Discussion Paper Series No.30
Voluntary abatement for transboundary
pollution and international
redistribution scheme
Hiroshige Tanaka
Tomoyuki Hasegawa
September

19,

2002

Voluntary abatement for transboundary pollution and international
redistribution scheme
Hiroshige Tanaka a , Tomoyuki Hasegawa baFaculty of Economics, Chuo University, 742-1 Higashinakano, Hachioji-shi, Tokyo
192-0393, Japanb
Chuo University Graduate School

Abstract
The transboundary pollution requires some kind of international cooperation. Theinternational agreements for the environmental problems consume a large amount oftime and laborious bargaining. Considering that the international agreement is noteasily achieved for many types of environmental pollution and that a large part ofpollution is related with economic activities of pollutants, environmental regulation
using market is expected to bring about efficient solution. Employing a theory ofvoluntary provision of public goods, we propose a redistributional scheme to attainthe efficient solution to abate transboundary pollution.

Keywords: Transboundary Pollution; Voluntary Provision of Public Goods; Subsidy
and Tax Redistribution; Stackelberg Model

1. Introduction
Acid rain caused by economic activities of neighboring countries, water pollution
in a going through some countries and an ocean pollution damaging ashore fishery ona large range are classified as transboundary pollution. The pollution appears todamage limited district to some extent and might be distinguished from global
environmental problems. But the transboundary problems as well as the global
environmental problems require international cooperation to abate effectively
emission of pollutants. To investigate the transboundary pollution in the context ofpublic economics, protecting or maintaining environment is assumed to be provisionof public goods in neighboring countries.
The transboundary pollution involves complicated interests of some countries, aparticular country could not directly decide any other country environmental policy
such as regulation requirements, pollution tax and emission permit. These related
countries should perform cooperative environmental policy from theoretical1perspective. The cooperation seems to be complemented by integration ofenvironmental policy. The international coordination needs to spend a great amountof efforts and times. A non-cooperative abatement of pollution is practically expected
to substitute the cooperative approach. On the other hand, the well-known prisoner ’s
dilemma shows that the non-cooperative competition probably leads to inefficientconsequences. To employ non-cooperative instruments for the transboundary
pollution, we need carefully find out effective scheme.
Abatement of pollution is classified into public goods. Hoel (1990) points out thatthe theoretical results in voluntary provision of public goods are applicable to asolution in global warming agreement. Many authors such as Bergstrom, Blume andVarian (1986) argue the well-known result that voluntary provision could not achieve
efficient provision in a Cournot-Nash framework. Although the negative results arewidely accepted in public economics, Andreoni and Bergstrom (1996) propose aredistribution scheme by which efficient public goods is attained in the voluntaryprovision mechanism. Kirchsteiger and Puppe (1999) research further the
redistribution scheme and demonstrates the existence of efficient provision by using
non-cooperative Nash equilibrium analysis. They indicate the possibility that theefficient interior solution is unstable and easily replaced by inefficient boundary
solution. The severe pollution in the international aspect might appear in thisinefficient solution. In this paper, using the two-country model we propose a schemethat turns the inefficient solution into efficient one. It is argued that relatively
advanced country should make a policy more benefiting for the less developed
country so as to improve abatement of pollution.
This paper is organized as follows. In 2, the redistribution scheme is formulated
for the environmental policy in the views of international repercussion. In 3, thecondition of efficient abatement is defined and feature of the efficient solution is
explained. Especially, as the population grows, the efficient abatement would be
more likely to be achieved by lower tax rate. In 4 and 5, we investigate inefficientboundary solution and propose the international redistribution policy that turns
inefficient abatement into efficient one. The existence of abatement is proved in 6.
Applying the result of this paper, 7 states that environmental policy to initiatetechnological innovation is closely related with global industrial strategy for eachgovernment. The relationship between the environmental and industrial policy should
be discussed in another opportunity.

2. ModelTo simplify following argument, we consider two-country model. The twoneighboring countries denoted by i and j are assumed to make an effort to abate2pollution. i stands for developed country and j states under or less developed country.
In recent literatures of environmental economics, abatement of pollution is supposed
to provide public goods. Representative individual of each country abates emissionof pollutants g i , g j ( ≥ 0 ) and the numbers of agents of country i and j are n i , n j . n
represents the total number of individuals and is defined byn = ni + n j .

(1)i and j satisfy the inequalities,i ≡ h , for all h , 1 ≤ h ≤ n i ,j ≡ k , for all k , n i +1 ≤ k ≤ n .
The total abatement of emission is depicted byn

G = ∑ gh .

