HIAS-E-106

Trade, Consumption Pollution and Tax
Haitao Cheng (a)(a) Hitotsubashi Institute for Advanced Study, Hitotsubashi University

This version: April 2021
First version: October 2018

Hitotsubashi Institute for Advanced Study, Hitotsubashi University
2-1, Naka, Kunitachi, Tokyo 186-8601, Japan
tel:+81 42 580 8668 http://hias.hit-u.ac.jp/
HIAS discussion papers can be downloaded without charge from:https://hdl.handle.net/10086/27202
https://ideas.repec.org/s/hit/hiasdp.html

All rights reserved.

Trade, Consumption Pollution and Tax?
Haitao Cheng
Hitotsubashi Institute for Advanced Study, Hitotsubashi University

This version: April 2021
First version: October 2018

Abstract
Consumption is an important source of greenhouse gas (GHG) emissions. This study theoreticallyanalyzes how trade liberalization and consumption tax affect firm locations across countries and
GHG emissions originating from consumption. Introducing consumption-originated emissions ina standard footloose capital model, we find several novel results that extend previous analysesof production-originated GHG emissions. First, trade liberalization has a non-monotonic effecton global emissions; that is, as trade costs decline, global emissions initially decrease and thenincrease. Second, consumption taxes cause carbon leakage; that is, the tax on one country reduces
emissions in that country, while increasing it in the rest of the world. Third, optimal consumption
taxes that maximize global welfare must be neutral about firm location decisions. In particular,
even if firms are asymmetrically distributed across countries in the absence of a consumption tax,
the optimal tax level must be identical across countries.
Keywords: Asymmetric market sizes; Consumption pollution; Consumption tax harmonization;
Footloose capital model; Trade liberalization
JEL classification: F18; Q54; Q58?
I am deeply indebted to Professors Jota Ishikawa and Yoichi Sugita for their valuable comments and constantencouragement. I would like to thank Professors Hayato Kato, James Markusen, Hirofumi Okoshi, Hajime Takatsuka, Kensuke Teshima, Eiichi Tomiura and Dao-Zhi Zeng for helpful suggestions. Thanks also go to the participantsat the 78th Annual Meeting of the JSIE, IEFS Japan Annual Meetings 2019 (Poster Session) and 2020 and seminars at Hitotsubashi University. Financial support from Hitotsubashi Institute for Advanced Study is gratefully
acknowledged. All remaining errors are my own. E-mail address: haitaoecon@gmail.com.

1. Introduction
Previous research on trade and the environment strongly focuses on emissions from the production
side; however, less attention is paid to the consumption side.1 Consumption is an importantsource of greenhouse gas (GHG) emissions such as fossil fuel combustion for cooking, heating, andtransportation, and it also leaks from refrigerants in businesses and homes. According to the US
Environmental Protection Agency, direct GHG emissions from residents and businesses, excluding
agricultural and industrial activities, accounted for 11.6 percent of US GHG emissions in 2017.
This proportion is even larger in Japan; the Japanese Ministry of the Environment announced thatthe commercial and residential sectors generated 33.4 percent of Japanese CO2 emissions in 2016.
GHG emissions from the production and consumption sides should be distinguished. Production emissions occur when dirty goods are produced, while consumption emissions occur when they
are consumed. Owing to this difference, the behaviors of consumers, firms, and countries can also
differ in the presence of environmental regulations. For instance, if a country becomes a peripherywith no firms, its domestic environmental regulation no longer affects production emissions becauseof the lack of production there. However, it still affects consumption emissions as long as residents
consume imported goods.
Against this background, we investigate the environmental issues of consumption in this study.
Specifically, we examine how trade liberalization and environmental taxes affect GHG emissions aswell as how heterogeneous countries choose their tax levels cooperatively and non-cooperatively.
To do so, we employ the footloose capital model of Martin and Rogers (1995), which emphasizes
the diversity of goods and endogenous firm locations, key features in today’s trade liberalization.
To conduct the policy analysis, we assume an ad valorem consumption tax on consumers as an(indirect) environmental instrument. Changing the consumption tax to an emission tax has no
impact on our main conclusions; however, the tractability and feasibility of the analysis diminishes.
An example of a consumption tax functioning as an environmental regulation is the tax on the
consumption of fossil fuels. Several governments such as those in Norway and the United Kingdom
impose a fuel tax—a type of ecotax—to control CO2 emissions from vehicles. We consider not only
developed countries but also developing countries, as both are obliged to control GHG emissions
under the Paris Agreement.
To analyze how trade liberalization and consumption taxes affect GHG emissions, we decompose
the total effect into a firm relocation effect and a demand effect. The firm relocation effect describes
1

Examples of studies dealing with production pollution are Markusen et al. (1993, 1995) and Copeland andTaylor (1994, 1995b). Compared with the little attention paid to consumption emissions in the theoretical literature,
the empirical literature is extensive, including Druckman et al. (2008), Wiedmann (2009), and Davis and Caldeira(2010).

2

the changes in GHG emissions due to the relocation of firms. This differs from the composition
effect—discussed in previous research—that measures the reallocation of production factors acrossrelatively clean and dirty goods. The net firm relocation effect is always neutral in the model. The
demand effect captures the changes in GHG emissions due to the changes in the consumption of
dirty goods.
Given a consumption tax, as trade costs decline, the demand effect tends to initially decrease global emissions and then increase them. We can understand the intuition behind thisnon-monotonicity as follows. The consumption of dirty goods under free trade is equal to that
under autarky because there are no trade costs in either case. However, under trade with costs,
consumers have to pay extra trade costs, which decreases consumption globally. Hence, GHG emissions are lower than in the two extreme cases. The literature has not reached a consensus on how
trade affects the environment. Previous theoretical analyses with neoclassical settings show that
free trade can increase world pollution (e.g., Copeland and Taylor, 1994, 1995b). On the contrary,
Antweiler et al. (2001) empirically find that openness to the international goods market appears
to be good for the environment because trade increases income and induces the development ofcleaner production technology. Our findings suggest an alternative answer to this question throughthe substitution between variety and quantity. Trade may reduce world consumption and pollution
by increasing the variety of consumption goods.
Given trade costs, as the consumption tax increases in either country, local emissions decrease inthat country and increase in the other country; global emissions always decline because the demand
effect is always negative. Many studies have examined carbon leakage under production emissions,claiming that a more stringent environmental regulation in a country increases other countries’
production emissions (e.g., Markusen et al., 1993, 1995). Our findings indicate that carbon leakage
still exists under consumption pollution. Intuitively, an increase in the consumption tax in acountry decreases its consumption and thus its emissions from consumption. However, it is notstraightforward why consumption emissions in the other country increase.
In the welfare analysis, we first focus on the global optimum to determine what countries
should do cooperatively. The analysis shows how a supranational regime designs an environmental
tax to control GHG emissions. We find that optimal consumption taxes must be neutral to firm
location decisions. In particular, if firms initially disperse across countries under no environmental
regulation, identical consumption taxes are globally desirable regardless of market size. This finding
is related to the literature on environmental tax harmonization, which seeks to construct a simple
policy to deal with complicated environmental problems, especially in the presence of heterogeneous
countries (e.g., Vlassis, 2013; Cremer and Gahvari, 2004; Cheng et al., 2020). Among others, Chenget al. (2020) examine whether environmental tax harmonization is globally desirable in global value3

