Discussion Papers In Economics
And Business

Ecological dumping under foreign investment
quotasYasuyuki Sugiyama and Muneyuki Saito

Discussion Paper 08-31

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANEcological dumping under foreign investment
quotasYasuyuki Sugiyama and Muneyuki Saito

Discussion Paper 08-31

September 2008

この研究は「大学院経済学研究科・経済学部記念事業」
基金より援助を受けた、記して感謝する。

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANEcological dumping under foreign investment
quotas *Yasuyuki Sugiyama † and Muneyuki Saito ‡Abstract
In this paper, we examine the discrimination of emission taxes between the export andnontradable sectors in a small country. A few articles indicate that there should be
no differentiation of environmental policies between sectors in a small country if thegovernment uses indirect instruments as emission taxes. However, we show that thediscrimination of emission taxes may occur in a small country that imposes foreign
investment quotas. In particular, the possibility that ecological dumping occurs ishigher if export goods are more labor intensive than import goods, as in developing
countries. Moreover, in the case where imported goods are most capital intensive, bothemission tax rates may be lower than marginal environmental damage, and ecologicaldumping may occur. It is also shown that easing foreign capital quotas may deteriorate
the small country’s welfare.
Key words: ecological dumping, emission tax, nontraded goods, international

trade, capital movement
JEL classification: F18, F20* Acknowledgment: We are indebted to Kenzo Abe for advice and encouragement. We
also wish to thank Katsuhiko Suzuki, Akihiko Yanase, and Laixun Zhao for their helpful andconstructive comments.
† Graduate School of Economics, Osaka University, 1-7 Machikaneyama, Toyonaka, Osaka
560-0043, Japan. E-mail: jk802sy@srv.econ.osaka-u.ac.jp‡ Graduate School of Economics, Osaka University, 1-7 Machikaneyama, Toyonaka, Osaka
560-0043, Japan. E-mail: bg063sm@srv.econ.osaka-u.ac.jp

1

Introduction

Environmental preservation is an important contemporary issue, and many
countries are attempting to develop institutional design and policies to deal
with this issue. However, environmental preservation is difficult in countries
that place high priority on economic growth, because such countries are concerned about the decline in the international competitiveness of domestic firms.
Thus, the government in such countries may impose lax environmental regulations on firms so that they are able to retain their competitiveness. Thissituation is characterized by the term “ecological dumping”.
Definitions of ecological dumping are given in Rauscher (1994, 1997, Ch.2).
For example, Rauscher (1997, Ch.2) defines dumping as “an environmental legislation that does not fully internalize the domestic social cost of pollution and,
thereby gives domestic producers an advantage in international markets”. Moreover, Rauscher (1994, 1997, Ch.2) proposes the utilization of nontradable goods
as a criterion to evaluate ecological dumping, because trade-related measures ofenvironmental policy are primarily targeted at the sectors that produce traded
goods. In such a case, ecological dumping is defined as “the discrimination of
the nontraded goods sectors against the exporting sectors in terms of higher
pollution-abatement requirements for the same pollutants”. 1
According to the latter definition, Rauscher (1994, 1997, Ch.5) shows thatwhether the government pursues differentiation of environmental policies between these sectors depends on how the country’s terms of trade are affected bythese policies. Hence, the government does not have an incentive to differentiate
environmental policy between the export and nontradable sectors in the case ofa small country, because the distortions other than environmental externalities
do not exist in this economy. However, this discussion may be modified if other

1 As denoted in Rauscher (1994, 1997, Ch.2), the government must implement a sectorspecific environmental policy to enable dumping. Actual examples of differential tax systems
are offered by the OECD (2001). In addition, refer to Hoel (1996) for differentiation of carbon
taxes across production sectors, and see Richter and Schneider (2003) about the discriminationof energy taxes between households and the production sector.

