Policy-Induced Environmental Technology Transfer
Takeshi Iidaa and Kenji Takeuchia∗
a Graduate School of Economics,
Kobe University, Hyogo, 657-8501, Japan

Abstract
We investigate how environmental and trade policies aﬀect the transfer ofenvironmental technology in a two-country model with global pollution. By comparing free trade and tariﬀ policy without commitment, the following results are
obtained. First, the existence of an environmental policy in a local country induces technology transfer from a foreign country. Second, there is a possibility
that free trade is preferable to a tariﬀ policy for both countries even though free
trade lowers the environmental tax rate. Third, the quantity of the local ﬁrm’s
product decreases for higher environmental damage. On the other hand, importof environmentally eﬃcient goods from the foreign country increases.

JEL classiﬁcation numbers: D43; F13; L13; Q56
Keywords: Environmental technology transfer; Free trade; Tariﬀ protection

1

Introduction

The importance of technology transfer for a global environmental policy has been
well recognized.1 For instance, the United Nations Framework Convention on Climate
Change includes provisions calling for the transfer of environmental technologies and∗Corresponding author. E-mail address: takeuchi@econ.kobe-u.ac.jp
Popp (2008) considers public funding and private ﬁrm behavior as sources of technological transfer.
A representative example of public funding is aid from governments or non-governmental organizationsin the form of oﬃcial developmental assistance. Private transfer of technology can take place in three
ways: trade, foreign direct investment, and licensing to a local ﬁrm.
1

1

know-how related to environmentally sound technologies. However, there seems to be
disagreement on how this transfer can be achieved. Developing countries often claimthat compulsory licensing, by which a government forces a patent holder to grant theuse of the technologies to the state or others, is eﬀective for transferring environmental
technologies. On the other hand, industrialized countries tend to prefer a free trade
policy, in which technology is indirectly transferred through the trade of commodities
produced in their countries. From this standpoint, it is necessary to remove tariﬀs andother trade barriers to decrease the price of environmental technology.2
It is important to note that these transfers of technology, either through licensing contract or through import of environmentally eﬃcient goods, are aﬀected by thedesign of environmental and trade policies. If a developing country implements an environmental policy, it provides an incentive for the local ﬁrm to adopt environmental
technology. Stronger environmental regulation would lead to higher value being set on
the environmental technology, which in turn would bring higher revenue to the licensor.
In the context of studies on trade and environment, it is often pointed out that a
trade liberalization may induce weaker environmental regulation as a means of compensating the domestic ﬁrm (see Rauscher, 1994; Ulph and Valentini, 2001). If the weakerenvironmental regulation discourages the ﬁrm from adopting cleaner technology, thevalue of the technology might decrease. Our main question is whether a developed
country still prefers diﬀusion of environmental technology through free trade, even if
trade liberalization leads to weaker environmental regulation in the developing country.
To answer this question, we consider an international duopoly model with global
pollution and investigate how environmental and trade policies aﬀect the transfer ofenvironmental technology. We extend the model of Iida and Takeuchi (2010) to include
the possibility of an environmental policy in the local country.
2

3

The main results

A World Bank (2008) summary of applied tariﬀs for solar photovoltaic technology in 18 highGHG-emitting developing countries found that except in one case, import tariﬀs range from 32 to 6
percent. These are much higher than the average tariﬀs in high-income OECD countries (4%). Tariﬀ
barriers on ﬂuorescent lamps in these 18 countries are also high, varying from 30 to 5 percent, again
with one exception. The tariﬀ on ﬂuorescent lamps is the highest across all clean technologies assessed.
3
Iida and Takeuchi (2010) do not consider environmental policy instruments on the assumptionthat it is politically diﬃcult to implement an environmental tax. See other studies that consider the
trade policy as the second best policy tool, for example, Copeland (1996), Ludema and Takeno (2007)
and Regibeau and Gallegos (2004).

2

can be summarized as follows. First, the existence of an environmental policy in a
local country induce technology transfer from a foreign county. Second, free trade ispreferable to a tariﬀ policy for both country when the environmental damage is high.
This has signiﬁcant policy implications when one considers the claim for environmental degradation caused by trade liberalization. Third, technological transfer throughlicensing contract decrease for higher environmental damage by the decrease in quantity of the local ﬁrm’s product. On the other hand, import of environmentally eﬃcient
goods from the foreign country increases.
The impact of strategic trade and environmental policies has been previously investigated by several authors. Walz and Wellisch (1997) compare free trade and export
subsidies with a third-market model in the context of local pollution. They showthat free trade (which means a ban on export subsidies) enhances the social welfare
of symmetric exporting countries. Although reducing the export subsidy lowers theenvironmental tax to compensate the ﬁrm, the compensation is less than the export
subsidy reduction. Therefore, free trade raises the price of the ﬁnal product and extracts rent from consumers of the third market. The exporting countries beneﬁt fromthis. However, because the higher price of the product lowers the consumer surplus of
the third market, free trade is not preferable from the perspective of world welfare.
Tanguay (2001) extends the analysis to trans-boundary pollution under the reciprocalmarkets model. He shows that tariﬀ is preferable to free trade. In the case of free trade,the government sets the environmental tax rate lower than that under a tariﬀ policy toprotect its own ﬁrm. Moreover, because of transboundary pollution, the government
does not have an incentive to set a higher environmental tax in order to shift the pollution activity to another country. Therefore, free trade leads to a lower environmental
tax rate and worsens the social welfare.
Although many other studies have investigated the interaction between trade andenvironmental policies (see, e.g., Burguet and Sempere, 2003; Lai and Hu, 2008; Ohori,
2006; Ray Chaudhuri and Baksi, 2009; Riveiro, 2008), to our knowledge there is no
study that analyzes the interaction regarding the impact on environmental technology
transfer. The most important contribution of our study is that we consider the roleof licensing contracts. The earlier studies argue that the strength of an environmental3policy resulting from a trade policy signiﬁcantly impacts on environmental damage.
Therefore, if free trade leads to a lower environmental tax, it lowers social welfare
through deterioration of the environment. In contrast, we show that the strength ofan environmental policy resulting from a trade policy signiﬁcantly aﬀects the level oflicense fees. If licensing occurs and eliminates environmental damage, the environmental
impact of free trade can be mitigated. We show that there is a possibility that free
trade is better than a tariﬀ policy for both countries even though free trade lowers theenvironmental tax rate.
The remainder of this paper is organized as follows. In Section 2, we present aninternational duopoly model with global pollution. In Section 3, we investigate a free
trade policy. In Section 4, we investigate a tariﬀ policy without a commitment to thetariﬀ level. In Section 5, we compare free trade with no commitment from the viewpointof equilibrium quantity and revenue, and social welfare. The case of tariﬀ policy withpre-commitment is also examined. The ﬁnal section concludes.

2

The model

We consider a duopoly model with one foreign and one local ﬁrm. We suppose the goods
are homogeneous except for their environmental properties. The goods produced by the
local ﬁrm generate global external diseconomy. The foreign ﬁrm has clean technology
and its product does not adversely aﬀect the environment. The clean technology of theforeign ﬁrm is transferable. If the technology is transferred by a licensing agreement to
the local ﬁrm, its product does not cause environmental damage. We assume that thelicense fee is paid by royalties.
The proﬁts of the foreign ﬁrm and the local ﬁrm are πfj,k = (pj,k − tk )qfj,k + rj qlj,kand πlj,k = (pj,k − τ j − rj )ql , respectively, where j = {F, T } represents the trade policy
with F denoting free trade and T denoting the tariﬀ policy, and k = {L, N } represents
the state of licensing contract with L denoting licensing and N denoting no licensing.
The parameter t denotes the tariﬀ rate imposed on the product of the foreign ﬁrm,
τ j is the environmental tax rate imposed on one unit of pollution, and r > 0 is theroyalty rate. Note that when there is no licensing, r = 0. Further, in the case of
free trade, t = 0. Following Qiu and Yu (2009), we assume a linear inverse demand4

function pj,k = α − qfj,k − qlj,k , and standardize the marginal private cost of production
to zero. The social welfare of the foreign country is the sum of the producer surplus
minus the environmental damage: SWfj,k = πfj,k − (γ/2)EDj,k .4 The social welfare of
the local country is the sum of the consumer surplus, the proﬁt of the local ﬁrm, theenvironmental tax, and the tariﬀ revenue minus the environmental damage: SWlj,k =(qfj,k +qlj,k )2 /2+πlj,k +τ j qlj,k +tk qfj,k −(γ/2)EDj,k . We assume that one unit of production
generates one unit of pollution. The environmental damage is represented as EDj,k =(qlj,k )2 and is common for both countries.5 The evaluation of the environmental damage
is denoted by γ/2.6 Since the licensing contract eliminates the environmental damage,
EDj,L = 0.