chains given that countries differ in their average cost advantages of input production. They findthat environmental tax harmonization is socially optimal when unbundling costs are high, but
not when unbundling costs are low. Compared with theirs, our findings do not depend on thelevels of trade costs; moreover, the model has different production processes, market structures,
environmental issues, and country heterogeneity.
Under consumption tax competition, we investigate how countries choose their taxes in thepresence of endogenous firm locations and how market sizes affect their decisions. We show that a
Nash equilibrium may exist in which firms disperse across countries and that the consumption tax
is always higher in the larger country. The analysis is related to the literature on environmental
tax competition in the presence of imperfect competition and endogenous firm locations (e.g.,Markusen et al., 1995; Rauscher, 1995; Hoel, 1997; Dong et al., 2012). Markusen et al. (1995)
and Hoel (1997) claim that optimal environmental taxes at the Nash equilibrium depend on themarginal environmental damage, which is also revealed in our results. Dong et al. (2012) show thatcountries’ choices are relevant to their market sizes, which are assumed to be identical. In contrast
to their analyses, we emphasize the asymmetry of market size.
1.1. Related LiteratureThis study follows the literature on new economic geography and the environment. Examples
include Zeng and Zhao (2009) and Ishikawa and Okubo (2011, 2016, 2017). The basic setup in
this study is close to that of Ishikawa and Okubo (2011).2 However, they only analyze unilateralenvironmental product standards and do not look further through a welfare analysis. By contrast,
we investigate bilateral consumption taxes in both countries and derive the global and national
optima. The examination of how consumption taxes affect firm behaviors and GHG emissions
is similar to the analysis of full border tax adjustments by Ishikawa and Okubo (2017) in thatenvironmental regulation appears in the consumption country. However, they compare unilateralemission quotas with emission taxes in the presence of GHG emissions from production and derive
the neutral effect of border tax adjustments on firm locations, which is different from the findingsof this study.
Ishikawa and Okubo (2016) also find a non-monotonic effect of trade liberalization on GHG
emissions in a model in which emissions originate from production. Our mechanism differs fromtheirs. First, in their model, trade liberalization affects global emissions only when the emission
tax is strictly positive; if the tax rate is zero, global emissions are independent of trade costs.
2
The other three papers cited here all focus on production pollution. Zeng and Zhao (2009) investigate the effectof production pollution on agricultural productivity, while Ishikawa and Okubo (2016, 2017) investigate the effect of
production pollution on residents.

4However, our results hold even without an environmental tax. Second, if our model is modified sothat emissions originate from production instead of consumption, trade liberalization has no effecton global emissions. Therefore, the distinction between consumption and production emissions isimportant.
However, few studies have examined trade and consumption pollution (e.g., Krutilla, 1991;
Copeland and Taylor, 1995a; Ishikawa and Kuroda, 2007; Ishikawa and Okubo, 2010, 2011; Hu
and McKitrick, 2016). Krutilla (1991) derives a series of second-best consumption taxes with theexistence of production and consumption pollution and concludes that environmental production
and consumption taxes affect the world price and trade balance in opposite directions. Ishikawa andKuroda (2007) and Ishikawa and Okubo (2010) examine and compare the effectiveness of various
taxes in reducing emissions from production and/or consumption. They find that emission taxes
may be less effective at decreasing consumption emissions than other taxes such as production taxes
and tariffs. Hu and McKitrick (2016) compare production and consumption pollution with a model
similar to that of Antweiler et al. (2001) and find that trade liberalization affects the two kindsof pollution differently through trade-induced composition effects. Copeland and Taylor (1995a)
employ a Heckscher–Ohlin model and verify that the dirty industry migration hypothesis holds inthe presence of local consumption pollution. Compared with their findings, we demonstrate thatwhether firms migrate to countries with laxer environmental regulations also depends on market
size. Except for Ishikawa and Okubo (2011), the studies mentioned in this strand consider neither
endogenous firm locations nor monopolistic competition.
This study also complements the literature on conventional trade policy competition and coordination (e.g., Ludema and Wooton, 2000; Baldwin and Krugman, 2004; Haufler and Wooton,
2010; Haufler and Pflüger, 2004). The basic setup of this study is similar to the tax regime basedon the destination principle in Haufler and Pflüger (2004). However, they do not consider asymmetric market sizes, the full agglomeration of firms, or environmental issues. With consumption
externalities, governments consider not only the consumer surplus and tax revenue, but also environmental damage. If environmental damage is large, governments are likely to impose stringent
environmental regulations (or lower consumption subsidies), even though this harms the consumer
surplus.
The remainder of this paper is organized as follows. Section 2 introduces the basic model
setup. Section 3 derives the equilibrium in trade with footloose capital and investigates how
trade liberalization and consumption taxes affect firm locations, consumption, and GHG emissions.
Section 4 discusses the global optimum. Section 5 discusses consumption tax competition. Finally,
Section 6 concludes.
5

2. Basic Model
The basic model extends the footloose capital model of Martin and Rogers (1995) by including the
GHG emissions from consumption and consumption taxes. Consider a world with two countries,
Home and Foreign, and two factors, capital and labor. The individuals in each country consume two
types of goods: a dirty manufacturing good with different varieties and a clean agricultural good.
Each firm produces a variety of dirty goods at a fixed cost of one unit of capital; in addition, one
unit of dirty goods requires one unit of labor.3 Dirty goods are traded with symmetric trade costs
τ of the “iceberg” form such that τ units of dirty goods are traded for one unit that is eventuallyconsumed. The clean good is the numéraire. It is homogeneous and freely tradable. The productionof clean goods is subject to constant returns to scale and each unit is produced with only one unitof labor. The wage rates across countries are equalized because of the existence of the numéraire,
and they are normalized to 1 for simplicity. Denote the labor and capital stock in Home as L and
K and those in Foreign as L∗ and K ∗ , respectively.4 The two production factors are distributed
proportionately across countries and capital is distributed uniformly across the residents withineach country. Denote s as the share of the world’s labor and capital belonging to Home, that
is, L/(L + L∗ ) = K/(K + K ∗ ) = s. Without loss of generality, total capital and labor are bothnormalized to unity; Home is assumed to have a larger market size (s > 1/2). Labor is immobile
across countries, but can freely move across sectors and firms. Capital is mobile across countries
and capital rents are paid to local owners. GHG emissions are generated during the consumptionof dirty goods, with one unit of dirty goods emitting one unit of GHG. Governments impose advalorem consumption taxes on consumers to control GHG emissions under the requirements ofenvironmental agreements such as the Paris Agreement.
The utility of a representative individual in Home is described as a quasi-linear function:

where

U = µ ln M + A − D(E G )

(1)


 σ
1
1
σ−1
HH 1− σ∗ F H 1− σM ≡ nx+n x(2)

is the constant elasticity of substitution composite consumption of the dirty manufacturing varieties
and A is the consumption of the numéraire. D(·) is the environmental damage function thatmeasures the disutility of emissions. E G represents the global emission level. n is the number (orratio) of differentiated varieties in Home and n∗ is that in Foreign. xHH denotes the quantity of
3
4

The term “firm” only refers to the producer of dirty goods throughout the paper.
Variables with asterisks are Foreign-related.

