Global COE Hi-Stat Discussion Paper Series 013

Research Unit for Statisticaland Empirical Analysis in Social Sciences (Hi-Stat)

Greenhouse-gas Emission Controls and International
Carbon Leakage through Trade Liberalization

Hi-Stat Discussion Paper

Jota Ishikawa
Toshihiro Okubo

November 2008

Hi-Stat
Institute of Economic Research
Hitotsubashi University
2-1 Naka, Kunitatchi Tokyo, 186-8601 Japan
http://gcoe.ier.hit-u.ac.jp

Greenhouse-gas Emission Controls and International
Carbon Leakage through Trade Liberalization∗
Jota Ishikawa (Hitotsubashi University and RIETI)α
Toshihiro Okubo (Kobe University)β
October 2008

ABSTRACT. This paper studies greenhouse-gas (GHG) emission controls

in the presence of carbon leakage through international firm relocation.
The Kyoto Protocol requires developed countries to reduce GHG
emissions by a certain amount. Comparing emission quotas with emission
taxes, we show that taxes coupled with lower trade costs facilitate more
firm relocations than quotas do, causing more international carbon
leakage. Thus, if a country is concerned about global emissions, emission
quotas would be adopted to mitigate the carbon leakage. Firm relocationentails a trade-off between trade liberalization and emission regulations.
Emission regulations may be hampered by trade liberalization, and viceversa.
JEL: F18, Q54
Keywords: trade liberalization, global warming, Kyoto Protocol, emission
tax, emission quota, carbon leakage∗

We are grateful to seminar participants at Nagoya University and attendees at the Hitotsubashi
COE/RES Conference on International Trade & FDI 2007, the APTS 2008 Sydney, and the ETSG
2008 Warsaw for helpful comments and suggestions. Any remaining errors are our own responsibility.
We acknowledge financial support from the Ministry of Education, Culture, Sports, Science andTechnology of Japan under the COE Projects.

αβjota@econ.hit-u.ac.jp
okubo@rieb.kobe-u.ac.jp

1. INTRODUCTION
Global environmental problems have recently attracted considerable
worldwide attention. In particular, global warming caused by greenhouse-gas (GHG)
emissions has been the central issue among the problems. To cope with global
warming, an international environmental treaty, the United Nations Framework
Convention on Climate Change (UNFCCC), was made at the Earth Summit held in
Rio de Janeiro in 1992. Then the Kyoto Protocol was adopted at the third session of
the Conference of Parties to the UNFCCC (COP3) in December 1997.1 In the protocol,
the industrialized countries called Annex I Parties made a commitment to decrease
their GHG emissions by 5.2% compared to their 1990 baseline levels over the 2008 to2012 period. However, the United States, which is a signatory to the protocol, has not
ratified the protocol. Moreover, developing countries including China and India haveno obligation to the reduction.
There is no doubt that the Kyoto Protocol is a significant step towards the
reduction of GHG emissions. Obviously, however, the partial participation of certain
countries in the framework of GHG emission reduction is a vital drawback. In
particular, the United States and China are the largest GHG emitters in the world.2
Moreover, with partial participation, a serious concern is international carbon leakage.
That is, the reduction of GHG emissions in some countries increases those in othercountries. As a result, worldwide emissions may rise.
International carbon leakage occurs through a number of channels. For
example, it may occur through fuel price changes (Ishikawa and Kiyono, 2000;
Kiyono and Ishikawa, 2004). When a country adopts policies to reduce GHG
emissions, its demand for fossil fuels is likely to decrease. If their world prices fall asa result, the demand for fossil fuels rises in other countries with weak regulations.
Carbon leakage may also arise through the changes in a country’s industrial structures(Copeland and Taylor 2005; Ishikawa and Kiyono, 2006). With stringent GHG
emission regulations, the comparative advantage of the emission-intensive industry
may shift abroad. This is the so-called pollution haven hypothesis. In particular, in

1

The Kyoto Protocol came into force in February 2005.

2

In 2005, the shares of world CO2 emissions were 21.4% for the United States and 18.6% for China,
respectively.

2

response to environmental policy differences across countries, firms may relocate tocountries with lax environmental regulations (Markusen et al., 1993, 1995). Recent
improvements in transportation and communications technology as well as tradeliberalization allow firms to relocate their plants more easily.
In this paper, we compare emission taxes with emission quotas (including
creation of a competitive emission-permit market) in the presence of the possibility offirm relocation. Specifically, using a new economic geography (NEG) framework, we
examine the effects of trade costs on emission taxes and quotas. In our model, there
are two countries (North and South), two sectors (agriculture and manufacturing), andtwo factors (capital and labour). The agricultural product, which perfectly competitive
firms produce from labour alone with constant-returns-scale (CRS) technology, isfreely traded internationally. The manufactured products are subject to the Dixit–
Stiglitz (1977) type of monopolistic competition and are costly to ship internationally.
Following Martin and Rogers (1995), we assume that only capital is mobile acrosscountries and determines plant location.3
To make our point as clearly as possible, in the benchmark case North’s
market is larger than South’s market and all firms in the manufacturing sector are
located in North in stable equilibrium because of small or intermediate trade costs.
The North government unilaterally adopts an environmental policy, either an emission
tax or an emission quota. Then we consider the effects of these policies when trade
costs fall and firms are free to relocate to South.
One of our main results is as follows. If North cares only about local
emissions, then North prefers emission taxes to emission quotas. On the other hand, if
North is concerned about global emissions, then emission quotas should be adopted.
This result has interesting implications for the Kyoto Protocol when regarding Annex
I Parties as North. As mentioned above, the target for GHG emission reductions set by
Annex I Parties in the protocol is a local one. In the presence of firm relocation fromAnnex I Parties to the other countries, therefore, trade liberalization may induce
Annex I Parties to adopt emission taxes rather than emission quotas to achieve the3This model is known as the footloose capital model, which is the simplest model in NEG. See
Baldwin et al. (2003).