3Free Trade

First, we consider the free trade case. The timing of the game is as follows. In the ﬁrst
stage, the foreign ﬁrm oﬀers royalty r to the local ﬁrm. In the second stage, the local
ﬁrm decides to accept the oﬀer. In the third stage, if licensing does not occur in theprevious stage, the local government determines environmental tax rate τ . In the ﬁnal
stage, the ﬁrms engage in quantity competition. The equilibrium concept is SPE. The
game is solved backwards.
To clarify the eﬀect of the tariﬀ policy on technology transfer, we consider only
the case in which the local government determines the optimal environmental tax after
the licensing contract. Recent studies have pointed out that the regulator may change
the pre-committed environmental standard because of a lack of credibility (see, e.g.,
Conrad 2001; Puller 2006).
In the ﬁnal stage, each ﬁrm determines its output. The equilibrium quantity and4

We omit the consumption in the foreign country for convenience. Because the markets are segmented between local and foreign, the result holds even if we include the foreign market.
5
Since we consider global pollution including climate change resulting from the emission of carbon
dioxide, environmental damage is assumed to be the same for both the foreign country and the local
country.
6
The γ should be diﬀerent between the foreign and local countries depending on the situations andcharacteristics of the environmental issues. For example, assuming a higher γ for the foreign country
and including the foreign environmental policy would allow us to address the issue of a competitiveenvironmental policy between countries. However, under the present framework of analysis, we obtain
qualitatively the same results even with the diﬀerent γ. We assume γf = γl = γ/2 to simplify the
analysis.

5

proﬁt with and without licensing are qfF,L = (α + r)/3, qlF,L = (α − 2r)/3, πfF,L =
)2
)2
(
(
qfF,L + rqlF,L and πlF,L = qlF,L ; and qfF,N = (α + τ )/3, qlF,N = (α − 2τ )/3, πfF,N =
(
)2
(
)2
qfF,N
and πlF,N = qlF,N , where superscripts F , L and N represent free trade,licensing, and no licensing, respectively.
In the third stage, if the local ﬁrm has not accepted a licensing contract, the local
government imposes an environmental tax on the local ﬁrm. The social welfare of the
(
)2
(
)2
local country in the third stage is SWlF,N = QF,N /2 + πlF,N + τ qlF,N − (γ/2) qlF,Nwhere QF,N = qfF,N + qlF,N . The optimal environmental tax that maximizes SWlF,N isτF =α(−3 + 2γ).
3 + 4γ(1)

If γ > 1.5, then τ F > 0. Since ∂τ F /∂γ > 0, the local government increases the optimal
environmental tax for higher environmental damage. The equilibrium quantity and)2(
proﬁt without licensing are qfF,N = 2αγ/(3 + 4γ), qlF,N = 3α/(3 + 4γ), πfF,N = qfF,N)2(
and πlF,N = qlF,N .
In the licensing stage, the foreign ﬁrm oﬀers the license fee rF , which maximizes
its proﬁt subject to πlF,L ≥ πlF,N . The optimal license fee is a corner solution and isderived as rF = τ F such that qlF,L = qlF,N . Then, if πfF,L (rF ) ≥ πfF,N , the foreign ﬁrm
licenses its environmental technology to the local ﬁrm. Because qfF,L (rF ) = qfF,N , theproﬁt of the foreign ﬁrm is denoted as πfF,L = πfF,N + rF qlF,L . Therefore, the foreign ﬁrm
licenses its technology to the local ﬁrm if rF > 0, and in turn τ F > 0. We obtain thenext proposition.
Proposition 1. When γ > 1.5, licensing occurs. Otherwise, licensing does not occur.
We depict the equilibrium environmental tax and license fee in Figure 1. The left
and the right panels of the ﬁgure are the equilibrium environmental tax and licensefee, respectively. The vertical axis of the left panel is the environmental tax rate andthat of the right panel is the license fee, and the horizontal axes are the evaluationof the environmental damage. When γ ≤ 1.5, the environmental tax rate is negative
and the local ﬁrm receives the subsidy (τ F < 0). When γ > 1.5, the local ﬁrm incurs
the license fee to avoid the tax payment. The dotted line in the left panel implies
that the environmental tax is avoided by the licensing contract. In contrast to the

6

rF

τF

0

1.5

γ

γ
0

1.5

Figure 1: The equilibrium environmental tax and license fee in free tradeﬁnding of Iida and Takeuchi (2010), licensing occurs even under free trade. This can be
attributed to the existence of an environmental policy in the local country that gives
a local ﬁrm an incentive to adopt the environmental technology. Indeed, if τ F > 0,licensing occurs. This obviously means that the incentive for the local ﬁrm to accept
the contract is avoidance of regulation. When γ ≤ 1.5, licensing does not occur andthe local government subsidizes the polluting local ﬁrm.
Corollary 1. When γ ≤ 1.5, the local government subsidizes the polluting local ﬁrm,
therefore, τ F ≤ 0.
Under the free trade regime, the local government does not have the means toprotect the local ﬁrm directly. The government, therefore, uses an environmental tax
as an instrument to protect the local ﬁrm.
Figure 2 shows the equilibrium value of quantity (the left panel) and proﬁt (theright panel). The quantity and proﬁt of the local ﬁrm decrease, and those of the foreign
ﬁrm increase in γ. On the other hand, import of environmentally eﬃcient goods fromthe foreign country increases in γ.
When γ ≤ 1.5, because the local ﬁrm receives a subsidy (τ F < 0), the quantityof the local ﬁrm is larger than that of the foreign ﬁrm. When γ > 1.5, the local ﬁrm
adopts the environmental technology and pay the license fee. Since a larger γ implies
that the value of the environmental technology is higher, the license fee rises (Figure

7

qfF , qlF

πfF , πlF

qfF

qlF

πfF
πlF

qfF

qlF

πlF

πfF
γ

0

γ

1.5

1.5

0

Figure 2: The equilibrium quantity and proﬁt in free trade
SWfF , SWlF

CS F

SWlF

SWfF
SWlF

SWfF
0

1.5

γ

γ
0
Figure 3: The equilibrium consumer surplus and social welfare in free trade1). This drawback to the local ﬁrm results in an equilibrium quantity being less thanthat of the foreign ﬁrm.
Figure 3 shows the equilibrium consumer surplus (the left panel) and the social
welfare (the right panel). Although the quantity of the foreign ﬁrm increases in γ, thereduction of the quantity of the local ﬁrm dominates. Therefore, consumer surplus
decreases in γ.
When γ < 1.5, because the licensing contract does not occur, the social welfare of
the local country decreases in γ. While the proﬁt of the foreign ﬁrm increases, theenvironmental damage also increases in γ. The social welfare of the foreign country8depends on these two eﬀects. When γ is small, the eﬀect of environmental damage
dominates that of the proﬁt. As a result, the social welfare of the foreign country
initially decreases and then begins to increase in γ. At γ = 1.5, the social welfare
of both countries increases discontinuously. This is because licensing eliminates theenvironmental damage. After the licensing contract, there is no tariﬀ revenue and thesocial welfare of the local country decreases. The social welfare of the foreign country
becomes equal to the proﬁt of the foreign ﬁrm and increases in γ.

