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Three-Win Strategies of Trade
and Domestic Tax Reforms in the
Presence of Pollution
Michael S. Michael and Panos Hatzipanayotou
CESifo GmbH
Poschingerstr. 5
81679 Munich
Germany
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Three-Win Strategies of Trade and Domestic Tax Reforms in the Presence of
Pollution
Michael S. Michael♣ and Panos Hatzipanayotou♠
February 2009
Abstract
This paper builds a small open economy trade model where there is pollution from
production and consumption of all goods. The paper identifies sufficient conditions
under which tax reforms improve welfare, increase government tax revenue and
reduce pollution. In particular we examine, first, a piecemeal and a radial consumerprice-neutral reform of tariffs and consumption taxes whereby either the consumer
price of a selected commodity remains constant, or the consumer prices for all goods
remain constant. Second, a piecemeal and a radial producer-price-neutral reform of
export and production taxes whereby either the producer price of a selected
commodity remains constant, or the producer prices for all goods remain constant.
Keywords: Domestic and trade tax reforms, Production and consumption generated
pollution, Government tax revenues, Welfare.
J.E.L Classification: F13, H20
♣
Department of Economics, University of Cyprus; P.O. Box 20537 Nicosia, CY
1678, Cyprus, and CESifo (Center for Economic Studies and the Ifo Institute of
Economic Research), Email: [email protected], Tel.: 0035722892433; Fax:
0035722892432
♠
Department of International and European Economic Studies, Athens University of
Economics and Business; 76, Patission str., Athens 104 34, Greece, and CESifo, Email: [email protected], Tel: 0030 210 8203189; Fax: 0030 210 8214122.
Acknowlegements: We thank B. Copeland, P. Neary, P. Raimondos-Møller, P. Sgro, E. Yu, and
participants of the Workshop on Growth, Trade and Environment at the Venice International
University, June 2008, and of ETSG 2007 for useful comments and suggestions. For remaining
shortcomings the authors are solely responsible.
Three-Win Strategies of Trade and Domestic Tax Reforms in the Presence of
Pollution
1. Introduction
During the past couple of decades, there is a general consensus regarding the
reform of national tax systems. For example, international institutions such as the
GATT/WTO, the IMF and the World Bank encourage governments to reform their
indirect tax structures requiring the reliance for raising public sector revenues
primarily on taxes such as income taxes, consumption taxes, and VATs, rather than
tariffs and export taxes. Such tax reforms, however, are likely to reduce government
revenues for many LDCs which historically have relied on tariffs for their tax
revenues. Given such undesirable revenue implications of indirect tax reforms,
designing reform strategies which improve welfare without, however, eroding
government tax revenues, has been an important issue both in theoretical research and
in policy agendas.
Motivated by such considerations, a theoretical literature identifies sufficient
conditions under which proposed indirect tax reforms, e.g., reduction in trade taxes
and increase in domestic taxes, improve welfare and either retain constant or increase
government tax revenues, e.g., see, Michael et al. (1993), Hatzipanayotou et al.
(1994), Keen and Lighthart (2002), Emran (2005), Naito (2006), and Naito and Abe
(2008). 1
In the process of economic development and growth an emerging literature
has extensively examined the relationship between expanding economic activity (e.g.,
international intensification of production, or growing volumes of international trade)
and environmental quality. Yet, only a small number of studies addresses the welfare
implications of tax reforms in the presence of pollution generated from production or
consumption activities. On the other hand, most of the studies doing so, abstract from
government revenue considerations, e.g., Copeland (1994), Beghin et al. (1997),
Turunen-Red and Woodland (2004). Notable exceptions, within a static general
equilibrium framework of an open economy, are Beghin and Dessus (1999), and
1
Kreickemeier and Raimondos-Møller (2008) examine whether a consumer-price-neutral radial
reduction in tariffs and increase in consumption taxes improves the market access of a small open
economy. Moreover, they note that such a reform scheme is less efficient, both in terms of welfare and
market access considerations, compared to a reform of only tariffs (e.g., see Ju and Krishna, 2000).
See, among others, Anderson and Neary (2007) for the welfare and market access implications of tariff
reforms.
1
Kayalica and Kayalica (2005), who examine the welfare implications of trade and
domestic tax reforms with a non-decreasing government revenue constraint. Naito
(2005) does so in a dynamic framework of an open economy.
In the present study, we construct a general equilibrium model of a small open
economy producing many traded goods, whose production and consumption entail the
emission of pollutants that adversely affect households’ utility. The country’s
structure of indirect taxes consists of trade, production and consumption taxes. We
identify sufficient conditions under which selective tax reforms improve welfare,
increase government tax revenue, and lower pollution emissions.
Specifically, we consider the following reforms of indirect taxes. First,
consumer-price-neutral reforms whereby we reduce the tariff rate on a given good
and increase its consumption tax, leaving its consumer price unchanged, or where we
reduce all tariffs and increase all consumption taxes leaving all consumer prices
unchanged. Second, producer-price-neutral reform whereby we reduce the export tax
on a given good and increase its production tax, leaving its producer price unchanged,
or where we reduce all export taxes and increase all production taxes leaving all
producer prices unchanged.
2. The Model
Consider a small open, perfectly competitive economy, which produces and
consumes K internationally traded goods. There are pollution emissions associated
with the production and consumption of all goods. Let z j and rj , j = 1, 2,....K ,
denote respectively the levels of production and consumption generated pollution
from the j th good.