3

target. From the viewpoint of worldwide emission reduction, however, emission
quotas are more effective.
Another main result is that when emission taxes are adopted in North to attaina target of global emission reduction, trade costs and tax rates must satisfy certain
conditions. Intuitively, lower trade costs coupled with tougher regulations facilitate
firm relocation, which leads to carbon leakage. Thus, free firm relocation entails a
trade-off between trade liberalization and emission regulations. Emission regulations
may be hampered by trade liberalization, and vice versa.
There are many papers that examine the pollution haven hypothesis. In theframework of an open economy, the first theoretical analysis on the hypothesis isPethig (1976).4 Then Markusen et al. (1993, 1995) investigate the hypothesis in thepresence of foreign direct investment (FDI). In Markusen et al. (1993), two polluting
firms (one is local and the other is foreign) choose the number of plant and plant
locations when only the home country adopts emission taxes. They are primarily
concerned with market structures induced by taxes. In Markusen et al. (1995), a single
firm decides the plant number and locations when both countries adopt environmental
policies non-cooperatively. The governments have an incentive to lower (raise)environmental standards to attract (deter) investment if the benefit from investment isgreater (less) than the loss (i.e., the environmental damage).5
Firm locations and trade costs are central issues in the NEG literature. A few
NEG studies investigate environmental policies (Pfluger, 2001; Venables, 2001;
Elbers and Withagen, 2004).6 Pfluger (2001) considers Pigouvian emission taxes in a

4

Evidence on the pollution haven hypothesis is mixed. According to Jaffe et al. (1995), differences inenvironmental policy have little or no effect on trade patterns, investment or firm location. However,Henderson (1996), Becker and Henderson (2000), Greenstone (2002), and List et al. (2003) find thatpollution-intensive plants are responding to environmental regulations. Smarzynska and Wei (2004)
discuss factors that may make the evidence of the hypothesis weak. Levinson and Taylor (2008) pointout that the pollution haven effects have been underestimated.
5

When a country adopts too lax environmental policies in order to keep its competitive advantage, its
strategy is sometimes called “environmental (or ecological) dumping.” On the other hand, when acountry adopts too stringent environmental policies in order to reduce local pollution, this strategy iscalled “Not in my back yard (NIMBY).” There are a number of studies which, following Markusen etal. (1995), analyse environmental dumping and NIMBY. See, for example, Rauscher (1995) and Ulphand Valentini (2001).
6

Venables (2001) studies the impact of tax on equilibrium in a vertical linkage model. In the case ofenergy taxes that are unilaterally introduced in one country, he discusses hysteresis in location but does
not investigate any environmental policies. Elbers and Withagen (2004) study the impact of anemission tax on agglomeration in the presence of labour migration.

4

NEG model similar to ours. However, his analysis is along the line of Markusen et al.
(1995). Thus, environmental damages are local and governments can detect emitters,
estimate the damage and can impose optimal emission taxes. In contrast, emissions in
our model are global and hence it is hard to identify polluters and estimate emissions
damage. This makes it impossible to levy a tax on each polluter and compensate thepublic through tax reimbursement. In our paper, global warming is an impending
issue and each country is required to reduce total emissions by a certain amount.
A key mechanism of environmental policies is agglomeration rent, which is
discussed somewhat similarly in the literature of tax competition. The NEG literature
has been exploring taxation on agglomeration rent (Kind et al., 1998; Ludema andWooton, 2000; Baldwin and Krugman, 2004). However, our environmental policies
are substantially different from corporate tax competition and agglomeration rent inspirit and purpose: 1) A reduction of emissions is an obligation in international
agreements. Taxation is aimed at reducing emissions to a certain level rather thanaffecting tax revenue. On the other hand, corporate taxation is intended to absorb
agglomeration rent and raise tax revenue; 2) Tax competition is not plausible in ourpaper. Only developed countries ratify the international agreements and thus taxationis unilateral in our North–South model. The environmental policies are mandatory
across ratified countries so as to reduce emissions to satisfy the agreements. Thus, theinternational environmental agreements leave no room for tax competition to increase
government revenue, i.e., a race-to-top or race-to-bottom in the tax rate; and 3) Our
discussion involves how to reduce global emissions while refraining from using apollution haven under trade liberalization. In contrast, tax competition studies show
how each government seeks to maximize tax revenue by attracting more firms andwidening the tax base.
Turning to the environment and trade literature, Ishikawa and Kiyono (2006)
analyse the potential effects of choices over emission controls in an open economy.
They specifically compare emission taxes, quotas and standards in a perfectlycompetitive general equilibrium trade model. Their analysis is somewhat similar toours in the sense that one of two countries unilaterally imposes environmental policies,

5which generates cross-border carbon leakage,7 and that North’s emission level isendogenously determined under emission taxes. However, their model is based on
traditional trade models (i.e., both Ricardian and Heckscher–Ohlin models) and does
not take firm relocation into account.
In an analysis of global warming, Copeland and Taylor (2005) explore therelationship between international trade in goods and emission permits using a
Heckscher–Ohlin framework. They also consider partial participation in the Kyoto
protocol. Interestingly, they show that unilateral emission reductions in North can
induce the unconstrained South to reduce emissions. This implies that, in contrast
with our analysis, international carbon leakage may not be a serious issue even
without universal participation in the protocol. This contrast basically stems from thepresence of an income effect as well as the absence of firm relocation in their analysis.
Here the income effect means that higher income reduces pollution.8
The rest of the paper is organized as follows. In Section 2, we present ourbasic model. Emission taxes and quotas are investigated in Sections 3 and 4,
respectively. Then, in Section 5, we compare emission taxes with emission quotas. In
Section 6, we explore the relationship between emission regulations and tradeliberalization. Section 7 concludes the paper.

2. BASIC MODEL
2.1.

Two-country, 2-sector, 2-factor model without environmental policies
We basically introduce GHG emissions into the footloose capital (FC) model

developed by Martin and Rogers (1995). There are two countries (North and South),
two production factors (labour, L, and physical capital, K) and two sectors(agriculture, A-sector, and manufacturing, M-sector). North is bigger than South inpopulation size. The agricultural product is produced from labour alone by perfectlycompetitive firms under CRS technology and is traded without any trade cost. This
product serves as a numéraire. The manufactured goods are subject to the Dixit–

7

Kiyono and Ishikawa (2004) focus on international interdependence of environmental management
policies in the presence of international carbon leakage.
8

Evidence of the income effect is also mixed. See, for example, Barbier (1997).