(2)

h =1

If individual of each country abate an identical abatement of pollution, (2) is simply
written by
G = ni g i + n j g j .
(3)
Marginal abatement cost is 1. In more general case, the marginal cost of the twocountries might not be identical. Since we investigate mainly efficient abatement ofidentical marginal cost countries, the identical marginal cost is supposed in this paper.
Individual i and j consume a private good xi , x j . The private good is supposed to bea numeraire. The price is denoted by 1. The private good and the abatement ofpollution are normal goods. Utility of i , j is expressed byu h ( x h , G ) , for h = i , j .
(4)
The utility functions are assumed to be strictly concave and continuously
differentiable. The marginal rate of substitution for i and j ( MRSh ≡ −

dx h
) are
dG

increasing with x h and decreasing with G ;
∂MRSh
∂MRSh
> 0 and< 0 1.
∂x h∂G
It is assumed that at zero abatement the marginal rate of substitution is larger thanmarginal cost 1.
Both countries might manage cooperatively a subsidy and tax scheme to attainefficient abatement of emission. Each agent is privileged to accept subsidy andrequired to pay tax based on calculating formula under voluntary abatement
1

These inequalities are straightforward from∂MRShu Gx u x − u G u xx
=−
> 0,
∂x h
[u x ]2∂MRShu GG − u G u Gx
=−
< 0.
∂G
[u x ]2u Gx , u x , u G and u xx mean partial derivative of utility function u h , h = i , j .
3

distribution of individuals. Incomes of individuals i and j are initially endowed withmi and m j . Kirchsteiger and Puppe (1997) formulate a general linear form ofsubsidy and tax redistribution.

x h + [1 − σ h ]g h = m h − ∑ t hk g k , h = 1,..., n .
n

(5)

k≠h

Abatement effort of individuals is supported by a rate σ h ( 0 ≤ σ h ≤ 1 ) of subsidy andabatement costs of other individuals are partially shared by a constant ratet hk ( 0 ≤ t hk ≤ 1 ) of tax. Budget equilibrium condition for the subsidy and tax scheme
is represented by
n

n

h =1

h =1 k ≠ hn∑ σ h g h = ∑ ∑ t hk g k .

(6)Each individual is assured to obtain a positive post tax income. The condition isreferred as no-bankruptcy and defined bynm h − ∑ t hk g k ≥ 0 , h = 1,..., n .

(7)

k≠h

In the case that individuals of country i , j abate identical pollution g i , g j , therate of subsidy are assumed to be equal to σ i , σ j for individual of country i , j .
Suppose that government of country i founds the redistribution scheme to initiate
abatement. The subsidy for abatement of i is probably financed through the tax on
individuals of foreign country j as well as domestic country i . To consider theinternational repercussion we suppose the following environmental oriented tax
system. The cost to equip facilities emitting lower pollution is partially subsidized by
the government of county i . This environmental redistribution scheme taxes heavily
on the individuals or firms using facilities to emit high pollution. The individuals or
the products of firms targeted to tax inevitably include foreign inhabitants andimports from j . The tax on import products might rise the consumer price anddecrease demand of the product. Consequently, the producers of j suffer the declineof revenue. That makes incomes of the individuals of j lower. Tax rate of i and j aredenoted by t ii and t ji for g i and t jj and t ij for g j . Since we do not attempt toinvestigate tax incidence here, t ji and t ij represent only ex-post international
effect of environmental redistribution policy. Subsidy and tax scheme (5) is
separately rewritten for individuals of country i and j ,xi + [1 − σ i ]g i = mi − [[n i − 1] t ii g i + n j t ij g j ] ,(8)x j + [1 − σ j ]g j = m j − [n j t ji g i + [n j − 1] t jj g j ] .
(9)The budget equilibrium condition of the scheme (6) is simply stated byn i σ i g i + n j σ j g j = [[n i − 1]n i t ii + n i n j t ji ]g i + [n i n j t ij + [n j − 1]n j t jj ]g i .

(10)(10) is transformed inton i [σ i − [n i − 1] t ii − n j t ji ]g i + n j [σ j − n i t ij − [n j − 1] t jj ]g j = 0 .

(11)

From the budget equilibrium condition (11), summing up (8) and (9) represents total
budget condition4∑ n h [x h + g h ] = ∑ n h m h .

h=i , j(12)h=i , jEach country h could decide domestic subsidy and tax rate σ h , t hh , and t kh andtransfer budget surplus of h to k .