The supply of factors of production is fixed. The country is a price taker in
world commodity markets.2 Thus, the international prices of all goods are fixed and
are denoted by the price vector p* ≡ ( p1* ..... pK* ) , a (1× K ) vector. Various restrictions
exist on all goods in the form of specific domestic taxes, i.e., production and
consumption taxes, and of specific trade taxes, i.e., export taxes and import tariffs.3
2
We follow a standard practice of the literature of indirect tax reforms, which, for analytical
convenience confines the analysis of such tax reforms in the context of small open economies.
3
The qualitative results hold regardless of whether it is assumed that there is a numeraire commodity,
either from the class of the exported or of the imported goods, which may be taxed or untaxed,
polluting or not. Because of this, the analysis treats all goods as polluting and taxed.
2
Thus, for the j th commodity, the domestic prices for consumers (q j ) and producers
( p j ) are respectively given by q j = p*j + τ j + t j and
p j = p*j + τ j − s j , where
τ j > 0(< 0) denotes a specific import tariff (export tax), t j and s j respectively denote
a consumption and production tax on the same good.
The economy’s production side is represented by the function R( p) , which
captures the economy’s maximum revenue from production of the traded goods, with
producers’ price vector p . The R( p ) function is convex and homogeneous of degree
one in producer prices, and by the envelop theorem R p j (= ∂R / ∂p j ) is the supply
function of the j th good. We define z j = α j R p j ( p ) to be the level of pollution
associated with the production of the j th good and α j ≥ 0 are the units of pollution
per unit of output of the j th good.
The demand side of the economy comprises identical households which
consume the K commodities, whose utility is adversely affected by production and
consumption generated pollution. A representative household’s preferences are
captured by the expenditure function E (q, z , r , u ) denoting the minimum expenditure
on goods achieving a level of utility (u ) , at consumer price vector q ≡ (q1.....qK ) , and
vectors of production generated pollutants z and of consumption generated
pollutants r . The E (q, z , r , u ) function is increasing in z , r , and u , non-decreasing and
concave in q , i.e., Eqq is a ( K × K ) negative semi-definite matrix. The derivative
Eq j (= ∂E / ∂q j ) is the compensated demand for good ( j ) , and the derivatives Ez j and
Erj , respectively, denote the household’s marginal damage caused by the pollutants z j
and rj , thus capturing the household’s marginal willingness to pay for reducing the
production or consumption generated pollutant by one unit (e.g., see Copeland,
1994).4 We define rj = β j Eq j (q, r , z , u ) to be the level of pollution associated with the
consumption of the j th good and β j ≥ 0 are the units of pollution per unit of
consumption of the same good. It is assumed that all consumption activities generate
The E (.) function is increasing in z and r since an increase in any type of pollutant is assumed to
harm the households’ utility. Therefore, to attain a given level of utility, u , private spending on
4
consumption must rise. Moreover, Eu ( = ∂E / ∂u ) denotes the reciprocal of the marginal utility of
income, and it is assumed to equal to one.
3
the same type of pollution (e.g., air pollution) and all the production activities
generate the same type of pollution (e.g., water pollution). 5
The government’s tax revenue (T ) is lump-sum distributed to domestic
households, and it equals the sum of production, consumption and trade tax revenues.
That is,
T = s′R p ( p) + t ′Eq (q, z , r , u ) + τ ′ ⎡⎣ Eq (q, z , r , u ) − R p ( p) ⎤⎦ ,
(1)
where Eq and R p , respectively, are the vectors of compensated demand and supply
functions, τ , s and t are the vectors of trade, production and consumption taxes. A
prime (′) denotes a transposed vector or matrix.The country’s income-expenditure
identity requires that private spending on goods must equal income from production
plus income from lump-sum distributed tax revenue. That is,
E ( q, z , r , u ) = R ( p ) + T .
(2)
Equations (1) and (2) are the main equations of the model, used to examine
what we call the “three-win” strategies of indirect tax reform programs. That is,
designing reforms of production or consumption taxes, and of trade taxes, which
result to an improvement of welfare, an increase in government tax revenue, and to a
decrease in the level of pollution. In the analysis to follow, two reform programs are
considered.
Case I: An indirect tax reform that entails a simultaneous small increase in
consumption taxes and a decrease in import tariffs, so that consumer prices are held
constant. This we call a “consumer-price-neutral” indirect tax reform.
Case II: An indirect tax reform that entails a simultaneous small increase in
production taxes and a decrease in export taxes, so that producer prices are held
constant. This we call a “producer-price-neutral” indirect tax reform.
5
The assumption that all consumption activities and all the production activities generate the same type
of pollution between activities is a simplified assumption and it is only needed in our effort to examine
the effects of various reforms programs on total pollution. The results do not change if consumption
and production activities generate the same type of pollution.
4
We conclude this section by deriving the effects of changes in domestic and
trade taxes on welfare, tax revenues and the levels of pollution. Differentiating
equations (1) and (2), we obtain:
dT = θ ′dEq + (dt + dτ )′ Eq − ϕ ′dR p + (ds − dτ )′ R p , and
(3)
Eu du = − ( β Er − θ )′ dEq − (α Ez + ϕ )′ dR p ,
(4)
where, θ = t + τ and ϕ = τ − s . In the case of imported goods θ > 0 , and ϕ > 0 (i.e., a
net production subsidy) if τ > s . In the case of exported goods ϕ < 0 , and θ < 0 (i.e., a
net consumption subsidy) if −τ > t . Also, changes in the levels of production and
consumption
generated
pollution
are,
respectively,
given
by
dz = α ′dR p and dr = β ′dEq , where:
dEq = Eqq (dt + dτ ) + Eqr dr + Eqz dz + Equ du , and
(5)
dR p = R pp (dτ − ds ) .