1

distortions exist. 2 In fact, while allowance of foreign capital inflows progresses
gradually through negotiations with international groups such as the World
Trade Organization, both developed and developing countries still regulate investment from abroad or impose trade-related investment measures (TRIMs)
in order to protect domestic industries. Therefore, we need to investigate how
environmental policy should be implemented in the case where not only external
diseconomies from pollution emissions exist but also where distortions causedby regulation against foreign capital inflows are present.
In the case of a small open economy, Beladi, Chao, and Frasca (1999) examine the welfare effects of foreign investment quotas in addition to emission
taxes. 3 If foreign investment quotas are implemented, the optimal emission
tax rate is higher than the marginal environmental damage because an increasein the emission tax reduces the rate of return on capital, and, thus, the payments to foreign capital owners are decreased. Meanwhile, an easing of foreign
investment quotas does not change the rate of capital return and accelerates thedischarge of pollutants. Then, if the emission tax is higher than the marginal
damage, the lax quotas improve the country’s welfare because pollution tax revenue is increased. However, their research does not involve nontraded goods;
thus, whether differentiation of emission taxes between export and nontraded
goods sectors is optimal has not been revealed.
On the other hand, Schneider and Wellisch (1997) apply Rauscher’s discussion to the case of a small country with international capital movement, andshow that, if the country’s government regulates the aggregate level of pollution emissions in each sector, then allocates its permits to firms according totheir capital employment, then such direct controls that achieve social welfare
maximization may be differentiated in the case of the opposite of ecological
2 Many researchers have examined the effects of environmental policies in models involving pollution and trade distortions, for instance, Copeland (1994), Ulph (1997), and Neary(2006). While Copeland (1994) considers gradual policy reforms, Ulph (1997) and Neary(2006) demonstrate that, in view of the optimal policy, environmental policies deviate fromthe first-best policy if trade taxes cannot be removed, and that free trade may not be executed
if first-best environmental policies are absent.
3 See Rauscher (1997, Ch.3) and Chao and Yu (1998) for the economic and environmental
impacts of a tax on foreign capital.

2

dumping between the export and nontraded goods sectors. However, in contrast to the direct controls, environmental rents do not accrue to producers if
the small country’s government uses price instruments such as emission taxes.
Thus, even according to Schneider and Wellisch (1997), it is not optimal thatthe government discriminates the tax rates between these sectors as in Rauscher(1994, 1997, Ch.5). 4
In this paper, we investigate whether ecological dumping can arise in a model
involving foreign investment quotas, and examine the welfare effect of the quotas. 5 Our model generalizes those of Rauscher (1994, 1997, Ch.5) and Schneider
and Wellisch (1997) in that not only are export and nontraded goods produced
and consumed in the country, but also imported goods. Then, we show that,unless foreign capital inflows are zero, either ecological dumping or the opposite
of ecological dumping may take place even if the host country’s government uses
emission taxes. In particular, we derive the following results. First, the possibility that ecological dumping occurs is higher if the export sector is more labor
intensive than the import sector, such as in developing countries. Moreover, inthe case where the import sector is most capital intensive, both optimal emission
tax rates may be lower than the marginal damage, and the emission tax rate on
the nontradable sector may be higher than that on the export sector. Secondly,
the opposite of ecological dumping can occur if the export sector is more capital intensive than the import sector, such as in developed countries. However,in the case where the import sector is most labor intensive, both emission tax
rates are higher than the marginal damage, and the emission tax rate on the
nontradable sector may be higher than that on the export sector. Thirdly, a
relaxation of foreign investment quotas may reduce the small country’s welfare.
4 Recently, Withagen et al. (2007) examined whether preferential treatment of the export sector is optimal under several market structures. They introduce an upper bound on
emissions, and assume that the target corresponding to the upper bound is implemented byemission taxes. Their model is discriminative in that ‘n’ varieties are produced in the export
sector. However, ecological dumping still does not occur in the case of a small country.
5 We assume perfectly competitive markets throughout this paper. For the analysis ofimperfect competitive markets, refer to, e.g., Walz and Wellisch (1997), Ulph and Valentini(2001), and Greaker (2003) for the case of oligopoly in addition to Withagen et al. (2007)
cited above, and see Pflüger (2001) for the case of monopolistic competition.

3

The paper is organized as follows. Below, we reconsider the definition of
ecological dumping to clarify the subsequent discussion. Section 2 presents theframework of our model. Section 3 obtains some comparative static resultswith respect to emission taxes. In Section 4, we derive the combination of
optimal emission taxes levied against the export and nontraded goods sectors,
then analyze whether each of the jointly optimal emission tax rates is higher orlower than the marginal environmental damage. We analyze the effect of easing
foreign investment quotas on a nation’s welfare in Section 5. The final section
gives concluding remarks.
Definition of ecological dumping
As shown in Rauscher (1994, 1997, Ch.2), ecological dumping occurs whenenvironmental policies are less strict in the tradable goods sector than in the nontradable goods sector. We can easily confirm the direction of the discrimination
if either of the environmental taxes is higher than the marginal environmental
damage, and the other is lower than the damage. However, in our general model,
it is possible that both emission taxes imposed on the export and nontradable
sectors are higher or lower than the marginal environmental damage, and thesetax rates are discriminated. Hence, by elaborating the definitions of Rauscher(1994, 1997, Ch.2), we redefine ecological dumping in a model involving thenontraded goods sector as follows.
Definition 1: Strong ecological dumping
Strong ecological dumping means that the emission tax of the export sector islower than the marginal damage and that of the nontradable sector is higher.
Definition 2: Weak ecological dumping:
Weak ecological dumping means that both emission taxes are either lower orhigher than the marginal damage, and the emission tax of the export sector islower than that of the nontradable sector.