3. Efficient abatement of emission
In this section, we consider an efficient condition of abatement. For the first,
representative individual of one country is assumed to obtain Nash conjecture.
Individual h ( = i , j ) maximizes (4) subject to budget constraint (8) or (9). Individuals
consume positive private goods ( x h > 0 ). Individual i in the developed county could
be willing to abate a positive pollution ( g i > 0 ). It is afraid in extreme case that j in
the less developed country unfortunately could not afford to contribute abatement ofpollution ( g j ≥ 0 ).
Employing Lagrange multiplier λ , the first order conditions are stated by (12),(13), (14), (8) or (9) for h = i , j .
∂ uh− λh = 0 ,
∂x hi

(12)

∂u h
= λ h [[1 − σ h ] + [n h − 1]t hh ] ≤ 0 ,
∂G

(13)

 ∂ uh(14)gh − λ h [[1 − σ h ] + [n h − 1] thh ] = 0 .
 ∂G(13) satisfies equality, and directly derives (14) for i . (14) is not independent for i .
Regarding j , it is possible that (13) hold with the strict inequality. In this boundary
solution, (14) is the independent equation. Let us consider this corner solution later
on, we suppose that ( g i , g j ) is the interior solution for a while. The interior
solution satisfies Samuelson efficient condition for the abatement of pollution;∂u j∂ui
n i ∂G + n j ∂G = ∑ n h [[1 − σ h ] + [n h − 1]t hh ] = 1 .
∂ui∂u j
h=i , j
∂xi
∂x j

(15)

Reminding that [1 − σ h ] + [n h − 1] t hh > 0 for each h , the necessary condition for (15)is[1 − σ h ] + [n h − 1] t hh ≤ 1 , for h = i , j .
nh

(16)

(16) is interpreted as follows. As population of each country increases, addition ofown share rate of par capita abatement cost [1 − σ h ] and total tax rate of own
country [n h − 1] t hh must be set lower to attain efficient allocation.
For the next, we consider the equilibrium budget condition of subsidy and tax
5scheme. From rearrangement of (15)n j σ j − n j [n j − 1] t jj = n j − 1 + n i [[1 − σ i ] + [n i − 1] t ii ],is obtained. To substitute (17) into (11),n j − 1 + n i [[1 − σ i ] + [n i − 1] t ii ] − n i n j t ij
gi
=−
.
gj
n i [σ i − [n i − 1] t ii − n j t ji ]

(17)

(18)

follows. Suppose that the developed county i pays overpayment which subtract thesubsidy from the payment in this redistribution scheme. The denominator of (18) is
negative. (18) is positive for interior solution, therefore the numerator must be
positive. From [1 − σ h ] + [n h − 1] t hh > 0 the sufficient condition of efficiency yields
n j − 1 − n i n j t ij > 0 .
(19)
From the signs of the denominator and (19),σ i − [n i − 1] t ii
< t ji ,
nj

nj −1
1
=
> t ij ,nj
ni n j(20)(21)

are satisfied so that the two country voluntarily abate pollution for a positive amount.
The interpretation of (20) is that individual of advanced country i should sharesufficiently own abatement cost ( t ii ). In addition, as the population ratio of theadvanced country to the less developed country rises to extremely high, theconstraint of (20) becomes less restrictive. (21) implies that the larger the populationof both country become, the less cost share of i due to the less developed country
should be set.

4. Improving abatement for an inefficient solution
In transboundary pollution, some polluting countries could not attain an efficientabatement for the shortage of technology and money. In the previous model, theboundary solution ( g i > 0 , g j = 0 ) states an inefficient abatement. In this boundary
solution, for j (13) holds with strict inequality. Hence, the value of (15) is strictly
less than one. Samuelson efficient condition is not satisfied. In this inefficient case,from budget equilibrium condition (11) the equality;
σ i − [n i − 1] t ii − n j t ji = 0 ,(22)
is derived. The tax rate of the less developed country j ( t ji ) is not assumed to be zero.
Suppose that the redistribution tax of country i is charged in lump sum on somecommodities. The commodities are exported to the country j and the people of jpurchase those at a price including the lump sum tax. The effect of redistribution
scheme of the country i spills over the other country j . But the effect is too restrictive
for the government i to achieve the efficient allocation. Even if the developed
country constructs one own subsidy and tax scheme for abatement, efficient
6abatement could not be obtained by the single country. To improve efficiency, afavorable approach is that j raises subsidy rate σ j or lower tax rate t jj . An interior
solution is probably obtained. The boundary solution will be simply substituted withinterior one. However, j owns the right to alter domestic rates of subsidy σ j and tax
t jj . Therefore, it is not necessary that j alters efficiently its domestic rate as i intend
to be. The less developed country j is easily supposed to prefer consumption ofprivate goods to abatement of pollution. By dividing (13) by (12), the boundary
solution shows that the marginal rate of substitution of abatement for the private
good is less than the marginal cost of abatement after the redistribution tax. In thiscontext, j is not willing to adopt the scheme planed by i to abate pollution, but sustain
the way to assure more economic profits. The inefficient corner solution remains.