(6)
For the rest of the analysis, we assume, for simplicity, that goods and clean
environment are independent in consumption, i.e., Eqr = Eqz = 0 .6,7 Moreover, Equ is a
vector whose all elements are positive assuming that all goods are normal in
consumption, i.e., Eq j u > 0, ∀j ∈ K .
3. Reforms of tariffs and consumption taxes
In this section, we assume that that the government pursues a consumer-priceneutral reform policy by simultaneously reducing tariffs and increasing consumption
6
Subscripts on the functions, i.e., Eqp , Eqz , Eqr , Equ and R pp denote partial derivatives. For example,
Eqq = ∂Eq / ∂q , R pp = ∂R p / ∂p .
7
The assumption that the demand for goods is independent of the environmental quality is often made
in the literature (i.e., Bovenberg 1999, Beghin and Dessus 1999). In the analysis to follow we
assume Eqr = Eqz = 0 while Equ > 0 . This result emerges if the expenditure function has the
following form E ( q, u , z , r ) = g ( q )u + z + r . Among others, Wilson (1991) considers an example
of a direct utility function and Copeland and Taylor (2004) an example of an indirect utility function by
which ordinary, not compensated, demand functions for goods are independent of public good and
pollution, respectively.
5
taxes by the same amount. Export and production taxes are held constant. Using
equations (3)-(6), we get the welfare and tax revenue effects of the proposed reform
policy as follows:
dT = θ ′Equ du − (ϕ ′R pp + R p′ )dτ , and
(7)
Λdu = −(αE z + ϕ ) R pp dτ ,
(8)
where Λ = Eu + ( β Er − θ )′ Equ , and is assumed to be positive.
3.1 Consumer-price-neutral piecemeal reform of a tariff and a consumption tax.
We examine the implications on welfare, government revenues and on the
level of pollution of simultaneously reducing the tariff rate and increasing the
consumption tax on the k th imported good so that its consumer price remains constant,
i.e., dτ k < 0 and dtk > 0 , so that dqk = dtk + dτ k = 0 . Using equation (8) and the
above assumptions, the welfare effect of the consumer-price–neutral tax reform is
given as follows:
Λ
du
= − (α Ez + ϕ )′ R ppk = −(α k Ezk + ϕk ) R pk pk − ∑ (α j Ezj + ϕ j ) R pk p j .
dτ k
j≠k
(9)
Equation (9) can be further elaborated on by using the properties of the revenue
function, i.e., output supply functions are homogeneous of degree zero in prices.
K
Specifically, ∑ p j R p j pk = 0 yields R pk pk = −∑ ( p j / pk ) R p j pk , and by the reciprocity
K
j ≠k
conditions we have R p j pk = R pk p j . Using the above properties in equation (9), the
welfare effect of the proposed consumer-price-neutral tax reform, after some
manipulations, is given as follows:
Λ
du
= −∑ (γ j − γ k ) p j R p j pk ,
dτ k
j≠k
(10)
6
where γ i =
α i E z + ϕi
i
pi
, i = j , k . The net production subsidy of the i th good, ϕ i , is
negative (i.e., net production tax) if the i th good is an exported, and it is positive (i.e.,
net production subsidy) if it is an imported good and τ i > s i . The term α i E zi is the
marginal damage of pollution created by the production of one unit of the i th good or
is the marginal willingness to pay for reducing the pollution generated from the
production of one unit of the i th good. Thus, the term γ i denotes the adjusted for
production generated pollution, total net production subsidy burden on the i th good as
a fraction of its producer price. That is, in the present context of pollution and of a
consumer-price-neutral reform of tariffs and consumption taxes, the total burden on
the i th good consists of the net production subsidy distortion created by the tariff and
the damage caused by the production generated pollution. We call γ i the total net
production subsidy burden ratio for the i th good.
Equation (10) indicates that the proposed consumer-price-neutral reduction in
the tariff rate on the k th good increases social welfare if, first, the k th good is a
substitute in production with all other goods. Second, the total net production subsidy
burden ratio on the k th good is the highest. Intuitively, since a tariff is a production
subsidy and a consumption tax, then reducing the tariff rate on the k th good and
equally increasing the consumption tax levied on it, leaves its consumer price
unchanged, reduces the production subsidy and thus the producer’s price of this good.
Production of the k th good falls and that of all other goods increases since we assume
that goods are substitutes in production. Consumption of all goods remains
unchanged. Since the k th good whose production decreases has the highest total net
production subsidy burden ratio (γ k ) compared with the other goods whose
production increases, implies that social welfare increases.