4

2

The model

We consider a small open economy. Three types of final goods are produced in
the economy, and one of them is a nontraded good. 6 Production in each sector
is assumed to exhibit constant returns to scale. We represent the productionof an imported good, an exported good, and a nontraded good as y0 , y1 , andy2 , respectively. 7 The economy is endowed with labor (¯l) and capital (k̄) as
primary factors of production, which are supplied inelastically. We assume that
capital inflows from abroad are regulated by foreign investment quotas. Then,if we denote the restricted level of capital inflows as k ∗ , then the total supplyof capital in the economy is k̄ + k ∗ .
Pollution is generated as a by-product in the production processes of theexported and nontraded goods, and only has an effect within the country. We
denote pollution emissions as zI (I = 1, 2). Emissions of each sector are associated with their own output. We describe the relation as zI = ei yI , where eI
is pollution emissions per unit of output and is assumed to be constant. The
total amount of pollution (z) with which the country is confronted is written
as the sum of each sector’s emissions (z = z1 + z2 ). The government imposesemission taxes. We denote the tax rates imposed on the export and nontradable
sectors by t and τ , respectively. The revenue from these taxes is redistributed
in a lump-sum fashion to consumers.
We assume a representative consumer whose utility function is quasilinear.
The utility function is additively separable with respect to pollution damage
and consumption of each good. Namely, it is written by u = x0 + u1 (x1 ) +u2 (x2 ) − φ(z), where xI (I = 0, 1, 2) is the consumption level of I good, and uIis the utility function received from the consumption of I good. Moreover, thesubutility function uI (xI ) is continuously differentiable, increasing, and strictly
concave. The damage function φ(z) is continuously differentiable, increasing,and strictly convex. We represent the relative price of the exported good as p
6 For example, see Komiya (1967) for the role of nontraded goods in international trade

theory.
7 In the following analysis, we designate the imported good as the numeraire.

5and the price of the nontraded good as q. Hence, the minimum expenditure
function is defined as:E(p, q, z, u) ≡ min {px1 + qx2 + u + φ(z) − u1 (x1 ) − u2 (x2 )}.
x1 ,x2(1)

If the expenditure function is continuously twice differentiable, the first- andsecond-order derivatives for the function have the following properties: 8
Ep = h1 (p), Eq = h2 (q), Eu = 1, Ez = φ0 (z),Epp = h01 (p) < 0, Eqq = h02 (q) < 0, Ezz = φ00 (z) > 0,
where h1 (p) and h2 (q) are compensated demand functions for the exported andnontraded goods, respectively. 9 All of the other second-order derivatives are
zero except for Epp , Eqq , and Ezz .
Noticing the assumptions of a small country and constant returns-to-scaletechnology, the zero-profit conditions are expressed as:
1 = c0 (w, r),(2)

p = c1 (w, r) + te1 ,(3)

q = c2 (w, r) + τ e2 ,(4)where cI is the unit cost function with respect to labor and capital in the i-th
sector, w is the wage rate, and r is the domestic rental rate.
The factor market equilibrium conditions for labor and capital are:¯l = c0 (w, r)y0 + c1 (w, r)y1 + c2 (w, r)y2 ,
w
w
w

(5)

k̄ + k ∗ = c0r (w, r)y0 + c1r (w, r)y1 + c2r (w, r)y2 ,(6)where cIj (I = 0, 1, 2, j = w, r) is the partial derivative of the unit cost functions
with respect to factor prices, and denotes the factor requirements for producing
a unit of the i-th good from Shepard’s lemma. In addition, the market clearing
8 Throughout the paper the subscripts on expenditure, unit cost, and the GDP functions
represent the partial derivative with respect to the corresponding variables.
9 The compensated demand function accords with an ordinary demand function because
we assume a quasilinear utility function.

6

condition for the nontraded good, and the total amount of pollution in the
country are written as follows:y2 = h2 (q),(7)

z = e1 y1 + e2 y2 .

(8)Note that the nontraded good’s demand does not depend directly on the utility
level and the pollution damage under our assumption.
There are seven endogenous variables, w, r, q, y0 , y1 , y2 , and z from (2)to (8). In the next section, we confirm the effects of emission taxes t and τon these variables, and thereafter examine the welfare effects of the taxes andderive the conditions arising from the ecological dumping or the opposite of
ecological dumping.

3

Preliminaries

3.1

Prices of labor, capital, and a nontraded goodFirst of all, we consider the influences of the emission tax imposed on the export sector on the prices of labor, capital, and the nontraded good. The total
derivatives of (2) and (3) yield:
·

c0w
c1w

c0r
c1r

¸·

dw
dr

¸

·
=

0
−e1

¸
dt,

(9)

where the determinant of the coefficient matrix (|A|) in (9) is given by:|A| ≡ c0w c1r − c0r c1w = c0w c1w (κ1 − κ0 ).

