GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No. 288

Environmental regulation and technology transfers

Takao Asano and Noriaki Matsushima

December 2012GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

Environmental regulation and technology transfers∗
Takao Asano†
Faculty of Economics, Okayama University
Noriaki Matsushima‡
Institute of Social and Economic Research, Osaka University
This Version: December 13, 2012

Abstract
This paper analyzes the situation in which a national government introduces environmental regulations. Within the framework of an international duopoly with environmental regulations, this paper shows that an environmental tax imposed by the government
in the home country can induce a foreign firm with advanced abatement technology tolicense it to a domestic firm without this technology. Furthermore, when the domestic
firm’s production technology is less efficient than that of the foreign firm, the foreign
firm may freely reveal its technology to the domestic firm. These improvements throughthe voluntary transfer of technology support the Porter hypothesis, which states thatenvironmental regulations have positive impacts on innovation.
JEL Classification Numbers: Q56, F18, H23, L13
Key Words: Environmental regulation; Technology transfer; International competition;
Duopoly.

∗
We would like to thank Akihisa Shibata for his helpful comments. Financial support from Grant-in-Aid
for Scientific Research (JSPS) is greatly acknowledged. Needless to say, we are responsible for any remaining
errors.
†Takao Asano, Faculty of Economics, Okayama University, 3-1-1 Tsushimanaka, Kita-ku, Okayama 7008530, Japan. e-mail: asano@e.okayama-u.ac.jp. Phone: +81-86-251-7558.
‡
Correspondence author: Noriaki Matsushima, Institute of Social and Economic Research, Osaka University, 6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan. Phone: +81-6-6879-8571. Fax: +81-6-6879-8583.
E-mail: nmatsush@iser.osaka-u.ac.jp

1. Introduction
This paper analyzes the situation in which a national government introduces environmental regulations. Based on an international duopoly model with environmental regulations,this paper shows that an environmental tax imposed by the government in the home country
can induce a foreign firm with advanced abatement technology to license it to a domestic
firm without this technology. Furthermore, when the domestic firm’s production technology
is less efficient than that of the foreign firm, the foreign firm may freely reveal its technology
to the domestic firm.
Although the importance of environmental regulations has been recognized, many national governments, especially those in developing countries, seem hesitant to impose thembecause it is believed that these regulations can lower domestic firms’ production (Ekins,
1999; European Commission, 2001).1 If such regulations were imposed, these firms would
need support from foreign firms with advanced environmental technologies to overcome them.
Thus, policymakers must understand whether the necessary advanced environmental technologies would be transferred from foreign firms to domestic firms. Because both abatement
and production technologies play an important role in firms’ activities, we also investigate
whether foreign firms that license their advanced abatement technologies would also provide
or license their production technologies.
This second question is important because technology transfers from developed countries
to developing countries have received extensive attention (Horiuchi and Ishikawa, 2009).
Substantial north-south technology spillovers have been well established empirically (Coeet al., 1997; Miller and Upadhyay, 2000), but these spillovers were involuntary. If foreign
firms have incentives to voluntarily provide production technology to domestic firms, we can1Contrary to this tendency, most European countries do have high levels of environmental taxationcompared to the United States and some other countries (Sterner and Köhlin, 2003). In fact, as reportedby the OECD (2012), the revenues from environmentally related taxes measured as a percent of GDP in2009 were, for example, 3.99% in Denmark, 3.50% in Turkey, 2.85% in Sweden, 1.32% in Argentina, 1.27% in
China, and 0.81% in the United States. For a discussion of environmental taxation in the United Kingdom,
see Dresner et al. (2006).

1

conclude that these foreign firms would not have to fear involuntary production technology
spillovers through north-south trade when they can license their environmental technologies
to domestic firms.
To analyze these situations, we consider an international duopoly model with environmental regulations.2 We suppose that one domestic firm and one foreign firm exist and thatthe foreign firm is more efficient than the domestic one. The domestic firm does not have anabatement technology to reduce pollutants, whereas the foreign firm does have such a technology. To reduce pollutants, the government in the home country imposes an environmental
tax if the foreign firm does not transfer its abatement technology.
Using a simple duopoly model, we show that the abatement technology can be transferred from the foreign firm to the domestic firm. Moreover, if the foreign firm has a chance
to transfer its production technology before it determines whether to license its abatement
technology, it may reveal its production information freely. It may seem like this production technology transfer would not benefit the foreign firm because it would improve theproduction efficiency of the rival domestic firm. However, this is not always true. Whenthe domestic firm is very efficient, the government tends to set a higher environmental tax
level to reduce the quantity supplied by the domestic firm. The foreign firm can therefore
charge higher royalties for the abatement technology license because the domestic firm has
a stronger incentive to escape the environmental tax. Anticipating this higher royalty fee,the foreign firm has an incentive to provide its production technology before it determines
whether to license its abatement technology. This transfer is Pareto improving given that theforeign firm will license its abatement technology irrespective of the production technology
transfer decision. This property of free-revelation can hold true even when we consider thecase in which the licenser charges a lump-sum fee.3 Furthermore, we compare the two fee
2Burret and Sempere (2003), Lai and Hu (2008), and Baski and Chaudhuri (2009) investigate pollution

problems in the context of international competition. They do not discuss firms’ incentives to license abatement technologies, as discussed in this paper.
3

Several works compare fees and royalties in oligopoly models (Wang, 1998; Sen, 2005).

2

schedules and show that royalty licensing is more profitable for the licenser.
This result does not hold, however, when the government pre-commits itself to its environmental tax level. The production technology transfer is therefore more likely to occur if
the government intends to adjust its environmental standard to fit the market environment.
As mentioned earlier, many governments seem hesitant to impose environmental regulations, which reduces the possibility of a production technology transfer. A government’s
willingness to adjust its environmental standard also eliminates the foreign firms’ fear of
production technology spillovers because the effect of a production technology transfer is thesame whether it is voluntary or involuntary.
Furthermore, our result is related to the Porter hypothesis. The Porter hypothesis (Porterand van der Linde, 1995) states that stringent environmental regulations could affect both innovation that improves the environment and firms’ competitiveness. Many works empiricallyand theoretically discuss the validity of the Porter hypothesis by investigating the effects ofenvironmental regulations on the growth rate of total factor productivity (Hamamoto, 2006),
innovative activity (Hamamoto, 2006), global productivity (Bréchet and Jouvet, 2009), export competitiveness (Costantini and Mazzanti, 2011), the productivity of capital stock(Xepapadeas and de Zeeuw, 1999; Feichtinger et al., 2005), and endogenous technologicalchange (Mohr, 2002). Our paper investigates the relationship between environmental regulations and technology transfers, which clearly have a positive impact on productivity. To
the best of our knowledge, the effects of environmental regulations on technology transfers
have not been analyzed. Therefore, our result complements the previous discussions on thePorter hypothesis.
Some researchers have already pointed out that firms with superior production or abatement technologies have incentives to license their technologies to their competitors (Rockett,1990 and Regibeau and Gallegos, 2004). Rockett (1990) does not consider environmental
technology transfers. Papers that do consider environmental technologies do not investigate
production technology transfers, but, as in this paper, they do find that abatement technol-3ogy transfers occur in oligopoly models where licensers directly compete with licensees infinal product markets.
The possibility of technology transfers has been also investigated in the literature. Kabiraj and Marjit (2003) and Mukherjee and Pennings (2006) discuss the licensing incentives offirms with advanced production technologies. This paper is different from the other papers
in several ways. First, this paper considers a licenser’s incentive to transfer two types oftechnology, whereas previous papers only discuss production technology transfers. Second,
unlike previous papers, we show that the free revelation of production technology can occur.
Finally, these papers do not take into account pollution problems and instead focus on thepossibility that tariffs induce a technology transfer from an advanced foreign firm to domestic
firms.4
The organization of this paper is as follows. Section 2 provides our model. Section
3 analyzes two cases in which the host government imposes an environmental tax on thedomestic and foreign firms. In the first case, the foreign firm does not license its abatement
technology to the domestic firm, and in the second case, it does. In the latter case, bothproduction and abatement technology can be transferred. Section 4 discusses the case inwhich the foreign firm uses a lump-sum fee when it licenses its abatement technology. Section
5 analyzes a different timing structure to check the robustness of the results in Section 3.
Section 6 discusses further extensions. Section 7 concludes.
2. The ModelIn this section, we provide our model. We consider a market with two firms (f and h)that produce a homogeneous product. Firm f is in a foreign country, and firm h is in thehome country. Firm f produces a unit of product at no marginal cost, and firm h produces
at a constant marginal cost c ∈ (0, 1/2), so that firm h is less efficient than firm f . There
4