6

Home consumption of each variety produced by Home and xF H is the counterpart produced byForeign. The first capital letter in the superscripts represents the location of production and thesecond represents the location of consumption. σ > 1 is the constant elasticity of substitution
between the different varieties, as is usually observed in the constant elasticity of substitutionfunction. µ is the intensity of preference for good M . The larger the value of µ, the more theindividual spends on dirty goods.
The budget constraint of the representative individual in Home isnp(1 + t)xHH + n∗ τ p∗ (1 + t)xF H + A = I/L.

(3)

I = L+rK+T R denotes total income, where r is the capital rent in Home, T R = Lt npxHH + n∗ τ p∗ xF H
is total tax revenue, and t represents the Home ad valorem consumption tax. The term xF H , but
not xHF , enters total tax revenue because the consumption tax is imposed on consumers but not
producers. p and p∗ are the pre-trade prices of dirty goods in each country and τ p∗ is the importprice of Foreign dirty goods in Home, adjusted by trade costs. Similarly, the utility function andcorresponding variables for Foreign can be derived. For simplicity, µ and σ are assumed to be thesame across countries.
The aggregate price index facing the individual in Home is 1
P = (1 + t) np1−σ + n∗ (τ p∗ )1−σ 1−σ .

(4)Unlike a tax on producers, a country’s consumption tax cannot directly affect the aggregate pricein the other country. However, an indirect channel still exists through the effect of the consumption
tax on firm locations. On the contrary, trade liberalization can affect the aggregate prices in thetwo countries both directly and indirectly.
The consumption of each Home- and Foreign-produced variety in Home and Foreign is
xHH = µP σ−1 [p(1 + t)]−σ ; xF H = µP σ−1 [τ p∗ (1 + t)]−σ ;(5)xF F = µP ∗ σ−1 [p∗ (1 + t∗ )]−σ ; xHF = µP ∗ σ−1 [τ p(1 + t∗ )]−σ .

(6)For a representative firm in Home and Foreign, if any, its capital rent is
r = (p − 1)Y ; r∗ = (p∗ − 1)Y ∗ ;(7)

Y = sxHH + (1 − s)τ xHF ; Y ∗ = sτ xF H + (1 − s)xF F

(8)

where

7



are the total production of each variety. The markup pricing rule of the Dixit–Stiglitz monopolisticcompetition model in Dixit and Stiglitz (1977) still holds and the identical pre-tax prices acrossvarieties are derived as
p = p∗ = σ/(σ − 1).

(9)

3. Trade Equilibrium
In this section, we derive the trade equilibrium and examine how trade costs and consumption taxes
affect firm locations, consumption, and emissions. At the trade equilibrium, there are two possible
cases. In the first case, firms disperse across countries; in the second case, the full agglomerationof firms occurs in one country.
If the difference between consumption taxes is moderate, firms disperse across countries, thatis, sτ 1−σ /(1 − s) < (1 + t)/(1 + t∗ ) < sτ σ−1 /(1 − s). The difference between capital rents in thetwo countries is∆r = r − r∗ = (p − 1)Y − (p∗ − 1)Y ∗ = (Y − Y ∗ )/(σ − 1)


s
1−s
σ
= µ(τ − τ )−.
(1 + t)(nτ σ + n∗ τ ) (1 + t∗ )(nτ + n∗ τ σ )(10)

At the trade equilibrium, no arbitrage exists because capital is footloose across countries. Therefore,
capital rents are the same (r = r∗ ), which in turn equalizes the total production of each variety(Y = Y ∗ ).
Along with the condition that n + n∗ = K + K ∗ = 1, the number of firms (or varieties) in Homeand Foreign is derived asn=s(1 + t∗ )τ σ−1 − (1 − s)(1 + t)
; n∗ = 1 − n.
τ σ−1 − 1 s(1 + t∗ ) + (1 − s)(1 + t)
1

(11)

Lemma 1. Suppose firms disperse across countries.
(i) An increase in a country’s consumption tax induces firms to relocate to the other country, i.e.,
dn/dt < 0, dn∗ /dt∗ < 0.
(ii) How trade liberalization affects firm locations depends on the strengths between the market
sizes and consumption taxes, i.e.,dn(σ − 1)τ σ−2 (1 + t)(1 + t∗ )
= σ−1
dτ
(τ
− 1)2 [s(1 + t∗ ) + (1 − s)(1 + t)]

8



1−s
s
−
∗
1+t
1+t


.

(12)

To understand the intuitions behind the findings, we first investigate how the number of firms
and consumption tax affect the capital rent difference in equation (10). First, as more firms arelocated in Home, the Home market becomes more competitive, lowering the capital rents of eachfirm (∂∆r/∂n < 0). Second, as the consumption tax in Home increases, residents consume fewerof each variety of dirty goods and capital rents in both Home and Foreign decrease; however, firms
suffer more in Home because residents in Home consume more of each Home variety, which makes
Foreign more attractive (∂∆r/∂t < 0). At the trade equilibrium, ∆r = 0. In Lemma 1-(i), as tincreases, capital rents in Foreign become relatively high and firms relocate from Home to Foreign
until the capital rents are equalized again. In Lemma 1-(ii), if there are no consumption taxes,
our model collapses to the conventional footloose capital model. Firms locate in the larger country
more than proportionately and trade liberalization strengthens this tendency until firms fully agglomerate in the larger country, that is, ∂∆r/∂τ |t=t∗ =0 < 0, ∂∆r/∂n|t=t∗ =0 < 0, dn/dτ |t=t∗ =0 < 0.
However, the relationship between trade liberalization and the capital rent difference is ambiguousin the presence of consumption taxes because they play a role in shrinking the market. Therefore,
how trade liberalization affects firm locations depends on the extent to which the consumption tax
shrinks the market. Suppose t > t∗ . If t is sufficiently high that (1 − s)/(1 + t∗ ) > s/(1 + t), firms
relocate to Foreign under trade liberalization because the effective market size is larger in Foreign.
If t is not so high that (1 − s)/(1 + t∗ ) < s/(1 + t), trade liberalization induces firms to relocate toHome, which has a higher consumption tax. If t fully offsets Home’s market size advantage, thatis, (1 − s)/(1 + t∗ ) = s/(1 + t), trade liberalization has no effect on firm locations, which is thesame as the case of symmetric market sizes in the conventional footloose capital model.
The levels of each type of consumption arex

HHµ(σ − 1) τ σ=
σ
τσ + τFFµ(σ − 1) τ σ=
σ
τσ + τ



x

1
1−s 1
+
1+t
s 1 + t∗



1
s
1
+
∗
1+t
1−s1+t;

xF H =

xHH
;
τσ

(13)

;

xHF =

xF F
.
τσ

(14)

Lemma 2. When firms disperse across countries,(i) xHH > xF H , xF F > xHF ;(ii) dxdτ

HH> 0, dxdτ

dxij

dxij
dt∗

(iii)

dt

FH

< 0,

FF

< 0, dxdτ

HF> 0, dxdτ< 0;< 0, where i, j = H, F .