6

Stiglitz type of monopolistic competition and are traded with trade costs. Firms in Msector in Martin and Rogers (1995) can move between countries, but there is no entry
and exit. M-sector uses labour, a variable cost, and exclusively employs capital, afixed cost. Specifically, each firm is required to use one unit of capital, which
represents fixed costs, and “a” units of labour. The cost function for firm j is given by

TC j = π + awx j , where π, i.e., the fixed cost part of total cost, represents capital
return. M-sector emits GHGs in the process of production. Specifically, theproduction of one unit of an M commodity entails one unit of GHG emissions. Tradecosts, τ(> 1), are iceberg type. The freeness of trade, φ, can be defined as φ ≡ τ 1−σ .
This implies that free trade, τ = 1, can be expressed as φ= 1 whereas φ= 0 represents
autarchy (τ = ∞).
Turning to the demand side, a representative consumer has the following
quasi-linear utility function:(1)(

U = µ ln M + A − f ( χ N + χ S ), M ≡ nc1−1 / σ + n * c *1−1 / σ)

1 /( 1-1/σ ),1 > µ > 0, σ > 1 ,where M and A stand for consumption of M-sector varieties and that of A-sector,
respectively, and µ is the intensity of preference towards M-sector goods. n and n* arethe number of differentiated varieties, and c and c* are the quantities of consumption
for each variety. σ in the CES function for differentiated varieties denotes the constantelasticity of substitution between two varieties.9 The disutility is expressed as anincreasingly monotonic function of GHG emissions, f( χ N + χ S ), where χ N and χ S
are GHG emissions in North and South, respectively. Each consumer has one unit ofcapital as well as one unit of labour and gets income from both factors, w + π .
However, the quasi-linear utility function has no income effect and thus eachconsumer buys a certain number of units of M-goods regardless of his/her income andM-goods prices.
Labour is mobile between sectors but immobile between countries. While
capital is mobile between two nations, capital owners are immobile and thus capital9

The equilibrium path in the FC model with a quasi-linear utility function is identical to that of the
Cobb–Douglas utility function. The quasi-linear function eliminates the income effect (See Baldwin, etal. 2003).

7

rewards are repatriated to the country of origin. Because capital endowment isinitially allocated in proportion to labour endowment (market size), North’s share of
initial capital and labour endowments are given by sK = K / K W = sL = L / LW .

However, after the firm has relocated, capital share is generally not equal topopulation share, whereas population share always corresponds to labour share, sL,
and capital share is always identical to firm share, n / N W = sK. This is because eachfootloose firm needs one unit of capital. Because no income effect exists, the quasilinear utility function ensures s ≡ sE = sL, where North’s expenditure share is defined
as sE = E / E W . For simplicity, total expenditure E W and total labour and capitalendowments, LW and K W (thus the total number of firms, N W ), are normalized toone. Thus, n is North’s share of firms.10
2.2.

Initial equilibrium

Because the A-sector good is the numéraire and is freely traded internationally,
wage rates in both countries are normalized to one, w = w* = 1. Utility maximization
results in the well-known CES demand function. As a result of maximization, local
and export prices of the product variety of the North-based M-sector firm are givenby:(2) p =a,1 − 1/ σp* =τa1 − 1/ σ,where “a” is unit labour requirement, equal to marginal cost, which is exogenously
given as a constant. Consumption per variety is:(3) c =

µp −σ E
np 1−σ + n * p *1−σ

and c * =µp *−σ E *np 1−σ + n * p *1−σ.

Using (2) and (3), pure profit for a representative firm in North is given by:⎞µ⎛ a 1−σφa 1−σE +E * ⎟⎟ ,*∆ [ n]⎠σ⎝ ∆[n]

π [n] = ⎜⎜10

Importantly, we use a quasi-linear utility function. The income effect is eliminated. The total numberof households (population) is one in the world, because each individual has one unit of labour andcapital. The level of demand depends on population size rather than income.

8

where E (E*) represents the North’s (South’s) expenditure, and ∆ and ∆* are definedas ∆[n] = na 1−σ + φ (1 − n)a 1−σ and ∆* [n] = φna 1−σ + (1 − n)a 1−σ .11
Because our model has asymmetric market size, E(= s) > E*(= 1 – s), i.e., s >0.5, pure profit of a North-based firm is higher than that of a South-based firm withpositive trade costs. Therefore, allowing for free relocation, the pure profits areequalized and then firm shares, n are determined as locational equilibrium.
(4) π [n] − π * [n] = a 1−σ1− s ⎞µ (1 − φ ) ⎛ s⎜⎜− * ⎟⎟ = 0 .
σ ⎝ ∆[n] ∆ [n] ⎠Solving (4), we obtain n =1 ⎛1+ φ ⎞1⎟⎟( s − ) .
+ ⎜⎜2 ⎝1−φ ⎠2

As trade costs fall (a rise in φ), n increases: more South firms go to North, so-called
gradual agglomeration. Then, below a certain trade cost, called the sustain point (φ=(1 – s)/s ), all firms concentrate in North, i.e., full agglomeration. That is, trade costs
above the sustain point (small trade costs) create full agglomeration in the big country
as a stable equilibrium. For simplicity, we first consider full agglomeration before
considering any environmental policy. Accordingly, trade costs discussed in our paper
are assumed to be from the sustain point through free trade: (1 – s)/s <φ< 1.
2.3.

Production and GHG emissions

The quantity produced by each North-based firm (j) for the North market isgiven by x j =µp −σ
np 1−σ + n * p *1−σ

, which is identical to c. Turning to the export market,

only x/τunits arrive for export because of iceberg trade costs. While North’s
consumption is equal to the quantity produced in North for each variety, i.e., x j = c j ,11⎛ a1−σa1−σ *⎞ µ . Note that each firm’s
+
E
E⎟
⎜ ∆
∆* ⎟⎠σ⎝Likewise, pure profits for South-based firms are π*[n] =⎜φprofit is 1/σ times firm revenue. The (1 – 1/σ) terms cancel out in the price of a variety and in CES
composition.