(10)

On the right-hand side of (10), κI denotes the capital–labor ratio in each sector,
and is defined by κI ≡ cIr /cIw . The sign of the determinant depends on thefactor intensity of the import and export sectors. If κ0 > (<)κ1 , the sign of |A|
is negative (positive).
The effects of t on w and r are as follows:
wt ≡ dw/dt = |A|−1 e1 c0r , rt ≡ dr/dt = −|A|−1 e1 c0w .

7

(11)

A rise in the emission tax rate on the export sector decreases the return to thefactor that is intensively used in the export sector and increases the return tothe factor that the import sector intensively uses. That is, if κ0 > (<)κ1 , we
get wt < (>)0 and rt > (<)0.
Next, considering (11), the change of the nontraded good’s price is derived
from (4):qt ≡ dq/dt = |A|−1 e1 c0w c2w (κ0 − κ2 ).

(12)Thus, it is clear that the effect of a rise in t on q depends on the order of factor
intensities between the three sectors. We can classify the effect on the nontraded
good’s price as follows:(
qt > 0 if(
qt < 0 if

condition (Ia) : κ2 > κ0 > κ1 ,condition (Ib) : κ2 < κ0 < κ1 ,(13)

condition (IIa) : κ0 > κ1 and κ2 ,condition (IIb) : κ0 < κ1 and κ2 ,(14)

where ‘a’ and ‘b’ in these conditions represent the classification based on thefactor intensity of the import and export sectors: ‘a’ denotes that κ0 > κ1 and‘b’ that κ0 < κ1 .
In the case of condition (Ia) (condition (Ib)), we get wt < (>)0 and rt > (<)0
from (11). In addition, the nontraded goods sector is more capital intensive(labor intensive) than the import sector. Thus, the unit cost in the nontraded
goods sector rises because of an increase in the return to the factor intensively
used in the nontradable sector, which then increases the nontraded good’s price.
Alternatively, suppose that condition (IIa) (condition (IIb)) is satisfied so that
we obtain wt > (<)0 and rt < (>)0, and the nontradable sector is more capitalintensive (labor intensive) than the import sector. Hence, we can show thata decrease in the return to the factor that is used in the nontradable sector
reduces the unit cost in the nontradable sector, and reduces the price.
On the other hand, the effects of the emission tax in the nontradable sector
are very clear. From (2) and (3), we can confirm that the emission tax does notchange factor prices (dw/dτ = dr/dτ = 0). Then, the influence on the price of8the nontraded good is derived from (4):dq/dτ = e2 > 0.

(15)

With regards to payments to foreign capital, (11) indicates that a rise in theemission tax rate on the export sector increases the payment, while an increasein the emission tax on the nontraded goods sector does not influence the rental
rate of capital from (15).

3.2

Outputs of exported and nontraded Goods

Secondly, we consider the effects of emission taxes on output in each sector.
Noticing that the price of the nontraded good varies with the emission taxes,
from (7), the change in y2 is given as:
dy2 /dj = h02 (dq/dj), j = t, τ.

(16)

The emission tax on the nontraded goods sector definitely decreases this
sector’s output (dy2 /dτ = h02 e2 < 0). On the other hand, an increase in theemission tax on the export sector affects the output of the nontraded good
through a change in the good’s price. Noticing h02 < 0 and the conditions forthe sign of qt given in (13) and (14), we can classify the sign of dy2 /dt as follows:
dy2 /dt < 0

if condition (Ia) or condition (Ib),(17)

dy2 /dt > 0

if condition (IIa) or condition (IIb).

(18)

The demand for the nontraded good decreases (increases) if qt > (<)0, and,thus, output of the nontraded good also decreases (increases).
Next, let us examine the effects of emission taxes and easing foreign investment quotas on the production of an export good. Totally differentiating (5)and (6), we get the following simultaneous equation: 10
·

c0w
c0r

c1w
c1r

¸·

dy0
dy1

¸

·
=

δl
δk

¸

·
dt − h02 e2

c2w
c2r

¸

·
dτ +

0
1

¸
dk ∗ ,(19)

10 To simplify the notation, we define the partial derivatives of w, r, and q with respect toj (j = t, τ ) as wj , rj , and qj , respectively.

