =2τ − 2A + Bφ + 2k 2 τ − 2Bk + Akφ − 2kτ φ.
φ2 − 4The eﬀect of a change in the emission tax on the total emissions is given bydeτ
2k(φ − k) − 2
=
< 0,
dτ
4 − φ2(5)which implies that the total emissions fall and hence emission taxes are eﬀective to reduce
the total emissions.

7

Consumer surplus (CS) is
CSτ

=

=

(xτ )2 + (yτ )2+ φxτ yτ2Ã
−3A2 φ2 + 4A2 + 2ABφ3 − 2Akτ φ3 + 6Aτ φ2 − 8Aτ − 3B 2 φ2 + 4B 2

+6Bkτ φ2 − 8Bkτ − 2Bτ φ3 − 3k 2 τ 2 φ2 + 4k2 τ 2 + 2kτ 2 φ3 − 3τ 2 φ2 + 4τ 2¡
¢2
2 φ2 − 4!

Diﬀerentiating CS with respect to τ and evaluating it at τ = 0, we have the eﬀect of an
introduction of a small emission tax on CS as follows:¯∂CSτ ¯¯
4A − 3Aφ2 + Bφ3 + 4Bk + Akφ3 − 3Bkφ2=−< 0.
∂τ ¯τ =0
(φ − 2)2 (φ + 2)2

Thus, a small emission tax decreases CS.

We next consider the eﬀect on domestic welfare which now includes tax revenues.
Wτ= CSτ + π dτ + τ eτ − V (eτ )(xτ )2 + 3(yτ )2+ φxτ yτ + τ (xτ + kyτ ) − V (eτ ).
=2Here we examine the welfare eﬀect of introducing a small emission tax. Diﬀerentiating
domestic welfare with respect to τ and evaluating it at τ = 0, we have¯∂Wτ ¯¯
A − Bk2k(φ − k) − 2=− V 0 (eτ ).
¯2∂τ τ =04−φ
4 − φ2

If A − Bk ≥ 0, ∂W/∂τ |τ =0 > 0 holds, that is, a small emission tax raises domestic

welfare. A − Bk ≥ 0 is likely to hold when B and/or k are relatively small. A relatively
small B implies a relatively small demand for good Y .13 A relatively small k meansthat firm d’s per unit emissions are small. Thus, when B and/or k are relatively small,the detrimental eﬀect on the domestic producer and consumers led by a tax is relatively
small.
Therefore, we obtain
Proposition 1 An emission tax decreases the total emissions. Firm f necessarily loses
from an emission tax, while firm d loses if and only if φ < 2k. When an emission tax
is introduced at a marginally small rate, CS necessarily decreases and domestic welfare
improves if A − Bk ≥ 0.
13

Since B ≡ β − cy , B becomes smaller as β becomes smaller and/or cy becomes larger. One may

expect that α ≈ β holds when φ is suﬃciently close to 1. However, α ≈ β does not necessarily imply
A ≈ B.

8

3.2

TariﬀsWe now suppose that a tariﬀ is introduced instead of an emission tax. The outputs undera tariﬀ are given byxt =2(A − t) − φB
2B − φ(A − t)
, yt =,
24−φ
4 − φ2where subscript t denotes the tariﬀ equilibrium. The changes in the outputs of firms f
and d are, respectively, given by
dxt
2
φ
dy
=−
< 0, t =
> 0.
2
dt
dt
4−φ
4 − φ2The output of firm f decreases, while that of firm d increases. The total emissions areet =2t − 2A + Bφ − 2Bk + Akφ − ktφ.
φ2 − 4Thus, the eﬀect of a tariﬀ on the total emissions is given bydet
kφ − 2=< 0,dt
4 − φ2(6)which implies that a tariﬀ decreases the total emissions. As expected, a tariﬀ harms firm
f , benefits firm d and reduces the emissions.
CS is

CSt =

−3A2 φ2 + 4A2 + 2ABφ3 + 6Atφ2 − 8At − 3B 2 φ2 + 4B 2 − 2Btφ3 − 3t2 φ2 + 4t2.
¡¢2
2 φ2 − 4

The introduction of a small tariﬀ decreases CS, because the following holds:¯
4A − 3Aφ2 + Bφ3∂CSt ¯¯=−<0¯∂t t=0(φ − 2)2 (φ + 2)2
Although consumers lose, a small tariﬀ always enhances domestic welfare
Wt = CSt + π dt + txt − V (et )(xt )2 + 3(yt )2+ φxt yt + txτ − V (eτ )=2by reducing the emissions and shifting rent from abroad:¯∂Wt ¯¯Akφ − 2=− V 0 (et )> 0.
∂t ¯t=0 4 − φ2
4 − φ2Thus, the following proposition is established.
9