9the quantities produced for the foreign market need x = c τ =
*
j

*
j

µτp *−σnp 1−σ + n * p *1−σ

. Itfollows that the total quantity produced by a North-based firm, firm j, is written as:
x j + x *j =µp −σnp 1−σ + n * p+*1−σµτp *−σnp 1−σ + n * p *1−σ

⎛
⎞ −σ
1− s
s
⎟p .
φ
= µ ⎜⎜ 1−σ+* *1−σ1−σ* *1−σ ⎟
+
+
np
n
p
np
n
p
⎝
⎠

For simplicity, we assume that producing one unit of goods entails one unit of
GHG emissions. Thus, the amount of local emissions in each country corresponds toeach country’s total quantity produced. Local emission levels in North and South are,respectively, defined as:

1− s ⎞⎛s⎛ s 1− s ⎞+ φ * ⎟a −σ and χ S ≡ n * ( x j + x *j ) = n *b⎜ φ + * ⎟a −σ ,
∆ ⎠
∆ ⎠
⎝∆
⎝ ∆

χ N ≡ n( x j + x *j ) = nb⎜
where b ≡µ
(1 − 1 / σ )is exogenously given and constant. Without loss of generality,

by an appropriate choice of units we can normalize b = 1 . Note that GHG emissions
in North and South correspond to quantities produced in each country. In sum, world
1− s ⎞⎛ s 1− s ⎞⎛semissions are χ ≡ χ N + χ S = n⎜ + φ * ⎟a −σ + n * ⎜ φ + * ⎟a −σ . Utilising these
∆ ⎠
∆ ⎠
⎝∆
⎝ ∆
specifications, emissions at the initial no-policy equilibrium (full agglomeration in
North) can be written as χ

initial=χ

initialNa −σ
1= 1−σ = because of ∆ = a 1−σ and ∆* = φ∆ .
aaNote that GHGs are initially emitted only in North because of North’s full
agglomeration and the emissions remain constant and are independent of trade costs.12
Proposition 1: The total amount of emissions is unaffected by trade costs atfull agglomeration (no environmental policy) equilibrium.

12

More generally, ignoring a stable equilibrium path, if all firms hypothetically concentrate in one
country, either North or South, the amount of emissions can be kept constant. For instance, if all firms
are forced to relocate to South by policy, global emissions can be derived as⎛ s 1 − s ⎞ −σ ⎛ 1 ⎞ −σ 1 , which is the same level as with North’s+ * ⎟a = ⎜ * ⎟a =
a
∆ ⎠
⎝ ∆
⎝∆ ⎠

χ ≡ χ N + χ S = χ S = ⎜φfull agglomeration. Hence, the global level of emissions is independent of location in the case of full
agglomeration, irrespective of a stable equilibrium path.

103. EMISSION TAX
3.1.

Taxation without relocation

Now we introduce environmental policies. Because of international
environmental agreements such as the Kyoto Protocol, an industrialized country,
which has manufacturing agglomeration, namely North, is required to limit emissions
to a certain fixed level. To satisfy the upper bound of emissions, we assume that
North introduces either an emission tax or quota. In this section, we examine anemission tax.
Starting from full agglomeration, North imposes an emission tax so as toreduce emissions and implement the international agreement. At this moment,
relocation is prohibited (infinitive relocation costs). Because one unit of GHG
emissions corresponds to one unit of quantity produced in our model, an emission tax
needs to be levied on each unit of production rather than prices, pure profits or sales.
Thus, the emission tax is equivalent to a specific production tax, t. Then the total costs
and prices are expressed as:
TC j = π + (a + t ) x j and p =a+t;
1 − 1/ σp* =τ ( a + t).
1 − 1/ σ

The tax increases total costs and prices.13 Thus, pure profit of a North-based firm andthe North’s emissions without relocation are given as:⎛s(5) π = ⎜⎝∆+⎛s(6) χ = χ N = ⎜⎝∆φ (1 − s) ⎞ µ (a + t )1−σ µ
= ,
⎟
σ
σ
∆* ⎠
+

φ (1 − s) ⎞∆*⎟(a + t )
⎠

−σ

=

1
,
a+t

where North’s full agglomeration leads to ∆ = a 1−σ and ∆* = φa 1−σ . Note that
taxation without relocation, i.e., without carbon leakage, results in reducing emissions
from 1/a to 1/(a + t).

13

Note that we assume a + t < 1.

11

3.2.

Equilibrium with free relocation

Next, we allow for free firm relocation. Because taxation decreases profits inNorth, firms may have an incentive to move to the non-taxed country, i.e., South,
regardless of a small market size. When tax rates are set at a substantial level suchthat π < π*, i.e., (a + t 1−σ
1− s, full agglomeration is not stable any more and) < φs +φasome firms relocate to South. Firm share, n, is determined so as to equalize pureprofits between countries:(7) π − π * =µ⎛sφ (1 − s ) ⎞µ ⎛ s 1 − s ⎞ 1−σ
1−σ+⎜⎟( a + t ) − ⎜ φ + * ⎟ a = 0 ,*σ ⎝∆σ⎝ ∆ ∆ ⎠∆ ⎠where ∆ = na1−σ + (1 − n)φ (a + t )1−σ and ∆* = nφa 1−σ + (1 − n)(a + t )1−σ .
Figure 1 plots firm share, n, in terms of freeness of trade φ, Given a fixed low
rate of tax, the firm share locus is hump-shaped. Taxation causes international carbon
leakage: firm relocation occurs from North (taxed country) to South (non-taxedcountry). Stated differently, it is necessary to have intermediate levels of trade costs tokeep full agglomeration, φ NL < φ < φ NU , which can be written as:(8) φ NU =(9) φ NL =(a + t )1−σ + (a + t ) 2 (1−σ ) − 4 s(1 − s)a 2 (1−σ )2a 1−σ s(a + t )1−σ − (a + t ) 2(1−σ ) − 4s (1 − s)a 2 (1−σ )2a 1−σ s,.