4

Tariﬀ policy

Next, we consider the case of tariﬀ policy. While the optimal tariﬀ will depend onwhether the tariﬀs can be pre-committed before the licensing decisions, it is natural
to assume that a government has the incentive to change a pre-announced tariﬀ rate
(Mukherjee and Pennings, 2006; Neary and Leahy, 2000). Thus, we analyze a nocommitment regime as a probable tariﬀ policy.
In this case, the timing of the game is as follows. In the ﬁrst stage, the foreign ﬁrm
oﬀers a licensing contract with royalty rT to the local ﬁrm. In the second stage, the local
ﬁrm decides to accept the oﬀer. In the third stage, if licensing does not occur in theprevious stage, the local government determines the tariﬀ rate tT,N and environmental
tax rate τ T . If licensing does occur, the local government only determines the tariﬀ
rate tT,L . In the ﬁnal stage, the ﬁrms engage in quantity competition. The equilibrium
concept is SPE. The game is solved backwards.
In the ﬁnal stage, each ﬁrm determines its output. The equilibrium quantity andproﬁt with and without licensing are qfT,L = (α + r − 2tT,L )/3, qlT,L = (α − 2r + tT,L )/3,
(
)2
(
)2
T,L
T,L
T,L
T,L
T,L
π f = qf
+ rql , and πl = ql
; and qfT,N = (α − 2tT,N + τ )/3, qlT,N =
(
)2
(
)2
(α+tT,N −2τ )/3, πfT,N = qfT,N , and πlT,N = qlT,N , respectively. The social welfare)2(of the local country with and without licensing is SWlT,L = QT,L + πlT,L + tT,L qfT,L
(
)2
(
)2
and SWlT,N = QT,N + πlT,N + τ T qlT,N + tT,N qfT,N − (γ/2) qlET,N , respectively. In
the third stage, when licensing does not occur, the local government determines the9environmental tax rate and the tariﬀ rate to maximize SWlT,N . The FOCs yieldtT,N (3 + 2γ) − α(3 − 2γ),
3 + 4γτ T,N (3 + 2γ) + α(3 − γ)=.
9+γτ̂ T,N =

(2)

t̂T,N

(3)

Since ∂ 2 SWlT,N /∂τ ∂t > 0, there is a complementary relationship between τ T,N and tT,N .
When the tariﬀ rate is high, the environmentally friendly goods produced by the foreign
ﬁrm cannot be diﬀused. Thus, the local government sets a high environmental tax while
protecting the competitiveness of the local ﬁrm by setting a high tariﬀ. On the other
hand, when the tariﬀ rate is lower, the local government sets a lower environmental
tax. The lower environmental tax protects the local ﬁrm from competition with theforeign ﬁrm. From (2) and (3), we obtain the equilibrium environmental tax rate andtariﬀ rate;2α(−1 + γ),
2 + 3γα2α=−.
3 3(2 + 3γ)

τ T,N =

(4)

tT,N

(5)

When γ < 1, the environmental tax rate takes a negative value and the local government
actually subsidizes the local ﬁrm, despite the pollution caused by it.
The optimal tariﬀ rate takes its eﬀect on the environment into account. This is
conﬁrmed by tT,N = α/3 − 2α/3(2 + 3γ) = α/3 − (∂(γ/2)EDT,N /∂ql − τ T,N )∂ql /∂t.
The last term of the above equation corresponds to the environmental damage causedby the marginal increase in the tariﬀ rate.
When licensing occurs, the optimal tariﬀ rate is tT,L = α/3. We obtain the next
proposition.
Proposition 2. The optimal tariﬀ is higher with licensing than without licensing:tT,L > tT,N .
When licensing does not occur, the local government must consider protecting boththe environment and the local ﬁrm. On the other hand, the local country can concentrate on protecting the local ﬁrm when licensing occurs and environmental damage
is internalized. The diﬀerence leads to a higher optimal tariﬀ under the no licensing

10

regime. The relationship between the diﬀerence in tariﬀs, tT,L −tT,N , and the evaluationof environmental damage is as follows.
Corollary 2. The diﬀerence between the tariﬀ rate with and without licensing issmaller when γ is higher: ∂[tT,L − tT,N ]/∂γ < 0
The local government enhances its regulation when environmental damage is large.
Therefore, from (2), (3), the tariﬀ rate tT,N is also enhanced to protect the local ﬁrm,
which reduces the diﬀerence tT,L − tT,N . In contrast, when the implementation ofenvironmental tax is restricted as in Iida and Takeuchi (2010), it sets a lower tariﬀ rate
for higher γ to diﬀuse the environmentally friendly goods produced by the foreign ﬁrm.
The third stage equilibrium quantity and proﬁt with and without licensing are qfT,L =
(
)
T,L
T,L
T,L
T,L
2
2
(3r + α)/9, ql = 2(2α − 3r)/9, πf = (α + 42rα − 45r ) /81, and πl = ql
;
(
)2
(
)
and qfT,N = αγ/(2 + 3γ), qlT,N = 2α/(2 + 3γ), πfT,N = qfT,N , and πlT,N = qlT,N ,respectively.
In the licensing stage, the foreign ﬁrm oﬀers a license fee rT that maximizes its proﬁt
subject to πlT,L ≥ πlT,N . When γ ≤ 4.333, the optimal license fee is a corner solution
and is derived as rCT = α(−5 + 6γ)/(6 + 9γ) such that qlT,L = qlT,N .
When γ > 4.333, the interior solution is derived as rIT = 7α/15. When γ is small,because environmental damage is small, the value of the environmental technology (thelicense fee) is also small; therefore, when γ ≤ 4.333, the optimal license fee is derived
as a corner solution. However, when γ is large, because the value of the environmental
technology is higher, rCT is larger than rIT , which is independent of γ. Since the foreign
ﬁrm incurs a tariﬀ payment that increases the marginal cost of its product, it is nolonger beneﬁcial to require as large a license fee as possible when γ > 4.333.
The proﬁt of the foreign ﬁrm licensing the environmental technology to the local ﬁrm
is πfT,L (rCT ) = α2 (−29 + 30γ + 9γ 2 ) /9(2+3γ)2 (when γ ≤ 4.333) and πfT,L (rIT ) = 2α2 /15(when γ > 4.333). When γ ≥ 0.967, πfT,L (rCT ) ≥ πfT,N and the foreign ﬁrm licenses thetechnology to the local ﬁrm. Moreover, since πfT,L (rIT,L ) ≥ πfT,L (rCT,L ), πfT,L (rIT,L ) > πfT,Nwhen γ > 4.333. Hence, we obtain the next proposition.
Proposition 3. When γ ≥ 0.967, licensing occurs. Otherwise, licensing does not occur.

11

τT

0

rT

0.967

1

4.333

γ

0

0.967

4.333

γ

Figure 4: The equilibrium environmental tax and license fee in tariﬀ policy
We depict the equilibrium environmental tax and license fee in Figure 4. The left
and the right panels of the ﬁgure are the equilibrium environmental tax and license fee,
respectively. The vertical axis of the left panel is the environmental tax rate and thatof right is the license fee, and the horizontal axis is the evaluation of environmental
damage. The dotted line is the environmental tax rate if the licensing does not occur.
The local ﬁrm receives the subsidy (τ T < 0) when γ < 0.967. The local ﬁrm pays thelicense fee when γ ≥ 0.967. The environmental tax rate and license fee are the marginal
cost of production for the local ﬁrm, and increase in γ.
As we have already examined, the optimal tariﬀ rate is tT,L = α/3 under a licensing
contract (Figure 5).
The left and the right panels of Figure 6 show the equilibrium quantity and proﬁt,
respectively. The quantity of the local ﬁrm decreases in γ. This is because the marginal
cost of production increases in γ, as illustrated in Figure 4. Since the license fee isdetermined such that qlT,L = qlT,N , the quantity decreases continuously in spite of adiscontinuous increase in the marginal cost of production at γ = 0.967.
Although the tariﬀ rate increases in γ when γ < 0.967, the quantity of the foreign
ﬁrm increases. This is because the local government increases the environmental tax
rate more than the tariﬀ rate. Consequently, there is a larger downward shift in thereaction function of the local ﬁrm than that of the foreign ﬁrm. It decreases the quantityof the local ﬁrm and increases that of the foreign ﬁrm. At γ = 0.967, where licensing

12

tT

α
3

0

0.967

4.333

γ

Figure 5: The equilibrium tariﬀ rate in tariﬀ policy
occurs, there is a discontinuous increase in the tariﬀ rate and the quantity of the foreign
ﬁrm drops down. However, because of the license revenue, the proﬁt of the foreign ﬁrm
keeps increasing in γ. When γ > 4.333, the license fee and therefore each ﬁrm’s quantity
do not depend on γ.
We depict the equilibrium consumer surplus (the left panel) and social welfare (theright panel) in Figure 7. As is in the case of free trade, consumer surplus decreases
in γ because the reduction of the quantity of the local ﬁrm dominates the increasein the foreign ﬁrm’s output. At γ = 0.967, consumer surplus drops oﬀ because of adiscontinuous decrease in the quantity of the foreign ﬁrm. When γ > 4.333, consumer
surplus does not depend on γ.
The social welfare of the local country decreases in γ. The social welfare of theforeign country initially decreases, and then begins to increase in γ. This interpretation
is similar to that of free trade. After the licensing contract, the social welfare of thelocal country decreases and the social welfare of the foreign ﬁrm (which equals the proﬁtof the foreign ﬁrm) increases. However, unlike what happens in the case of free trade,the social welfare of the local country is always larger than that of the foreign country.
This is because of the tariﬀ revenue.

