Global Relative Prices in the Face of a Pollution Transfer Problem

doi:10.4236/tel.2012.25102

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Theoretical Economics Letters, 2012, 2, 557-560

http://dx.doi.org/10.4236/tel.2012.25102 Published Online December 2012 (http://www.SciRP.org/journal/tel)

Global Relative Prices in the Face of a Pollut ion Transfer

Problem

John Dogbey

Department of Economics, University of Nebraska at Omaha, Omaha, USA

Email: jdogbe[email protected]

Received September 22, 2012; revised October 23, 2012; accepted November 25, 2012

ABSTRACT

This study focuses on the relationship between trade and relative prices of pollution intensive goods. Seminal to this

idea is the transfer problem. It is based on the idea that environmental quality of two countries that engage in trade

could be affected and this could also have possible environmental quality transfer effects in a third country (geographic

neighbors or trade partners) and a result, terms of trade effects. The paper makes the case that whether the relative price

of a pollutant would suffer during trade will depend on the kind of pollutant it is, distance between the countries in-

volved, countries’ marginal propensity to consume and substitutability of the good. The nature of the pollutant (whether

it is spatially separable in production and or consumption) determines whether it can spillover to trade neighbors or

whether it is transferable to a trade partner with ramifications to its relative price. The paper uses indirect utility func-

tions and compensated demand functions to analyze the terms of trade effects.

Keywords: Relative Prices; Spatially Separable; Trade; Substitutability; Pollutant; Transfers

1. Introduction

The debate on the role of trade in environmental pollu-

tion has attracted a lot of attention in recent years. Many

believe that trade has a debilitating effect on the envi-

ronment and others hold contrary views. For example,

research has been done to determine whether reduction in

trade barriers alters the composition of economic activity,

or leads to a change in the techniques of production and

thus have an effect on the environment. The environ-

mental impacts of trade policies as well the trade impacts

of environmental policies have also been investigated.

These researchers find that trade liberalization may in-

crease specialization in sectors that cause little pollution.

These studies include Grossman and Krueger [1], and

Huang and Labys [2].

The relationship between economic growth and envi-

ronmental pollution has also gained much attention. Re-

searchers find that a liberal trade regime leads to in-

come growth and that economic growth reduces pollu-

tion once a country reaches a certain income threshold.

Other findings are that as trade increases and growth

increases, environmental pollution also increases. The

other side of the coin is that environmental policies

reduce trade and growth. Stricter environmental stan-

dards are also considered necessary for a U-shaped

relationship between pollution and income during

growth as discussed in Grossman and Krueger [1],

Huang and Labys [2], and Grossman and Krueger [3],

and McConnell [4].

On the effect of trade on countries’ Environmental

Kuznets Curve (EKC), a myriad of research has been

carried out. A theoretical work finds that during the tran-

sition from autarky to international trade, the EKC U-

shape relationship may hold for a cross-section of coun-

tries but may not hold for individual economies. The

extent to which consumer preferences and structures

such as education level, sectoral composition of the

economy, and unemployment can spatially and inter-

temporally affect the EKC relationship has been explored

with the result that the level of income at which house-

holds decide to reduce their exposure to pollution de-

pends on the nature of the pollution. For goods that are

spatially separable (i.e., goods which do not generate

pollution during either their production or consumption),

such as SO2 and PM10, there is significant evidence of

such relationship while there is little evidence for non-

spatially separable pollutants such as CO3, O3 and NOx.

Khanna [5], and Khanna and Plassmann [6] document

these views.

Other researchers in the area of welfare and trade ana-

lyze the welfare effects that arise when rich countries

make bilateral or multilateral transfers to poor countries

and conclude that there is a transfer problem in that poor

countries get impoverished when they receive transfers

from rich countries. These researchers include Band-

yopadhay and Majumdar [7], and Bandyopadhyay and

J. DOGBEY

558

Munemo [8], and Bhagwati, Brecher, and Hatta [9], and

Bhagwati and Brecher [10,11].

While a plethora of literature looks at the link between

trade and the environment, or trade and relative prices,

no research has made the link between pollution, trade

and relative prices. This paper attempts to fill the gap by

providing a comparative statistics analysis to examine

what happens to relative prices during trade when the

good in question is a pollutant. It establishes a relation-

ship between pollution, trade, welfare and relative prices.