<Figure 1>

In reverse, given a fixed φ, a low tax can sustain full agglomeration. The condition
for the low tax rate is given as:t ) 2 (1−σ ) − 4s(1 − s )a 2(1−σ ) > 0 ⇔ ~t < a (4s(1 − s ))1 /( 2 (1−σ )) − a . When the tax rate is(a + ~
above ~
t , North never sustains full agglomeration for any trade cost and instead Southis more likely to achieve full agglomeration. Figure 2 illustrates the case of high tax
rates without North’s full agglomeration.

12

<Figure 2>

As shown in Figures 1 and 2, all firms relocate to South with a sufficiently
small trade cost, i.e., perfect carbon leakage. The critical value of trade costs, φ S , isanalytically given by:(10) φ S =a 1−σ + a 2(1−σ ) − 4s(1 − s )(a + t ) 2 (1−σ )2a 1−σ (1 − s ).

As the tax rate, t, rises, the critical value, φ S , decreases and full agglomeration inSouth is more likely to occur. A sufficiently small trade cost coupled with a high tax
rate accelerates international carbon leakage, relocating to the country without
environmental regulation. Note that φ S > φ NU > φ NL is always ensured. φ S is a real
number, because a 2(1−σ ) − 4s (1 − s)(a + t ) 2 (1−σ ) > 0 . We can also verify that φ S isalways larger than φ NU .14
Proposition 2: An emission tax may lead to international carbon leakage.
Full agglomeration in North (taxed country) can be sustained if the tax rate
is low and/or trade costs are intermediate. However, when the tax rate ishigh and/or trade costs are sufficiently small, all North firms move to South(non-taxed country).

Note that the standard FC model (without any taxation) has hump-shaped
agglomeration rents, which is a net benefit from agglomeration (see Baldwin andKrugman, 2004): when trade costs decrease, the rents first rise and then fall. Free
trade has no agglomeration rents. Taxation on the rents reduces the net benefit fromagglomeration. Thus, large or small trade costs lead to a negative net agglomeration
benefit, which causes firm relocation to South.
Turning to emission levels, Figures 3 and 4 plot them for North, South and theworld, which are given by:

14

This is because 4(1 – s)s < 1 for s > 0.5 and a2 (1−σ )13> (a + t ) 2(1−σ ) .

1− s ⎞⎛s+ φ * ⎟(a + t ) −σ ,∆ ⎠⎝∆

χ N = n⎜⎛ s 1 − s ⎞ −σ
+ * ⎟a ,∆ ⎠⎝ ∆χ S = n * ⎜φ⎛s⎝∆

χ = χ N + χ S = n⎜+φ (1 − s ) ⎞∆*⎟( a + t )⎠−σ⎛ s 1− s ⎞+ n * ⎜ φ + * ⎟a −σ ,∆ ⎠⎝ ∆where ∆ = na1−σ + (1 − n)φ (a + t )1−σ and ∆* = nφa 1−σ + (1 − n)(a + t )1−σ .

<Figure 3><Figure 4>

Allowing firm relocation entails more GHG emissions than the target of theinternational agreements, 1/(a + t), because of international carbon leakage when
trade costs are either large or small. That is, when trade costs are either large or small,
North’s emissions fall and South’s emissions rise (Figure 3). The carbon leakage
decreases North’s emissions, which are less than the target, 1/(a + t), and South’s
emissions increase by relocation, and then reach a maximum of 1/a with South’s full⎛ sagglomeration: χ = χ S = n * ⎜ φ⎝ ∆+1 − s ⎞ −σ 1
a = , where ∆ = φ∆* and n* = 1.
* ⎟
a
∆ ⎠

Note that South’s emissions exceed North’s for certain levels of φ. As trade costs fall,
firm relocation decreases n and then, when n <a+t
holds, the South’s emissions
2a + texceed the North’s. Lower tax rates lead to a critical n of 0.5, and higher tax rates
increase the critical n. This means that lowering tax rates can moderate carbon
leakage.
Figure 4 shows global emissions, which are the sum of North’s and South’s
emissions. Because small and large trade costs allow more relocation to the non-taxedcountry, global emissions increase. In particular, above φ S all firms concentrate inSouth and no firms pay tax, and thus the emission level becomes 1/a. Note that this is14

identical to the initial no-policy level. North’s emission policy is nullified and theglobal amount of emissions returns to the initial equilibrium (no environmental
policy). We can say that the only impact of taxation with small trade costs is totransfer GHG emissions from North to South through the relocation of all firms. With
small trade costs, unilateral emission taxation results in perfect carbon leakage (fullagglomeration in South) and taxation cannot control pollution any more.
Proposition 3: With emission taxation, the global emission level is generally
U-shaped in terms of freeness of trade. Emission taxation has no impact on
the global emission level when trade costs are sufficiently small.

4. EMISSION QUOTA
4.1.

Quota without relocation

Now we discuss the other policy, an emission quota. In this case, starting fromfull agglomeration, North unilaterally introduces an emission quota so as to satisfy
international environmental agreements. To make a strict comparison of policy impact
on carbon leakage in the tax case, the quota is set so that the emission level under thequota is the same as that under taxation at the initial equilibrium (North’s full
agglomeration), i.e., χ =1(constant). Moreover, the quota is assumed to bea+t

accompanied by creation of a competitive emission-permit market in North. The
quota is implemented by the North government via a fee. Purchasing one unit of thepermit allows one unit of production for a North firm. Using (6), the level of the quota
is given by:⎛s
1− s ⎞
1
1⎟(a + q ) −σ =+=.
(11) χ = ⎜⎜
1−σ
1−σ ⎟
a+q a+t(a + q ) ⎠⎝ (a + q )Thus, the price of emission permit q is equal to t at full agglomeration (initial
equilibrium), i.e., q = t.
The following should be noted. The price of permit, q, is endogenously
determined by the number of firms located in North and trade costs so as to satisfy⎛sNorth’s emission-permit market clearance, n⎜
⎝∆
15

+

φ (1 − s ) ⎞∆*⎟( a + q )⎠−σ− χ = 0,although tax rates are invariant, exogenously given by international agreements.
( ∆ = na 1−σ + (1 − n)φ (a + q)1−σ and ∆* = nφa 1−σ + (1 − n)(a + q)1−σ ).
This results in different impacts on firm location and emission level. Total
costs and price are written as TC j = π + (a + q) x j , p =a+qτ (a + q)
and p * =.
1 − 1/ σ1 − 1/ σFirm location is determined by profit equalization and the size of the quota.