Using equation (7) and the homogeneity properties of the revenue function,
changes in the level of government revenue, due to the proposed tax reform program,
are given as follows:
dT
du
du
= θ ′Equ
− ϕ ′R ppk + R pk = θ ′Equ
− R pk − ∑ ( µ j − µ k ) p j R p j pk , (11)
dτ k
dτ k
dτ k
j≠k
(
)
7
where µi =
ϕi
pi
, i = j , k is the net subsidy in production of the i th good as a fraction of
its producer price. From the above expression it is clear that sufficient (but not
necessary) conditions for the consumer-price-neutral decrease in the tariff rate on the
k th good to increase the total government tax revenue are that (i) the k th good is a
substitute in production with all other goods, (ii) the net production subsidy on the
k th imported good as a fraction of its producer price is the highest, and (iii) the reform
is welfare improving. Alternatively, the proposed consumer-price-neutral tax reform
entails a positive effect on government revenue if welfare rises and the cost of
production subsidies implied by the tariff does not increase due to the tariff reduction,
(
i.e., the term − ϕ ′R ppk + R pk
) is not positive.
Finally, the effect on the proposed consumer-price-neutral tax reform on
pollution
is
given
as
follows.
Using
the
definitions
of z j (= α j R p j ( p ))
and rj (= β j Eq j (q, r , z , u )) , the properties of the revenue and expenditure functions, and
our assumption that Eqr = Eqz = 0 , we obtain:
⎛ α j αk ⎞
=
⎜⎜ − ⎟⎟ p j R pk p j , and
∑
∑
pk ⎠
j =1 dτ k
j≠k ⎝ p j
K
K
dz j
drj
∑ dτ
j =1
k
K
= ∑ β j Eq j u
j =1
du
.
dτ k
(12.a)
(12.b)
Equation (12.a) captures the reform induced changes in production generated
pollution. It indicates that the proposed consumer-price-neutral decrease in the tariff
rate on the k th good decreases the production generated pollution if the k th good is a
substitute in production to all other goods, and if the units of production generated
pollution of one unit of the k th good per unit of money are the highest. Intuitively, a
tariff on a good entails a subsidy to its production. Thus, reducing the tariff rate on the
k th good reduces its production and raises the production of all other goods if the k th
good is a substitute to all other goods in production. Moreover, if the k th good is
burdened with the highest rate of production pollution per unit of money, then the
decrease in its production and increase in production of all other goods reduces the
8
overall production generated pollution. Equation (12.b), on the other hand, shows that
when the consumer-price-neutral reform improves welfare, consumption increases
and thus it exacerbates the consumption generated pollution.
The previous results of equations (10)-(12.b) are summarized in the following
proposition:
Proposition 1: Consider a small open economy where there exists production and
consumption generated pollution, and whose structure of indirect taxes consists of
trade, production and consumption taxes. Let also the k th imported good be a
substitute in production to all other goods. Then, a tax reform entailing a
simultaneous small decrease of the tariff rate of the k th good and a small increase in
its consumption tax, leaving its consumer price unchanged,
•
increases social welfare if the k th good has the highest total net production
subsidy burden ratio,
•
increases total tax revenue if the tax reform is welfare improving and the k th good
carries the highest net subsidy in production as a fraction of its producer price,
•
reduces pollution generated from production if the production of the k th good
generates the most units of production pollution per unit of money, and it
exacerbates the consumption generated pollution.
The above results can be compared to related results of the tax reform
literature in the absence of pollution. For example, assuming substitutability of goods
in production, Keen and Ligthart (2002), Corollary 1.c, demonstrate that reducing the
highest tariff rate and increasing the consumption tax on the same good so that its
consumer price remains constant, improves welfare and raises government revenues.
In our analysis, again under the assumption of substitutability of goods in production,
the proposed welfare improving, revenue increasing consumer-price-neutral reform
of tariffs and consumption taxes requires lowering the tariff rate and equally
increasing the consumption tax on the good exhibiting the highest net production
subsidy burden ratio. This ratio accounts not only for the net production subsidy
burden, due to the presence of tariffs and production taxes, but also for the
households’ willingness to pay for reducing production generated pollution.
9
3.2 Radial consumer-price-neutral reform in tariffs and consumption taxes
Another type of reform of the trade and consumption taxes considered in the
literature is that of the simultaneous radial reduction of tariffs and of an equal increase
in consumption taxes, leaving all consumer prices unchanged. In what follows we
examine the implications of such a reform exercise on welfare, government revenues
and on the levels of pollution. In the present context of pollution, however, we set the
radial reduction of tariffs and the simultaneous equal increase in consumption taxes to
equal a small amount λ of the total burden of the net production subsidy of the
imported goods. That is, dt = − dτ = λ (α Ez + ϕ ) . Substituting this equal change in
equation (8) gives:
Λdu = λ (α Ez + ϕ )′ R pp (α Ez + ϕ ) .
(13)
Equation (13) shows that a consumer-price-neutral radial reduction of all tariffs and a
simultaneous equal increase of all consumption taxes by an amount
λ of the total
burden of the net production subsidy of the imported goods increase social welfare.
Next we examine whether the aforementioned tax reform increases total
government revenue. Changes in government tax revenues are given as follows:
dT = θ ′Equ du − ( R′p + ϕ ′R pp )dτ = θ ′Equ du + λ ( R p + ϕ ′R pp )′(α ′Ez + ϕ ) .
(14)
It is well known that a tariff is a consumption tax and a production subsidy, and thus a
reduction in tariffs is a reduction in production subsidies. The term −( R p + ϕ ′R pp )dτ
is the change in the cost of the net production subsidies implied by the reduction in
tariffs. Thus, any reduction in tariffs that does not increase the total cost of the net
production subsidies implied by them, increases total government revenue (sufficient
but not necessary condition).