Furusawa, Higashida, and Ishikawa (2004) and Ishikawa and Okubo (2009) investigate the effects ofseveral governmental policies in international oligopoly models with externalities. Iida and Takeuchi (2009)
investigate the effect of a tariff on the incentives of a foreign firm in an international duopoly model.

4are no fixed costs to production. We consider quantity competition.
Let xi be firm i’s output level (i = f, h). The inverse demand function for the homogeneous products is
p = 1 − xf − xh .

(1)

In the production process, firm h generates pollutants that damage the environment of
the home country. The environmental pollutants generated by firm h with output level xhareED ≡ γx2h ,(2)where γ denotes the degree of environmental damage. For analytical simplicity, we assume
that γ > 1/2. In order to reduce pollutants that affect social welfare in the home country,
the government in the home country imposes an environmental tax that maximizes thedomestic surplus. Because firm f has advanced abatement technology, firm f does not emit
any pollutants, which implies that the environmental tax is not imposed on firm f . The
amount of tax paid by firm h is txh , where t is a constant value. In this paper, t canbe negative because of the government’s incentive to protect the domestic firm, as in thecontext of strategic trade policy (Brander and Spencer, 1985). As shown in the next section,
this assumption is not necessary to derive the main results, but it allows us to simplify the
exposition. In this case, firm f ’s marginal cost of production is zero, and firm h’s marginal
cost of production is c + t.
Firm h can escape the pollution tax if firm f licenses its abatement technology, which
eliminates pollutants. Firm f licenses this technology at a royalty rate r. The total royalty
firm h must pay depends on the quantity of the product that it supplies. In this case, firm
f ’s marginal cost of production is zero, and firm h’s marginal cost of production is c + r.
3. Royalty Licensing
In this section, we consider an environmental tax both without and with licensing. In thefirst case, the game is a simple two-stage quantity-setting model; the regulator imposes the5tax rate t, and each firm simultaneously determines its quantity supplied. In the second case,firm f first decides whether to license its technology to firm h, the regulator then imposes
the tax rate t if licensing does not occur, and finally, each firm simultaneously determines
its quantity supplied.
3.1. No licensing versus licensing
We first consider the case in which firm f does not license its abatement technology.
Suppose that the marginal costs of firms f and h are cf and ch , respectively. Applying thestandard calculation in Cournot competition to this problem, we have xf = (1 + ch − 2cf )/3,
xh = (1 + cf − 2ch )/3, πf = x2f , and πh = x2h . Now, the marginal costs of firms f and h are
0 and c + t, respectively. The profits of the firms and the consumer surplus are
πf = x2f =(1 − 2c − 2t)2
(2 − c − t)2(1 + c + t)2, πh = x2h =, CS =
.
9
9
18

(3)

The domestic social surplus (the objective of the government) is
SW = CS + πh + txh − γx2h=3(2 − 4c + 3c2 ) − 2(1 − 2c)2 γ − 2(3(1 − c) − 4(1 − 2c)γ)t − (3 + 8γ)t2
.
18

(4)

Solving the first-order condition, we find the optimal tax rate tn :tn = −

3(1 − c) − 4(1 − 2c)γ.
3 + 8γ(5)The superscript “n” denotes the case of no licensing. The profits of the firms are obtained
as follows:πfn =4(c + 2γ)2(3 − 4c)2
n
,
π
=
.
h
(3 + 8γ)2(3 + 8γ)2(6)

Next, we consider the case in which firm f licenses its abatement technology to firm h
if possible. The marginal costs of firms f and h are 0 and c + r. Firm f earns additional
profits (rxh ) from the licensing. The profits of the firms areπf =1 − 2c − 2r
(1 − 2c − 2r)2
(1 + c + r)2+r, πh =
.
9
3
9
6

(7)

When firm f licenses its abatement technology, it faces the constraint that the ex post profit
of firm h must be larger than πhn in (6). Otherwise, firm h would reject the offer and pay theenvironmental tax. This condition is (1 − 2c − 2r)2 /9 > (3 − 4c)2 /(3 + 8γ)2 , which implies
that r < tn . Under this constraint, firm f licenses its technology if and only if tn > 0.5 Thatis, if the environmental tax is positive and does not function as a subsidy to protect firmh from firm f , firm f has an incentive to license its abatement technology to firm h. The
optimal royalty rate rl is equal to the optimal tax rate tn , where the superscript “l” denotes
licensing. This is because firm f sets its royalty rate so that firm h is indifferent between
accepting and rejecting f ’s offer.
Proposition 1. If tn > 0 (γ > 3(1−c)/4(1−2c) or c < (4γ −3)/(8γ −3)), firm f licenses its
technology to firm h. The royalty rate rl is equal to the optimal tax rate tn , that is, rl = tn .
Then, the profits of the firms and the domestic surplus are given by:πfl =(3 − 4c)2(3 − 4c)(−3(1 − c) + 4(1 − 2c)γ) + 4(c + 2γ)2
l
,
π
=
,
h
(3 + 8γ)2(3 + 8γ)2

27 − 60c + 36c2 + 8(3 − 2c)γ + 16γ 2.
SW =2(3 + 8γ)2(8)l3.2. Free revelation of production technology
We consider whether firm f has an incentive to freely give its efficient production technology to firm h. We consider the following stage game. First, firm f determines whether
to provide its production technology to firm h. Second, firm f decides whether to license its
abatement technology to firm h. Third, the regulator imposes tax rate t if the transfer of
the abatement technology does not occur. Finally, each firm simultaneously determines its
quantity supplied. That is, we add the first stage to the game discussed in the previous subsection. By comparing πfl |c=0 and πfl , we obtain the following proposition (the calculation
is available in the Appendix).
Firm f licenses its abatement technology if its ex post profit is greater than πfn , that is, (1 + c + r)2 /9 +r(1 − 2c − 2r)/3 > (1 + c + t)2 /9. Because the optimal royalty rate is equal to the optimal tax rate andxh = (1 − 2c − 2r)/3 ≥ 0, it follows that f licenses its technology if and only if tn > 0.
5

