This paper studies the environmental tax and trade liberalization in a mixed duopolistic market wherein environmental damage is associated with consumption. In particular, we consider the effect of privatization on environmental tax and the effect of trade liberalization on the environment in an importing country. The results show that the optimal environmental tax in a mixed duopoly is higher than the Pigouvian level and the optimal tax in a pure duopoly. Furthermore, trade liberalization does not alter the environment.

Shuichi Ohori

English

Research Papers in Economics

 
 
 
 
 
 
 
Discussion Paper No. 622 
 
“Environmental Tax and Trade Liberalization in a Mixed Duopoly” 
 
by   
Shuichi Ohori 
  
 
June 2006 
KYOTO UNIVERSITY 
KYOTO, JAPAN 
http://www.kier.kyoto-u.ac.jp/index.html 
KYOTO INSTITUTE 
OF 
ECONOMIC RESEARCH 
KIER DISCUSSION PAPER SERIES Environmental tax and trade liberalization in a
mixed duopoly∗
Shuichi Ohori†
Kyoto Institute of Economic Research, Kyoto University, JAPAN.‡
This version: June 2006
Abstract
This paper studies the environmental tax and trade liberalization in
a mixed duopolistic market wherein environmental damage is associated
with consumption. In particular, we consider the eﬀect of privatization on
environmental tax and the eﬀect of trade liberalization on the environment
in an importing country. The results show that the optimal environmental
tax in a mixed duopoly is higher than the Pigouvian level and the optimal
tax in a pure duopoly. Furthermore, trade liberalization does not alter
the environment.
∗All remaining errors and ambiguities remain my responsibility.
†E-mail: ohori@kier.kyoto-u.ac.jp
‡Address: Kyoto Institute of Economic Research, Kyoto University, Yoshida Hommachi
Sakyo, Kyoto, 606—8501, Japan.
11. Introduction
It is observed that in many developing and eastern European countries, state-
owned enterprises are faced with issues related to poor environmental quality
and competition from foreign ﬁrms.1 Although the privatization of such ﬁrms is
expected to foster environmental beneﬁts as well as greater production eﬃciency,
privatization has been deterred by the poor environmental quality caused by
the failure of the centrally planned economies to control pollution. This is
because governments and investors are concerned about the potential liability
of accumulated environmental contamination and the cost of cleanup (Lovei and
Gentry 2002). Additionally, they are exposed to the dominance of foreign ﬁrms
within the privatized markets that result from trade liberalization. There is
concern that the inﬂow of foreign ﬁrms into these markets leads to the expansion
of consumption and production in the importing countries and consequently
results in environmental degradation.
This paper investigates the optimal environmental tax and the environmen-
tal eﬀect of trade liberalization in a mixed duopoly wherein one public ﬁrm
competes with one private ﬁrm.2 As a benchmark, we use the study conducted
by Lai (2004) to compare the optimal environmental tax before privatization
with that after privatization. Lai (2004) considers the case of the environmen-
tal damage associated with consumption in a pure duopoly wherein one home
private ﬁrm competes with one foreign private ﬁrm. Although it has been ar-
gued that trade liberalization results in the environmental degradation of the
importing country,3 Lai (2004) demonstrates that trade liberalization on the
dirty good leads to environmental improvement.
In this paper, we ﬁnd that when pollution is associated with environmentally
harmful consumption, the optimal environmental tax rate in the case of a mixed
duopoly is higher than both the standard Pigouvian level and the optimal tax
rate in the case of a pure duopoly. This result implies that the privatization
of the public ﬁrm decreases the optimal environmental tax. In addition, trade
liberalization does not aﬀect the environment. The remainder of this paper is
organized as follows. Section 2 explains the basic model. Section 3 includes the
1For theoretical studies on environment-privatization relations, see Bluﬀstone and Panay-
otou (2000), Chimeli (2003), and Ohori (2006). Alternatively, for empirical studies, see Boyd
(1996), Anderson and Zylicz (1999), Auer et al. (2001), and Lovei and Gentry (2002), among
others.
2For some analyses of mixed oligopoly models in a foreign context, see Fjell and Pal (1996),
Pal and White (1998), and Fjell and Heywood (2002).
3For previous theoretical studies regarding the issue, see, for example, Krutilla (1991),