Finally, changes in production and consumption generated pollution due to the
proposed tax reform are given by:
K
∑ dz
j =1
j
= α ′dR p ( p ) = −λα ′(α Ez + ϕ ) R pp , and
(15.a)
10
K
∑ dr
j =1
j
= β ′Equ
du
′ .
= Λ −1λβ (α Ez + ϕ )′ R pp (α Ez + ϕ ) Equ
dτ
(15.b)
Equation (15.a) indicates that a consumer-price-neutral radial reduction of all tariffs
and a simultaneous equal increase in consumption taxes by an amount λ of the total
burden of the net production subsidy of the imported goods, may not reduce the level
of production generated pollution, since −λα (α Ez + ϕ )′ R pp cannot be signed
unambiguously. On the other hand, equation (15.b) indicates that the proposed
consumer-price-neutral reform program unambiguously exacerbates consumption
generated pollution.
Proposition 2: Consider a small open economy where there exists production and
consumption generated pollution, and whose structure of indirect taxes consists of
trade, production and consumption taxes. Then, a consumer-price-neutral radial
reduction of tariffs and a simultaneous equal increase in consumption taxes by a
small amount λ of the total burden of the net production subsidy of the imported
goods,
•
increases social welfare,
•
total government revenue increases if this reform does not increase the total cost
of the net production subsidies implied by the tariffs (sufficient but not necessary
condition),
•
has an ambiguous effect on production generated pollution and exacerbates
consumption generated pollution.
The results summarized in Proposition 2 can be again compared to the related
results of the tax reform literature in the absence of pollution. For example,
Hatzipanayotou et al. (1994), Proposition 2, Keen and Ligthart (2002), Corollary 1.b,
conclude that a radial consumer-price-neutral tariff reduction and increase in
consumption taxes raises welfare and government revenues. In the present context of
pollution, the consumer-price-neutral radial reduction in tariffs and increase in
consumption taxes is welfare improving if all tariffs are reduced and all consumption
taxes are raised by the same small amount (λ ) of the total burden of the net production
subsidy on all goods. On the other hand, this reform of tariffs and consumption taxes
11
also raises government revenue, if it does not increase the total cost of production
subsidies implied by the tariffs.
Two special cases of the above general model are those where there is (i)
“clean” production, i.e., α j = 0∀j ∈ K and only consumption generated pollution, or
(ii) “clean” consumption i.e., β j = 0∀j ∈ K and only production generated pollution.
In the first case, either with a piecemeal or a radial consumer-price-neutral reform,
the conditions leading to a welfare improvement or to an increase in government
revenues are the same as those emerging in standard literature models without
pollution externalities. Since welfare improves with either reform program,
consumption generated pollution worsens. In the second case, the impact of the
reform programs on welfare, government revenue and on production generated
pollution are the same as those stated in Propositions 1 and 2.
3.3 Zero cross-price substitution effects in production
We conclude this section by considering another special case of the above
results, whereby it is assumed that all “cross-substitution price effects” in production
are zero.8 In the case of the consumer-price-neutral piecemeal reform of the tariff and
consumption tax on the k th good, equations (9), (11), (12.a) and (12.b) become:
⎛ du
Λ⎜
⎝ dτ k
⎞
⎟ = −(α k Ezk + ϕk ) R pk pk ,
⎠
dT
du
= θ j Eq j u
− ϕ k R pk pk − R pk ,
dτ k
dτ k
K
dz j
∑ dτ
j =1
K
drj
∑ dτ
j =1
k
k
=
dzk
= α k R pk pk > 0 , and
dτ k
K
= ∑ β j Eq j u
j =1
du
.
dτ k
(16)
(17)
(18.a)
(18.b)
Equations (16) and (17) respectively indicate that if there is a net production
subsidy on the k th imported good, i.e., ϕk > 0 , then the proposed consumer-priceneutral tariff reduction improves welfare and increases government tax revenues. If,
8
This special case is examined by Emran (2005) in the context of producer-price-neutral tax reforms.
12
however, ϕk < 0 , i.e., the k th imported good is burdened by a net production tax, then
the proposed indirect tax reform improves welfare if the marginal willingness to pay
for reducing the pollution generated from the production of one unit of the k th good is
larger than the net production tax i.e., −ϕ k < α k Ezk . Government tax revenue rises
(
if − µk < ε k−1 , where ε k = ∂R pk / ∂pk
)( p
k
/ R pk
)
(a sufficient but not necessary
condition). In case where sk = 0 , i.e., no production tax is levied on the k th imported
good, then ϕk = τ k > 0 and the proposed indirect tax reform unambiguously improves
welfare and raises government tax revenues. As indicated by equation (18.a),
production pollution unambiguously falls, while consumption generated pollution, as
depicted by equation (18.b) exacerbates as long as the proposed reform improves
welfare.
Similarly, with zero cross-substitution price effects in production, R pp is a
diagonal matrix with all its elements positive. Thus equations (13)-(15.b) give again
the welfare, revenue and pollution effects of a consumer-price-neutral radial reform
in tariffs and consumption taxes by a small amount λ of the total burden of the net
production subsidy of the imported goods. This reform program always improves
welfare and increases the consumption generated pollution. The government revenue
increases and the production generated pollution decreases if all goods carry net
production subsidies (i.e., ϕ > 0 ) (sufficient but not necessary condition). If some
goods carry net production taxes (i.e., ϕ i < 0 ), then production generated pollution
decreases if − ϕ i < α i E Z I for all i th goods with a net production tax. Similarly, the
above uniform reform program increases government revenue if for all the k th goods
with a net production tax we have
−ϕ k < α k Ezk and − µk < ε k−1 . The following
Corollary summarizes the previous findings.