7

Proposition 2. Suppose that firm f uses a royalty to license its abatement technology.
When c < min {(4γ − 3)/(8γ − 3), 3(8γ − 7)/8(4γ − 1)}, the profits of the firms, the consumer surplus, and the social surplus are larger when firm f freely reveals its production
technology.
When γ is large, as the marginal cost of firm h decreases, the profits of firms h and f
increase. In other words, firm h’s efficiency improvements benefit firm f when the degree ofenvironmental damages generated by firm h (γ) is large. When c is small (firm h is efficient),
the quantity supplied by firm h is large. Because more production leads to more pollution,
firm h must pay more taxes as it improves. This higher taxation level allows firm f to set ahigher royalty rate. This effect is represented by the difference between rl = tn in (5) whenfirm h’s marginal cost is zero and when it is c: rl |c=0 −rl = (8γ −3)c/(8γ +3). This differenceis larger as the value of γ increases. Therefore, when γ is large (γ > 3(1 − c)/4(1 − 2c) or
c < (4γ − 3)/(8γ − 3)), a decrease in c can be Pareto improving.
As shown in Proposition 2, if firm f provides its production technology to firm h, thenfirm h’s marginal cost changes from c to zero, increasing the profits of both firms h and f .
Disclosing the efficient technology can therefore be Pareto improving. Our result implies thatenvironmental regulation can improve production technology through a voluntary technology
transfer and supports the well-known Porter hypothesis (Porter and van der Linde (1995)).
Many works empirically and theoretically discuss the validity of the Porter hypothesis, andour result complements these previous discussions.
We implicitly assume that the government knows the efficiency levels of the firms (thatis, the marginal costs of the firms) and the significance of the environmental damage causedby pollutants (that is, the value of γ). These implicit assumptions are not particularly
restrictive. The first assumption is not restrictive if the government is able to observe thequantities supplied by the firms because these quantities reflect the efficiency levels of thefirms. The more efficient a firm is, the more it produces. The second assumption is also
not restrictive if governments are able to evaluate the effectiveness of firms’ environmental
8technologies. In the automobile industry, governments set many grades of environmental
standards because they are able to certify the emissions generated by products. Finally, theassumption of linear demand is not crucial to the results if the convexity of the environmental
damage function, or in other words, γ, is large enough (this result is available in the Appendix(not for publication)).
4. Lump-Sum Licensing
We consider the case in which firm f uses a lump-sum fee to license its abatement
technology to firm h. To discuss the incentives of firm f , we compare the case where it does
not license to the case where it does.
4.1. Licensing
The case in which firm f does not license has already been discussed in section 3.1. The
profits in this case are provided in (6).
Thus, we only consider the case in which firm f licenses. The profits when firm f licenses
its abatement technology are given as πf = (1 + c)2 /9 + F and πh = (1 − 2c)2 /9 − F , where
F is the lump-sum fee from firm h to firm f . As in the case of royalties, we assume thatfirm f (the licenser) has full bargaining power over firm h (the licensee). Firm h accepts thelicensing contract if doing so does not lower its profit. Therefore, firm f sets the maximum
value of F such that πh ≥ πhn , that is,F∗ =4(3(1 − c) − 4(1 − 2c)γ)(−3(2 − 3c) − 4(1 − 2c)γ).
9(3 + 8γ)2(9)We derived the condition under which the environmental tax level is positive in Proposition
1, which is equivalent to c < (4γ − 3)/(8γ − 3). The value of F in (9) is positive if −3(2 −3c) − 4(1 − 2c)γ < 0, that is, if c < 2(2γ + 3)/(8γ + 9). This inequality is satisfied if
the environmental tax level is positive, that is, if c < (4γ − 3)/(8γ − 3). Therefore, if
c < (4γ − 3)/(8γ − 3), F ∗ is positive. In other words, if the environmental tax level is9positive, F ∗ is also positive. The profits of the firms are
πfL =



1+c
3

2

∗

πhL =

+F ,



1 − 2c3

2− F ∗,(10)

where the superscript “L” denotes licensing with a lump-sum payment.
We now check whether firm f has an incentive to license its abatement technology, whichis the case if the profit from licensing with a lump-sum fee is greater than that of no licensing(the calculation is available in the Appendix).
Proposition 3. If c < min{(4γ − 3)/(8γ − 3), (21 − 4γ)/(5(8γ + 9))}, firm f has an incentive
to license its abatement technology to firm h through a lump-sum fee.
The first inequality, c < (4γ − 3)/(8γ − 3), is the condition under which firm h has anincentive to accept the licensing contract. This is similar to the case of a royalty. The second
inequality, c < (21 − 4γ)/(5(8γ + 9)), is the condition under which firm f has an incentive
to offer the licensing contract. In the case of a royalty, firm f always has an incentive tooffer its technology if firm h has an incentive to accept the licensing contract. This result
does not always hold when firm f uses a lump-sum fee. When firm f uses a royalty, the net
marginal cost of firm h is c + rl = c + tn if firm h accepts this offer. Firm f keeps its costadvantage and earns the licensing revenue. When firm f uses a lump-sum fee, however, thenet marginal cost of firm h is c, not c + tn , if firm h accepts this offer. Firm f loses its costadvantage even though it earns the licensing revenue.6
When c is large, this negative effect is significant. The licensing contract lowers theequilibrium market price because the marginal cost of firm h decreases. A larger firm has
more output over which it can apply a decrease in price. Because the production level offirm f is large when c is large (when firm h is less efficient), a decrease in price has a morenegative impact on firm f . Therefore, when c is large, firm f has weak incentives to license
its abatement technology.
6

The right-hand side of the inequality in Proposition 3 can be rewritten as c < (21 − 4γ)/5(9 + 8γ). Whenc is large enough, this inequality does not hold.

10

4.2. Free revelation of production technology
We now check the conditions under which firm f has an incentive to give its advanced
production technology to firm h. As shown in the Appendix, the following proposition gives
the result.
Proposition 4. Suppose that firm f uses a lump-sum fee to license its abatement technology.

If c < min{(4γ − 3)/(8γ − 3), (21 − 4γ)/(5(9 + 8γ))} and c < 2 −99 + 48γ + 64γ 2 /(−99 +240γ + 320γ 2 ), firm f has an incentive to give its production technology to firm h.

Firm f does not give its production technology when c is large. When firm f uses a
lump-sum fee, the net marginal cost of firm h is c rather than c + tn . The free revelation of
production technology eliminates firm f ’s cost advantage. When the production technology
is revealed, the revenue from licensing, F ∗ in (9), increases, but when c is large, the costs ofincreased competition outweigh the benefits from the licensing revenue.
4.3. Lump-sum fee versus royalty
We now compare the cases where firm f charges a royalty and where it charges a lumpsum fee. Given that the environmental tax level tn in (5) is positive, πfl in (8) is greaterthan πfL in (10), which leads to the following proposition.7
Proposition 5. Firm f prefers a royalty to a lump-sum fee.
A royalty contract keeps firm h in a less competitive position because it needs to pay a
positive r to firm f , which increases its marginal cost. On the other hand, a lump-sum fee
contract makes firm h more competitive because the contract does not increase its marginalcost. This difference is the key to this proposition.
5. Extensions
7

A simple calculation leads to πfl −πfL = ((4(1 − 2c)γ − 3(1 − c))(3(2 + 3c) + 4(1 + 10c)γ)) /9(3+8γ)2 > 0.