Walz and Wellisch (1997), and Damania et al. (2003).
2results of the analysis. Section 4 presents conclusions.
2. The model
The present model follows Lai’s (2004) basic set-up. Consider one public ﬁrm
(ﬁrm 0) located in a home country and one private ﬁrm (ﬁrm 1) located in a for-
eign country. It is assumed that the public ﬁrm maximizes the sum of consumer
surplus and its own proﬁt, while the private ﬁrm maximizes only its proﬁt.4
The home and foreign ﬁrms produce a homogeneous good and compete in the
home country’s market by choosing their quantity levels. It is assumed that
the consumption of the good, given by qi (i = 0,1) , leads to pollution. Some
examples of consumption-type negative externalities are medical waste and the
eﬄuent gas generated by cars and motorbikes. The home government sets the
environmental tax t to control the pollution that results from environmentally
harmful consumption. In order to shapen the study, we assume that the inverse
demand function is linear, p ≡ p(q0 + q1) with p￿ < 0 and p￿￿ = 0. The proﬁt
function of ﬁrm i is given as
π0 = (p − c0 − t)q0 and (1)
π
1 = (p − c1 − t − r)q1, (2)
where ci is the constant marginal production cost and r is the tariﬀ rate.5 We
assume r ≥ 0. It is also assumed that the marginal production cost of the
domestic ﬁrm is higher than that of the foreign ﬁrm (c0 > c1 > 0) because
public ﬁrms are generally less eﬃcient than private ﬁrms.6 Furthermore, this
paper considers trade liberalization to be tariﬀ reduction.
The public ﬁrm’s objective function is deﬁned as the sum of consumer surplus
and the ﬁrm’s proﬁt and is given as
U =
￿ q0+q1
0
p(η)dη − p(q0 + q1) + π0. (3)
The environmental damage function is given by D = θ(q0 + q1), where θ
denotes the marginal environmental damage. We assume θ ≥ 1. It should be
noted that an increase in environmentally harmful consumption results in an
4In this paper, the public ﬁrm’s purpose is not assumed to be the maximization of social
welfare, including environmental damage, because the public ﬁrm would ﬁnd it diﬃcult to
control the environmental damage associated with consumption.
5For simplicity, this paper neglects the ﬁxed cost. However, this has no bearing on my
discussions.
6See Cremer et al. (1989) for a justiﬁcation of this assumption.
3increase in environmental damage. Social welfare in the home country is thus
written as
W =
￿ q0+q1
0
p(η)dη − p(q0 + q1) + π
0 + t(q0 + q1) + rq1 − D. (4)
The structure of the game is as follows: In the ﬁrst stage, the government sets
the environmental tax, anticipating how ﬁrms will react to the policy. In the
second stage, each ﬁrm strategically sets its output level.
3. Analysis
First, we derive the optimal environmental tax in the mixed duopoly. Under
the Cournot-Nash assumption, the domestic ﬁrm selects its output in order to
maximize the sum of consumer surplus and its own proﬁt U, while the foreign
private ﬁrm chooses its output in order to maximize its own proﬁt π1. Dif-
ferentiating (3) and (2) with respect to each output, we obtain the following
ﬁrst-order conditions:
p − p￿q1 − c0 − t = 0, and (5)
p + p
￿q1 − c1 − t − r = 0. (6)
Following this, the output eﬀects of the taxes can be obtained by diﬀerentiating
(5) and (6) with respect to t and qi to obtain δq0/δt = 1/p￿ and δq1/δt = 0. This
demonstrates that an increase in the environmental tax reduces the market share
of the less eﬃcient public ﬁrm. Having obtained the results, it becomes possible
to solve the optimal environmental tax in the mixed duopoly. Diﬀerentiating
(4) with respect to t yields
dW
dt
=
δW
δt
+
δW
δq0
δq0
δt
+
δW
δq1
δq1
δt
= q1 + (t − θ)
1
p￿. (7)
By setting dW/dt = 0 in (7) and using (5) and (6), we obtain the following
optimal environmental tax:7
tMN = −p￿q1 + θ =
c0 − c1 − r
2
+ θ. (8)
We then state the following proposition.
7We use the superscripts MN and PN for the mixed Cournot-Nash and pure Cournot-Nash
duopolies, respectively.
4Proposition 1. Suppose that the marginal production cost of the domestic
ﬁrm is higher than that of the foreign ﬁrm. In an international mixed duopoly
wherein the environmental damage is associated with consumption, the optimal
environmental tax is higher than the marginal environmental damage (the stan-
dard Pigouvian level).
As a benchmark, we consider the optimal environmental tax in the pure
duopoly. In the regime, each ﬁrm selects its output in order to maximize its
own proﬁt πi. Following the same procedure as that for the case of the mixed