13

qfT , qlT

πfT , πlT
πlT

qlT

qfT

qfT
qlT

qfT

πfT

πfT

qlT

πlT

πfT

πlT

γ
0

0.967

γ

4.333

0

0.967

4.333

Figure 6: The equilibrium quantity and proﬁt in tariﬀ policy

CS T

SWfT , SWlT
SWlT

0
0

0.967

4.333

γ

0.967

SWlT

SWlT

SWfT

SWfT

4.333

γ

SWfT

Figure 7: The equilibrium consumer surplus and social welfare in tariﬀ policy

145

Discussions

5.1

ComparisonFirst, we compare free trade with tariﬀ policy on the range where the licensing contract
occurs. Licensing occurs when γ > 1.5 under free trade and γ ≥ 0.967 under tariﬀ
policy. The range under tariﬀ policy is larger than that under free trade.
Previous literature on the strategic environmental policies have pointed out that
free trade lowers environmental regulation to compensate the domestic ﬁrm (Tanguay,
2001; Walz and Wellisch, 1997). Therefore, in such a case, the incentive of the local ﬁrm
to adopt environmental technology may be weakened, and it may cause social welfare
loss. However, we can show that there is a case where free trade is Pareto improving
to tariﬀ policy, although it leads to weaker environmental regulation.
Proposition 4. World welfare under tariﬀ policy is higher than (resp. lower than oreven with) that under free trade, when γ ∈ (0, 0.203) and when γ ∈ [0.967, 1.5] (resp.
otherwise ).
Figure 8 illustrates the situation by comparing the social welfare of each country.
The upper part represents the policy preferred by the foreign country and the lower
represents that by the local country. Initial T means tariﬀ policy and F means free
trade.
When γ ∈ (0, 0.967), licensing does not occur under either regime. As a result,the foreign ﬁrm does not pay a tariﬀ and the foreign country prefers free trade to tariﬀ
policy. On the other hand, the local country prefers tariﬀ policy to free trade because of
the tariﬀ revenue. When γ ∈ [0.967, 1.5], licensing occurs only under tariﬀ policy. The
foreign country prefers tariﬀ policy in this case, because there is revenue from a license
fee and no environmental damage. The local country also prefers tariﬀ policy becauseof the tariﬀ revenue. When γ ∈ (1.5, 4.333], licensing occurs under both regimes. The
foreign country prefers free trade to tariﬀ policy because there is no tariﬀ payment.
The local country also prefers free trade to tariﬀ policy as long as γ ∈ (1.5, 4.301].
This is because of the lower license fee under the free trade. Since free trade promote
the diﬀusion of technology embodied in the product, the local government can place a15

Foreign Country
F

T

F
γ

0

0.967
T

1.5
T

4.301
F

T

Local Country
Figure 8: Comparison between each country’s social welfare under free trade and tariﬀ
policylower environmental tax. It means that the local ﬁrm has less incentive to adopt aninnovative environmental technology under such a regime.
When γ > 4.301, the local country prefers tariﬀ policy to free trade. Since higher
γ implies higher license fee, as illustrated in the previous section, the quantity of thelocal ﬁrm decreases and that of the foreign ﬁrm increases in γ (see the left panel of
Figure 6). Consequently, the local country earns larger tariﬀ revenue when γ is higher
under tariﬀ policy. When γ > 4.301, this beneﬁt exceeds the cost of the higher license
fee and the local country prefers tariﬀ policy to free trade. Moreover, when γ > 4.333,
the license fee is determined by interior solution and independent of γ. While the local
country’s social welfare decreases in γ under free trade (see the right panel of Figure3), it is not aﬀected under tariﬀ policy (see the right panel of Figure 7). Thus, the local
country prefers tariﬀ policy to free trade when γ > 4.333. The foreign country prefers
free trade because there is no tariﬀ payment. To sum up, a comparison of the social
welfare of each country under each regime leads to the following proposition.
Proposition 5. When γ ∈ [0.967, 1.5] both countries prefer tariﬀ policy to free trade.
When γ ∈ (1.5, 4.301] both countries prefer free trade to tariﬀ policy.
Our main result can be summarized as follows. When the evaluation of the environmental damage (γ) is small, the tariﬀ policy is useful to encourage the environmental
technology transfer. However, when the evaluation of the environmental damage is large
enough that the local country adopts environmental regulation, free trade is beneﬁcial
for the world welfare.

16

5.2

Commitment to a tariﬀ

So far, the tariﬀ rate is assumed to be determined after the licensing contract. If theregulator could commit itself in advance to a speciﬁc tariﬀ rate, how does the previous
result change? In this subsection, we consider the case of commitment to a tariﬀ. We
show that our main result does not change, except that there is a situation where thelocal country subsidizes the foreign ﬁrm to lower the license fee. Here we show only the
result. The proof is in the Appendix.
We obtain the ﬁrst stage equilibrium where the local government determines the
optimal tariﬀ rate as follows.
Proposition 6. When γ ∈ (0, 0.5], the optimal tariﬀ rate is tC,N and licensing does notoccur. When γ ∈ (0.5, 1.823], the optimal tariﬀ rate is t̄C,Land licensing occurs. WhenCγ ∈ (1.823, 5.266], the optimal tariﬀ rate is tC,Land licensing occurs. When γ > 5.266,
C
the optimal tariﬀ rate is tC,Land licensing occurs.
I
Figure 9 illustrates Proposition 6. The vertical axis is the tariﬀ rate and the horizontal axis is the evaluation parameter of environmental damage. We also depict theequilibrium environmental tax and license fee in Figure 10. The left and the right panelsof the ﬁgure are the equilibrium environmental tax and the license fee, respectively. The
dotted line is the environmental tax rate when licensing contracts are not entered into.
In the case of commitment, the local government can induce licensing contracts throughthe tariﬀ rate. Because the license fee is equal to the environmental tax rate (rC = τ C )and ∂τ C /t > 0, the local government lowers the tariﬀ rate to suppress the license fee.
Moreover, because ∂τ C /γ > 0, to suppress the license fee to low levels (almost zero; see
the left panel of Figure 10), the local government puts a lower tariﬀ rate for higher γ
when γ ∈ (0.5, 1.823) (Figure 9). When γ > 1.5, the tariﬀ rate becomes negative andworks as an import subsidy for the foreign ﬁrm. We obtain the next corollary.
Corollary 3. When γ ∈ (1.5, 2.303), the optimal tariﬀ rate is negative.
When γ > 1.823, it is not beneﬁcial for the local country to apply a negative tariﬀ(tC < 0) anymore. Although the license fee also increase, the local government increases
the tariﬀ rate to increases tariﬀ revenue. We compare the world welfare under free tradewith that under commitment.