11

In this section, to analyze whether commitment to the environmental tax affects our
results, we change the timing structure of the game. First, the government sets the tax
level. Second, observing the tax level, firm f determines whether to license its abatement
technology and sets royalty rate r when it licenses. Finally, given the decisions of thegovernment and firm f , each firm sets its quantity supplied.
First, we consider the subgame in which firm f does not license its abatement technology.
We only consider the case where t ≤ 0 because firm f has an incentive to license its technology
if t > 0. When t ≤ 0, the outcome in this subgame is similar to that in the previous section.
That is, πf , πh , and CS are described in (3), and SW is described in (4). Given the outcome,the optimal tax is tn in (5), and the welfare level is SW cn = (3 − 6c + 4c2 + 2γ)/2(3 + 8γ),
where the superscript “cn” denotes the case of commitment with no licensing. tn in (5) is
negative if and only if c > (4γ − 3)/(8γ − 3).
Second, we consider the subgame in which firm f licenses its abatement technology. If
the government induces firm f to license its technology, then the optimal tax level is t = ε,where ε is a sufficiently small positive value. To simplify the analysis, we assume that t iszero and firm f licenses its technology with r = t = 0. Substituting r = 0 and γ = 0 into
SW in (4), we have SW cl = (2 − 4c + 3c2 )/6, where the superscript “cl” denotes the case ofcommitment with licensing. In this case, the profit of firm f monotonically increases in c.
As shown in the Appendix, the following proposition holds.
Proposition 6. When the government pre-commits itself to the environmental tax, firm fdoes not have an incentive to give its superior production technology to firm h.
From the difference between SW cn and SW cl , we find that the government sets t = 0 if
γ > 3(1 − c)2 /2(1 − 2c)(5 − 6c). The right-hand side is smaller than 3(1 − c)/4(1 − 2c), whichis the threshold at which the tax rate is negative when the government does not commit to
the tax rate. That is, when the government is able to commit to the tax rate, firm f tends
to license its abatement technology.

12Commitment versus No commitment

The domestic welfare ranking in the two gameswith different timing structures is ambiguous. The difference between SW cl and SW l |c=0
(because of the production technology transfer) is
SW cl − SW l |c=0 =(4(1 − 2c)γ − 3(1 + c))(21 − 9c + 5(5 − 6c)γ).
6(3 + 8γ)2This difference is negative if (4γ − 3)/(8γ + 3) < c. That is, when the inequality holds,
pre-committing to the tax rate does not improve the domestic surplus because it has two
conflicting effects. On the one hand, when the government sets its tax rate in advance, firm
f always licenses its abatement technology if the tax rate is positive. Anticipating firm f ’s
reaction, the government sets the tax rate at a positive but sufficiently small level. Therefore,pre-commitment can reduce the royalty rate r, which increases domestic welfare. On theother hand, pre-commitment does not induce firm f to transfer its technology as it would
when the government cannot commit its tax rate. Because the tax rate is pre-determined,
firm f cannot raise the royalty rate r through a production technology transfer, which
lowers domestic welfare. Those two effects trade off. As the value of γ increases, licensing
the abatement technology becomes more important for domestic welfare. As the value of cincreases, the production technology transfer becomes more important for domestic welfare.
When γ is large enough, pre-committing to the tax rate is beneficial because licensing isrelatively more important than the production technology transfer. When c is large enough,pre-committing to the tax rate is not beneficial because the production technology transfer
is relatively more important than licensing.
6. Discussions
In this section, we discuss further extensions. The details of the discussions are available
in the Appendix (not for publication).
Cost and quality

In the previous sections, we investigated the effects of licensing on

firms’ behaviors by incorporating production cost heterogeneity into the standard Cournot
13

model. The main results still hold even when we incorporate a quality difference between
the firms by the following formulation. The utility of the representative consumer is given
by U = xf + (1 − c)xh − (xf + xh )2 /2 + m, where m is a numeraire good. The inverse demand
functions are given by pf = 1 − xf − xh and ph = 1 − c − xf − xh , where c represents thequality disadvantage of firm h. Under this assumption, we have the same results as those in
the main text. Therefore, we can apply our main results to the case where firm f can giveits high quality technology to firm h.
Package license

In the previous sections, we separately analyzed firm f ’s decisions totransfer its abatement technology and its production technology to firm h. However, it
could offer both technologies as a package. When we incorporate the possibility of offering a
package license into the model, as in the case of Section 3.2, firm f licenses its technology tofirm h except the case in which c and γ are small. However, the optimal royalty rate is greaterthan the optimal tax rate, which is a stark contrast to the result obtained in Proposition 1.
On the other hand, the welfare level is equivalent to that under the abatement technology
licensing case.
Tariff and subsidy

We next analyze the case in which the government imposes an export

tariff on firm f as well as an environmental tax on firm h. For that purpose, we suppose thatafter the licensing contract is determined, the government imposes the tariff on firm f . Firmf has an incentive to provide its production technology and its abatement technology to firm
h when c is small. That is, the main result does not qualitatively change even when we take
into account a tariff on firm f . We can also consider the case in which the government gives
a subsidy to firm h and imposes an environmental tax on firm h. We can derive a result
which is qualitatively similar to Proposition 2 although the outcome in the case where firm
f licenses differs from that in the basic model.

14

Global welfare

We can obtain some implications about global welfare using the basicmodel when an environmental tax is set to maximize the global social surplus. When firm fdoes not freely reveal its production technology, the global social surplus increases because
the tax setter internalizes the profit of firm f . When firm f does freely reveal its production
technology, the tax level set by a global welfare maximizer is higher than that set by adomestic welfare maximizer. Because firm f sets its licensing fees at the tax levels in thetwo cases, the licensing fee in the former case is higher than that in the latter one. The
production technology transfers induce the production costs of the two firms to be zero inboth cases, which implies that the global surplus in each case monotonically increases withthe total quantity supplied by the firms. The difference between the licensing fees in the twocases leads to the welfare difference in the two cases. As a result, the global surplus in which
the tax setter maximizes the global surplus is smaller than that in which it maximizes the
local surplus.
7. Conclusion
Using a duopoly model with environmental regulations, this paper has analyzed whether
governmental environmental regulations induce advanced abatement technology transfersfrom a foreign firm to a local firm. In this setting, if the local firm produces without advanced
abatement technologies, then it has to pay an environmental tax for generating pollutants.
This paper has shown that abatement technology transfer does occur, enabling the local
firm to produce without generating pollution and to avoid paying the environmental tax.
Furthermore, this paper has shown that the foreign firm may transfer production technology
as well as abatement technology because the foreign firm can increase its royalties fromproviding the environmental technology when the local firm produces more efficiently. The
result supports the well-known Porter hypothesis (Porter and van der Linde (1995)), andthus this paper complements previous discussions of the Porter hypothesis.