The consumption of each domestic variety of dirty goods is always larger than that of each
imported variety because of the existence of trade costs. Trade liberalization raises the consumption9

of each imported variety and decreases that of each domestic variety because the imported varieties
become relatively cheap as trade costs decline. In addition, an increase in the consumption tax
of either country always reduces the consumption of all varieties of dirty goods. Suppose that t
increases; then, the after-tax price of each variety of dirty goods increases in Home. Therefore,
xHH and xF H decrease. Moreover, an increase in t lowers P ∗ , which in turn decreases xF F andxHF , as shown in equation (6).
Each country’s emissions are the sum of the emissions from the dirty goods consumed in acountry and global emissions are the sum of the emissions from the two countries:
E = nsxHH + n∗ sxF H ; E ∗ = n(1 − s)xHF + n∗ (1 − s)xF F ; E G = E + E ∗ .

(15)

In the following part, we show how trade liberalization affects global emissions.
Proposition 1. The effect of trade liberalization on global emissions can be non-monotonic. As
trade costs decline, global emissions first decrease and then increase.
The impact of trade liberalization on global emissions can be decomposed into the firm relocation and demand effects. The firm relocation effect measures the impact of firm relocation, as
shown in Lemma 1, and the demand effect captures the impact of changes in consumption, as
shown in Lemma 2.
dE G
dE dE ∗
=
+
dτ
dτ
dτ
dn
dn∗
dn
dn∗
= sxHH+ sxF H+ (1 − s)xHF+ (1 − s)xF F
+
dτ
dτ
dτ
dτ}
|
{z
0

n
|

dsxHH

∗

d(1 − s)xF F

∗ dsx

FH

d(1 − s)xHF
+n
dτ
{z
}

(16)

+n
+n
dτ
dτ
{z
} |
+
−


σ
µ(σ − 1)s
1 − s (σ − 1)τ − στ σ−1 − 1+.
=σ
1 + t 1 + t∗(τ σ + τ )2dτ

The firm relocation effect in each country can be positive, negative, or neutral depending on
the relationship between consumption taxes and market size. However, the net firm relocation
effect of trade liberalization is always neutral because the consumption of each domestic variety
and imported variety is the same separately across countries, that is, sxHH = (1 − s)xF F andsxF H = (1 − s)xHF . A change in emissions in one country caused by firm relocation is offset by thechange in emissions in the other country. Thus, how trade liberalization affects global emissions10

is determined by the demand effect of dirty goods. As trade costs decline, the consumption ofeach imported variety increases and that of each domestic variety decreases. When trade costs
are high, the increase in GHG emissions from the consumption of imported goods is dominatedby the decrease in the consumption of domestic goods; hence, total emissions tend to decrease.
However, when trade costs are low, the case can be reversed and total emissions increase. The
non-monotonic effect is likely to occur when (1 + t)/(1 + t∗ ) is close to s/(1 − s). Otherwise, global
emissions continue to decrease until firms fully agglomerate in Home or Foreign.
We now examine how the consumption tax affects GHG emissions. In this section, the consumption tax is exogenous. The endogenous case is described in Sections 4 and 5.
Proposition 2. An increase in the consumption tax in one country reduces the emissions in thatcountry and raises the emissions in the other country. Global emissions always decrease.
Note that

dE
dsxHH
dn
dn∗
dsxF H+n< 0;= sxHH+ sxF H
+ n∗
dt
dt {z
dt} | dt {z
dt }
|

(17)

dE ∗
dn
dn∗
d(1 − s)xHF
d(1 − s)xF F= (1 − s)xHF+ (1 − s)xF F
+n
+ n∗
> 0;
dt
dt {z
dt} |
dt
dt
|
{z
}

(18)

dE G
dE dE ∗
=
+
< 0.
dt
dt
dt

(19)

−

−

−

+

The impact of the consumption tax on emissions can also be decomposed into the firm relocationand demand effects. The demand effect is always negative because an increase in the consumption
tax decreases demand for both domestic and imported dirty goods. The firm relocation effect isnegative in one country and positive in the other country because of the relatively high consumptionof domestic goods compared with imported goods. The net firm relocation effect of a consumption
tax is also neutral because the total consumption of dirty goods is the same in the two countries.
As a result, the total effect of the consumption tax on global emissions is always negative. In
addition, the total effect of t on emissions is negative for Home and positive for Foreign, which
verifies the existence of carbon leakage under consumption pollution. The intuition behind thisfinding is as follows. An increase in the Home consumption tax increases the aggregate price index
in Home and decreases that in Foreign. Since the expenditure on dirty goods is constant in eachcountry, the total consumption of dirty goods decreases in Home and increases in Foreign, that is,
sµ/P decreases and (1 − s)µ/P ∗ increases.
If the consumption tax in Home is sufficiently smaller than that in Foreign, firms fully ag11

glomerate in Home to benefit from the larger market and laxer environmental regulations, andvice versa. For (1 + t)/(1 + t∗ ) ≤ sτ 1−σ /(1 − s), all firms agglomerate in Home, Foreign specializes in the production of the clean good, and Foreign imports dirty goods from Home. For(1 + t)/(1 + t∗ ) ≥ sτ σ−1 /(1 − s), all firms agglomerate in Foreign, Home specializes in the production of the clean good, and Home imports dirty goods from Foreign. Consumption and emissions
under full agglomeration are shown in Appendix A1.
4. Global OptimumThis section studies how the social planner maximizes global welfare by deciding on the consumption taxes in each country. For simplicity, we make several assumptions. First, we assume
that environmental damage is increasing and convex with respect to global emissions, that is,
D0 (E G ) > 0 and D00 (E G ) > 0, following Copeland and Taylor (1994, 1995b). Second, we assume
that firms disperse across countries when there is no consumption tax, that is, s/(1 − s) < τ σ−1 .
This assumption ensures that the market size across countries is similar or that trade costs are not
too low.5 Lastly, we define global welfare as the sum of individual utility globally:
W G = sU + (1 − s)U ∗ .