17

t

tC,L
I
t1
tC,L
C

tC,N
1.823

γ

0
0.5

1.5

2.303

5.266

Figure 9: The optimal tariﬀ under commitment to a tariﬀ
Proposition 7. World welfare under commitment is higher than (resp. lower than oreven with) that under free trade, when γ ∈ (0, 0.203) and when γ ∈ (0.5, 2.303) (resp.
otherwise).
Therefore, free trade is preferable to a tariﬀ policy with commitment when theevaluation of the environmental damage is high (when γ ≥ 2.303).
Figure 12 compares the social welfare of each country. Interpretation of the ﬁgure
is mostly the same as that of the no commitment case, except for γ > 1.5, where
licensing occurs under both cases. If the local government can commit itself to a tariﬀ,
it sets a tariﬀ rate that attracts the lowest possible license fee. Therefore, the local
country always prefers commitment to free trade. When γ ∈ (1.5, 2.303), the foreign
ﬁrm receives a subsidy in the form of negative tariﬀ. So the foreign country also prefers
commitment to free trade. When γ ≥ 2.303, the foreign ﬁrm incurs a positive tariﬀ
again and prefers free trade to tariﬀ policy with commitment. Hence, a comparison of
the social welfare of each country leads to the following proposition.
Proposition 8. When γ ∈ (0.5, 2.303) both countries prefer commitment to free trade.
Unlike the case of free trade or tariﬀ policy, there is a range where consumer surplus
increases in γ (see Figure 11). This is because the optimal tariﬀ decreases in γ when

18

τC

0

rC

0.5

1.823

5.266

γ

γ
0

0.5

1.823

5.266

Figure 10: The equilibrium environmental tax and license fee under commitment to a tariﬀ

CS C

SWfC , SWlC
SWlC

SWlC

SWlC
SWfC

SWfC

SWlC
SWfC
γ

0.5
γ
0

0.5

1.823

5.266

0

1.823

5.266

SWfC

Figure 11: The equilibrium consumer surplus and social welfare under commitment to a tariﬀ

19

Foreign Country
F

C

F
γ

0

0.5

Local Country

2.303
C

Figure 12: Comparison between each country’s social welfare under free trade andcommitment to a tariﬀγ ∈ (0.5, 1.823]. Consequently, the increase in the foreign ﬁrm’s output dominates
the decrease in the local ﬁrm’s output. The proﬁt of the local ﬁrm decreases and thesubsidy to the foreign ﬁrm (tC < 0) increases in γ. Since these costs are less than theincrease in consumer surplus, the social welfare of the local country initially increases
in this range of γ.
The range over which licensing occurs under tariﬀ policy with commitment is larger
than that under free trade or under tariﬀ policy without commitment. Through its
commitment, the local government can encourage licensing contracts by its tariﬀ policy. The local government sets the environmental tax rate higher than it would underno commitment, thereby inducing licensing contracts. Therefore, licensing contracts
are promoted by committing to a tariﬀ rate. In the case of no commitment, the decision of the licensing contract is already made when the local government sets the tariﬀ
rate. Therefore, if licensing does not occur, the local government sets a lower environmental tax to protect the local ﬁrm, which discourages the agreement of environmental
technology transfer.

6

Conclusion

This paper has examined the welfare implications of a free trade regime and a licensing
agreement within a framework of international duopoly involving global pollution. We
have shown that although free trade lowers environmental regulation relative to a tariﬀ
policy, free trade is preferable to a tariﬀ policy for world welfare when the evaluation of
the environmental damage is higher. Moreover, we have shown that there is a possibility

20that free trade dominates a tariﬀ policy in the Paretian sense when the environmental
damage is within a certain range. The cost of free trade for the local country is that
there is no tariﬀ revenue. The beneﬁt is the lower license fee that is the result of lower
environmental regulation. When the environmental damage is within a certain range,
the beneﬁt dominates the cost, and the local country prefers free trade to a tariﬀ policy.
When the developing country cares less about the environmental damage, a tariﬀ
policy is beneﬁcial to transferring environmental technology and enhancing the world
welfare. If the concern of the developing country is high enough to conduct environmental regulation, free trade is preferable to a tariﬀ policy for world welfare.

21

Appendix
The equilibrium value under free trade
We obtain the following result for the case of free trade when 0 < γ ≤ 1.5 where
licensing does not occur as follows:
2αγ
2αγ
3α
, qfF =
, qlF =,
3 + 4γ
3 + 4γ
3 + 4γ
4α2 γ 2
9α2
F
=
,
π
=
,
l
(3 + 4γ)2(3 + 4γ)2α2 (3 + γ)
α2 γ(−9 + 8γ)
F
,
SW
=
,
=
l
2(3 + 4γ)2
6 + 8γ3α2 (3 + 2γ + 4γ 2 )=.
2(3 + 4γ)2

pF =

(6)

πfF

(7)

SWfF
SWwF

(8)
(9)

When γ > 1.5, the result where licensing occurs is denoted as follows:
2αγ
2αγ
3α
, qfF =
, qlF =,
3 + 4γ
3 + 4γ
3 + 4γα2 (−9 + 6γ + 4γ 2 )
9α2
F
=
,
π
=
,
l
(3 + 4γ)2(3 + 4γ)2α2 (−9 + 6γ + 4γ 2 )α2 (27 + 12γ + 4γ 2 )F=, SWl =,
(3 + 4γ)22(3 + 4γ)23α2 (3 + 8γ + 4γ 2 ).
=2(3 + 4γ)2

pF =

(10)

πfF

(11)

SWfF
SWwF

(12)
(13)

The equilibrium value under tariﬀ policy without commitment
We obtain the following result for the case of tariﬀ policy when 0 < γ < 0.967] where
licensing does not occur as follows:
2αγ
αγ
2α
, qfT =
, qlT =,
2 + 3γ
2 + 3γ
2 + 3γ
α2 γ 2
4α2
T
=
=
,
π
,
l
(2 + 3γ)2(2 + 3γ)2α2 (2 + γ)
α2 (−2 + γ)γT, SWl =,=
(2 + 3γ)2
4 + 6γα2 (4 + 4γ + 5γ 2 )=.
2(2 + 3γ)2

pT =

(14)

πfT

(15)

SWfT
SWwT

22

(16)
(17)

When 0.967 ≤ γ ≤ 4.333, the result where licensing occurs is denoted as follows:
α + 6αγα(−1 + 3γ)
2α, qfT =
, qlT =,
6 + 9γ
6 + 9γ
2 + 3γα2 (−29 + 30γ + 9γ 2 )
4α2
T
=
,
π
=
,
l
9(2 + 3γ)2(2 + 3γ)2α2 (−29 + 30γ + 9γ 2 )α2 (31 + 12γ + 9γ 2 )
T
=
,
SW
=
,
l
9(2 + 3γ)26(2 + 3γ)2α2 (35 + 96γ + 45γ 2 )=.
18(2 + 3γ)2

pT =

(18)

πfT

(19)

SWfT
SWwT

(20)
(21)

When γ > 4.333, the result where licensing occurs is denoted as follows:
3α
4α
2α, qfT =
, qlT =
,
5
15
15
2α2
4α2
, πlT =
,
=
15
225
2α2
14α2
=
, SWlT =
,
15
75
8α2
=
.
25

pT =

(22)

πfT

(23)

SWfT
SWwT

(24)
(25)

The equilibrium value under tariﬀ policy with commitment
We obtain the following result for the case of commitment to a tariﬀ when γ ∈ (0, 0.5]
where licensing does not occur as follows:
2αγ
αγ
2α
, qfC =
, qlC =,
2 + 3γ
2 + 3γ
2 + 3γ
α2 γ 2
4a2
C
=
,
π
=
,
l
(2 + 3γ)2(2 + 3γ)2α2 (−2 + γ)γ
α2 (2 + γ)
C
,
SW
=
,
=
l
(2 + 3γ)2
4 + 6γα2 (4 + 4γ + 5γ 2 )=.
2(2 + 3γ)2

pC =

(26)

πfC

(27)

SWfC
SWwC

23

(28)
(29)

When γ ∈ (0.5, 1.823], the result where licensing occurs under the tariﬀ rate t1 + ε isdenoted as follows:2αα(−1 + 2γ)
2α, qfC =
, qlC =,
3 + 2γ
3 + 2γ
3 + 2γ4α2α2 (1 − 2γ)2
C
=
,
π
=
,
l
(3 + 2γ)2(3 + 2γ)2α2 (1 − 2γ)2α2 (3 + 20γ − 4γ 2 )
C
=
,
SW
=
,
l
(3 + 2γ)22(3 + 2γ)2α2 (5 + 12γ + 4γ 2 ).
=2(3 + 2γ)2

pC =

(30)

πfC

(31)

SWfC
SWwC

(32)
(33)

When γ ∈ (1.823, 5.266], the result where licensing occurs under the tariﬀ rate tC,LisC
denoted as follows:2α(−1 + γ)
α (1 + γ + γ 2 )α + 2αγ, qfC =
, qlC =,3γ
3γ(1 + γ)
3γ + 3γ 2α2 (−2 − 4γ + 5γ 2 + γ 3 )(α + 2αγ)2
C
=
,
π
=
,
l
9γ 2 (1 + γ)
9γ 2 (1 + γ)2α2 (4 + γ + γ 2 )α2 (−2 − 4γ + 5γ 2 + γ 3 )
C
,
SW
=
,
=
l
9γ 2 (1 + γ)
6γ(1 + γ)
α2 (−4 + 8γ + 5γ 2 )
=
.
18γ 2

pC =

(34)