9where δ l and δ k are defined by:δ l ≡ −(Σi cIww yI )wt − (Σi cIwr yI )rt − h02 c2w qt ,
δ k ≡ −(Σi cIrw yI )wt − (Σi cIrr yI )rt − h02 c2r qt .
Thus, the influence of emission taxes on the output of the export good are
written as:
dy1 /dt = |A|−2 e1 {h02 (c0w )2 (c2w )2 (κ0 − κ2 )2 − (c0r Ωl + c0w Ωk )} < 0,(20)

dy1 /dτ = |A|−1 h02 e2 c0w c2w (κ0 − κ2 ),(21)

where Ωl and Ωk are defined as follows:Ωl ≡ c0w (Σi cIwr yI ) − c0r (Σi cIww yI ) > 0,
Ωk ≡ c0r (Σi cIrw yI ) − c0w (Σi cIrr yI ) > 0.
The signs of Ωl and Ωk follow from the well-known properties of the unit costfunction.
We can confirm that the emission tax on the export sector definitely decreases this sector’s output from (20). On the other hand, considering that theemission tax on the nontraded good’s sector raises this good’s price, we find thatthe effect of the emission tax on the export sector depends on the capital–laborratio between the three sectors. Hence, utilizing the above conditions, we canclassify the effects of the emission tax on the exported products as follows:
dy1 /dτ < 0

if condition (Ia) or condition (Ib),(22)

dy1 /dτ > 0

if condition (IIa) or condition (IIb).

(23)

Next, we investigate the effect of the easing of foreign investment quotas.
In our model, the quotas do not change the prices of the nontraded good andproduction factor, and therefore production of the nontraded good is constant.
Considering these points, the effect of a relaxation of the quotas prices on the
production of the exported goods results in the following:dy1 /dk ∗ > (<)010

if κ1 > (<) κ0 .

(24)

That is, the export sector expands if the export sector is more capital intensive
than the import sector. This result is known as the Rybczynski effect. The
relaxing of foreign investment quotas influences only the outputs of the export
and import sectors.
Finally, by using these comparative static results about the output of eachsector, we can verify whether emission taxes and foreign investment quotas
reduce pollution emissions. In our model, because emissions per unit of output
are fixed, it is simply given as:zij ≡ dzI /dj = ei dyI /dj, (I = 1, 2, j = t, τ, k ∗ ).

4

(25)

Jointly optimal emission taxes

In this section, we analyze the welfare effects of emission taxes and whether
ecological dumping actually occurs or not.
Considering the expenditure function, the budget constraint of the country
is written as:
E(p, q, z, u) = y0 + p̃y1 + q̃y2 + tz1 + τ z2 − rk ∗ ,(26)

where p̃ ≡ p − te1 , q̃ ≡ q − τ e2 . Then, the effects of emission taxes on domestic
welfare are expressed as:
du/dt = (t − Ez )z1t + (τ − Ez )z2t − k ∗ rt ,(27)

du/dτ = (t − Ez )z1τ + (τ − Ez )z2τ .

(28)(27) and (28) show that the country confronts two kinds of distortions, that is,external diseconomies generated from each sector, and the deviation of the rental
rate between domestic and world capital markets caused by foreign investment
quotas. Noting that the level of the quotas is positive and constant, the government might use the emission taxes on the export sector in order to decrease thepayment to foreign capital, because the emission tax on the nontradable sector
cannot affect the rental rate.

11

Next, we derive the combination of optimal emission taxes (t∗ , τ ∗ ) for which
du/dt = du/τ = 0 are satisfied, and show that the optimal level of these taxes
is not equal even if a small country’s government uses a price instrument suchas an emission tax. We obtain the following simultaneous equations from (27)and (28):
·

z1t
z1τ

z2t
z2τ

¸·

t
τ

¸

·
=

k ∗ rt + Ez (z1t + z2t )Ez (z1τ + z2τ )

¸
,

(29)

where rt and zij (I = 1, 2, j = t, τ ) have already been given in (11) and (25),respectively.
We represent the determinant of the coefficient matrix in (29) as |B|. Considering zij , substituting (16), (20), and (21) into (25), |B| is written as:|B| = z1t z2τ − z1τ z2t = −|A|−2 h02 (e1 e2 )2 (c0r Ωl + c0w Ωk ) > 0.
The sign of |B| is positive despite the order of the factor intensities between thethree sectors. Then, jointly the optimal emission tax rates are expressed as:t∗ = Ez + |B|−1 k ∗ rt z2τ = Ez − |A|−1 |B|−1 k ∗ h02 e1 e22 c0w ,(30)

τ ∗ = Ez − |B|−1 k ∗ rt z1τ = Ez + |A|−2 |B|−1 k ∗ h02 e21 e2 (c0w )2 c2w (κ0 − κ2 ). (31)
From (30) and (31), we confirm that, as long as the foreign capital inflow is
not zero, the optimal emission tax of each sector should differ from the marginal
damage caused by domestic pollution emissions.
In the following subsection, considering the influences of emission taxes on
outputs of exported and nontraded goods depends on conditions (Ia), (Ib), (IIa),and (IIb), we classify the conditions into κ0 > (<)κ1 according to the capital–
labor ratio of import and export sectors, and concretely examine the discrimination of emission taxes under the conditions.