Appendix15

Proof of Proposition 2. The difference between πfl |c=0 and πfl is given by
πfl |c=0 − πfl =c(3(8γ − 7) − 8(4γ − 1)c),
(3 + 8γ)2(11)which is zero when c = 0 or c = 3(8γ − 7)/8(4γ − 1). Because πfl is a convex function
with respect to c, πfl is smaller than πfl |c=0 if and only if c < 3(8γ − 7)/8(4γ − 1). Under
this inequality, CS l and πhl decrease in c, and SW l is largest when c = 0, which proves
Proposition 2.
Proof of Proposition 3. πfL in (10) can be rewritten as−63 + 96γ + 128γ 2 − 2 −99 + 48γ + 64γ 2 c + c2 −99 + 240γ + 320γ 2L.
πf =9(3 + 8γ)2(12)Firm f has an incentive to license if and only if πfL in (12) is larger than πnf in (6), that is,
πfL ≥ πfn ⇔(3(1 − c) − 4(1 − 2c)γ)(−3(7 − 15c) + 4(1 + 10c)γ)≥ 0.
9(3 + 8γ)2(13)This is positive if −3(7 − 15c) + 4(1 + 10c)γ < 0, that is, c < (21 − 4γ)/5(8γ + 9), which
proves Proposition 3.
Proof of Proposition 4. Using πfL in (12), we derive the partial derivative of firm f ’s profit
with respect to c:
2 99 − 99c − 48γ + 240cγ − 64γ 2 + 320cγ 2=.
∂c9(3 + 8γ)2

∂πfL

The second partial derivative is given by∂ 2 πfL∂c2


2 −99 + 240γ + 320γ 2=.
9(3 + 8γ)2When γ > 3/4, this profit function is convex with respect to c. The lower bound of γ,
3/4, is derived using the condition under which the environmental tax level is positive,γ > 3(1 − c)/4(1 − 2c) in (5) for c ∈ [0, 1/2). The inequality γ > 3/4 fully covers the casethat we mainly discuss. From the first-order condition ∂πfL /∂c = 0, the following c minimizes
the profit of firm f :c=−99 + 48γ + 64γ 2.
−99 + 240γ + 320γ 2
16

If firm f gives its advanced production technology to firm h, the value of c becomes zero.
When c = 0, the profit of firm f is
πfL |c=0 =−63 + 96γ + 128γ 2.
9(3 + 8γ)2

We now derive the value of c such that the profit of firm f is equal to that when c = 0:c 198 − 99c − 96γ + 240cγ − 128γ 2 + 320cγ 2LLπf − πf |c=0 = 0 ⇔= 0.
9(3 + 8γ)2This equation is satisfied when c = 2 −99 + 48γ + 64γ 2 /(−99 + 240γ + 320γ 2 ). Because
πfL is a convex function with respect to c, πfL is smaller than πfL |c=0 if and only if
2 −99 + 48γ + 64γ 2,c<−99 + 240γ + 320γ 2which proves Proposition 4.
Proof of Proposition 6. We now show that when the government pre-commits to the environmental tax rate, firm f never gives its production technology to firm h.
When the government sets its tax rate at t, the maximum level of the licensing fee isr = min{t, r̄}, where r̄ = arg maxr x2f + rxh = (5 − 4c)/10. When r = t, the profit of firm f
is πf = (1 + c)2 + (5 − 4c)t − 5t2 /9. This is larger than πf |c=0 for any t < (1 − 2c)/2 (thisinequality ensures that the quantities supplied by the firms are positive). When r = r̄, theprofit of firm f is πf = (5 + 4c2 )/20. This is larger than πf |c=0 . These results imply thatfirm f is not willing to give its production technology to firm h.

References[1] Ambec, S. and P. Barla (2002): “A Theoretical Foundation of the Porter Hypothesis,”Economics Letters 75, 355-360.
[2] Baksi, S. and A. R. Chaudhuri (2009): “On Trade Liberalization and Transboundary
Pollution,” Economics Bulletin 29, 2605-2612.

17[3] Brander, J.A. and B.J. Spencer (1985): “Export subsidies and international market
share rivalry,” Journal of International Economics 18, 83-100.
[4] Bréchet, T. and P.-A. Jouvet (2009): “Why Environmental Management May Yield
No-Regret Pollution Abatement Options,” Ecological Economics 68, 1770-1777.
[5] Burguet, R. and J. Sempere (2003): “Trade Liberalization, Environmental Policy, andWelfare,” Journal of Environmental Economics and Management 46, 25-37.
[6] Coe, D. T., E. Helpman, and A.W. Hoffmaister, (1997): “North–South R and D
Spillovers,” Economic Journal 107, 134-49.
[7] Costantini, V. and M. Mazzanti (2012): “On the Green and Innovative Side of Trade
Competitiveness? The Impact of Environmental Policies and Innovation on EU Exports,” Research Policy 41, 132-153.
[8] Dresner, S., T. Jackson, and N. Gilbert (2006): “History and Social Responses toEnvironmental Tax Reform in the United Kingdom,” Energy Policy 34, 930-939.
[9] Ekins, P. (1999): “European Environmental Taxes and Charges: Recent Experoence,Issues, and Trends,” Ecological Economics 31, 39-62.
[10] European Commission (2001): Study of the Economic and Environmental Implicationsof the Use of Environmental Taxes and Charges in the European Union and Its Member
States.
[11] Feichtinger, G., R. F. Hartl, P. M. Kort, and V. M. Veliov (2005): “Environmental
Policy, the Porter Hypothesis and the Composition of Capital: Effects of Learning andTechnological Progress,” Journal of Environmental Economics and Management 50,
434-446.
[12] Furusawa, T., K. Higashida, and J. Ishikawa (2004): “Tariffs versus Quotas in the
Presence of Imperfect Competition and Cross-Border Externalities,” Canadian Journalof Economics 37, 445-458.
[13] Hamamoto, M. (2006): “Environmental Regulation and the Productivity of Japanese
Manufacturing Industries,” Resource and Energy Economics 28, 299-312.
[14] Horiuchi, E. and J. Ishikawa (2009): “Tariffs and Technology Transfer through an Intermediate Product,” Review of International Economics 17, 310-326.
[15] Iida, T. and K. Takeuchi (2009): “Environmental Technology Transfer via Free Trade,”
Economics Bulletin 30, 948-960.

18

[16] Ishikawa, J. and T. Okubo (2010): “Environmental and Trade Policies for Oligopolistic
Industry in the Presence of Consumption Externalities,” International Economy 14,
59-76.
[17] Kabiraj, T. and S. Marjit (2003): “Protecting Consumers through Protection: The Roleof Tariff-induced Technology Transfer,” European Economic Review 47, 113-124.
[18] Lai, Y. and C. Hu (2008): “Trade Agreements, Domestic Environmental Regulation,
and Transboundary Pollution,” Resource and Energy Economics 30, 209-228.
[19] Miller, S. M. and M.P. Upadhyay, (2000): “The Effects of Openness, Trade Orientation,and Human Capital on Total Factor Productivity,” Journal of Development Economics
63, 399-423.
[20] Mohr, R. D. (2002): “Technical Change, External Economies, and the Porter Hypothesis,” Journal of Environmental Economics and Management 43, 158-168.
[21] Mukherjee, A. and E. Pennings (2006): “Tariffs, Licensing and Market Structure,”
European Economic Review 50, 1699-1707.
[22] OECD (2012): “The OECD/EEA database on instruments used for environmental policy and natural resources management,” (May 5, 2012).
[23] Porter, M. E. and C. van der Linde (1995): “Toward a New Conception of theEnvironment-Competitiveness Relationship,” Journal of Economic Perspectives 9, 97118.
[24] Regibeau, P. M. and A. Gallegos (2004): “Managed Trade, Trade Liberalisation andLocal Pollution,” Advance in Economic Analysis and Policy 4 (2) Article 5.
[25] Rockett, K. (1990): “The Quality of Licensed Technology,” International Journal ofIndustrial Organization 8, 559-574.
[26] Sen, D. (2005). “Fee versus Royalty Re-Considered,” Games and Economic Behavior
53, 141-147.
[27] Stern, T. and G. Köhlin (2003): “Environmental Tax in Europe,” Public Finance andManagement 3, 117-142.
[28] Wang, X. W. (1998): “Fee versus Royalty Licensing in a Cournot Duopoly Model,”Economics Letters 60, 55-62.
[29] Xepapadeas, A. and A. de Zeeuw (1999): “Environmental Policy and Competitiveness:
The Porter Hypothesis and the Composition of Capital,” Journal of Environmental
Economics and Management 37, 165-182.