duopoly, we ﬁnd the eﬀect of the environmental tax on outputs to be δqi/δt =
1/3p￿. This indicates that setting the environmental tax leads to a decrease in
output. After diﬀerentiating (4) with respect to t and rearrenging, we obtain
the following
t
PN =
1
2
(p
￿q0 − p
￿q1 + 2θ − r) =
c0 − c1
2
− r + θ. (9)
Clearly, this is the same as the optimal environmental tax rate derived by Lai
(2004).
We now turn to a comparison between the optimal environmental taxes.
Using (8) and (9), we have
tPN − tMN = −
r
2
< 0. (10)
Therefore, we can describe the following proposition:
Proposition 2. In an international mixed duopoly wherein the environmental
damage is associated with consumption, the optimal environmental tax is higher
than that in an international pure duopoly.
This proposition implies that privatization decreases the optimal environ-
mental tax.
Next, we consider the impact of a change in the tariﬀ rate on the outputs
of both the domestic and foreign ﬁrms in the mixed duopoly. Diﬀerentiating
(3) and (2) with respect to r and qi, we obtain δq0/δr = 0 and δq1/δr =
1/2p￿, respectively. This indicates that a reduction in the tariﬀ rate leads to an
increase in the market share of the foreign ﬁrm. We use this result to derive
the total impact of trade liberalization on the environment. Diﬀerentiating the
environmental damage function with respect to r yields
dθ(q0 + q1)
dr
=
δθ(q0 + q1)
δr
+
δθ(q0 + q1)
δt
δt
δr
= 0, (11)
5where δt/δr = −1/2, from equation (8).8 The ﬁrst term in the middle section of
equation (11) denotes the direct eﬀect on the environmental damage. The sec-
ond term demonstrates the indirect eﬀect on the environmental damage caused
by the positive impact that a decrease in the tariﬀ has on the environmental
tax. Equation (11) demonstrates that when considering the indirect eﬀect, a
decrease in the tariﬀ rate does not aﬀect the environmental damage on the dirty
good because the indirect eﬀect oﬀsets the direct eﬀect by the same amount.
It is important to note that in the pure duopoly, a decrease in the tariﬀ
rate will lead to a decrease in the environmental damage associated with con-
sumption because the indirect eﬀect of tariﬀ reduction on the environmental
damage exceeds the direct eﬀect, as Lai (2004) demonstrates.9 The diﬀerence
between the results for these two regimes implies that from the viewpoint of
environmental improvement, tariﬀ reductions should be implemented after pri-
vatization. One reason for the diﬀerence is that the absolute value of the eﬀect
of a change in the tariﬀ on the optimal environmental tax in the mixed duopoly
(δtMN/δr = −1/2) is less than that in the pure duopoly (δtPN/δr = −1).
The following proposition summarizes the above discussion.
Proposition 3. A tariﬀ reduction has no eﬀect on the environmental damage
associated with consumption.
4. Conclusion
Using the simple linear model, we have investigated the optimal environmental
tax and trade liberalization in a mixed duopolistic market wherein the environ-
mental damage is associated with consumption. The analysis has yielded some
results that diﬀer from those that are obtained in a corresponding pure Cournot
duopoly. We have demonstrated that the optimal environmental tax in a mixed
duopoly is higher than both the Pigouvian level and the optimal environmental
tax in a pure duopoly. This implies that the privatization of the home public
ﬁrm will decrease the optimal environmental tax. Furthermore, tariﬀ reduc-
tion does not aﬀect the environment. This implies that from the viewpoint of
8Some papers have discussed the relationship between reductions in trade policy instru-
ments and the level of environmental tax. For example, see Walz and Wellisch (1997). In this
paper, we can say that in the mixed duopoly, a tariﬀ reduction increases the aggregate output
and hence the pollution, which in turn, leads to an increase in the environmental tax.
9Note that in the pure duopoly, the output eﬀect of a change in the tariﬀ rate is shown as
δqPN
0 /δr = −1/3p￿ and δqPN
1 /δr = 2/3p￿. Thus, the impact of a change in the tariﬀ on the
environment is dθ(q0 + q1)/dr = θ/3p￿ + 2θ/3p￿(−1) = −θ/3p￿ > 0.
6environmental improvement, trade liberalization should be implemented after
privatization.
7References
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8

Environmental tax and trade liberalization in a mixed duopoly

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Environmental tax and trade liberalization in a mixed duopoly

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