4.1

The case where an import sector is more capital intensive than an export sector (κ0 > κ1 )At the beginning, we consider the case (Ia). If condition (Ia), that is κ2 > κ0 >
κ1 is satisfied, the direction of the differentiation of optimal emission taxes is
12

t The case of ecological dumping
45o

Ez

A
B

t∗

0

Ez

τ∗

t = t0 (τ )τ
τ = τ 0 (t)Figure 1: Jointly optimal emission taxes under condition (Ia)clear. Noticing h02 < 0, the emission tax on the export sector depends on thesign of |A|, and therefore the sign of κ1 − κ0 . If we assume κ0 > κ1 , the optimallevel of the tax is lower than the marginal damage. That is, t∗ < Ez . On theother hand, the emission tax on the nontraded goods sector depends on thesign of κ0 − κ2 , so that the optimal level is higher than the marginal damage if
κ0 < κ2 . That is, τ ∗ > Ez .
The following proposition summarizes the argument concerning ecologicaldumping under condition (Ia).
Proposition 1: Suppose that the emission tax rates on the export and nontraded
goods sectors are jointly chosen to maximize domestic welfare. Then, strong
ecological dumping occurs under condition (Ia).
The diagram is useful to instinctively comprehend the patterns of the discrimination in optimal emission tax rates.
Setting du/dt = 0 in (27), we can derive the optimal tax rate on the export
sector given the nonoptimal emission tax rate on the nontradable sector. We
represent this relation as t = t0 (τ ). In the same way, we can obtain τ = τ 0 (t)by setting du/dτ = 0 in (28). As shown in Figure 1, we can draw t0 and τ 0schedules in the (t, τ ) space. From (27) and (28), the slopes of these schedules

13depend on the effects of the emission taxes on the production of export andnontraded goods, and the associated emissions discharged from these sectors.
Under condition (Ia), the nontraded goods sector’s emission tax decreases pollution emissions of its own sector and the export sector, z1τ < 0 and z2τ < 0,and the emission tax on the export sector also decreases pollution emissions ofthese sectors, z1t < 0 and z2t < 0. Hence, the slopes of the two schedules arenegative.
Moreover, if foreign capital inflow is zero (k ∗ = 0) in (27), the schedule ofthe export sector’s optimal emission tax is depicted as the dashed line throughpoint A in Figure 1. We can confirm that the dashed line is located below theline τ 0 comparing the vertical intercepts of these lines. 11 In this case, either ofthe optimal emission tax rates is equal to marginal environmental damage; andthus the tax rates do not differentiate between the export and nontraded goods
sectors.
Here, the payment to foreign capital can be decreased below (11) if the government reduces the export sector’s emission tax, while an increase in the emission
tax on a nontraded goods sector does not influence the rental rate of capital from
(15). Hence, the emission tax rate on the export sector tends to be set below
the marginal environmental damage, reflecting the influence on the rental rate.
This means that t < Ez must be satisfied to hold du/dt = 0 in (28) if τ = Ez ,and a reduction in the export sector’s emission tax causes a downward shift ofthe dashed line in Figure 1. As a consequence, the line t = t0 (τ ) corresponds tothe schedule of the export sector’s optimal emission tax in the case of k ∗ > 0.
However, total pollution emissions increase if the emission tax rate on theexport sector is set below the marginal damage. In contrast, because an increasein the emission tax on the nontraded goods sector decreases emissions in both
11 Setting τ = 0, we obtain the following relation with respect to the position of these lines:„t̃0 (0) − [τ 0 ]−1 (0) = Ez

z2t
z2τ
−
z1t
z1τ

«
=−

Ez |B|,
z1t z1τ

where t = t̃0 (τ ) denotes the export sector’s optimal emission tax under k∗ = 0, and [τ 0 ]−1 (τ )means the inverse function of τ = τ 0 (t). Hence, the dashed line is located below the line
τ 0 under condition (Ia), when we compare them at their vertical intercepts. Of course, this
discussion can be applied to other conditions.

14

sectors, the nontraded goods sector’s emission tax rate should be higher than themarginal damage in order to decrease total emissions. Hence, the government
has an incentive to set the lower emission tax rate on the export sector and thehigher one on the nontraded goods sector, so that jointly optimal emission taxes
are achieved at point B in Figure 1.
Next, we consider the case of condition (IIa). In contrast to condition (Ia),
whether the combination of the jointly optimal emission taxes is ecologicaldumping or not is ambiguous in condition (IIa). However, we can confirm
that both of these tax rates are set below the marginal damage under the condition given by (30) and (31). In addition, if we calculate t∗ − τ ∗ , the following
equation is derived with respect to the differentiation in the optimal emission
tax rates:t∗ − τ ∗ = |B|−1 k ∗ rt (z1τ + z2τ )
½ µ
¶
¶¾
µ 1
k ∗ h02 e1 e22 (c0w )2 c2w
e1
e1
c1w
cr
=−
κ
−
−
+
κ
.
0
2
|A|2 |B|
e2
c2w
c2r
e2