Corollary: Consider a small open economy with production and consumption
generated pollution and the use of consumption, production and trade taxes for
generating government revenues. Let all “cross-substitution price effects” in
production be zero. Then:
• A small consumer-price-neutral decrease in the tariff rate on the k th good and
increase in its consumption tax
13
(i)
unambiguously improves welfare and raises government revenues if the k th
imported good carries a net production subsidy. If the k th imported good
carries a net production tax, welfare improves
if −ϕ k < α k Ezk , and
government revenue increases if −ϕ k < α k Ezk and − µk < ε k−1 ,
(ii)
reduces the level of production generated pollution, and it exacerbates the
level of consumption generated pollution as long as the reform is welfare
improving.
• A small consumer-price-neutral radial reduction in tariffs and increase in
consumption taxes by a small amount λ of the total burden of the net production
subsidy of the imported goods
(i)
unambiguously improves welfare, and exacerbates consumption generated
pollution,
(ii)
raises tax revenues, and reduces production generated pollution, if all the
imported goods carry a net production subsidy,
(iii)
increases tax revenue if
− ϕ i < α i E Z I and − µi < ε i−1 , and reduces
production generated pollution if
− ϕ i < α i E Z I , for all the i th imported
goods with a net production tax.9
Consider for example, the case where all imported goods carry a net production
subsidy. Then, any reduction in the tariff rate of a good and an increase in its
consumption tax to keep its consumer price unchanged reduce the net production
subsidy implied by the tariff. The reduction in production subsidy causes its producer
price and output to decrease. The reduction of its output improves efficiency and
reduces pollution which improves welfare. The reduction in production reduces the
subsidy cost and increase government revenue. Similarly, in this case, a small radial
consumer-price-neutral reform of reducing tariffs and increasing consumption taxes
unambiguously improves welfare, raises government tax revenues, and it reduces
production generated pollution while it exacerbates consumption generated pollution.
When s = 0 , thus ϕ = τ > 0 , the proposed consumer-price-neutral radial reform in tariffs and
consumption taxes unambiguously raises government revenues and reduces production generated
pollution.
9
14
4. Reforms of export and production taxes
In this section, we assume that that the government pursues a producer-priceneutral reform by simultaneously reducing export taxes and increasing production
taxes by the same amount. Tariffs and consumption taxes are held constant. The
welfare and tax revenue effects of the proposed reform policy are given, using
equations (3)-(6), as follows:
dT = θ ′Equ du + (θ ′Eqq + Eq′ )dτ , and
(19)
Λdu = − ( β Er − θ )′ Eqq dτ ,
(20)
4.1 Producer-price-neutral piecemeal reform of an export and a production tax.
We examine the welfare, revenue and pollution effects of increasing the
production tax on the k th exported good, i.e., dsk > 0 , and of simultaneously reducing
its export tax, i.e., dτ k > 0 , so that its producer price is held constant, i.e.,
dpk = dτ k − dsk = 0 . Note that since we denote an export tax by τ i < 0 , a reduction of
its size implies that, algebraically, τ i rises.
Using equation (20), and the above assumptions, after some calculations, we
obtain the welfare effects of the producer-price-neutral tax reform as follows:
Λ
du
= − ( β Er − θ )′ Eqqk = −( β k Erk − θ k ) Eqk qk − ∑ ( β j Erj − θ j ) Eqk qj .
dτ k
j≠k
(21)
Equation (21) can be further elaborated on by using the properties of the expenditure
function, i.e., compensated demand functions are homogeneous of degree zero in
prices. Specifically,
∑q E
j
K
q j qk
= 0 yields Eqk qk = −∑ ( q j / qk ) Eq j qk , and by the
j≠k
reciprocity conditions we have Eq j qk = Eqk q j . Using the above properties and after some
manipulations, the welfare effect of the proposed producer-price-neutral tax reform is
given as follows:
Λ
du
= ∑ (σ j − σ k )q j Eq j qk ,
dτ k j ≠ k
(22)
15
where σ i = −
( β i Eri − θi )
qi
, i = j , k . The net consumption subsidy of the i th good, θ i is
positive (i.e., net consumption tax) if it is an imported good and it is negative (i.e., net
consumption subsidy) if it is an exported one and − τ i > si . The term β i E ri is the
marginal damage of pollution created by the consumption of one unit of the i th good
or is the marginal willingness to pay for reducing the pollution generated from the
consumption of one unit of the i th good. Thus, the term σ i denotes the adjusted for
consumption generated pollution total net consumption subsidy burden on the i th
good as a fraction of its consumer price. That is, in the present context, the total net
consumption burden on the i th good consists of the net consumption subsidy distortion
and the damage caused by the consumption generated pollution. We call σ i the total
net consumption subsidy burden ratio.