Proposition 2 A tariﬀ harms firm f , benefits firm d, and decreases the total emissions.
When a tariﬀ is introduced at a marginally small rate, CS falls but domestic welfare
improves.
Next we compare emission taxes with tariﬀs. We specifically make a comparison
when both taxes and tariﬀs result in the same emission levels. From (5) and (6), thetotal emissions are the same if the tariﬀ rate satisfies the following condition:t=

2k(φ − k) − 2
τ (≡ t).
φk − 2(7)

Thus, t ≷ τ if and only if φ ≶ 2k. To put it diﬀerently, when the emission tax rate
and the tariﬀ rate are the same, the total emissions are less under an emission tax if andonly if φ < 2k.
We obtain(Wt − Wτ )|t=t = −kτ

Ã ¡

¢ !
k3 φ2 − 12k 3 − 2k2 φ3 + 20k 2 φ − kφ2 − 20k + 4φ τ
−2 (kφ − 2) (2B − Aφ + 2Ak − Bkφ)
2 (φ − 2) (φ + 2) (kφ − 2)2,Noting −2 (kφ − 2) (2B − Aφ + 2Ak − Bkφ) > 0, (Wt − Wτ )|t=t > 0 holds as long asτ and hence t are suﬃciently small. Thus, a tariﬀ that satisfies (7) leads to higher
welfare. Also we should recall that tariﬀs always enhance welfare, while emission taxes
may worsen welfare. This implies that tariﬀs could be more attractive measures thanemission taxes.
We obtain:
Proposition 3 Suppose that the emission level under an emission tax is the same withthat under a tariﬀ. Then the tariﬀ rate is higher than the emission tax rate if and only
if φ < 2k. Domestic welfare under the tariﬀ is higher than under the emission tax if the
tax rates are suﬃciently small.

3.3

Consumption Subsidies

We consider consumption subsidies provided to good Y . The eﬀects of a consumption
subsidy are similar to those of a tariﬀ. As in the case of tariﬀs, a subsidy decreases theoutput of firm f and increases the output of firm d:xς =2A − φ(B + ς)2(B + ς) − φA
, yς =,
24−φ
4 − φ210

where subscript ς denotes the equilibrium with a subsidy. The changes in the outputs offirms f and d are, respectively, given by
dy
dxς
φ
2
=−
< 0, ς =
> 0.
2
dς
dς
4−φ
4 − φ2The total emissions areeς =Bφ − 2A − 2kς + ςφ − 2Bk + Akφ
φ2 − 4and hence the eﬀect on the total emissions is given bydeς
2k − φ=,dς
4 − φ2A subsidy increases the total emissions if and only if φ < 2k. Since a subsidy increases
the consumption of good Y more than a tariﬀ, the total emissions rise unless k is small.
CS is

CSς =

−3A2 φ2 + 4A2 + 2ABφ3 + 2Aςφ3 − 3B 2 φ2 + 4B 2 − 6Bςφ2 + 8Bς − 3ς 2 φ2 + 4ς 2.
¡
¢2
2 φ2 − 4

The change in CS is¯∂CSς ¯¯
4B + Aφ3 − 3Bφ2=
> 0.
∂ς ¯ς=0(φ − 2)2 (φ + 2)2

Although a consumption subsidy decreases the consumption of good X, a small subsidy
raises CS. The welfare eﬀect of a small subsidy is generally ambiguous:Wς= CSς + π dς − ςyς − V (eς )(xfς )2 + 3(yςd )2+ φxfς yςd − ςyςd − V (eς )
=
2
¯
∂W ¯¯
B
2k − φ=− V 0 (eς )
.
¯
2
∂ς
4−φ
4 − φ2(8)

ς=0

If 2k ≤ φ, then a small subsidy does not increase the emissions and raises domestic

welfare. Conversely, a small subsidy could increase the emissions and decrease domestic
welfare. This is likely to occur when B (i.e., the market for good Y ) is relatively small
and k is relatively large. When B is relatively small, the increases in both CS and thedomestic profits are relatively small. Thus, (8) could become negative. In this case, aconsumption tax on good Y rather than a subsidy could be justified from the viewpointof both welfare enhancement and emission reduction. We should mention that domestic
welfare deteriorates only if the total emissions increase (i.e.2k > φ).
Thus, we obtain the following result.
11

Proposition 4 A consumption subsidy to good Y decreases the total emissions if andonly if 2k < φ. Firm d gains from consumption subsidy, while firm f loses. When aconsumption subsidy ς is introduced at a marginally small rate, CS necessarily increases
and domestic welfare improves if φ ≥ 2k.