(32)

We need to examine the order of each factor’s ratio in the export and nontraded goods sectors to clarify the direction of the discrimination in the emission
taxes, because condition (IIa) merely denotes that the import good is most capital intensive. Then, we can summarize the discussion as the following proposition.
Proposition 2:

Suppose that the emission tax rates on the export and non-traded sectors are jointly chosen to maximize domestic welfare. Then, undercondition (IIa), both of the emission tax rates are lower than the marginal environmental damage. Moreover, weak ecological dumping (the opposite of weakecological dumping) occurs if c1w /c2w < (>)e1 /e2 < (>)c1r /c2r .
In the case of condition (IIa), either of the optimal emission tax rates islower than the marginal damage. The reason why the emission tax rate on theexport sector is lower than the marginal damage is the same as for the case of
condition (Ia). It reflects the influence on the rental rate. On the other hand,
15

The case of ecological dumpingtτ = τ 0 (t)
45o

A

Ez
t∗
0

t = t0 (τ )Bτ ∗ Ezτ

Figure 2: Jointly optimal emission taxes under condition (IIa)each emission tax reduces pollution emissions in its own sector, and increases
the other sector’s emissions under condition (IIa): z1t < 0, z2τ < 0, z1τ > 0
and z2t > 0. Hence, considering the influence on total emissions, the nontraded
goods sector’s emission tax rate should also be lower than the marginal damage,if the emission tax rate on the export sector is lower than the marginal damage.
Moreover, the increasing effect of the nontraded goods sector’s emission tax
on emissions from the export sector is larger (smaller) than the decreasing effecton its own emissions, if the nontraded goods sector is labor (capital) intensive
relative to the export sector. Hence, using the above definition of ecologicaldumping again, we can confirm that the opposite of weak ecological dumping
takes place if c1w /c2w < e1 /e2 < c1r /c2r , or weak ecological dumping arises if
c1r /c2r < e1 /e2 < c1w /c2w . 12
We draw the case of ecological dumping in Figure 2. From (27) and (28),the slopes of t0 and τ 0 are positive under condition (IIa) because z1j and z2j(j = t, τ ) have opposite signs. In addition, if foreign capital inflow is zero(k ∗ = 0) in (27), the dashed line is located above the line τ 0 comparing thevertical intercept of these lines because t̃0 (0) − [τ 0 ]−1 (0) = −Ez |B|/z1t z1τ > 0.
12 These conditions are often found in the traditional two-good and three-factor model; seee.g., Batra and Casas (1976) and Suzuki (1983).

16

Here, because k ∗ 6= 0, an increase in the export sector’s emission tax also causes
a downward shift of the dashed line in Figure 2 as in the case of condition (Ia),so that the jointly optimal emission taxes is achieved at point B.

4.2

The case where an import sector is more labor intensive than an export sector (κ0 < κ1 )Conditions (Ia) and (IIa) represent the case where the import sector is more
capital intensive than the export sector. However, we can derive different results
if the factor intensity of the import and export sectors is opposite to these
conditions. In this subsection, we demonstrate these results.
First, we consider the case of condition (Ib). For h02 < 0, the emission tax
on the export sector depends on the sign of |A| and κ1 − κ0 . If we assume
κ0 < κ1 , the optimal level of the tax is lower than the marginal damage. Thatis, t∗ > Ez . On the other hand, the emission tax on the nontraded goods sector
depends on the sign of κ0 −κ2 , and the optimal level is higher than the marginal
damage if κ0 > κ2 . That is, τ ∗ < Ez . This is a situation for the opposite ofstrong ecological dumping.
Next, let us check the case of condition (IIb). Under this condition, bothjointly optimal rates of emission taxes are higher than the marginal environmental damage. However, we have already derived (32) with respect to thedirection of the discrimination. Hence, the discussion under conditions (Ib) and(IIb) is summarized as the following proposition.
Proposition 3:

Suppose that the emission tax rates on the export and non-traded sectors are jointly chosen to maximize domestic welfare. Then, the opposite of strong ecological dumping occurs under condition (Ib). On the other
hand, under condition (IIb), both of the emission tax rates are higher than themarginal environmental damage. Moreover, weak ecological dumping (the opposite of weak ecological dumping) arises if c1w /c2w < (>)e1 /e2 < (>)c1r /c2r .
If we assume condition (Ib), rt < 0 because κ1 > κ2 . Namely, the rental
price falls when the emission tax of the export sector is increased. In this case,17the government has an incentive to ensure that the emission tax of the export
sector is higher than the marginal environmental damage. On the other hand,
the government can set the emission tax of the nontradable sector lower thanthe marginal damage, because this decreases total pollution emissions. Hence,
the opposite of strong ecological dumping arises.
On the other hand, in the case of condition (IIb), both optimal emission tax
rates are higher than the marginal damage of domestic pollution, because a risein t reduces the rate of return to foreign capital and has a positive impact on
domestic welfare. Then, a rise in t decreases the output of the export good andincreases the output of the nontraded good, whereas an increase of τ makes
the output of the export good increase and the output of the nontraded gooddecrease. As well as the case of condition (IIa), whether ecological dumping
arises in the country depends on the magnitude of c1w /c2w , e1 /e2 and c1r /c2r ,where the emission is the middle factor.