Equilibrium with free relocation

4.2.

At the equilibrium, n and q are determined by pure profit equalization as wellas the emission constraint:15(12) π − π * =⎛s(13) π = n⎜⎝∆µ⎛sφ (1 − s) ⎞µ ⎛ s 1 − s ⎞ 1−σ
1−σ+⎜⎟( a + q ) − ⎜ φ + * ⎟ a = 0 ,*σ ⎝∆σ⎝ ∆ ∆ ⎠∆ ⎠+φ (1 − s) ⎞∆*⎟( a + q )
⎠

−σ

=χ,

where ∆ = na 1−σ + (1 − n)φ (a + q)1−σ and ∆* = nφa 1−σ + (1 − n)(a + q)1−σ .
Figure 5 plots firm share, n, in terms of freeness of trade, φ. Similarly to taxation,
small or large trade costs lead to firm relocation and international carbon leakage,
while intermediate trade costs can sustain full agglomeration in North.

<Figure 5>

Because we assume that the emission level under a quota is the same as that
under taxation with full agglomeration, q = t and trade costs that result in full
agglomeration are fully equivalent to those under taxation:

15

In our model, the quota is always binding and has a positive permit price. If q is negative or zero,then no firms have an incentive to relocate and full agglomeration is achieved. In addition, the total
emission level is reduced by international regulation and thus the number of permits supplied by thegovernment is less than the quantities produced with full agglomeration. It follows that q should bepositive.

16

(14) φ NU =(15) φ NL =(a + q )1−σ + (a + q ) 2 (1−σ ) − 4s(1 − s )a 2 (1−σ )2a 1−σ s(a + q )1−σ − (a + q ) 2(1−σ ) − 4s(1 − s)a 2(1−σ )2a 1−σ s,.

However, unlike the effect of an emission tax, a quota does not involve South’s full
agglomeration with small trade costs. Some firms stay in North at any trade cost. As
plotted in Figure 6, q is positive for 0 ≤ φ < 1 and hump-shaped. As long as all firms
are in North (full agglomeration) with intermediate trade costs, quota prices equal thevalues of t (= q ). However, when agglomeration rents fall because of small trade
costs, firm relocation to South reduces q, while taxation t remains constant. Firm
relocation to South softens the quota constraint in North. The fall of the permit pricereduces the disadvantage of locating in North and mitigates relocation.

<Figure 6>

Proposition 4: With an emission quota, full agglomeration in North can besustained with intermediate trade costs. However, full agglomeration neveroccurs in South for any positive quota level.

Emission levels are written as:
1− s ⎞1⎛s, (constant)(16) χ N = n⎜ + φ * ⎟(a + q) −σ = χ =
a+t
∆ ⎠
⎝∆
⎛ s 1− s ⎞(17) χ S = n * ⎜ φ + * ⎟a −σ ,∆ ⎠⎝ ∆(18) χ = χ N + χ S =1⎛ s 1− s ⎞+ n * ⎜ φ + * ⎟a −σ .
a+t
∆ ⎠
⎝ ∆

Figures 7 and 8 plot emissions in terms of trade costs. Similarly to the tax case, aquota leads to U-shaped global emissions in terms of trade costs. More generally, inthe case of small/large trade costs, some firms relocate and emit GHGs in South,
although North’s emissions are kept at 1/(a + t) because of the emission constraint.
However, unlike the effect from taxation, global emissions never return to the no17

policy level, 1/a, for any positive trade costs. Because South never creates full
agglomeration and the quota is still binding in North, this diversification of firm
location results in less global emissions than the case without any policy and the caseof taxation.

<Figure 7><Figure 8>

Proposition 5: In the case of an emission quota, North’s GHG emissions arealways kept at the target level of international environmental agreements,
although South increases emissions via international carbon leakage under
trade liberalization.

5. EMISSION TAX VERSUS QUOTA
Here, we make a comparison with two-policy effects on emissions. The only
target of the North government is to implement the international environmental
agreement and reduce North’s local GHG emissions.
The first finding is related to tax rates and the quota price. Becauseinternational agreements allocate a certain amount of GHG emissions to North, χ , tax
rates and the price for the permit in the quota system are all equal (t = q ) as long as
all firms concentrate in North. For this reason, both policies have the same full
agglomeration range: the same levels of φ NL and φ NU . This implies that firm
relocation begins at the same critical trade costs. However, relocation to South causedby environmental regulations results in q being less than t for a givenφ(i.e., t > q)(see Appendix for an analytical derivation). The tax rate is fixed, but the fee for theemission permit is endogenously determined by the number of North firms. As more
firms relocate to South, the emission constraint can be more easily attained and thenthe permit price decreases. Furthermore, when many firms move to South, the permit
price drastically decreases, which hampers firm relocation. To summarize:
18

Proposition 6: The price of the emission permit under a quota is always
lower than the per unit emission tax rate in the presence of relocation.

In other words, we can say that the quota has a weaker relocation effect thantax. As is clear in Figure 9, carbon leakage is moderate under the quota. Because tax
has a stronger relocation effect, it always leads to more carbon leakage and full
agglomeration in South.

<Figure 9>

Turning to global emissions, this implies that the emission in North is larger
with a quota than with taxation for any φ (see Appendix for derivation).

<Figure 10>

Proposition 7: The GHG emission level in North is higher with quota thanwith tax policy in the presence of relocation. Compared with taxation, aquota can mitigate international carbon leakage.