4

Eﬀects of Standards

In this section, we consider the eﬀects of emission standards. The domestic government
introduces an emission standard, λ, which sets a maximum amount of emissions per unitof product consumption. If a product does not satisfy the standard, its sale is prohibitedin the domestic country. In our analysis, we specifically consider an emission standard
with λ = k and hence good X does not satisfy it but good Y does. In the presence ofthe standard, firm f has to give up exporting to the domestic country.

4.1

Monopoly

The standard leads firm d to be a monopolist in the market. In the equilibrium denotedby subscript M , the output and price are, respectively, given by
yM =

B
B
, pM =+ cy .
2
2(9)

In view of (3), we can easily verify that yM > y0 and yM < x0 + y0 . As expected,
therefore, the standard benefits the domestic firm and reduces emissions. The change in
CS is∆CSM ≡ CSM − CS0 =¡¢8A + 4Bφ − 6Aφ2 + Bφ3 (Bφ − 2A)
8 (φ + 2)2 (φ − 2)2< 0.

Since 2A − φB > 0, CS falls. Thus, the welfare eﬀect is generally ambiguous.

4.2

R&D

In the presence of the emission standard, firm f cannot serve the domestic market.
Hence firm f may have an incentive to produce a good which meets the standard. In
the following analysis, we assume for simplicity that firm f produces good Y to serve
the domestic market.14 We also assume that firm f can produce good Y by engaging in
R&D, the cost of which is fixed costs, F .
14

Even if the good produced by firm f is still diﬀerentiated from good Y , the essence of our main

result, Proposition 5, would not change.

12

As long as firm f can make a positive profit from R&D, it has an incentive to invest
in R&D. Since there is only good Y in the market, the inverse demand is:p = β − (y f + y d ),where yi is the output of firm i (i = d, f). The profits of firms f and d are:πf

= (p − cfy )yf − F,

π d = (p − cy )yd ,where cfy is the constant MC of firm f to produce good Y . In the R&D equilibrium
denoted by subscript R, we obtain:f=yR

B − 2δ dB+δ
, yR =,
3
3

where δ ≡ cfy − cy . We assume both B > max{2δ, −δ} and 0 < π fR (= (B − 2δ)2 /9 − F ) <π f0 .15

We compare the R&D equilibrium with the initial laissez-faire equilibrium. We firstconsider whether firm d gains from the standard. Noting that Lemma 1 is still valid forfirm d, we check whether the output rises:d∆yR ≡ yR
− y0d ==

B + δ 2B − φA−
3
4 − φ2

3Aφ − 2B − Bφ2 + δ(4 − φ2 ).
3(4 − φ2 )Thus, the R&D under the standard benefits firm d if and only if Ω ≡ 3Aφ − 2B − Bφ2 +δ(4 − φ2 ) > 0. This condition is likely to be satisfied when A is large relative to B, andδ and φ are large. A relatively large A implies relatively large demand for good X, andhence the prohibitive standard causes a relatively large demand shift to good Y . A large

δ implies that firm d is much more eﬃcient in production of good Y than firm f . Thus,
the entry of firm f into the good-Y market does not decrease the output of firm d much.
A large φ implies that goods X and Y are close substitutes. Thus, the entry of firm f
into the good-Y market caused by the elimination of good X does not aﬀect the output
of firm d much.
15

If πfR > π f0 , firm f has no incentive to produce good X even without standards.

13

The change in CS is given by
∆CSR

Ã
!
f
d )2
(yR
+ yR
(xf0 )2 + (y0d )2
f d−+ φx0 y0
≡ CSR − CS0 =22
Ã
!
28B 2 − 36A2 − 18ABφ3 + 27A2 φ2 − 5B 2 φ2 + 4B 2 φ4
+δ (φ − 2)2 (φ + 2)2 (δ − 4B)=

18 (φ + 2)2 (φ − 2)2.