Thus, it addresses the issue of global welfare effects or

terms of trade effects when countries engage in trade

involving pollutants. The rest of this paper is organized

as follows: In the next section I present the models and

derive the results, followed by the comparison of the

results and intuition behind them in Section 3, then pre-

sent the concluding remarks and policy recommendations

in Section 4.

2. The Model

2.1. The General Model

This paper uses compensated demand functions, indirect

utility functions and the overspending functions of coun-

tries to analyze bilateral trade in a pollutant in a multilat-

eral context. This model assumes a three-country world:

countries α, γ, β, namely the developed country, the de-

veloping country and the non-participant; only countries

γ and β could be neighbors (the developed country’s aim

is to transfer pollution, so it can only engage in such a

trade with a developing country that is not its neighbor).

The model also assumes a two-good world: Good X and

good Y; good X is the pollutant.

The paper considers three cases of the pollutant and

hence three models. The first two cases relate to a situa-

tion where consumption or production of the good is spa-

tially separable (either consumption or production does

not generate pollution) while the third case relates to a

situation where both production and consumption are

non-spatially separable. Case 1 involves a situation where

only consumption generates pollution (only consumption

is non-spatially separable) and it is assumed that the de-

veloped country transfers pollution by exporting good X

to the developing country. Case 2 is the one in which

only the production of good X generates pollution (only

production is non-spatially separable), and the developed

country is assumed to transfer pollution by exporting

production or the pollution generating activities to the

developing country, γ. Case 3 is a scenario where both

the production and consumption of good X generates

pollution (consumption and production are both non-

spatially separable). The developed country is assumed

to still export production to the developing country, with

the possibility of importing the finished goods, thereby

transferring the production emissions.

The cases above thus result in three models. The over-

spending (indirect utility) function of each country, ,

is its cost (expenditure) less its revenue.

Let = the relative price of good X;

= the welfare level of country ; i

= the value (cost) of the pollution in terms of good



= inverse distance between country β and γ; 0 ≤ δ <





equ = the expenditure function of country ; i





rq = the revenue function of country ; i





xqi

u = the compensated import-demand function

of good X by country .

Then the overspending function in autarky is given by:











1;,,,,.

iiiii

cueurqiqq







2.2. Case 1: Only Consumption Generates

Pollution

Introducing trade in good X, the budget equation for each

country will include P (the volume of trade in the pol-

lutant), which will be adding to the benefit (revenue)

component of the developed country (the exporter), but

reducing the revenue component (or adding to the cost

component) of the developing country (importer) and the

non-participant (depending on the distance between the

importer and the non-participant). In other words, the

export of the pollutant reduces the overspending function

of country α but increases the overspending functions of

countries γ and β. The model comprises of the budget

equations of the three countries and the market clearing

equation of good X:





,Pqcu



0 (2.1)





,Pqcu







 (2.2)





,Pqcu



0 (2.3)









,,,uuxq xqxqu





 (2.4)

As the developed and developing country trade the

production and, hence, the consumption of the pollutant

increases (so P increases). Taking total differentials of

Equations (2.1)-(2.4)4 and augmenting gives:

1During trade, a country’s overspending function will increase (de-

crease) if it is importing (exporting) good X.

2The budget equation of the non-participant is affected not by the full

value of the pollution, but by a fraction. The longer the distance be-

tween the non-participant and its neighbor, the smaller the value of δ

and hence the smaller the value of the pollution transfer or spillover.

When δ approaches zero, the non-participant’s overspending function

and budget equation will be the same.

3By Walras Law, the market clearing equation of good Y is omitted.

4Total differential of (2.1) is: , and (2.4) is:

ddd

cu cq P

 

0





dd0

x xqP

 

ddd

uuu q

xu xuxux

  





J. DOGBEY 559

100 1

010dd

001 1

xup

xxxx q





























where i

qqqq q

xxx x



 (2.5)

c (2.6)

uu i

ce u



 

 (2.7)

Equation (2.7) implies that a country will consume

good X until it reaches a point where the percentage in-

crease in its utility exactly equals the percentage increase

in its cost or expenditure. In Equation (2.5)6, q

is the

summation of the substitution effects, which are always

negative for a normal good.

Let Δ be the negative of the slope of the global excess

demand function. This represents the Marshall Lerner

Condition (MLC) and the Walrasian stability implies that

Δ > 07. Thus, where,

qu uu

xxxxx xx

 



x

The effect of an increase in P on the relative price of

the good using Cramer’s Rule is:

dΔ

uu u

xx x

 







(2.8)

(2.8) implies that the relative price of good X (when

consumption is non-spatially separable) increases as the

trade in X increases. Note that ,,

uu u





represent each

country’s marginal propensity to consume8, which is

always positive for normal goods.