(20)

Suppose that the social planner has no incentive to induce the full agglomeration of firms in acountry. The first-order conditions of global welfare concerning t and t∗ are derived as follows:


dW G
1
ζ∗
1 1−s ζ= µζ −1 + φζ −
+
= 0,
(21)
dt
σ − 1 ζ + ζ∗ σ − 1 s ζ + ζ∗


1
ζ
1
s
ζ∗
dW G
∗
∗
= µζ −1 + φ ζ −
+
= 0,
dt∗
σ − 1 ζ + ζ∗ σ − 1 1 − s ζ + ζ∗

(22)

where
s
1−s
, ζ∗ =,
1+t
1 + t∗(23)

1 σ − 1 1 σ − 1 τσ + 1 0+D,s σs σ τσ + τ

(24)

1 σ−1
1 σ − 1 τσ + 1 0
+
D.
1−s σ
1 − s σ τσ + τ

(25)

ζ=
φ=
φ∗ =

5
In Appendix A3, we study the case in which the firms fully agglomerate in a country initially, that is, s/(1−s) ≥τ σ−1 . Our main result does not change. That is, optimal consumption taxes that maximize global welfare are neutral
about firm location decisions.

12sNote that φ∗ = 1−sφ. Rearranging the first-order conditions gives



ζ∗
ζ
−
s 1−s



1
+ φs(ζ + ζ ∗ )
σ−1


= 0,

(26)

which implies identical consumption taxes
tGO = t∗GO .

(27)

Bringing the identical tax rates into equation (21) shows1+t=| {zGO}LHS

σ − 1 σ − 1 τσ + 1 0+D .
σσ τσ + τ
{z
}
|

(28)

RHS
0

G

0

G

G

dD
dD dE
00 dE
Under the condition that D00 > 0 and dE
dt < 0, dt = dE G dt = D dt < 0 holds. Thus, theoptimal tax rates are determined by the intersection shown in Figure 1.

Figure 1: Optimal consumption tax when RHS|t=0 > 1.

The optimal consumption taxes are identical regardless of the asymmetric market sizes because
the net firm relocation effect is neutral in our model. The social planner imposes identical taxes inboth countries to control emissions through the demand effect but does not adjust firm locations.
Moreover, the tax rates can be negative (tGO = t∗GO < 0), which implies consumption subsidies.
This case occurs when σ is sufficiently small such that RHS|t=0 < 1. Intuitively, if σ is sufficiently
small, the varieties are very differentiated. Firms have stronger market power and tend to produce
less. The social planner imposes consumption subsidies to encourage consumption and production.
13

If σ is sufficiently large, the varieties are close substitutes. Firms’ market power weakens andthey produce relatively more, which leads to more consumption emissions. In this case, the social
planner imposes consumption taxes to control demand for dirty goods.
As shown in the new economic geography literature, without environmental issues, global welfare can increase as more firms are located in a larger country. In the current setting with consumption emissions, we also examine whether the social planner has an incentive to induce full
agglomeration in Home. Since the firm relocation effect is neutral and emission targets can berealized by the demand effect, full agglomeration cannot be motivated by emission issues. In otherwords, even if full agglomeration occurs in Home, global emissions do not change. Since the emissions per unit of consumption are 1, the total consumption of dirty goods is the same. Therefore,
capital rents and total tax revenue are the same in the two cases. Inducing full agglomeration in
Home only reallocates tax revenue and consumption emissions across countries, but has no effecton their total levels. Denote the variables in the case of full agglomeration in Home with “H” inthe subscripts. We can obtain the following lemma.6
Lemma 3. In the two cases in which firms disperse across countries and fully agglomerate in∗∗
G = EG
Home, (i) EGO
GO,H ; (ii) rGO = rGO,H ; and (iii) T RGO + T RGO = T RGO,H + T RGO,H .

Therefore, whether the social planner has an incentive to induce full agglomeration depends
only on the consumer surplus given the consumption of dirty goods. In other words, the questionis how the social planner maximizes the total consumer surplus by distributing the firms (andthus the dirty goods) in the presence of asymmetric market sizes. The mass of firms affects theconsumer surplus through changes in the aggregate price indices (P and P ∗ ). When trade costs
are high, that is, s/(1 − s) < τ σ−1 , P ∗ would become too high and the consumer surplus in Foreign
would become too low if firms fully agglomerate in Home. Therefore, the social planner always
disperses firms.
Proposition 3. Optimal consumption taxes that maximize global welfare are neutral aboutfirm location decisions. In particular, if firms disperse across countries under no environmental
regulation, that is, s/(1 − s) < τ σ−1 , the consumption taxes (or subsidies) are identical regardlessof market size.

6

See Appendix A3 for the proofs of Lemma 3 and Proposition 3.

14

5. Discussion: Consumption Tax Competition
This section discusses how to derive the Nash equilibrium in a two-stage game. In the first stage,
countries simultaneously decide on the level of their consumption taxes. In the second stage,
firms determine their location and production patterns in response to environmental regulations.
In the main part of this paper, we investigated firm behavior under consumption tax. Here, weconcentrate on the first stage of the game. For simplicity, we assume that D(E W ) = δE W .7
Figure 2 describes the relationship between firm locations and environmental regulations, whereζ = s/(1 + t) and ζ ∗ = (1 − s)/(1 + t∗ ) are defined as the market size-adjusted inverse consumption taxes in Home and Foreign. The coordinate system consists of three areas: in area (i), full
agglomeration occurs in Home; in area (iii), full agglomeration occurs in Foreign; and in area (ii),firms disperse across countries.

Figure 2: Nash equilibrium when σ and τ are sufficiently large.

Denote Home welfare in each area as W(i) , W(ii) , and W(iii) , respectively. Foreign welfare still
has asterisks. With endogenous location patterns, Home cannot always choose consumption taxes
according to the first-order conditions with no constraint because location patterns may change
among the three areas, in which case Home has to behave at the threshold values of taxes. Home
7
A linear environmental damage function is often used in the analysis with endogenous firm locations. See, forexample, Markusen et al. (1993, 1995) and Dong et al. (2012).

15

then compares the welfare levels in the three areas to determine the optimal consumption tax withendogenous firm locations.
1ζ(i) = 1 1 σ−1s − σ + σ δ
1−σ ζ ∗


τ

√
σ
ζ∗
−(βζ ∗ −1)+ (βζ ∗ −1)2 +4β σ−1
ζBR =
2β




σ−1
∗

τ
ζ





1


ζ(iii) = 1 1 σ−1 δ
s − σ + σ τ

if 0 < ζ ∗ < ζ1∗
if ζ1∗ ≤ ζ ∗ < ζ2∗
if ζ2∗ ≤ ζ ∗ < ζ3∗ ,(29)