πfC

(35)

SWfC
SWwC

(36)
(37)

When γ > 5.266, the result where licensing occurs under the tariﬀ rate tC,L
is denotedI
as follows:
25α
14α
20α
, qfC =
, qlC =
,
33
99
99
47α2
196α2
=
, πlC =
,
363
9801
47α2
37α2
=
, SWlC =
,
363
198
689α2
=
.
2178

pC =

(38)

πfC

(39)

SWfC
SWwC

(40)
(41)

The proof of Proposition 4
We compare world welfare in the case of free trade with that in the case of tariﬀ policy.
We compare SWwF with SWwT when γ ∈ (0, 0.967) where licensing does not occur in24either case, and obtain
SWwF − SWwT

α2 γ 2 (−2 + 7γ + 14γ 2 )=.
(2 + 3γ)2 (3 + 4γ)2(42)

Solving (−2 + 7γ + 14γ 2 ) = 0 with respect to γ, we obtain γ ≈ 0.203. Therefore,
SWwF < SWwT if γ ∈ (0, 0.203) and SWwF ≥ SWwT if γ ∈ [0.203, 0.967).
We compare SWwF with SWwT when γ ∈ [0.967, 1.5] where licensing occurs only inthe case of tariﬀ policy and obtain the result
SWwF − SWwT =α2 (9 − 516γ − 1460γ 2 − 834γ 3 + 252γ 4 )> 0,18(2 + 3γ)2 (3 + 4γ)2(43)

if γ ∈ [0.966, 1.5].
We compare SWwF with SWwT when γ ∈ (1.5, 4.33] where licensing occurs in bothcases and obtain the result
SWwF − SWwT

α2 (3 + 10γ + 6γ 2 ) (3 + 34γ + 42γ 2 )=> 0.
18(2 + 3γ)2 (3 + 4γ)2(44)

We compare SWwF with SWwT when γ > 4.333 where licensing occurs in both casesand obtain the result
SWwF − SWwT =α2 (9 + 2γ)(9 + 22γ)
> 0.
50(3 + 4γ)2(45)
Q.E.D.

The proof of Proposition 5First, we compare the foreign country’s social welfare in the case of free trade withthat in the case of tariﬀ policy. We compare SWfF with SWfT when γ ∈ (0, 0.967) andobtainSWfF − SWfT =α2 γ 2 (2 + 31γ + 40γ 2 )> 0.
2(2 + 3γ)2 (3 + 4γ)2(46)

We compare SWfF with SWfT when γ ∈ [0.967, 1.5] and obtain
SWfF − SWfET =α2 (522 + 528γ − 1358γ 2 − 1257γ 3 + 360γ 4 )< 0,18(2 + 3γ)2 (3 + 4γ)2

if γ ∈ [0.967, 1.5].

25

(47)

We compare SWfF with SWfT when γ ∈ (1.5, 4.333] and obtain
SWfF − SWfT

α2 (−63 − 330γ − 274γ 2 + 222γ 3 + 180γ 4 )> 0,=
9(2 + 3γ)2 (3 + 4γ)2(48)

if γ ∈ (1.5, 4.333].
We compare SWfF with SWfT when γ > 4.333 and obtain
SWfF − SWfT

α2 (−153 + 42γ + 28γ 2 )= −> 0,15(3 + 4γ)2(49)

if γ > 4.333.
Next, we compare the local country’s social welfare in the case of free trade withthat in the case of tariﬀ policy. We compare SWlF with SWlT when γ ∈ (0, 0.967) andobtainSWlF − SWlT = −α2 γ 2< 0.
2(2 + 3γ)(3 + 4γ)(50)

We compare SWlF with SWlT when γ ∈ [0.967, 1.5] and obtain
SWlF − SWlT = −α2 (57 + 40γ − 42γ 2 + 9γ 3 )< 0,
6(2 + 3γ)2 (3 + 4γ)(51)

if γ ∈ [0.967, 1.5].
We compare SWlF with SWlT when γ ∈ (1.5, 4.333] and obtain
SWlF − SWlT = −α2 (−45 − 264γ − 344γ 2 − 60γ 3 + 36γ 4 ).
6(2 + 3γ)2 (3 + 4γ)2(52)

Solving (−45 − 264γ − 344γ 2 − 60γ 3 + 36γ 4 ) = 0 with respect to γ, we obtain γ ≈ 4.301.
Therefore, SWwF ≥ SWwT if γ ∈ (1.5, 4.301) and SWwF < SWwT if γ ∈ (4.301, 4.333].
We compare SWlF with SWlT when γ > 4.333 and obtain
SWlF − SWlT = −α2 (−1773 − 228γ + 148γ 2 )< 0,150(3 + 4γ)2(53)

if γ > 4.333.
Q.E.D.

26

Commitment to a tariﬀ
In the case of commitment to a tariﬀ, the timing of the game is as follows; in the ﬁrst
stage, the local government determines the tariﬀ rate tC ; in the second stage, the foreignﬁrm oﬀers a licensing contract with royalty rC to the local ﬁrm; in the third stage, thelocal ﬁrm decides whether to accept the oﬀer; in the fourth stage, if licensing does notoccur in the previous stage, the local government determines the environmental tax rate
τ C ; and in the ﬁnal stage, the ﬁrms engage in quantity competition. The equilibrium
concept is SPE. The game is solved backwards.
In the ﬁnal stage, each ﬁrm determines its output. The equilibrium quantity andproﬁt with and without the licensing contract are qfC,L = (α + r − 2t)/3, qlC,L = (α −2r + t)/3, πfC,L = (α2 + 5αr − 5r2 − 4αt − rt + 4t2 ) /9, and πlC,L = (qlC,L )2 ; and qfC,N =(α − 2t + τ )/3, qlC,N = (α + t − 2τ )/3, πfC,N = (qfC,N )2 , and πlC,N = (qlC,N )2 , respectively.
The social welfare of the local country, with and without licensing respectively, is
SWlC,L =SWlC,N =)1( 22α − 4αr + 3r2 + 2αt − 3t2 ,
6(54)

α2 (6 − γ) − t2 (9 + γ) + 2t(3 + 2γ)τ − (3 + 4γ)τ 2 + α(6t − 2tγ − 6τ + 4γτ )
.(55)
18

In the fourth stage, when licensing does not occur, the local government determines theenvironmental tax rate to maximize (55). The equilibrium environmental tax rate isτC =t(3 + 2γ) − α(3 − 2γ).
3 + 4γ(56)

When t > α(3 − 2γ)/(3 + 2γ) ≡ t1 , τ C > 0. The fourth stage equilibrium quantityand proﬁt where licensing does not occur are qfC,N = (2αγ − t − 2tγ)/(3 + 4γ), qlC,N =
(
)2
(
)2
(3α − t)/(3 + 4γ), πfC,N = qfC,N and πlC,N = qlC,N .
In the licensing stage, the foreign ﬁrm oﬀers a license fee rC that maximizes its
proﬁt subject to πlC,L ≥ πlC,N . The optimal license fee is a corner solution when t ≤15α/(11 + 8γ) ≡ t2 and is derived as rCC = τ C such that qlC,L = qlC,N . Hence, if
t > t1 , the local ﬁrm has an incentive to innovate environmental technology. So, if
πfC,L (rCC ) ≥ πfC,N , the foreign ﬁrm licenses environmental technology to the local ﬁrm.
Because qfC,L (rCC ) = qfC,N , the proﬁt of the foreign ﬁrm when it licenses the technology27

is denoted as πfC,L = πfC,N + rCC qlC,L . Therefore, the foreign ﬁrm licenses its technology
to the local ﬁrm when rCC > 0, and in turn t > t1 . The optimal license fee is an interior
solution when t > t2 and is rIC = (5α − t)/10. When t is higher, because ∂τ C /∂t > 0,
the license fee rCC rises. Moreover, the higher tariﬀ increases the production cost of
the foreign ﬁrm. Therefore when t > t2 , the interior solution rIC emerges. Thenthe proﬁt of the foreign ﬁrm is πfC,L (rIC ) = (5α2 − 10αt + 9t2 ) /20. Because t2 > t1 ,
πfC,L (rIC ) ≥ πfC,L (rCC ) and πfC,L (rCI ) > πfC,N when t > t1 , πfC,L (rIC ) > πfC,N when t > t2 .
To sum up, the foreign ﬁrm licenses its technology when t > t1
The second stage equilibrium social welfare of the local country when licensing
occurs under the license fees rCC and rIC and that when licensing does not occur are,respectively,
SWlC,L =α2 (27 + 12γ + 4γ 2 ) + 8αt (−3 − γ + γ 2 ) − 12t2 γ(1 + γ)
2(3 + 4γ)2(57)

(25α2 + 70αt − 99t2 )
200

(58)

2αtγ + α2 (3 + γ) − t2 (2 + 3γ)
6 + 8γ(59)

when t1 < t ≤ t2 ,SWlC,L =when t > t2 and
SWlC,N =when t ≤ t1 .