19

Appendix (not for publication)
1

Packaging

We consider the case in which firm f licenses its abatement technology and its production
technology as a package to firm h if possible. From (1), the profit functions of firms f and
h are
πf = (1 − xf − xh )xf + rxh , πh = (1 − xf − xh − r)xh .
(A.1)
The first-order conditions lead to
xf =

1+r
1 − 2r, xh =
.
3
3

(A.2)

From (A.1) and (A.2), the profits of the firms and the consumer surplus areπf =(1 + r)2
1 − 2r(1 − 2r)2(2 − r)2+r, πh =, CS =
.
9
3
9
18

(A.3)

When firm f licenses the package, it faces a constraint under which the ex post profit offirm h must be larger than πhn in (6). Otherwise, firm h would reject the offer and pay theenvironmental tax. The condition is(3 − 4c)2(1 − 2r)2>9(3 + 8γ)2→ r<−3 + 6c + 4γ.
3 + 8γUnder this constraint, firm f licenses its technology if and only ifr > 0.
Firm f can choose r to maximize πf in (A.3) under the above constraint on r. We easilyfind that this constraint is binding, thus, the optimal royalty rate rp is
rp =−3 + 6c + 4γ.
3 + 8γ(A.4)

The superscript “p” denotes package licensing. Contrary to the previous case, this optimal
royalty rate is not equal to the optimal tax rate tn in (5). We summarize this result in thefollowing proposition:
Proposition 7. If c > (3 − 4γ)/6, firm f licenses its technology to firm h. The royalty rateis rp in (A.4).

20

Licensing always occurs if abatement technology licensing occurs. Substituting (A.4) into(A.2) and (A.3), we have the equilibrium outcome in this case:2(c + 2γ)
3 − 4c(3 − 2c + 4γ)2, xph =, CS p =,3 + 8γ
3 + 8γ2(3 + 8γ)2(3 − 4c)2(3 − 4c)(−3 + 6c + 4γ) + 4(c + 2γ)2
p
=
,
π
,
πfp =
h
(3 + 8γ)2(3 + 8γ)2
27 − 60c + 36c2 + 8(3 − 2c)γ + 16γ 2.
SW p =
2(3 + 8γ)2
xpf =

(A.5)
(A.6)
(A.7)

The welfare level is equivalent to that in the abatement technology licensing case.

2

Tariff

We consider the case in which the government imposes an export tariff on firm f as well as
an environmental tax on firm h. We assume that after the licensing contract is determined,
the government imposes the tariff rate. That is, the government can revise the tariff rate
after the competitive environment has changed.
No licensing First, we consider the case in which firm f does not license its abatement
technology. From (1), the profit functions of the firms (the objectives of the firms) are
πf = (1 − xf − xh − τ )xf , πh = (1 − xf − xh − c − t)xh ,(A.8)

where τ is the tariff rate on firm f . The first-order conditions of the firms lead toxf =1 + c + t − 2τ
1 − 2c − 2t + τ
1+c+t+τ, xh =
, p=
.
3
3
3

(A.9)

From (A.8) and (A.9), the profits of the firms and the consumer surplus areπf =(1 + c + t − 2τ )2(1 − 2c − 2t + τ )2(2 − c − t − τ )2
, πh =, CS =.
9
9
18(A.10)The domestic social surplus (the objective of the government) isSW =(xf + xh )2+ πh + txh + τ xf − γx2h .
2(A.11)

Solving the maximization problem of the government, we have the optimal tax rate tT andthe optimal tariff rate τ T :tT =(2 − 3c)(1 − 2γ)
c + 2γ, τT =.
2(1 + 3γ)
2(1 + 3γ)
21

(A.12)

The superscript “T ” denotes the case in which the government imposes a tariff as well as
an environmental tax. Substituting tT and τ T in (A.12) into (A.9), (A.10), and (A.11), we
have the equilibrium outcome in this case:c + 2γ2 − 3c(1 − c + γ)2, xTh =, CS T =,2(1 + 3γ)
2(1 + 3γ)
2(1 + 3γ)2(2 − 3c)22 − 4c + 3c2 + 2γ
(c + 2γ)2
T
T
,
π
=
,
SW
=
.
πfT =
h
4(1 + 3γ)24(1 + 3γ)24(1 + 3γ)
xTf =Licensing(A.13)(A.14)

Second, we consider the case in which firm f licenses its abatement technology.

From (1), the profit functions of the firms are
πf = (1 − xf − xh − τ )xf + rxh , πh = (1 − xf − xh − c − r)xh ,(A.15)

where τ is the tariff rate. The first-order conditions of the firms lead toxf =1 + c + r − 2τ
1 − 2c − 2r + τ
1+c+t+τ, xh =
, p=
.
3
3
3

(A.16)

From (A.15) and (A.16), the profits of the firms and the consumer surplus areπf =(1 − 2c − 2r + τ )2(2 − c − r − τ )2
(1 + c + r − 2τ )2, πh =, CS =.
9
9
18(A.17)The domestic social surplus (the objective of the government) isSW =(xf + xh )2+ πh + τ xf .
2

(A.18)

Solving the maximization problem of the government, we have the optimal tariff rate τ T l :1τTl = .
3

(A.19)The superscript “T l” denotes the case in which the government imposes a tariff after the
licensing negotiation is achieved. Substituting τ T l in (A.19) into (A.16), (A.17), and (A.18),
we have the outcome given that the licensing term is r:
1 + 3c + 3r
2(2 − 3c − 3r)(5 − 3c − 3r)2
, xh =, CS =,
9981(1 + 3c + 3r)2 2r(2 − 3c − 3r)4(2 − 3c − 3r)2πf =+, πh =,
81
9
81
7 − 12c + 9c2 − 6(2 − 3c)r + 9r2
.
SW =
18
xf =

(A.20)

When firm f licenses the abatement technology, it faces a constraint under which the expost profit of firm h must be greater than or equal to πhT in (A.14). Otherwise, firm h would
22

reject the offer and pay the environmental tax. Firm h accepts the licensing term r if andonly if(2 − 3c)24(2 − 3c − 3r)2≥.
πh in (A.20) ≥ πhT in (A.14) ⇔81
4(1 + 3γ)2
We can rewrite it asr≤(2 − 3c)(12γ − 5).
12(1 + 3γ)

When firm f sets r to maximize πf in (A.20) without considering the constraint, the optimalrate is7 − 6cr=.
15
If this r is smaller than the value on the right-hand side of the inequality, this rate is optimal.
Otherwise, the right-hand side value is the optimal rate. This is summarized in the following
equation:(2 − 3c)(12γ − 5)
if γ ≤ 13/6 or c ≥ 2(6γ − 13)/(3(12γ − 11)),
12(1 + 3γ)
rT l =(A.21)
7−6c

if γ ≥ 13/6 and c ≤ 2(6γ − 13)/(3(12γ − 11)).
15
Substituting it into (A.20), we have the outcome:

1. If γ ≤ 13/6 or c ≥ 2(6γ − 13)/(3(12γ − 11)),xTf l =

2 − 3c(10 − 9c + 12γ)2−2 + 9c + 12γ, xTh l =, CS T l =,12(1 + 3γ)
2(1 + 3γ)
288(1 + 3γ)2

πfT l =

(2 − 3c)2(−2 + 9c + 12γ)2 (2 − 3c)2 (12γ − 5)
Tl
+
,
π
=
,
h
144(1 + 3γ)224(1 + 3γ)24(1 + 3γ)2

SW T l =(A.22)

124 − 324c + 243c2 + 96γ + 144γ 2,
96(1 + 3γ)2

2. If γ ≥ 13/6 and c ≤ 2(6γ − 13)/(3(12γ − 11)),2(1 − 3c)4(1 − 3c)(2 − c)2, xTh l =, CS T l =
,
15
15
50
(4 + 3c)2 2(1 − 3c)(7 − 6c)4(1 − 3c)2
πfT l =+
, πhT l =
,
225
225
225
28 − 18c + 27c2.
SW T l =150
xTf l =

(A.23)

We now check the conditions in which firm f has an incentive to give its advanced production technology to firm h before the licensing contract is achieved. If firm f gives its

23

advanced production technology to firm h, the value of c becomes zero. When c = 0, theprofit of firm f is
−29 + 60γ + 36γ 2If γ ≤ 13/6,
36(1 + 3γ)2
πfT l |c=0 =(A.24)
 2
If γ ≥ 13/6.
15
We now derive the value of c such that the profit of firm f is equal to that when c = 0:3c (24(1 − c) − (12 − 7c)),if γ ≤ 13/6,
16(1 + 3γ)2







676 − 1620c + 945c2 − 24(26 − 135c + 135c2 )γ + 144γ 2>0720(1 + 3γ)2Tl
Tl
πf |c=0 − πf =if γ ≥ 13/6 and c ≥ 2(6γ − 13)/(3(12γ − 11)),






c(2 − 3c)


>0



15

if γ ≥ 13/6 and c ≤ 2(6γ − 13)/(3(12γ − 11)).
From this equation, πfT l |c=0 − πfT l > 0 if and only ifc<

12 (2γ − 1).
24γ − 7

Because πfT l is a convex function with respect to c, we have the following proposition.
Proposition 8. If c < 12(2γ − 1)/(24γ − 7), firm f has an incentive to give its production
technology to firm h. The profit of firm f , πfT l , is given by (A.24).

3

Subsidy

We consider the case in which the government gives a subsidy to firm h and imposes anenvironmental tax on firm h. We assume that after the licensing contract is determined, thegovernment sets the subsidy rate. That is, the government can revise the subsidy rate after
the competitive environment has changed.
No licensing First, we consider the case in which firm f does not license its abatement
technology. From (1), the profit functions of the firms (the objectives of the firms) are
πf = (1 − xf − xh + s − t)xf , πh = (1 − xf − xh − c)xh ,(A.25)

where s is the subsidy rate on firm h. The first-order conditions of the firms lead toxf =1+c+t−s1 − 2c − 2t + 2s
1+c+t−s, xh =
, p=
.
3
3
3
24

(A.26)

From (A.25) and (A.26), the profits of the firms and the consumer surplus areπf =(1 − 2c − 2t + 2s)2(2 − c − t + s)2(1 + c + t − s)2, πh =, CS =.
9
9
18(A.27)The domestic social surplus (the objective of the government) isSW =(xf + xh )2+ πh + txh − sxh − γx2h .
2(A.28)In this case, a negative subsidy and a positive environmental tax have the same effect on thedomestic social surplus. Both equivalently reduce the quantity supplied by firm h. Solving
the maximization problem of the government, we have the optimal tax rate tS and the
optimal subsidy rate sS :tS − sS = −3(1 − c) − 4(1 − 2c)γ.
3 + 8γ(A.29)The superscript “S” denotes the case in which the government imposes a subsidy as well as
an environmental tax. This is equivalent to the tax level in (5). Therefore, the profits of thefirms are those in (6):πfS =Licensing(3 − 4c)24(c + 2γ)2
S
,
π
=
.
h
(3 + 8γ)2(3 + 8γ)2(A.30)

Second, we consider the case in which firm f licenses its abatement technology.

The profit functions of the firms are
πf = (1 − xf − xh )xf + rxh , πh = (1 − xf − xh − c − r + s)xh ,(A.31)

where s is the tariff rate. The first-order conditions of the firms lead toxf =1+c+r−s1 − 2c − 2r + 2s
1+c+t−s, xh =
, p=
.
3
3
3

(A.32)

From (A.31) and (A.32), the profits of the firms and the consumer surplus areπf =(1 + c + r − s)2(1 − 2c − 2r + 2s)2(2 − c − r + s)2, πh =, CS =.
9
9
18(A.33)The domestic social surplus (the objective of the government) isSW =(xf + xh )2+ πh − sxf .
2(A.34)

Solving the maximization problem of the government, we have the optimal subsidy rate τ Sl :sSl = 1 − c − r.
25

(A.35)

The superscript “Sl” denotes the case in which the government imposes a subsidy after the
licensing negotiation is achieved. Substituting sSl in (A.35) into (A.32), (A.33), and (A.34),
we have the outcome given that the licensing term is r:
3 − 4c − 4r
(3 − 2c − 2r)22(c + r), xh =, CS =,3
3
18
4(c + r)2 r(3 − 4c − 4r)(3 − 4c − 4r)2πf =+, πh =
.
9
3
9

xf =

(A.36)

When firm f licenses the abatement technology, it faces a constraint under which the expost profit of firm h must be greater than or equal to πhS in (A.30). Otherwise, firm h would
reject the offer and pay the environmental tax. Firm h accepts the licensing term r if andonly if(3 − 4c)2(3 − 4c − 4r)2≥.
πh in (A.36) ≥ πhS in (A.30) ⇔9(3 + 8γ)2
We can rewrite it as2(3 − 4c)γ.
r≤
3 + 8γWhen firm f sets r to maximize πf in (A.36) without considering the constraint, the optimalrate is9 − 4c.
r=
16
If this r is smaller than the value on the right-hand side of the inequality, this is the optimalrate. Otherwise, the right-hand side value is optimal. This is summarized in the following
equation:
2(3 − 4c)γ

if c ≥ 1/4 or γ ≤ (9 − 4c)/(8(1 − 4c)),
3 + 8γSl(A.37)r = 9 − 4c
if c < 1/4 and γ ≥ (9 − 4c)/(8(1 − 4c)).
16
Substituting it into (A.36), we have the profit of firm f :
2(1 + 8γ)c2 − 16γc + γ(9 + 8γ)
if c ≥ 1/4 or γ ≤ (9 − 4c)/(8(1 − 4c)),(3 + 8γ)2
Sl
πf =
2


 9 − 8c + 16c
if c < 1/4 and γ ≥ (9 − 4c)/(8(1 − 4c)).
32(A.38)
We now check the conditions in which firm f has an incentive to give its advanced production technology to firm h before the licensing contract is achieved. If firm f gives its
advanced production technology to firm h, the value of c becomes zero. When c = 0, theprofit of firm f isγ(9 + 8γ)
if c ≥ 1/4 or γ ≤ (9 − 4c)/(8(1 − 4c)),(3 + 8γ)2(A.39)
πfSl |c=0 =9
if c < 1/4 and γ ≥ (9 − 4c)/(8(1 − 4c)).
32
26

We now derive the value of c such that the profit of firm f is equal to that in which c = 0:2c(8γ − (1 + 8γ)c), if c ≥ 1/4 or γ ≤ (9 − 4c)/(8(1 − 4c)),(3 + 8γ)2SlSl
πf |c=0 − πf =
 8c(1 − 2c) > 0,
if c < 1/4 and γ ≥ (9 − 4c)/(8(1 − 4c)).
32

From this equation, πfSl |c=0 − πfSl > 0 if and only ifc<8γ.
8γ + 1

Because πfSl is a convex function with respect to c, we have the following proposition.
Proposition 9. If c < 8γ/(8γ + 1), firm f has an incentive to give its production technology
to firm h. The profit of firm f , πfSl , is given by (A.39).