if ζ3∗ ≤ ζ ∗ < ζ4∗
if ζ ∗ ≥ ζ4∗σ
τ 1−σ
1 + σ−1
τ 1−σ
∗
,
ζ
=
,
2
1
σ−1
β(1 + τ σ−1 )s − σ + σ δwhere ζ1∗ = τ 1−σ ζ(i) = 1σ
τ σ−1
1 + σ−1
τ σ−1
∗
σ−1
,
ζ
=
τ
ζ
=
,
(iii)
4
1
1
σ−1 δ
β(1 + τ 1−σ )s − σ + σ τ
1 1 σ − 1 τσ + 1
δ.
β= − +s σ
σ τσ + τζ3∗ =How Home responds to the Foreign consumption taxes depends on the relative strengths of theconsumer surplus, capital rents, tax revenue, and environmental damage. The consumer surplus
decreases in the Home consumption tax because the aggregate price of dirty goods in Home in
1−sscreases in its tax rates. Capital rents, derived as r = Y /(σ − 1) = σµ 1+t+ 1+t∗ , also decrease int. However, tax revenue, T R = µt/(1 + t), always increases in t. In addition, as shown above, anincrease in consumption tax decreases environmental damage.
When the Foreign consumption tax is high (0 < ζ ∗ < ζ2∗ ), Home imposes consumption taxes
so that firms fully agglomerate there. By doing so, Home benefits from a high consumer surplus
and high capital rents, which dominate low tax revenue and high environmental damage. As
the Foreign tax decreases (ζ2∗ ≤ ζ ∗ < ζ3∗ ), Home also decreases its tax to increase its consumer
surplus. During this process, capital rents and environmental damage continue to increase, while
tax revenue continues to decrease. When Foreign tax falls (ζ ∗ ≥ ζ3∗ ), Home induces all firms
to relocate to Foreign; otherwise, its tax revenue and environmental quality would be too low.
For ζ2∗ ≤ ζ ∗ < ζ3∗ , Home responses are strategic complements to Foreign consumption taxes. An
increase in Foreign consumption taxes drives Home’s marginal loss below the marginal benefit from
2

R)−D]
µ
decreasing emissions, that is, d [(CS+r+T= (σ−1)(ζ+ζ∗ )2 > 0; therefore, Home has an incentivedζdζ ∗

to further decrease its emissions by increasing the consumption tax.

16

Analogously, Foreign best responses are

∗
ζBR
=


1
∗


ζ(iii)
= 1

1
σ−1


1−s − σ + σ δ





τ σ−1 ζ√−(β ∗ ζ−1)+






τ 1−σ ζ






∗

ζ(i) =(β ∗ ζ−1)2 +4β ∗2β ∗if 0 < ζ < ζ1
if ζ1 ≤ ζ < ζ2σζσ−1

if ζ2 ≤ ζ < ζ3 ,(30)

if ζ3 ≤ ζ < ζ4
1
1
1
σ−1 δ
1−s − σ + σ τ∗=where ζ1 = τ 1−σ ζ(iii)

if ζ ≥ ζ4σ
τ 1−σ
1 + σ−1
τ 1−σ
,
,
ζ
=
2
1
1
σ−1
β ∗ (1 + τ σ−1 )1−s − σ + σ δσ
τ σ−11 + σ−1
τ σ−1
σ−1 ∗
,
=
ζ3 = ∗
,
ζ
=
τ
ζ
4
(i)
1
1
σ−1 δ
β (1 + τ 1−σ )1−s − σ + σ τβ∗ =11 σ − 1 τσ + 1
− +
δ.
1−s σ
σ τσ + τ

The intuition behind Foreign best responses is the same as Home. Generally, as Home consumption taxes increase, Foreign also increases its consumption taxes because of the relative strengths
between the consumer surplus, capital rents, tax revenue, and environmental damage. Correspondingly, location patterns shift from full agglomeration in Home to dispersion across countries andeventually to full agglomeration in Foreign. Figure 2 shows the reaction curves of Home (denotedby red curves) and Foreign (denoted by blue curves). As long as σ and τ are sufficiently high, aunique Nash equilibrium always exists in which firms disperse across countries.8
The consumption taxes at the equilibrium are derived astN E =2(ββ ∗ − β 2 )s
q
− 1;
4σ 2
∗
β ∗ − 3σ−1(β ∗ − β)2 + (σ−1)
2 ββ
σ−1 β +

(31)t∗N E =2(β ∗2 − ββ ∗ )(1 − s)q
− 1;
3σ−1 ∗∗ − β)2 + 4σ 2 ββ ∗
β
−
β
−
(β
σ−1
(σ−1)2(32)

which are strongly dependent on the market size of each country. If the market sizes are identical,
β = β ∗ holds, leading to the equalization of consumption taxes across countries, that is, tN E =t∗N E = 2βs(σ−1)
2σ−1 − 1. However, if the market sizes are asymmetric, the advantage of a larger market
size encourages Home to impose a higher consumption tax or a lower consumption subsidy than8
σ and τ are sufficiently large so that T3∗ < T4∗ and T3 < T4 hold. Otherwise, the reaction curves of Home andForeign when firms disperse would expand outward, in which case the model becomes intractable.

17Foreign, that is, tN E > t∗N E .9
6. Conclusion
In this study, we extended the footloose capital model to answer several ongoing questions in theliterature on trade and the environment under consumption pollution. Specifically, we explored how
trade liberalization and consumption taxes affect firm locations, consumption and GHG emissions
and how countries decide on their consumption taxes cooperatively and non-cooperatively in thepresence of monopolistic competition, endogenous firm locations, and asymmetric market sizes.
We found that when firms disperse across countries, an increase in a country’s consumption tax
drives firms to move to the other country. However, how trade liberalization affects firm location
patterns is ambiguous and depends on the tension between consumption tax and market size.
If the market size is sufficiently large, firms may relocate to the country with more stringent
consumption taxes. Trade liberalization can decrease GHG emissions initially and subsequently
increase them. An increase in a country’s consumption tax always decreases its own and global
emissions, while increasing the emissions of other countries. In the global optimum, the social
planner imposes identical consumption taxes across countries to maximize global welfare if firms
disperse across countries under no environmental regulation. Firm locations are unchanged. Underconsumption tax competition, if the elasticities of substitution among different varieties and trade
costs are sufficiently high, a Nash equilibrium exists in which firms disperse across countries andthe consumption tax is higher in the larger country.
Finally, we emphasize two potential extensions of this study. As an essential source of consumption pollution, gasoline is always at the center of this issue. Gasoline is crucial not only
because its consumption is massive, but also because changes in its price have been demonstrated
to be an important channel of carbon leakage (e.g., Kiyono and Ishikawa, 2013). Further analysis
should be performed to study how policymakers design policies to control GHG emissions with theexistence of carbon leakage stemming from the price changes of natural resources. The other issue
is the choice of firms between abatement investment and FDI. If environmental regulation is notstringent compared with abatement costs, firms may prefer to pay for their emissions. However, if
environmental regulation is strict but not as strict as the costs of FDI, firms may abate their emissions by investing in expensive equipment and machines. If environmental regulation is sufficiently
stringent, firms may choose FDI instead of investing in abatement. Such endogenous choices areimportant, especially when firms have different productivity levels, mobility, emission intensities,
and abatement technologies.
9

See Appendix A4.

18

References
Antweiler, W., Copeland, B. R., and Taylor, M. S. (2001). Is free trade good for the environment?