In general, the sign of ∆CSR is ambiguous. ∆CSR > 0 is likely to hold when when A issmall relative to B. With ∆CSR > 0, a negative eﬀect due to the decrease in variety isdominated by a positive eﬀect due to the increase in good Y .
The change in emissions is given byfd+ yR) − (x0 + ky0 ) = (k∆eR ≡ k(yR

2A − φB
2B − δ
2B − φA
)−(
+k
).
2
3
4−φ
4 − φ2

If k is suﬃciently small, then ∆eR < 0, that is, the emission standard decreases the total
emissions. However, if k is close to 1, the total emissions may increase. Evaluating ∆eRat k = 1, we have
2A − φB 2B − φA
2B − δ
)−(+)
34 − φ24 − φ2B − 3A + 2Bφ − δ(φ + 2).
3 (φ + 2)∆eR |k=1 = (=From the continuity argument, the total emissions increase if Ψ ≡ B − 3A + 2Bφ −δ(φ + 2) > 0 and k is suﬃciently close to 1. This condition is likely to be satisfied when
A is small relative to B, δ is small and φ is large. A prohibitive standard eliminates

the consumption of good X, but increases that of good Y through the foreign R&D.
Although the emission per unit of consumption of good Y is lower than that of good X,
this could be dominated by the increase in the total consumption of good Y and hence
the total emissions could rise. A small A, a small δ and a large φ tend to increase theoutput of good Y relative to the laissez-faire equilibrium when a prohibitive standard
induces firm f to enter the good Y -market.
Again, the welfare eﬀect is generally ambiguous. If A = B and δ = 0, for example,
then ∆yR < 0, ∆CSR < 0 and ∆eR < 0 holds, that is, the profits of firm d andCS decrease but the environmental damage is mitigated. Thus, if the mitigation ofenvironmental damage is large (small), domestic welfare could improve (deteriorate).
The above analysis establishes the following proposition:

14

Proposition 5 Suppose that an emission standard leads firm f to incur fixed R&D
costs to develop good Y . By comparing the R&D equilibrium with the equilibrium without
the standard, there exists a range of parameterization under which the total emissions
increase. Firm d gains from the standard if and only if Ω > 0. Domestic welfare may or
may not improve.

5

Concluding Remarks

Using an international duopoly model with diﬀerentiated products, we have analyzed theeﬀects of environmental and trade policies in the presence of consumption externalities.
Both domestic and foreign products generate emissions during consumption, but theforeign product results in more damage to environment than the domestic product.
Emission taxes reduce negative externalities. The foreign firm necessarily loses fromsuch taxes, while the domestic firm could gain. Tariﬀs also reduce negative externalities.
Interestingly, however, tariﬀs could reduce externalities more eﬀectively than taxes. Thisis because tariﬀs directly impact on the foreign good alone which is environmentally lessfriendly. A small tariﬀ always enhances domestic welfare, while a small emission tax
may worsen welfare. Consumption subsidies provided to the domestic good may raise
the total emissions and lower domestic welfare. This implies that under some situation,
consumption subsidies to environmentally friendly goods such as hybrid and electric cars
should be abolished or replaced by taxes.
Stringent environmental policies may induce the foreign firm to supply an environmentally friendly good through R&D. Such policies may not reduce the externalities.
We should mention that the analysis of R&D can be applied to the case with production
externalities.
We have explored non-cooperative environmental and trade policies in this paper.
As Professor Kojima argues, however, a certain supranational regime may be required
to handle global environmental issues. Designing such a regime is an important research
topic left for us.

Appendix
We have assumed Cournot competition in the above analysis. In the appendix, we showthat the essence of the main results obtained with Cournot competition would not changewith Bertrand competition.
15

From (1a) and (1b), demands becomex =y =(α − φβ) − px + φpy,
1 − φ2(β − φα) − py + φpx.
1 − φ2

Then the FOCs for profit maximization under Bertrand competition are:
dπ f
dpx

=

dπ d
dpy

=

α − px − φ(β − py ) − px + (cx + τ + t)
= 0,
1 − φ2β − py − φ(α − px ) − py + (cy + kτ − ς)
= 0.
1 − φ2In the laissez-faire Bertrand equilibrium, we have
pB
x0 =
xB
=
0