5. A bargaining solution and a redistribution scheme
In this paper, we consider the international abatement where the cooperative
redistribution scheme is not well established. When the abatement of pollution is theinefficient boundary solution stated above, the more developed country would be
required to contribute positively to the improvement of abatement. However, it is
only an optimistic perspective that the international abatement program planed andexecuted by the more developed country could show the expected performance. Even
if the more developed country makes a plan to increase abatement, it is unfortunately
possible that international abatement will not appear to increase abatement. We must
make clear the possibility that the more developed country induces the less developed
country to increase abatement of pollution.
We adapt Stackelberg model for the international abatement of pollution. The moredeveloped country i is the leader. The less developed country j is the follower. i could
arrange coefficients of the redistribution scheme for own country σ i , t ii , t ij . The
coefficient regarding j , σ j , t jj , t ji are exogenous for i . Figure 1 and 2 illustrate theoptimal consumption for the country i and j .
Initially, suppose that j is not willing to abate pollution. The abatement vector of iand j is a boundary solution n i g i* , 0 . This solution is expressed by the point A’s in
the two Figures. Country i lowers the cost share t ji of j to t ′ji . (22) is transformed

(

)

into

n j t ′ji = σ i′ − [n i − 1] tii′ .
(23)
The decrease of cost share for j ( n j t ji ) increases the slope of the budget constraint

line of i with a constant income mi . The budget line of i turns downward clockwise.
Using the first order condition of abatement and the assumption of normal goods forabatement, it is straightforward from the income effect that the optimal abatement ofi ( n i g i* ) decreases to n i g i** . The optimal point A in Figure 1 is replaced by the point7

B.
For the second step, since the post tax income of j ( m j − n i t ji g i** ) increases in (9),the marginal substitution regarding j rises for the relatively small abatement n i g i**from the income effect. (13) is possibly satisfied with equality ( h = j ) for a positiven j g *j* . We consider the interior solution (n i g i** , n j g *j * ). In (11) positive coefficient of
n i g i for the positive n j g *j* . As the tax share of j ( n j t ji ) decreases over certain point,
the coefficient of g i might be positive. In this case, the negative coefficient of g jmeans decrease of σ j − [n j − 1] t jj or increase of n i t ij . The slope of budget line for j
becomes steeper or a part of abatement cost in j is taxed on i . A part of income incountry i is redistributed to j . The income effect in the country j the boundary optimal
point A in Figure 2 might move upwardly to the interior optimal point B.
Consequently, the positive abatement of j moves point B in Figure 1 to an efficient
point C.

6. Existence of efficient abatement
The explanation in the previous section roughly illustrates the process that theboundary solution turns into interior one. In this section, we thoroughly inquire into
improving efficiency of abatement in the context of theoretical analysis. g i* , 0means G = n i g i** + 0 . xi and x j are expressed by a function of t ij and t ji . Using()

the budget condition (8) and (9), for the boundary solution (12) and (13) are restatedby
MRSi n i g i* , xi* ; t ij = 1 − σ i + [n i − 1] t ii ,MRS j n j g *j , x *j ; t ji < 1 − σ j + [n j − 1] t jj .
To state simply, constant parameters mi , m j , n i , n j are omitted. MRSh stands for
marginal rate of substitution of G regarding x h for h ( = i , j ). We are mainly

(
(

)

)

concerned with redistribution policies for inefficient abatements. Since theabatement of the boundary solution is inefficient, we suppose that an efficientabatement exists. The existence condition for efficient abatement ensure aparticipation condition for i and j ,(24)
u h n i g i** + n j g *j * , x h** ≥ u h n i g i* + n j g *j , x h* , h = i , j .
In the boundary solution g j = 0 is satisfied. (9) is transformed intox j = m j − n j t ji g i .
(25)