AmericanEconomic Review, 91(4):877–908.
Baldwin, R. E. and Krugman, P. (2004). Agglomeration, integration and tax harmonisation. European Economic
Review, 48(1):1–23.
Cheng, H., Kato, H., and Obashi, A. (2020). Is environmental tax harmonization desirable in global value chains?
The B.E. Journal of Economic Analysis & Policy, 1(ahead-of-print).
Copeland, B. R. and Taylor, M. S. (1994). North-south trade and the environment. Quarterly Journal of Economics,
109(3):755–787.
Copeland, B. R. and Taylor, M. S. (1995a). Trade and the environment: a partial synthesis. American Journal of
Agricultural Economics, 77(3):765–771.
Copeland, B. R. and Taylor, M. S. (1995b). Trade and transboundary pollution. American Economic Review,
85(4):716–737.
Cremer, H. and Gahvari, F. (2004). Environmental taxation, tax competition, and harmonization. Journal of Urban
Economics, 55(1):21–45.
Davis, S. J. and Caldeira, K. (2010). Consumption-based accounting of CO2 emissions. Proceedings of the National
Academy of Sciences, 107(12):5687–5692.
Dixit, A. K. and Stiglitz, J. E. (1977). Monopolistic competition and optimum product diversity. American Economic
Review, 67(3):297–308.
Dong, B., Gong, J., and Zhao, X. (2012). FDI and environmental regulation: pollution haven or a race to the top?
Journal of Regulatory Economics, 41(2):216–237.
Druckman, A., Bradley, P., Papathanasopoulou, E., and Jackson, T. (2008). Measuring progress towards carbon
reduction in the uk. Ecological Economics, 66(4):594–604.
Haufler, A. and Pflüger, M. (2004). International commodity taxation under monopolistic competition. Journal of
Public Economic Theory, 6(3):445–470.
Haufler, A. and Wooton, I. (2010). Competition for firms in an oligopolistic industry: The impact of economic
integration. Journal of International Economics, 80(2):239–248.
Hoel, M. (1997). Environmental policy with endogenous plant locations. Scandinavian Journal of Economics,
99(2):241–259.
Hu, B. and McKitrick, R. (2016). Decomposing the environmental effects of trade liberalization: The case of
consumption-generated pollution. Environmental and Resource Economics, 64(2):205–223.
Ishikawa, J. and Kuroda, T. (2007). How effective are emissions taxes in an open economy? Review of Development
Economics, 11(2):359–368.
Ishikawa, J. and Okubo, T. (2010). Environmental and trade policies for oligopolistic industry in the presence ofconsumption externalities. International Economy, 2010(14):59–76.
Ishikawa, J. and Okubo, T. (2011). Environmental product standards in north–south trade. Review of Development
Economics, 15(3):458–473.
Ishikawa, J. and Okubo, T. (2016). Greenhouse-gas emission controls and international carbon leakage through tradeliberalization. International Economy, 19:1–22.
Ishikawa, J. and Okubo, T. (2017). Greenhouse-gas emission controls and firm locations in north–south trade.
Environmental and Resource Economics, 67(4):637–660.

19

Kiyono, K. and Ishikawa, J. (2013). Environmental management policy under international carbon leakage. International Economic Review, 54(3):1057–1083.
Krutilla, K. (1991). Environmental regulation in an open economy. Journal of Environmental Economics andManagement, 20(2):127–142.
Ludema, R. D. and Wooton, I. (2000). Economic geography and the fiscal effects of regional integration. Journal ofInternational Economics, 52(2):331–357.
Markusen, J. R., Morey, E. R., and Olewiler, N. D. (1993). Environmental policy when market structure and plant
locations are endogenous. Journal of Environmental Economics and Management, 24(1):69–86.
Markusen, J. R., Morey, E. R., and Olewiler, N. D. (1995). Competition in regional environmental policies whenplant locations are endogenous. Journal of Public Economics, 56(1):55–77.
Martin, P. and Rogers, C. A. (1995). Industrial location and public infrastructure. Journal of International Economics, 39(3-4):335–351.
Rauscher, M. (1995). Environmental regulation and the location of polluting industries. International Tax and Public
Finance, 2(2):229–244.
Vlassis, N. (2013). The welfare consequences of pollution-tax harmonization. Environmental and Resource Economics,
56(2):227–238.
Wiedmann, T. (2009). A review of recent multi-region input–output models used for consumption-based emission
and resource accounting. Ecological Economics, 69(2):211–222.
Zeng, D.-Z. and Zhao, L. (2009). Pollution havens and industrial agglomeration. Journal of Environmental Economics
and Management, 58(2):141–153.

20

Appendix
A1. Consumption and Emissions under Full Agglomeration.
1+ts1−σ , all firms agglomerate in Home, Foreign specializes in the production of
For 1+t∗ ≤ 1−s τ

the clean good, and Foreign imports the dirty goods from Home. In this case, n = 1, n∗ = 0;
1
1
HF = µ(σ−1)
F H = xF F = 0; E = µ(σ−1) s , E ∗ = µ(σ−1) 1−sxHH = µ(σ−1)σ
1+t ,h x
σ i τ (1+t∗ ) , xσ
1+tστ (1+t∗ )µ(σ−1)
s
s
1−s
1+t
G
σ−1
and E =, all firms agglomerate in Foreign, Homeσ1+t + τ (1+t∗ ) . For 1+t∗ ≥ 1−s τspecializes in the production of the clean good, and Home imports the dirty goods from Foreign.
11
F H = µ(σ−1)
In this case, n = 0, n∗ = 1; xF F = µ(σ−1), xHH = xHF = 0; E ∗ =σ1+th∗ , xiσ τ (1+t)µ(σ−1) 1−sµ(σ−1)µ(σ−1) 1−sssGσ1+t∗ , E =σσ1+t∗ + τ (1+t) .
τ (1+t) and E =A2. Proof of Proposition 1.
Consider a case where (1 + t)/(1 + t∗ ) = s/(1 − s) so that consumption taxes do not affect firm
locations. Differentiating global GHG emissions in trade with footloose capital with respect to τ
gives
dE G
µ(σ − 1)
=
dτ
σ



s
1−s
+
1 + t 1 + t∗(σ − 1)τ σ − στ σ−1 − 1.
(τ σ + τ )2d[(σ−1)τ σ −στ σ−1 −1]= σ(σ − 1)τ σ−2 (τ − 1) > 0 always holds, therefore, (σ − 1)τ σ − στ σ−1 − 1 isdτ
an increasing function of τ for τ > 1. When τ = 1, the polynomial is -2; when τ = σ+1
σ−1 , theGdE
σ+1
polynomial is equal to τ σ−1 − 1 > 0. Thus, dτ = 0 exists for 1 < τ < σ−1 . Denote the certain
point as τ0 , then E G decreases for 1 < τ < τ0 and increases for τ > τ0 . In other words, as trade

costs decline from infinity to unity, global GHG emissions initially decrease and then increase.
A3. Global Optimum
Global Optimum: Firms Disperse
Define global welfare as the sum of individual welfare around the world:
W G = sU + (1 − s)U ∗21

whereU = µ ln M + I/s − µ − D(E G )= µ ln µ − µ ln P + 1 + r + T R/s − µ − D(E G )