2(β + cy ) − βφ2 − φA2(α + cx ) − αφ2 − φB B
,
p
=
,
y0
4 − φ24 − φ2(2 − φ2 )A − φB B
(2 − φ2 )B − φA
,
y
.
=
0
(1 − φ2 )(4 − φ2 )(1 − φ2 )(4 − φ2 )where superscript B stands for Bertrand competition. The total emissions areeB
0 =(2 − φ2 − kφ)A + (2k − φ2 k − φ)B.
(1 − φ2 )(4 − φ2 )By using the FOCs, the profits of firms f and d are
π f0 B =(py0 − cy )2(px0 − cx )2
2
2
dB
=
(z
)
(1
−
φ
),
π
=
= (y0 )2 (1 − φ2 ).
00
1 − φ2
1 − φ2

When an emission tax is introduced, the equilibrium is given by
pB
xτ

=

=
xB
τ

2(β + cy + kτ ) − βφ2 − φ(A − τ )2(α + cx + τ ) − αφ2 − φ(B − kτ ) B
,
p
=
,
yτ
4 − φ24 − φ2(2 − φ2 )(A − τ ) − φ(B − kτ ) B(2 − φ2 )(B − kτ ) − φ(A − τ )
,
y
.
=
τ
(1 − φ2 )(4 − φ2 )(1 − φ2 )(4 − φ2 )Thus, we have
∂pB
xτ
∂τ

=

∂xB
τ
∂τ

=

∂pB
2 + φk2k + φyτ> 0,
2 > 0, ∂τ =4−φ
4 − φ2φk − (2 − φ2 )φ − k(2 − φ2 )
∂yτB
=
<
0,
.
∂τ
(1 − φ2 )(4 − φ2 )(1 − φ2 )(4 − φ2 )The profits of firms f and d with an emission tax are
π fτ B =(pyτ − cy − kτ )2(pxτ − cx − τ )2
2
2
dB
=
(x
)
(1
−
φ
),
π
=
= (yτ )2 (1 − φ2 ).
ττ
1 − φ2
1 − φ216

Thus, firm f always loses from the tax, but firm d loses if and only if φ < k(2 − φ2 ).
The total emissions areeB
τ = xτ + kyτ .
The change in the total emissions is∂eB
φk − (2 − φ2 ) + {φ − k(2 − φ2 )}kτ.
=∂τ(1 − φ2 )(4 − φ2 )We can prove ∂eBτ /∂τ < 0 as follows. Since the denominator is positive, we show thenumerator is negative. First, by fixing φ, the numerator becomes a function of k:f (k) ≡ −(2 − φ2 )k2 + 2φk − (2 − φ2 ).
f (k) < 0 holds as long as 0 < φ < 1, because −(2 − φ2 ) < 0 holds and f (k) =0 does not have real number solutions, which can be confirmed by φ2 − (2 − φ2 )2 =− (φ − 1) (φ − 2) (φ + 2) (φ + 1) < 0. Next, by fixing k, the the numerator becomes afunction of φ:h(φ) ≡ (1 + k2 )φ2 + 2kφ − 2 − 2k2 .
√√h(φ) = 0 holds at −(k± 5k2 + 2k 4 + 2)/(k2 +1). Since −(k− 5k 2 + 2k4 + 2)/(k 2 +1) ≥1 holds for any k (equality holds at k = 1), h(φ) < 0 for 0 < φ < 1. Therefore, thenumerator is negative if 0 < φ < 1 and 0 < k < 1 hold.
Domestic welfare is
B
BWτB ≡ CSτB + π dB
τ + τ eτ − V (eτ )
2
2
B 2
(xB
τ ) + (3 − φ )(yτ )
B
B
B
B
+ φxB
=
τ yτ + τ (xτ + kyτ ) − V (eτ ).
2

Diﬀerentiating domestic welfare with respect to τ and evaluating it at τ = 0, we have¯
22∂WτB ¯¯A − Bk0 B φk − (2 − φ ) + {φ − k(2 − φ )}k
.
=
−
V
(e
)
τ
∂τ ¯τ =04 − φ2(1 − φ2 )(4 − φ2 )Therefore, if A − Bk ≥ 0, domestic welfare improves by introducing a small emission tax.
When a tariﬀ is introduced, we have
pB
xt =
=
xB
t

2(β + cy ) − βφ2 − φ(A − t)2(α + cx + t) − αφ2 − φB B
,
p
=
,
yt
4 − φ24 − φ2(2 − φ2 )(A − t) − φB B
(2 − φ2 )B − φ(A − t)
,
y
.
=
t
(1 − φ2 )(4 − φ2 )(1 − φ2 )(4 − φ2 )17

Hence,
∂pB
xt
∂t

=

∂xB
t
∂t

=

∂pB
2
φ
yt
=
>
0,
> 0,
2
∂t
4−φ
4 − φ2−(2 − φ2 )
φ
∂ytB
=
<
0,
> 0.
2
2
2
∂t
(1 − φ )(4 − φ )(1 − φ )(4 − φ2 )The profits of firms f and d with a tariﬀ are
2
2
(pB
(pB
yt − cy )fB
zt − cz − t)
B 22dB
= (xt ) (1 − φ ), π t == (ytB )2 (1 − φ2 ).
πt =
2
2

1−φ

1−φ

Thus, firm f loses from a tariﬀ, while firm d gains. The total emissions areBBeB
t = xt + kyt .