(

)

(

)

Substituting (22) into (8), the budget constraint for i is arranged into
xi + [1 − n j t ji ]g i = mi .
Using (25) and (26),dg idxi= − [1 − n j t ji ]+ n j gi ,
dt ji
dt ji
8

(26)

dx j
dg i


= −  n j t ji
+ n j gi 
dt ji
dt ji


are obtained. When t ji decreases, the post tax price of abatement ( 1 − n j t ji )increases. Since the abatement is normal goods, consumption of abatement decreases.
dx j
dg i
That is,> 0 is obtained. It is straightforward that
< 0 is satisfied.
dt ji
dt ji
Differentiating MRS j with t ji ,dMRS j∂MRS j dg i
∂MRS j dx j
= ni
+
dt ji
∂G dt ji
∂x j dt ji(27)

is derived. Since MRSi and MRS j are decreasing with G and increasing with xi or
x j , it is assured that (27) is negative. As t ji decreases, MRS j rises monotonously.
Suppose that g j remains zero. When t ji approaches to zero, the absolute slope ofbudget constraint (26) becomes approximately equal to 1. Remaining that MRS j iscontinuous with G , MRS j is greater than 1 for sufficiently small G from theassumption with MRS j . If subsidy rate is large enough, or if tax rate is small enough,inequality 1 − σ j + [n j − 1] t jj < 1 is derived. For some G ** to satisfy (23) for j
MRS j = 1 − σ j + [n j − 1] t jj
could be obtained. However, i never decide to lower t ji so much. Because to lower
t ji means to decreases consumption of abatement G and private good xi at zeroabatement of j ( g j = 0 ) and at sufficiently large g i . In this case, lowering t ji
dx j
dg i
> 0 and> 0 . If the country icontradicts the participation condition from
dt ji
dt ji
propose to increase t ji , the income effect decreases utility of the country j . To avoid
such a proposal of i , the country j should decide to abate in order to attain an
allocation satisfying (24).
An interior solution could be achieved the redistribution scheme stated in thispaper. We complete the existence proof of the efficient solution.

7. A Condition for an efficient abatement
In previous section, we have argued that redistributional scheme in the model has
the international effect and efficient abatement of transboundary pollution could beachieved even if individual j in less developed country could not contribute theabatement. It was also shown that relevant value of t ′ji should be employed to attainthis interior solution. In this section, we examine the model in detail to derive sucht ′ji that ensures the existence of efficient abatement.
To simplify the analysis, it is assumed that individuals of each country has
Cobb-Douglas utility function9

u i ( xi , G ) = xiα G 1 − α , 0 < α < 1 , i ,u j ( x j , G ) = x βj G 1− β , 0 < β < 1 , j .
Since individuals of country i contribute positive amount of abatement, the first orderconditions are described asα xiα − 1G 1 − α − λ i = 0 ,n i [1 − α ]x iα G − α − λ i [1 − σ i + [n i − 1] t ii ] = 0 .
On the other hand, individual of country j is supposed not to contribute, it implies
that equation (13) holds with inequality. First order condition for j is given asβ x βj − 1G 1 − β − λ j = 0 ,n j [1 − β ]x βj − λ j [1 − σ j + [n j − 1] t jj ] < 0 ,[]g j n j [1 − β ]x βj G − β − λ j [1 − σ j + [n j − 1] t jj ] = 0 .
These conditions give a corner solution[1 − α ]mi
xi* = α mi , g i* =,1 − σ i + [n i − 1] t ii

x *j = m j −n i t ji [1 − α ]mi, g *j = 0 .
1 − σ i + [n i − 1] t ii

(25)

From assumption, t ji in (25) is not zero.
At this corner solution, the government of i is supposed to lower t ji to achieve
efficient abatement of pollution. It is given in equation (23). When (23) applies,
decision problem of individual i is described by
max u i ( x i , G ) = x iα G 1−αs.t. x i + [1 − n j t ′ji ]g i = m i ,G = ni g i .
We could obtain

xi** = αmi , g i** =[1 − α ]mi .
1 − n j t ′ji(26)

From (26), g i** < g i* is confirmed. Since g i** is assumed to be positive,
1 − n j t ′ji > 0
holds.
While individual i reduces the contribution, due to lowered tax rate, it is possiblethat individual j starts to contribute positive amount of abatement. To observe this,note that maximization of j ismax u j ( x j , G ) = x βj G 1− βs.t.