2.3. Case 2: Only Production Generates

Pollution

This is the case where country α exports raw materials to

country γ and or engages in pollution generating active-

ties in it since the production of good X emits pollution

as opposed to its consumption. This model is only an

extension of Case 1 in that an emission tax,

, is applied, which reduces the amount of

pollution generated in country γ and the possible amount

of pollution spillovers in country β.



π0π1



The model is as follows:



,Pqcu



 (3.1)









1π0,cu Pq







 (3.2)









1π0,cu Pq





 (3.3)









,0,,cucuqqcuq





 (3.4)

The corresponding augment after taking total differ-

enttials and making similar assumptions as in Case 1 is:



100 1

010 1π

0011π

xuP

xxxx q





























The effect of an increase in P on the relative price of

the good using Cramer’s Rule is:









1π1π

dΔ

xxx











 (3.5)

From Equation (3.5) above, it is apparent that the rela-

tive price of the good (when production is non-spatially

separable) falls as trade in the pollutant increases.

2.4. Case 3: Both Consumption and Production

Generate Pollution

This is the case where production and consumption of the

pollutant are non-spatially separable. In this case, the

developed country still shifts production to the develop-

ing country but imports the good for consumption and

hence reduces the total amount of pollution by the pro-

duction emissions. The budget equations are:





,Pqcu



 0 (4.1)









2π0,cu Pq







 (4.2)









2π0,cu Pq





 (4.3)









,0,,cucuqqcuq





 (4.4)

The overspending function and the compensated de-

mand functions remains the same as in Cases 1 and 2.

Using the same conditions and assumptions as above and

totally differentiating and augmenting, gives:



100 1

010 2π

001 2π

xuP

xxxx q

































5Shephard Lemma.

6This is the substitution effect; it is assumed that X and Y are substi-

tutable in production and consumption.

7The slope of the excess demand function is: qu uu

xx xxxx





 The determinant of the above is same as before, and

the effect of an increase in P on the relative price of the



The MLC is thus the negative of this and it is positive. See Bhagwati,

Brecher, and Hatta [9].

8The Marginal Propensity to Consume is given by ii i

uu u



,since

, from Equation (2.7). 1

e

9Since the developing country’s production of the pollutant will be

affected by the emission but not consumption its budget equation









1π0,qcu PP







which simplifies to Equation (4.3).

J. DOGBEY

560

good using Cramer’s Rule is:







2π12π

dΔ







 



(4.5)

From Equation (4.5) above, it is obvious that the rela-

tive price of the good (when consumption and production

are both non-spatially separable) falls as the pollution

generating activity increases.

3. Comparing Results for All Cases

This section compares the comparative static analysis for

all three cases and provides intuition behind the results

obtained.

If the good is non-spatially separable in consumption

only (Case 1) the relative price of the good increases. If

the good is non-spatially separable in production (Case 2)

or non-spatially separable in both consumption and

production (Case 3) the relative price of the good falls.

Note that even though Cases 2 and 3 have same direction

(sign) for the relative price of the good, the magnitude is

higher for former than the latter case. The results there-

fore indicate that goods that are nonspatially separable in

at least production have relatively lower relative prices.

The intuition behind the above result is that ways of

restraining firms from increasing pollution emissions are

more effective than ways of restraining consumers. Cou-

pled with government regulations, specialization can

enable firms find efficient ways of producing the good in

order to reduce emissions considerably. Lower pollution

levels cost society and firms less and this causes the

global relative price of the good to fall. As there is little

or no specialization in or restraint on consumption, in-

crease trade in goods that are non-spatially separable in

consumption reflects directly in the relative price of the

goods. Second, relatively lower emission tax on firms in

the developing country reduces the cost of production

and hence the fall in the relative price of the good.

4. Concluding Remarks

This study investigates the direction of global relative

prices during bilateral trade involving a pollutant in a

multilateral context. The results suggest that increased

trade in goods that generate pollution in production or in

both production and consumption will reduce relative

prices as opposed to goods that generate pollution in

consumption only. Thus even though a good may be a

pollutant, depending on how spatially separable it is,

trade and specialization can still cause it’s relative price

to fall. This is true for the good in question even in coun-

tries that are non-participants.

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