σ
µ
µ
1−s 1+t
1−σ= µ ln µ − µ ln(+1)−
ln(1 + τ) + µ ln(1 + t) +ln 1 +σ−1
σ−1
σ−1
s 1 + t∗


s
t
µ
1−s
+µ
+
+
− µ − D(E G ).
∗σ 1+t 1+t
1+t
and


σ
µ
µ
s 1 + t∗1−σ∗
+1
U = µ ln µ − µ ln()+
ln(1 + τ) − µ ln(1 + t ) −ln 1 +σ−1
σ−1
σ−1
1−s 1+t


µ 1−s
s
t∗
+
+
+
µ
− µ − D(E G ).
σ 1 + t∗ 1 + t
1 + t∗∗

Remind that for s/(1 − s) < τ σ−1 ,1 + tGO =σ − 1 σ − 1 τσ + 1 0 G+
D (E ),σσ τσ + τ

global emissions at the social optimum are determined byGEGO=µ(1 + τ σ ).
G )τ σ + τ + (1 + τ σ )D0 (EGO

Global Optimum: Full Agglomeration in Home
If the social planner induces full agglomeration in Home, global welfare becomesσ
WHG = WH,H + WH,F = µ ln µ − µ ln() − µ(1 − s) ln τ + 1 − µs ln(1 + t) − µ(1 − s) ln(1 + t∗ )
σ
−
1


µ(σ − 1)
s
1−s
G
−
+
− D(EH).
σ
1 + t 1 + t∗
WH,H and WH,F denote Home and Foreign welfare as follows:
WH,H = µ ln µ − µ ln(σµ) − µ ln(1 + t) + 1 +
σ−1
σ



s
1−s
+
1 + t 1 + t∗σµWH,F = µ ln µ−µ ln()−µ ln(1+t∗ )−µ ln τ +1+
σ−1
σ

22




+µ

t
G
− µ − D(EH
);
1+t


s
1−s
t∗
G
+
+µ
−µ−D(EH).
1 + t 1 + t∗
1 + t∗

Solving the first-order conditions with respect to t and t∗ givest=Note that(σ − 1)(1 + D0 )σ−1
− 1; t∗ =
σ
σ



D0
1+
− 1.
τ

1+t
τ (1 + D0 )s=>1>τ 1−σ .
∗
0
1+t
τ +D
1−s

The taxes are not available because full agglomeration in Home never happens if the consumption
1+t
s
1−σ .
taxes are imposed. So the social planner acts at the threshold value where 1+t∗ = 1−s τProof of Lemma 3s1+t1−σ into W G and solving the welfare maximization problem give
Taking 1+t∗ = 1−s τHs(σ − 1)
1 + tGO,H =σ
1 + τσ 0 G
1−σ
1+τ
+
D (EH ) .
τσ

Hence, global emissions at the global optimum when full agglomeration occurs in Home are
G
EGO,H
=

µ(1 + τ σ ),G)
τ σ + τ + (1 + τ σ )D0 (EGO,H

W . For both E G and E G
which takes the same form as EGO
GO
GO,H , their left hand sides increase inglobal emissions and their right hand sides decrease in global emissions (i.e., D00 > 0). There exists
G = EG
only one solution for the equation, which implies that EGO
GO,H as shown in Figure A.1.
1+ts
1−σ and E G = E GWith 1+t∗ = 1−s τGOGO,H , we can get the optimal consumption taxes whenfirms fully agglomeration in Home.
tGO,H = s(1 + τ 1−σ )(1 + tGO ) − 1; t∗GO,H = (1 − s)(1 + τ σ−1 )(1 + tGO ) − 1.
Note that
s
1−s
s
1−s
+
=
+
.
(33)
∗
1 + tGO
1 + tGO
1 + tGO,H
1 + t∗GO,H


µt
µt∗
s
1−s
Therefore, capital rents r = σµ 1+t+ 1+t
and total tax revenue T R + T R∗ = 1+t+ 1+t∗∗ are thesame in the two cases.

23

G
G
must hold.
= EGO,H
Figure A.1: EGO

Proof of Proposition 3
For s/(1 − s) < τ σ−1 , the difference between global welfare in the two cases is
G
G
WGO− WGO,H=µσ s ln s + (1 − s) ln(1 − s) + ln(1 + τ 1−σ ) + (1 − s)(σ − 1) ln τ ) .
σ−1G − WG
d WGO
GO,H
dτ

= 0 =⇒ τ σ−1 =

G
G
G
G
WGO
− WGO,H> WGO− WGO,H



s
.
1−s

s
τ σ−1 = 1−s= 0.

Therefore, the social planner never has an incentive to induce full agglomeration in Home.
In the case where s/(1 − s) ≥ τ σ−1 holds, firms fully agglomerate in Home when there is no environmental regulation. The social planner has no incentive to make firms disperse across countries
because trade costs are low. Consequently, P ∗ would not be so high under full agglomeration in
Home. The increase in Home consumer surplus due to a lower P can dominate the decrease in Foreign consumer surplus due to a higher P ∗ . Hence, the social planner maintains full agglomerationin Home and sets a higher consumption tax in Home than in Foreign.
Firm locations remain unchanged in the two cases of dispersion and full agglomeration.

24

A4. Consumption Tax Competition
Comparison of Consumption Taxes at the Nash Equilibrium
We compare tN E and t∗N E as follows:q
4σ 2∗(β ∗ − β)2 + (σ−1)
2 βββs1 + tN Eq= ∗1 + t∗N E
β (1 − s) β ∗ − 3σ−1 β + (β ∗ − β)2 + 4σ2 ββ ∗σ−1(σ−1)23σ−1 ∗
σ−1 β − β −2s − 1+ β.
s(1 − s)Because σ and τ are sufficiently large, β > 1/s holds. Therefore,

where β ∗ =βsβ ∗ (1 − s)

= 2s−1sβs
1= 2s−1 1−s > 1.
+ β(1 − s)+ sβs2Moreover,
s
(
)
2
2
4σ
3σ
−
1
4σ
(β ∗ − β)2 +ββ ∗ − β ∗ −
β + (β ∗ − β)2 +ββ ∗(σ − 1)2σ−1(σ − 1)2
s
2σ
4σ 2
2σ ∗
β +
β − 2 (β ∗ − β)2 +ββ ∗ > 0=σ−1σ−1(σ − 1)2

3σ − 1 ∗
β −β−
σ−1

s

because


2σ ∗
2σ
β +
β
σ−1
σ−1

s

2
−

2

4σ 2
(β ∗ − β)2 +ββ ∗(σ − 1)2!2=

4(2σ − 1) ∗(β − β)2 > 0.
(σ − 1)2

As a result,

Therefore,

3σ−1 ∗
σ−1 β − β −q4σ∗(β ∗ − β)2 + (σ−1)
2 βββ ∗ − 3σ−1
σ−1 β +q4σ∗(β ∗ − β)2 + (σ−1)
2 ββ

2

2

1 + tN E> 1 stands, implying that tN E > t∗N E .
1 + t∗N E

25> 1.