Equation (22) shows that the proposed producer-price-neutral decrease in the
export tax rate on the k th exported good increases social welfare (i.e., ( du / dτ k ) > 0 ),
if (i) it is a substitute in consumption to all other goods, and (ii) the total net
consumption subsidy burden ratio on this good is the highest. Intuitively, since the
export tax is a production tax and consumption subsidy, then by reducing the export
tax on the k th good and equally increasing the production tax levied on it, leaves its
producer price constant, reduces the consumption subsidy and increases the consumer
price of this good. Production of all goods remains unchanged, while the higher
consumer price of the k th exported good causes its consumption to decrease and
increases the consumption of all other goods since commodities are assumed
substitutes in consumption. The k th exported good has the highest total net
consumption subsidy burden ratio
(σ )
k
compared with all other goods. Thus, the
reduction in its consumption causes total welfare to increase.
Using equations (19) and (21), and the homogeneity properties of the
expenditure function, changes in the level of government revenue, due to the proposed
tax reform program, are given as follows:
dT
du
= θ ′Equ
+ Eqk + θ ′Eqqk = Eqk + Λ −1 ∑ (−ξ k + ξ j )q j Eq j qk ,
dτ k
dτ k
j≠k
(
)
(23)
16
where ξi =
θi
qi
, i = j , k is the net subsidy in consumption of the i th exported good as a
fraction of its consumer price. From the above expression it is clear that sufficient
(but not necessary) conditions for the producer-price-neutral decrease in the export
tax on the k th good to increase the total government tax revenue, i.e., dT / dτ k > 0 , are
that (i) the k th good is a substitute in consumption to all other goods, and (ii) its net
subsidy in consumption as a fraction of its consumer price is the highest. Intuitively,
since the export tax is a consumption subsidy and production tax, by reducing the
export tax on the k th good reduces its consumption subsidy, and thus it reduces its
consumption and raises the consumption of all other goods since goods are substitutes
in consumption. Moreover, assuming that the k th exported good carries the highest
net consumption subsidy ratio relative to all other goods, the cost of the subsidy
decreases and total tax revenues increase.
Finally, because dR p = 0 due to the producer-price-neutral tax reform, the
only source of change in pollution is from changes in consumption. Using the
definition of rj (= β j Eq j ) , the properties of the expenditure function and equation (21),
the effect of the producer-price-neutral tax reform on pollution emissions is given by:
⎛ βk β j ⎞
⎛
du ⎞
−1
β
=
+
=
Λ
+ ⎟ q j Eq j qk .
E
E
⎜⎜ −
⎜
⎟
∑
∑
∑
j
q j qk
q ju
dτ k ⎠
qk q j ⎟⎠
j =1 dτ k
j =1
j≠k ⎝
⎝
K
drj
K
(24)
Sufficient conditions for the producer-price-neutral tax reform to reduce the
consumption generated pollution, thus the overall level of pollution, are, first, that the
units of consumption generated pollution of one unit of the k th good per unit of
money are the highest. Second, that the k th good is a substitute to all other goods in
consumption. This condition is in line with the results in equations (22) and (23) for
the producer-price-neutral tax reform to improve welfare and to raise government tax
revenue. The following proposition summarizes the results of this section:
Proposition 3: Consider a small open economy where there exists production and
consumption generated pollution, and whose structure of indirect taxes consists of
17
trade, consumption and production taxes. Let also the k th exported good be a
substitute in consumption to all other goods. Then, a tax reform entailing a small
decrease of the export tax of the k th good and a small increase in its production tax,
leaving its producer price unchanged,
•
improves social welfare if the k th good has the highest total net consumption
subsidy burden ratio,
•
increases government tax revenue if the this good has the highest net consumption
subsidy as a fraction of its consumer price,
•
reduces consumption generated pollution, thus the aggregate level of pollution, if
the units of consumption generated pollution of the k th good per unit of money
are the highest.
The results from proposition 3 can be compared to existing results of the relevant
literature of producer-price-neutral reforms in export and production taxes.
Specifically, Keen and Ligthart (2002) note that such a reform increases welfare and
public revenue if the increased consumer prices reduce the value of compensated
demand at world prices, and all goods are Hicksian substitutes. Emran (2005)
examines the effects of a welfare-improving and revenue-increasing producer-priceneutral reform in export and production taxes in an economy where the administration
of taxes is costly but there is no pollution.10 In his analysis, the producer-priceneutral reform in export and production taxes increases government revenues and
welfare if the k th good (i) bears the lowest tax burden in consumption,11 (ii) is a
substitute to all other goods in consumption, and (iii) the cost of administering taxes is
lower than a threshold.
4.2 Radial reform of export and production taxes
We now examine the welfare, pollution and government revenue effects of a
radial producer-price-neutral reform in export taxes and production taxes, which
10
In Emran's terminology tax administration is costly in the sense that when a $1 of tax revenue is
raised, only an amount $ (1 − δ ) , where δ ∈ (0,1) is the cost of administering taxes, actually ends up
to the government’s treasury.
11
In Emran (2005) the consumption of each commodity is burdened by a consumption tax (t j ) and an
export tax ( −τ j < 0) . The indirect tax burden on consumption of a j commodity,
th
θ j = t j − τ j is
positive, implying that the consumption tax is greater than the consumption subsidy implied by the
export tax.
18
leaves all producer prices constant. We set the radial reduction of export taxes and the
simultaneous equal increase in production taxes equal to a small amount λ of the total
net
consumption
subsidy
burden
of
the
exported
goods.
That
is, − ds = dτ = λ ( β Ez − θ ) . Substituting this equal change in equation (20) gives:
Λdu = −λ ( β Er − θ )′ Eqq ( β Er − θ ) .