An increase in the tariﬀ decreases the total emissions, becausekφ − (2 − φ2 )
∂eB
t
=
< 0.
∂t
(1 − φ2 )(4 − φ2 )Domestic welfare is
B
B
WtB ≡ CStB + π dBt + txt − V (et )
2
2
B 2
(xB
t ) + (3 − φ )(yt )
B
B
+ φxB
=
t yt + txt − V (et ).
2

Diﬀerentiating domestic welfare with respect to t and evaluating it at t = 0, we have¯
∂WtB ¯¯A
φ2 − 2
0 B
=
−
V
(e
)
> 0.
t
∂t ¯t=0 4 − φ2
(1 − φ2 )(4 − φ2 )Thus, a small tariﬀ improves domestic welfare.

Now we compare tariﬀs with emission taxes. If the tariﬀ rate satisfies the following
condition:

k2 φ2 + 2kφ + φ2 − 2k2 − 2
B(≡ t ),
2
kφ + φ − 2then the total emissions are the same. Using this, we obtaint=τ

(Wt − Wτ )|t=tBÃ ¡¢ !
−20k + 4φ − 8k 2 φ3 + 9k3 φ2 − 2k 3 φ4 − 2φ3 + 15kφ2 + 20k2 φ − 4kφ4 − 12k 3 τ¡¢+2 kφ + φ2 − 2 {(2 − φ2 )B − Aφ + k[(2 − φ2 )A − Bφ]}
= kτ
.
¡
¢¡
¢2
2 φ2 − 4 φ2 + kφ − 2¢¡Noting 2 kφ + φ2 − 2 {(2 − φ2 )B − Aφ + k[(2 − φ2 )A − Bφ]} < 0, the tariﬀ results inB

the higher welfare providing τ is suﬃciently small and t = t holds,
18

When a consumption subsidy is introduced, we obtain
pB
xς

=

=
xB
ς

2(β + cy − ς) − βφ2 − φA2(α + cx ) − αφ2 − φ(B + ς) B
,
p
=
,
yς
4 − φ24 − φ2(2 − φ2 )A − φ(B + ς) B
(2 − φ2 )(B + ς) − φA
,
y
.
=
ς
(1 − φ2 )(4 − φ2 )(1 − φ2 )(4 − φ2 )

Thus,
∂pB
xς
∂ς
∂xB
ς
∂ς

∂pB
φ
2ς
yς
=−
<
0,
< 0,
2
∂ς
4−φ
4 − φ2∂yςBφ
2 − φ2
= −
=
<
0,
> 0.
∂ς
(1 − φ2 )(4 − φ2 )(1 − φ2 )(4 − φ2 )= −The profits of firms f and d with a subsidy are
π fς B =

2
2
(pB
(pB
yς − cy + ς)xς − cx )
B 2
2
dB
=
(x
)
(1
−
φ
),
π
=
= (yςB )2 (1 − φ2 ).
ςς
1 − φ2
1 − φ2Thus, firm f loses from the subsidy, while firm d gains. The total emissions are
BBeBς = xς + kyς .

The change in the total emissions is∂eBk(2 − φ2 ) − φς,=∂ς
(1 − φ2 )(4 − φ2 )which is negative if and only if k(2 − φ2 ) < φ. Domestic welfare is
B
BWςB ≡ CSςB + π dB
ς − ςyς − V (eς )

=

2
2
B 2
(xB
ς ) + (3 − 2φ )(yς )
B
B
+ φxB
ς yς − ςyς − V (eς ).
2

Diﬀerentiating domestic welfare with respect to ς and evaluating it at ς = 0, we have¯
∂WςB ¯¯Bk(2 − φ2 ) − φ
0 B
=
−
V
(e
)
,
ς
∂ς ¯ς=0 4 − φ2
(1 − φ2 )(4 − φ2 )which is positive if k(2 − φ2 ) − φ ≤ 0.

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22