x j + [1 − σ j + [n j − 1] t jj ]g j = m j − n i t ′ji g i** ,G = n i g i** + n j g j ,10

g j > 0.
Solving this,x *j * =n i β [1 − σ j + [n j − 1] t jj ]g i**m j − n i t ′ji g i**

g *j * =− n j β [1 − σ j + [n j − 1] t jj ][1 − σ j + [n j − 1] t jj ]n i [1 − β ] − n j β [1 − σ j + [n j − 1] t jj ]1[1 − σ j + [n j − 1] t jj ],n i [1 − β ] n i β [1 − σ j + [n j − 1] t jj ]g i**1
m j − n i t ′ji g i**n i [1 − β ] − n j β [1 − σ j + [n j − 1] t jj ]1[1 − σ j + [n j − 1] t jj ](27)

are obtained. From the assumption of non-bankruptcy and value of each parameter,x *j * > 0 could be seen. However, the sign of g *j* could not be determined. We now
consider the condition to hold g *j * > 0 .
If efficient interior solution is achieved, from Samuelson condition,n i [1 − σ i′ + [n i − 1] t ii′ ] + n j [1 − σ j + [n j − 1] t jj ] = 1
must hold. (23) is used to substitute into (28) gives
1 − n i [1 − n j t ′ji ]1 − σ j + [n j − 1] t jj =njSince it is supposed that left-hand of (29) is positive, inequality
1 − n i [1 − n j t ′ji ] > 0 .

(28)

(29)

(30)

is satisfied. Substituting (29) into (27) gives

g

1
j

=

n i n j [1 − β ] m j [1 − n j t ′ji ] − n i2 n j [1 − α ][1 − β ] m i t ′ji − n i [1 − α ]β m i [1 − n i [1 − n j t ′ji ] ][n i [1 − β ] + n j β ][1 − n j t ′ji ] [1 − n i [1 − n j t ′ji ] ](31)
From n i , n j ≥ 1 , 0 < β < 1 and (30), the denominator of (31) is positive. To holdg *j * > 0 , it is required that the numerator of this equation should be positive.
Arranging gives(Numerator=)− n i n j [n i [1 − α ]mi + n j [1 − β ]m j ] t ′ji + n i [n j [1 − β ]m j − [1 − n i ][1 − α ]β mi ]. (32)(32) is linear in t ′ji . It could be seen that its gradient is negative and its intercept is
positive. Therefore there exists some t ′ji such that g *j * > 0 . The government of n j [1 − β ]m j − [1 − n i ][1 − α ]β mi  to attain the interiorcountry i can choose t ′ji ∈  0 ,n i [1 − α ] mi + n j [1 − β ] m jsolution.

11.

7. Concluding remarks
A large amount of researches are published in the field of transboundary pollution.
Hoel (1997) contrasts coordination with non-coordination of environmental policy.
Generally, the coordination of environmental policy is expected to bring about
profitable results for transboundary pollution. The coordination of environmental
policies is not easily achieved between different types of countries. In some cases,
the coordination seems to need a complicated arrangement of conflicting national
interests. Most of transboundary pollutions are derived from economic activities inneighboring countries. In the international free trade system, economic activities areoperated under the rule of international market mechanism. The effective policies tocontrol market activities affect abatement of transboundary pollution indirectly orunintended. The indirect solution through market mechanism is practical policies forabatement of transboundary pollution. Silva (1997) discusses optimal environmental
policy considering mobility of population. In international economies, mobility of
population is largely restricted by most countries. The redistributional scheme
considered in this paper could control transboundary pollution through theinternational market economy.
International redistribution of income such as economic aid is helpful fordeveloping many underdeveloped countries. We could suppose that a international
redistributional scheme is an alternative to improve abatement of global pollution.
We make clear that the more developed country could induce the less developed
country to take cooperative environmental policy by using a redistributional tax
scheme. Since some environmental tax policies are designed to initiate innovation ofenvironmental technology, these policies might work as the redistributional policy.
Considering the research regarding international industrial policy (Spencer and
Brander (1982)), the international welfare analysis remains as a problem toinvestigate. As Epple and Romer (1996) points out, it is remained also unclear that apolitical decision is consistent with the efficient abatement scheme.

12private goods

CB

A

nigi **

nigi *

nigi * * +njgj **Figure 1 Voluntary abatement of advanced country i

13abatemeprivate goods

BA

nigi *

nigi * * +njgj **Figure 2 Voluntary abatement of developing country j

14

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