The optimal tariﬀ rate
In the ﬁrst stage, the local government determines the optimal tariﬀ rate. We must
consider the tariﬀ rate that is compatible with the licensing decision of stage 2. Thismeans there are three cases. Case 1 is that the local government determines tariﬀ ratetC,L such that t1 < tC,L ≤ t2 , and then licensing occurs under the license fee rCC . Notethat we assumed t ≤ α/2 and because t1 ≥ α/2 when γ ≤ 0.5, there is no t such thatt > t1 . So when γ ≤ 0.5, licensing does not occur. Case 2 is that the local government
determines tariﬀ rate tC,L such that tC,L > t2 , and then licensing occurs under the
license fee rIC . Case 3 is that the local government determines tariﬀ rate tC,N such thattC,N ≤ t1 , and then licensing does not occur.

28

Case 1: licensing occurs under the license fee rCC in the next stage
First, we consider Case 1, in which the local government determines the tariﬀ rate thatwill maximize social welfare in the local country, in anticipation of a next stage in which
licensing will occur. The optimal tariﬀ rate that maximizes (57) is
tC,L
=
C

α (−3 − γ + γ 2 ).
3γ(1 + γ)(60)

If γ ∈ (1.823, 6.808] then t1 < tC,L
≤ t2 . Therefore, if γ ∈ (1.823, 6.808], tC,Lis theCC
equilibrium tariﬀ rate that is compatible with the licensing stage decision. Otherwise,tC,L
is incompatible with the licensing decision. However, if the local government deC
termines a tariﬀ rate such that t̄C,L= t1 + ε where ε > 0 is small enough, then licensingCoccurs under the tariﬀ rate t̄C,L
C . Moreover, if the local government determines the tariﬀ
C,Lrate such that t̄C,L
C2 = t2 , then licensing occurs under the tariﬀ rate t̄C2 .

Case 2: licensing occurs under the license fee rIC in the next stage
Next, we consider Case 2, in which the local government determines the tariﬀ rate thatwill maximize social welfare in the local country, in anticipation of a next stage in which
licensing will occur. The optimal tariﬀ rate that maximizes (58) is
tC,L
=
I

35α
.
99

(61)

If γ > 3.929 then tC,L
> t2 . Therefore, if γ > 3.929, tC,Lis the equilibrium tariﬀ rate
I
I
that is compatible with the licensing stage decision. Otherwise, tC,L
is incompatibleIwith the licensing decision. However, if the local government determines a tariﬀ rate
such that t̄C,L= t2 + ε where ε > 0 is small enough, then licensing occurs under theItariﬀ rate t̄C,LI .
Case 3: licensing does not occur in the next stage
Finally, we consider Case 3, in which the local government determines a tariﬀ rate in
anticipation of a next stage in which licensing will not occur. The optimal tariﬀ ratethat maximizes (59) is
tC,N =aγ.
2 + 3γ
29(62)

If γ ≤ 1 then tC,N ≤ t1 . Therefore, if γ ≤ 1, tC,N is the equilibrium tariﬀ rate that iscompatible with the licensing stage decision. Othewise, tC,N is incompatible with thenext stage decision. However, when γ > 1, if the local government determines a tariﬀ
rate such that t̄C,N = t1 , then licensing does not occur under the tariﬀ rate t̄C,N .
The local government will choose a tariﬀ rate that will induce the largest social
welfare. If the local government wants to obtain this result when licensing occurs, it
C,Lwill set the optimal tariﬀ rate at tC,Lor t̄C,Lor t̄C,Lor t̄C,LC
C
C2 or tII . If it does not, it will

set the optimal tariﬀ rate at tC,N or t̄C,N . From the above, we obtain Proposition 6.
The equilibrium environmental tax when licensing does not occur is τ C (tC,N ) =C,LC
2α(−1+γ)/(2+3γ). The equilibrium license fee when tC = tC,L
C and that when t = tI
2
C C,L
are rCC (tC,L
C ) = α (−3 − 2γ + 2γ ) /3γ(1 + γ), and rI (tI ) = 46α/99, respectively.

The decision of the optimal tariﬀ rate
The social welfare of the local country, under a tariﬀ rate when t = tC,L , when t = t̄C,LC ,and when t = tC,L
C2 is obtained from (57), respectively,
α2 (4 + γ + γ 2 )=,6γ(1 + γ)
α2 (3 + 4γ)2 (3 + 20γ − 4γ 2 ) + B)=
SWlC,L (t̄C,L,C
2(3 + 2γ)2 (3 + 4γ)2α2 (−77 + 128γ + 16γ 2 ),SWlC,L (t̄C,L)=
C2
2(11 + 8γ)2
SWlC,L (tC,L
C )

(63)
(64)
(65)

where B = 8α(−27 − 72γ − 42γ 2 + 20γ 3 + 16γ 4 )ε − 12γ(1 + γ)(3 + 2γ)2 ε2 .
The social welfare of the local country, under a tariﬀ rate when t = tC,Land thatI
when t = t̄C,L
is obtained from (58), respectively,
I
37α2
,
198
100α2 (−77 + 128γ + 16γ 2 ) + D
SWlC,L (t̄C,L)=,
I
200(11 + 8γ 2 )SWlC,L (tC,L
I ) =

(66)
(67)

where D = 40α(−605 − 286γ + 112γ 2 )ε − 99(11 + 8γ)2 ε2 .
The social welfare of the local country, under a tariﬀ rate when t = tC,N and, that30

when t = t̄C,N is obtained from (59), respectively,
α2 (2 + γ)
4 + 6γ2α (3 + 16γ − 4γ 2 )SWlC,N (t̄C,N ) =2(3 + 2γ)2
SWlC,N (tC,N ) =

(68)
(69)

We compare the social welfare of the local ﬁrm where licensing occurs with that
where licensing does not occur for γ > 0.5. There are ﬁve cases that we must con(
)
(
)
(
)
C,L
C,L
sider depending on the size of γ: (a) SWlC,L t̄C,L,SW
t̄, and SWlC,N tC,N
C
I
l
(
)
(
)
(
)
C,L
C,L
C,L
C,L
when γ ∈ (0.5, 1]; (b) SWlt̄C , SWlt̄I
, and SWlC,N t̄C,N when γ ∈
(
)
(
)
)
(
C,L
C,L
(1, 1.823]; (c) SWlC,L tC,L,SW
t̄
, and SWlC,N t̄C,N when γ ∈ (1.823, 3.929];
C
I
l
(
)
(
)
(
)
C,L
C,L
(d) SWlC,L tC,L,
SW
t
, and SWlC,N t̄C,N when γ ∈ (3.929, 6.808]; and (e)
C
I
l
(
)
(
)
(
)
C,L
C,L
C,L
C,L
SWl
t̄C2 , SWltI, and SWlC,N t̄C,N when γ > 6.808. Note that we consider ε small enough, therefore, the case in which ε → 0.
Case (a): 0.5 < γ ≤ 1
C,L C,L
We compare SWlC,L (t̄C,L(t̄I ) and obtain the result
C ) with SWl

SWlC,L

(

t̄C,L
C

)

− SWlC,L

(

t̄C,L
I

)

=−

16α2 (1 + γ) (−33 − 52γ − 6γ 2 + 10γ 3 ).
(33 + 46γ + 16γ 2 )2(70)

C,L C,LIf γ ∈ [0, 2.840), SWlC,L (t̄C,L(t̄I ). Next, we compare SWlC,L (t̄C,L
C ) > SWl
C ) with

SWlC,N (t̄C,N ) and obtainC,N C,N
SWlC,L (t̄C,L(t ) = −C ) − SWl

2α2 (3 − 4γ − 8γ 2 + 4γ 3 ).
(3 + 2γ)2 (2 + 3γ)(71)

C,N C,NIf γ ∈ (0.444, 2.293), SWlC,L (t̄C,L(t ). To sum up, if γ ∈ (0.5, 1], the local
C ) > SWlgovernment chooses t̄C,LC .
Case (b): 1 < γ ≤ 1.823
In this case, because t̄C,N is not the solution that maximizes SWlC,N , SWlC,N (tC,N ) ≥SWlC,N (t̄C,N ), from the results of (70) and (71), the local government chooses t̄C,L
C .