5

A Relaxation of Foreign Investment Quotas

In this section, we investigate the welfare effect of easing foreign investment quotas. The effect of k ∗ on the welfare of a nation under consideration is presented
from the differential of (26) using (25) as:
du/dk ∗ = (t − Ez )z1k .

(33)Thus, considering that the quotas do not influence the production of nontradables, the welfare effect of the quotas depends on the change in emissions fromthe export sector and the level of the emission tax rate on this sector.
The increase in foreign capital inflows makes the export sector contract andtotal emissions decrease if κ1 < κ0 . In this case, the relaxing of foreign investment quotas improves (deteriorates) welfare if the emission tax rate on theexport sector is (lower) higher than the marginal environmental damage. In
contrast, total emissions increase if κ1 > κ0 . Hence, welfare improves (deteriorates) if the emission tax rate of the export sector is higher (lower) than the18

marginal environmental damage.
Moreover, the welfare effect becomes clearer if we adopt the optimal tax level(t∗ ). Noticing that t∗ < (>)Ez if κ1 < (>) κ0 , a relaxation of foreign investment
quotas improves the country’s welfare irrespective of the factor intensity of theimport and export sectors.
The above discussion can be summarized as the following proposition.
Proposition 4:

An increase in foreign capital inflows reduces welfare if theemission tax rate on the export sector is higher (lower) than the marginal environmental damage and the export good sector is more labor intensive (capitalintensive) than the imported good sector. Meanwhile, suppose that the country
chooses the optimal emission tax. Then, easing of foreign investment quotas
improves the country’s welfare.
This conclusion expands the findings of Beladi, Chao, and Frasca (1999).
They showed that foreign investment quotas increase total emissions and improve welfare if the emission tax is more stringent than the marginal environmental damage. Our result in the case of κ1 > κ0 is very similar to that of
Beladi, Chao, and Frasca (1999). However, in our model, foreign investment
quotas can reduce total emissions if κ1 < κ0 . Thus, the easing of quotas increases welfare even if the emission tax on the export sector is lower than themarginal damage. Moreover, the optimal emission tax imposed on the export
sector satisfies this requirement.

6

Concluding Remarks

In this paper, we analyzed the effects of emission taxes on the export and nontradable sectors under foreign investment quotas and the effect of a marginal
opening of the quotas. As long as foreign capital inflows are not zero, differentiation of environmental policies between these sectors can arise even if we
consider a price instrument such as emission taxes in a small country, and relaxation of foreign investment quotas improves the country’s welfare irrespective of19the direction of the differentiation of the emission taxes if the country chooses
the optimal emission tax. On the other hand, that measure reduces welfare if
the emission tax rate on the export sector is higher (lower) than the marginalenvironmental damage, and the export sector is more labor intensive (capitalintensive) than the import sector.
In particular, our conclusions concerning jointly optimal emission taxes provide very interesting proposals from the perspective of developed and developing
countries. If the export goods are more labor intensive than the import goods
such as in developing countries, ecological dumping may be preferred from thestandpoint of domestic welfare. Moreover, in a country in which the import good
is most capital intensive, both emission tax rates are lower than the marginalenvironmental damage, and ecological dumping may arise. Meanwhile, the opposite of ecological dumping may be chosen if the export goods are more capitalintensive than the import goods such as in developed countries. In addition, if
the imported goods are the most labor intensive, the jointly optimal emission
taxes are both higher than the marginal damage of pollution emissions, and the
opposite of ecological dumping may occur.
Further research is required to address the following two points. First, we
do not consider pollution emissions from the import sector. If the emission
tax on this sector is also expected to influence the rental rate of capital, thenthe government may use the emission tax on the sector in order to reduce thepayment to foreign capital owners. Hence, we must analyze the combination of
optimal emission taxes including taxation to the import sector.
Second, there are two distortions that are brought about by domestic pollution emissions and foreign investment quotas in our model. However, theexistence of other distortions, e.g., trade taxes and minimum wages, may also
cause differentiation in emission taxes between the export and nontradable sectors. Thus, we need to further investigate the discrimination in the emission
taxes considering other types of distortions.

20

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