4

Global welfare

We can obtain some implications about global welfare using the basic model when an environmental tax is set to maximize the global social surplus. The objective function includes
the profit of firm f as well as the domestic surplus in country h, which is a departure fromthe basic model.
When firm f does not license, the environmental tax is set att=−1 + 5c + 4(1 − 2c)γ.
1 + 8γThe result is
πf =4(c + 2γ)2
(1 − 4c)2
1 − 2c + 4c2 + 6γ
,
π
=
,
GW
=
,
h
(1 + 8γ)2(1 + 8γ)22(1 + 8γ)

1 − 2c − 4c2 + 2(7 − 24c + 16c2 )γ + 16γ 2.
SW =2(1 + 8γ)2

(A.40)The global social surplus increases when the objective of the tax setter changes in the casewhere firm f never licenses its abatement technology.
When firm f does license its abatement technology, the licensing fee is set at the tax levelset when firm f does not license, that is,
r=t=−1 + 5c + 4(1 − 2c)γ.
1 + 8γ27

The result is
πf =4(c + 2γ)2 (−1 + 5c + 4(1 − 2c)γ)(1 − 4c)(1 − 4c)2
+
,
π
=
,
h
(1 + 8γ)2(1 + 8γ)2(1 + 8γ)2GW =(1 − 2c + 4c2 )(1 + 16γ) + 48γ 2,2(1 + 8γ)2SW =3 − 20c + 36c2 + 8(1 − 2c)γ + 16γ 2.
2(1 + 8γ)2

(A.41)

We find the change in the domestic and global surplus following licensing as follows:∆SW =(1 − 4c)2 γ(1 − 4c)(1 − 5c − (3 − 4c)γ), ∆GW =.
2
(1 + 8γ)(1 + 8γ)2Licensing can lower the domestic surplus when the tax setter maximizes the global social
surplus.
Finally, we compare the case where the tax setter maximizes the local surplus to thecase where it maximizes the global surplus. When γ is large, firm f not only licenses its
abatement technology but also gives its production technology to firm h. When it does soin these two cases, the difference between the global surpluses is∆GW =64γ 2 (1 + 4γ)
1 + 16γ + 48γ 2 9 + 48γ + 48γ 2
−
=
> 0.
2
2
2(1 + 8γ)2(3 + 8γ)
(1 + 8γ)2 (3 + 8γ)2That is, the global surplus in which the tax setter maximizes the global surplus issmaller
than that in which it maximizes the local surplus.

5

General demand function

We check how the functional form of the inverse demand affects the main result. We assume
that p(Q) is the inverse demand. As often assumed, p′ < 0 and p′′ ≤ 0.
The profit functions of the firms are given by
πh = (p(Q) − c − t)qh , πf = p(Q)qf .
The first-order conditions of the firms are given by
∂πh
∂qh
∂πf
∂qf
∂πh ∂πf+∂qh∂qf= p′ (Q)qh + p(Q) − c − t = 0,
= p′ (Q)qf + p(Q) = 0,
= p′ (Q)Q + p(Q) − c − t = 0.
28

The total differentials of the first and the third equations are given byp′′ (Q)qh dQ + p′ (Q)dqh + p′ (Q)dQ − dt = 0,(p′′ (Q)Q + 2p′ (Q))dQ − dt = 0.
Arranging the equations, we have
dQ
dqh
dQ
1
+ p′ (Q)
= 1,
= ′′
,
dt
dt
dt
p (Q)Q + 2p′ (Q)p′′ (Q)qf + p′ (Q)
dqh
= ′
.
dt
p (Q)(p′′ (Q)Q + 2p′ (Q))(p′′ (Q)qh + p′ (Q))→

The social surplus in the home country is given by
W =

Z Q∗
0

p(m)dm − p(Q∗ )Q∗ + (p(Q∗ ) − c − t)qh∗ − E(qh∗ ) + tqh∗ ,where E(·) is the economic cost of environmental damages. We assume that E ′ > 0 andE ′′ > 0. The first-order condition with respect to t is given by
∂W
∂t

dq ∗
dQ∗
+ (t − E ′ (qh∗ )) hdtdtp′′ (Q∗ )qf∗ + p′ (Q∗ )
1
′ ∗
+
(t
−
E
(q
))
,
= −p′ (Q∗ )Q∗ × ′′ ∗ ∗hp (Q )Q + 2p′ (Q∗ )p′ (Q∗ )(p′′ (Q∗ )Q∗ + 2p′ (Q∗ ))

1
′
∗ 2 ∗
′ ∗
′′
∗ ∗
′
∗
(p
(Q
))
Q
−
(t
−
E
(q
))(p
(Q
)q
+
p
(Q
))
= 0.
= − ′′ ∗ ∗hfp (Q )Q + 2p′ (Q∗ )= −p′ (Q∗ )Q∗

The equilibrium tax level is determined by the above equation. We define G ≡ (t −E ′ (qh∗ ))(p′′ (Q∗ )qf∗ + p′ (Q∗ )). The following figure captures how the tax level is determined.

G(p′ (Q∗ ))2 Q∗

0E ′ (qh∗ ))tUsing the first-order conditions of the firms, we have the following inequalities: dQ∗ /dc < 0,29dqh∗ /dc < 0, dqf∗ /dc > 0. We now check how ∂W/∂t changes with a decrease in c.
d((p′ )2 Q∗ )
dc

=

dQ∗
p′ (2p′′ Q∗ + p′ )< 0,|{z} |{z} |{z}
dc
(−)

dG
dc

(−)

(−)

dq ∗
= −E ′′ (qh∗ ) (p′′ (Q∗ )qf∗ + p′ (Q∗ )) h
| {z } |dc{z} |{z}
(−)

(−)

(−)





 ′′ ∗ dqf∗
dQ∗ 
′′′
∗ ∗
′′
∗
.
+
(p
(Q
)q
+
p
(Q
))
p
(Q
)
+ (t − E ′ (qh∗ )) f{z
} | {z } |{z}
|
dc
dc 
|
{z
} |{z}
(−)

(−)

(+)

(∗)

(−)

Both increase with a decrease in c when the inverse demand function is linear because thesecond term in dG/dc is zero (p′′ = p′′′ = 0). Under the linear demand assumption, when E ′′is large enough (γ in ED is large enough), the absolute value of dG/dc is larger than that ofd((p′ )2 Q∗ )/dc. That is, a decrease in c enhances the equilibrium tax level, t. Even though
the inverse demand is not linear, if the absolute value in the large parentheses is small, theabsolute value of dG/dc is more likely larger than that of d((p′ )2 Q∗ )/dc.

30