This suggests that if North seeks to reduce only the local emissions to satisfy
the international environmental agreements, North prefers taxation to a quota withsmall trade costs. While a quota keeps some firms in North, taxation with tradeliberalization can force all firms to South and thus North has no firms to emit GHGs,
perfectly satisfying international agreements. Then, North will import manufactured
goods from the fully agglomerated South with small trade costs.16 Accordingly, Northwill take taxation with pro-trade liberalization.
However, from a global viewpoint such an egoistic attitude by North may not
be acceptable. Regarding global emissions, as long as firms are allowed to relocate

16Note that South still has agriculture. Because our model adopts a quasi-linear utility function to

exclude any income effect and we assume that each consumer holds capital and labour, the expenditureon M-goods is not so high as to induce complete specialization in M-sector in the South.

19freely, international carbon leakage could be larger than the reduction in GHGs in
North. In particular, tax policy returns to the pre-agreement global emission level. For
this reason, with free relocation and small trade costs because of trade liberalization, aquota is a better policy scheme for reducing global emissions. A quota has a weaker
impact on firm relocation. The quota system could be more effective and make theemission level closer to the global target, although not only tax but also the quota
results in more global emissions than the target as long as some firms locate in Southand trade liberalization proceeds.
Proposition 8: An emission quota is a better policy scheme than an emission
tax in the sense of it being a more stringent constraint on global emissions
under free relocation with small trade costs.

6. GLOBAL EMISSIONS,ENVIRONMENTAL AGREEMENTS AND
TRADE LIBERALIZATIONFree relocation with small trade costs mitigates the effect of environmental
policy and consequently the global level of emissions is higher than the level
determined by international agreements. Now, we study what sorts of policies andagreements can properly control global GHG emissions as expected by international
agreements while accommodating international free relocation. One solution may be
to choose the combination of environmental tax rates as well as trade costs byinternational agreement.
Here, we keep the situation where only North ratifies international
environmental agreements. The policy stems from the outcomes so far. Given theinternational environmental agreement on total emissions χ = 1/(a + t), it isnecessary to prevent firm relocation and keep full agglomeration in North. To do so,
tax rates and trade costs should be in the shaded area in Figure 11: intermediate trade
costs and low tax rate.

<Figure 11>20

When any combination of both the tax rate and trade costs in the shaded area
is set up by international agreements and international organizations, the target levelof global emissions in international environmental agreements can be achieved. Tosummarize:
Proposition 9: When only North ratifies environmental agreements, itneeds to keep intermediate trade costs and levy a small environmental tax
to prevent international carbon leakage and achieve the target level ofglobal emissions in international agreements.

This result yields an important insight that, when the environmental
agreements are ratified only by North, the degree of North’s environmental policy
may be restricted by trade liberalization and vice versa. Free firm relocation entails a
trade-off between trade liberalization and environmental regulation.
Next, as another possibility, we consider the situation where both countries
ratify the international environmental agreements. If South ratifies an international
environmental agreement, things would be much easier. When global warming
becomes serious, South may have an incentive to ratify agreements so as to prevent
firm relocation from North. When the emission tax rates are the same across countries,
firms prefer to stay in the bigger market, North, and no firms locate to South.
Therefore, in this case the target level of global emissions can be achieved for any
trade cost: χ = 1/(a + t). It is necessary that international agreements specify thetarget level of emissions as well as the internationally levied tax rate. The common
tax rate is the key to the implementation. In this case, trade liberalization is nothampered by environmental policy, because there is no international carbon leakage.
If both countries ratify the agreement, global GHG emissions could be reduced
below the target, χ < χ = 1/(a + t). In addition to the given global target, χ = 1/(a+ t), international agreements state that tax rate, t, is a lower bound and allows for ahigher tax rate on the condition that full agglomeration can be kept in North.17 When17

If North imposes a sufficiently high rate of environmental tax, firms relocate to South (laxenvironment country) and emission increases because of the emission haven effect as discussed inprevious sections. Here, we assume that a marginal tax rate is allowed so as to promote the reduction of
local emissions but to prevent an emission haven.

21North suffers large damage from global warming, North will have an incentive to set
a tax rate higher than t by υ (i.e., υ + t). This tax rate is defined by:(199) (a + t + υ )1−σ=(φ 2 s + 1 − s )(a + t )1−σφ

⎛ ⎛ φ 2 s + 1 − s ⎞1 /(1−σ ) ⎞⎟⎟− 1⎟ ( a + t ) .
⇔ υ = ⎜ ⎜⎜
⎜⎝
⎟
φ
⎠
⎝
⎠

When freeness of trade is (1 – s)/s or 1, the additional tax rate υ is zero. Otherwise, υis strictly positive. υ is hump-shaped with respect to freeness of trade. As shown in
Figure 12, North’s (equivalently global) emission level is U-shaped. With positive
trade costs, the emission level could be less than χ .

<Figure 12>

Proposition 10: If international agreements voluntarily impose a more stringent(local) emission tax and if environmental damage in North is large, North has anincentive to set higher tax rates, which could make GHG emissions lower than
the target in the international agreements.

7. CONCLUSION
This paper studied the impact of environmental policies on firm location andcarbon leakage when international agreements such as the Kyoto Protocol require theratified countries to reduce emissions by a certain amount. We have compared twoenvironmental policy tools, emission tax and quota, under trade liberalization.
We have found the following. 1) When trade costs are small, either
environmental policy leads firms to relocate to a country without any environmental
regulation, which causes international carbon leakage. Thus, either environmental
policy causes carbon leakage with free trade and free relocations. 2) An emission tax
results in more firm relocation than a quota. Thus, an emission tax causes morecarbon leakage, increasing global emissions. If North is concerned with only local
emissions, a tax is adopted to attain the reduction target. On the other hand, if North isconcerned with global emissions, a quota is preferred. Thus, a quota is a better policy
22tool to cope with global warming. 3) Trade liberalization and environmental policies
are a trade-off when environmental agreements are unilateral. Trade liberalization
may hamper international environmental agreements. Under certain combinations oftax rates and trade costs, a target reduction in global GHG emissions can be attained.
Our paper is the first step in exploring the relationship between tradeliberalization and environmental policies in the presence of firm relocation. This
paper has some limitations. For example, the policy target in this paper is to reduce
GHG emissions to highlight the different policy effects of a tax and a quota. Of course,
it is plausible to think that governments maximize social welfare. Welfare analysis
and socially optimal policies are a subject for future research. Because our model
assumes one unit of emission per unit of quantity produced, production and emissions
are subject to a perfect trade-off: more production (consumption) positively affects
welfare but simultaneously has a negative effect through increased emissions. Theremight exist an optimal level of emissions and production, which hinges on thespecification of a social welfare function. To conduct welfare analysis formally, we
have to specify disutility in the utility function more rigorously, taking into accounttrans-boundary/local emissions and accumulation of emissions over time.
Furthermore, it might be worthwhile considering the negative impact of emissions on
A-sector productivity. A-sector might be subject to decreasing returns to scale byserious emissions. Future research should conduct a more rigorous analysis on theinternational environmental agreements and negotiation in Section 6 by using gametheory.
Moreover, we have assumed a quasi-linear utility function that excludes anincome effect. The total demand for manufactured goods remains constant even if
firms relocate and prices change through the absence of taxation or a quota in South.
The constant total demand implies constant total production and hence the global
emission level without any environmental policy is independent of trade costs. Thishas the advantage of highlighting the different effects of the two policies. We can get
analytical solutions allowing us to easily compare the relocation effects of a tax and aquota. Furthermore, even if we take into account tax/quota revenue reimbursement,