31

Case (c): 1.823 < γ ≤ 3.929
We compare SWlC,L (tLC ) with SWlC,L (t̄C,LI ) and obtain the result
SWlC,L (tLC ) − SWlC,L (t̄C,LI ) =2α2 (−11 − 12γ + 2γ 2 )2
> 0.
3γ(1 + γ)(11 + 8γ)2

(72)

C,N C,NWe also compare SWlC,L (tC,L(t̄ ) and obtain the result
C ) with SWl
C,N C,N
SWlC,L (tC,L(t̄ ) =
C ) − SWl

2α2 (9 + 12γ − 5γ 2 − 5γ 3 + 4γ 4 )> 0,3γ(1 + γ)(3 + 2γ)2(73)

for any γ > 0. Consequently, the local government chooses tC,LC .
Case (d): 3.929 < γ ≤ 6.808
C,L C,L
We compare SWlC,L (tC,L(tI ) and obtainC ) with SWl
C,L C,L
SWlC,L (tC,L(tI ) = −C ) − SWl

2α2 (−33 + γ + γ 2 ).
99γ(1 + γ)

(74)

C,L C,L
When γ ≤ 5.266, SWlC,L (tC,L(tI ). Moreover, from result (73), the local
C ) ≥ SWlgovernment chooses tLC , if γ ∈ (3.929, 5.266]. If γ ∈ (5.266, 6.808], from results (73) and(74), the local government chooses tLI .
Case (e): γ > 6.808
In this case, because SWlC,L (tC,L ) ≥ SWlC,L (t̄C,L
C2 ) and from result (74), we obtain
C,L C,L
SWlC,L (tC,L(t̄C2 ). Moreover, from results (73) and (74), SWlC,L (tCI ) >I ) > SWl

SWlC,N (t̄N ). Hence, the local government chooses tC,L
when γ > 6.808.
I
From the above, we obtain Proposition 6.

The proof of Proposition 7
We compare world welfare in the case of free trade with that in the case of commitment.
We compare SWwF with SWwC when γ ∈ (0, 0.5] where licensing does not occur in eithercase and obtain
SWwF − SWwC = −α2 γ 2 (2 − 7γ − 14γ 2 ).
(6 + 17γ + 12γ 2 )2

32

(75)

Solving (2 − 7γ − 14γ 2 ) = 0 with respect to γ, we obtain γ ≈ 0.203. Therefore,
SWwF < SWwC if γ ∈ (0, 0.203) and SWwF ≥ SWwC if γ ∈ [0.203, 0.5].
We compare SWwF with SWwC when γ ∈ (0.5, 1.5] where licensing occurs under only
commitment to a tariﬀ and obtain the result
SWwF − SWwC = −α2 (−18 + 33γ + 94γ 2 + 60γ 3 + 8γ 4 )< 0,(9 + 18γ + 8γ 2 )2(76)

if γ ∈ (0.5, 1.5].
We compare SWwF with SWwC when γ ∈ (1.5, 1.823] where licensing occurs in bothcases and obtain the result
SWwF − SWwC = −2α2 (1 + γ)(3 + γ)(−3 + 2γ)(1 + 2γ)< 0,(3 + 2γ)2 (3 + 4γ)2(77)

if γ ∈ (1.5, 1.823].
We compare SWwF with SWwC when γ ∈ (1.823, 5.266] and obtain the result
SWwF − SWwC =2α2 (9 + 6γ − 23γ 2 − 8γ 3 + 7γ 4 )< 0.
9γ 2 (3 + 4γ)2

(78)

Solving (9 + 6γ − 23γ 2 − 8γ 3 + 7γ 4 ) = 0 with respect to γ, we obtain γ ≈ 2.303.
Therefore, SWwF < SWwC if γ ∈ (1.822, 2.303) and SWwF ≥ SWwC if γ ∈ [2.303, 5.266].
We compare SWwF with SWwC when γ > 5.266 and obtain the result
SWwF − SWwC =2α2 (30 + 7γ)(30 + 73γ)
> 0.
1089(3 + 4γ)2

(79)
Q.E.D.

The proof of Proposition 8First, we compare the foreign country’s social welfare in the case of free trade with thatin the case of commitment. We compare SWfF with SWfC when γ ∈ (0, 0.5] and obtain
SWfF − SWfC =α2 γ 2 (2 + 31γ + 40γ 2 )> 0.
2 (6 + 17γ + 12γ 2 )2(80)

We compare SWfF with SWfC when γ ∈ (0.5, 1.5] and obtain
SWfF − SWfC = −α2 (18 + 57γ − 52γ 2 + 4γ 3 + 96γ 4 )< 0.
2(3 + 2γ)2 (3 + 4γ)2
33

(81)

We compare SWfF with SWfC when γ ∈ (1.5, 1.823] and obtain
SWfF − SWfC

2α2 (3 − 2γ) (−15 − 17γ + 8γ 2 + 12γ 3 ).
=(3 + 2γ)2 (3 + 4γ)2(82)

When γ > 1.5, (3 − 2γ) is negative and (−15 − 17γ + 8γ 2 + 12γ 3 ) is positive if γ >1.255. Therefore, if γ ∈ (1.5, 1.822], SWfF < SWfC .
We compare SWfF with SWfC when γ ∈ (1.823, 5.266] and obtain
SWfF − SWfC =2α2 (−3 − γ + γ 2 ) (−3 − 13γ + 3γ 2 + 10γ 3 ).
9γ 2 (1 + γ)(3 + 4γ)2

(83)

When γ > 1.111, (−3 − 13γ + 3γ 2 + 10γ 3 ) is always positive and (−3 − γ + γ 2 ) is
positve if γ > 2.303. Therefore, when γ ∈ (1.823, 2.303), SWfF < SWfC and SWfF ≥SWfC when γ ∈ [2.303, 5.266].
We compare SWfF with SWfC when γ > 5.266 and obtain
SWfF − SWfC =10α2 (−369 + 105γ + 70γ 2 )> 0,363(3 + 4γ)2(84)

when γ > 5.266.
Next, we compare the local country’s social welfare in the case of free trade withthat in the case of commitment. We compare SWlF with SWlC when γ ∈ (0, 0.5] andobtainSWlF − SWlC = −α2 γ 2< 0.
2(2 + 3γ)(3 + 4γ)(85)

We compare SWlF with SWlC when γ ∈ (0.5, 1.5] and obtain
SWlF − SWlC =α2 (18 − 27γ − 44γ 2 + 20γ 3 )< 0,2(3 + 2γ)2 (3 + 4γ)(86)

if γ ∈ (0.5, 1.5].
We compare SWlF with SWlC when γ ∈ (1.5, 1.823] and obtain
SWlF − SWlC =2α2 (−3 + 2γ) (−18 − 27γ − γ 2 + 10γ 3 ).
(3 + 2γ)2 (3 + 4γ)2

(87)

When γ > 1.5, (−3 + 2γ) is always positive and (−18 − 27γ − γ 2 + 10γ 3 ) is negative ifγ ∈ (1.5, 1.823]. Therefore, SWfF < SWfC .

34

We compare SWlF with SWlC when γ ∈ (1.823, 5.266] and obtain
2

SWlF − SWlC

2α2 (−3 − γ + γ 2 )= −< 0.
3γ(1 + γ)(3 + 4γ)2(88)

We compare SWlF with SWlC when γ > 5.266 and obtain
SWlF − SWlC

2α2 (585 + 75γ − 49γ 2 )=.
99(3 + 4γ)2

(89)

When γ > 4.304, (585 + 75γ − 49γ 2 ) is negative. Therefore, SWlF < SWlC .
Q.E.D.

35

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37