(25)
Equation (25) shows that social welfare improves with a producer-price-neutral radial
reduction of all export taxes and a simultaneous equal increase in all production taxes
by an amount λ of the total net consumption subsidy burden. However, this radial
producer-price-neutral reform in export and production taxes has an ambiguous effect
on both government tax revenues and on consumption generated, thus aggregate,
pollution.12 The following proposition summarizes the previous findings.
Proposition 4: Assume the existence of pollution, and the use of production,
consumption and trade taxes by the government for generating revenues. Then, a
producer-price-neutral radial reduction of export taxes and a simultaneous equal
increase in production taxes by a small amount λ of the total net consumption subsidy
burden of the exported goods,
•
increases social welfare,
•
has an ambiguous effect on government tax revenues and on consumption
generated, thus aggregate, pollution.
A special case of the above general model is the one where we have “clean”
consumption, i.e., β j = 0∀j ∈ K . In such a case, the conditions for welfare
improvement and revenue increase of the two reform programs are the same as the
ones we get in the absence of any pollution. That is, the piecemeal producer-priceneutral reduction in the export tax and increase in production tax burdening the
k th good improves welfare and raises government tax revenues if the k th good is a
12
It
that dr = βλΛ
is
easily
shown
−1
( β Er − θ )′ Eqq .
that dT
= λ ( β Ez − θ )′ ( Eq + Λ −1θ ′Eqq ) ,
and
The right-hand-side of both equations cannot be signed
unambiguously.
19
substitute in consumption to all other goods and it carries the highest net consumption
subsidy as a fraction of its consumer price.13 Whether production is a “clean” activity
or not bears no impact on the results, since the proposed producer-price-neutral
reform has no effect on levels of production, and thus on production generated
pollution.
Another special case, we briefly comment on, is when the cross-price substitution
effects in consumption are zero. In this case, as equation (21) shows, the producerpiece-neutral piecemeal reform, improves welfare if there is a net consumption
subsidy on the k th exported good, i.e., θ k < 0 . If, however, θ k > 0 , i.e., the k th
exported good is burdened by a net consumption tax, then, a sufficient and necessary
condition for the reform to improve welfare is that the marginal willingness to pay for
reducing the pollution generated from the consumption of one unit of the k th good is
larger than the net consumption tax i.e., θ k < β k Erk .
5. Concluding Remarks
This paper derives sufficient conditions under which specific reforms in trade
and domestic taxes achieve, what we call, a three-win objective. That is, an
improvement in welfare, an increase in government tax revenues, and a reduction in
pollution generated from production and consumption activities. This three-fold
objective set by the paper is being motivated by the fact that production and
consumption activities entail the emission of environmentally harmful pollutants
which affect negatively households’ welfare. Tax reform policies, on the one hand,
affect the aggregate levels of pollution due to the effects on economic activity, and on
the other hand, tax reform policies traditionally viewed as welfare improving and
revenue increasing may become less effective in achieving these objectives due to the
presence of these pollution externalities. By and large, the sizeable literature
examining the welfare and tax revenue implications of various indirect tax reforms
has overlooked these issues.
In light of the above considerations, the paper considers the welfare, tax
revenue, and pollution implications of a small piecemeal or a small radial (i)
consumer-price-neutral reform of reducing tariffs and increasing consumption taxes,
13
In equations (10) and (11) we now have σ i = ξi =
θi
qi
, i = j, k .
20
and (ii) producer-price-neutral reform of reducing export taxes and increasing
production taxes. The propositions and the corollary of the paper summarize the
sufficient conditions which ensure the three-win objectives of these tax reform
programs. These sufficient conditions, on the one hand, rely on certain relationships
of the standard tax reform literature, e.g., substitutability in production or
consumption between the imported or exported commodity whose taxes are reformed,
to all other goods. In this way, the results of equivalent consumer-price-neutral and
producer-price-neutral tax reforms of the standard tax reform literature are imbedded
in the present, expanded by pollution externalities, analytical framework. On the other
hand, the noted sufficient conditions rely on relationships resulting from the presence
of production and or consumption generated pollution, and from the comprehensive
indirect tax structure consisting of both trade and domestic taxes.
It appears from the previous analysis that in the context of piecemeal reforms,
a producer-price-neutral reform is more likely than a consumer-price-neutral reform
to reduce overall pollution. This result is attributed to the fact that the former reform
policy copes only with consumption generated pollution while production generated
pollution remains unchanged since producer prices and levels of production do not
change. On the other hand, a welfare improving piecemeal or radial consumer-priceneutral reform while it reduces production generated pollution, under the conditions
of the model, it unambiguously exacerbates consumption generated pollution, thus
rendering an ambiguous impact on the economy’s overall level of pollution.
Lastly, to enhance the understanding of the general results, we consider special
cases such as assuming only either production generated or consumption generated
pollution, or assuming zero cross-price substitution effects in production or
consumption. For example, in the case of a piecemeal consumer-price-neutral reform
of tariffs and consumption taxes, assuming “clean” consumption and only production
generated pollution, Proposition 1 gives the sufficient conditions under which we can
achieve the three objectives, i.e., increase welfare and government revenue and reduce
pollution. On the other hand, under the same assumption, a producer-price-neutral
reform of export and production taxes produces welfare and tax revenue effects
similar to those of standard literature model without pollution externalities.
21
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23