23

because we can ignore its impact, we can focus on the effects of each policy scheme
just on firm location and carbon leakage.18

APPENDIX: QUOTA PRICE AND TAX RATE
Here, we mathematically show the relationship between tax and quota policies
using analytical solutions. North’s emissions without relocation, which are the target
of international agreements, are denoted as:(A1) χ Ninitial =⎛s
11− s ⎞= ⎜⎜ + φ * ⎟⎟(a + t ) −σ ,a+t ⎝∆∆ ⎠*where ∆ = (a + t )1−σ and ∆ = φ ∆ . As mentioned in the main text, this target level ofemissions always corresponds to that of the quota case, regardless of
relocation: χ NQ = χ Ninitial =1
1. Note that at an initial equilibrium (full=a+t a+q

agglomeration without allowing for relocation), q is equal to t ( q = t ).
Next, allowing for relocation, North’s emissions under tax policy can be
written as:
1− s ⎞⎛s(A2) χ NT = n⎜ + φ * ⎟(a + t ) −σ ,∆ ⎠⎝∆where tax rate t is fixed. We compare (A1) and (A2):∆
1 − n 1−σ= (a + t )1−σ +φa ≥ ∆ = (a + t )1−σ ,nn∆*
1 − n 1−σ= φ (a + t )1−σ +a ≥ ∆* = φ (a + t )1−σ .
nn18However, it is certainly worthwhile examining the robustness of our results in the presence of an

income effect. The presence of an income effect caused by relocation may cause a complete
specialization in manufacturing (agriculture) in South (North), though it is an extreme and unrealistic
case. Agriculture is not the numéraire any more and factor prices are determined by the trade balance
and factor markets. In this case, market size and factor prices may determine emission levels.

24

Therefore, North’s emission level under a quota is higher than under a tax for any
trade costs, χ NQ ≥ χ NT .
Turning to q, because North’s emissions are always identical to the target in
the international agreements, by keeping a constant emission level through adjusting
quota prices, North’s emissions under free relocation are binding (13).

χN =11− s ⎞⎛s= n⎜ + φ * ⎟(a + q) −σ
a+t
∆ ⎠
⎝∆

The quota market clearance condition can be rewritten as:
⎛
⎞
⎜
⎟
s
1− s
1
⎜
⎟
+
= 0.
−⎜
1−σ
1−σ ⎟
a+t
φ (1 − n)a(1 − n)a⎜⎜ (a + q ) +⎟(a + q) +n(a + q) −σnφ (a + q ) −σ ⎟⎠⎝To satisfy the condition, we need q ≤ t because

φ (1 − n)a 1−σn(a + q ) −σ

≥ 0 and(1 − n)a 1−σ≥ 0 . Therefore, we show that an endogenously determined quota price isφn(a + q ) −σ
always less than the tax rate, given the same emission target in North.

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27

n

1

n=0
(1-s)/s

φ NL
Full Agglomerationin North

φ NU φS

φ
1

Full Agglomeration
in SouthFigure 1: Tax and Firm Share

n

1

n=0
(1-s)/s

φS

φ1

Figure 2: Tax and Firm Share (high tax rates)1χN, χS
1/a

North
χ=

South

1
a+t

n=0
(1-s)/s

φ NL

φ NU

Full agglomerationin northφS

1

φ

Full agglomeration
in southFigure 3: Local Emission Levels

χ
1/a

χ=

1
a+t

0

φ NL

φ NU

(1-s)/sFull agglomerationin northφS

φ
1

Full agglomeration
in southFigure 4: Global Emissions (Tax)

2

n

1

n=0

φ NL

(1-s)/s

φ

φ NU

1

Full Agglomerationin north

Figure 5: Quota and Firm Share

q

q

q=0
(1-s)/s

φ NL

φ NS

φ
1

Full agglomerationin north

Figure 6: Quota Prices

3χN, χS
1/a
North
χ=

1
a+q

South

φ NL

(1-s)/s

φ NS

φ1

Full agglomerationin north

Figure 7: Local Emission Levels (quota)

χ

Non-restriction 1/a

Quota χ =1a+q

0(1-s)/s

φ NL

φ NU

φ
1

Full agglomerationin north

Figure 8: Global Emissions (quota)

4

n
quota

1

tax

n=0

φ NL

φ NU

φ

φS

1

(1-s)/sFull agglomerationin north

Full agglomeration
in southFigure 9: Firm Share (Tax and Quota)

χ
tax
1/a
quota
χ=

1
1
=
a+t a+q

φ NL(1-s)/s

φ NU

φS

φ
1

Full agglomeration Full agglomerationin northin southFigure 10: Global Emissions
with Tax and Quota

5t
The set of policy variables

φ NL

φ NU

φ
1

(1-s)/s

Figure 11: Trade Liberalization and Tax

χ
χ=

1
a+t

φ
1
(1-s)/s

Figure 12: Emissions and Voluntary Tax

6