This version: July 24, 2011

Better technology may be sold for a lower fee:
The ad valorem tariﬀ and licensing contract
Tomomichi Mizuno†
Department of Economics, University of Nagasaki

Kazuhiro Takauchi‡
Department of Economics, Management and Information Science,
Onomichi University

Takeshi Iida
Graduate School of Economics, Kobe University

Abstract
The main purpose of this study is to investigate how a relationship arises between an advalorem tariﬀ and licensed technology in a licensing contract. To this end, we study a
two-country, two-ﬁrm duopolistic trade model. We consider a product market in whicha high-tech foreign ﬁrm can license its production technology to an importing country.
The government of the importing country chooses an ad valorem tariﬀ rate but has nocommitment power. In our model, the home government raises the tariﬀ rate as the licensed
technology improves. Our two main results in the case that a highly productive technology
is licensed are paradoxical: First, better technology is sold for a lower fee in a licensing
contract. Second, the proﬁts of both the licenser and licensee decrease as the licensed
technology improves. In other words, cost reduction reduces the proﬁts of both the licenser
and licensee. These ﬁndings indicate that because of the role played by the ad valorem tariﬀ,
technology licensing does not always beneﬁt both the licensee and the licenser.
JEL codes: D43; F13; L13
Key words: Licensing contract; Ad valorem tariﬀ; Fixed fee†

Tel.: +81-956-47-2191; fax: +81-956-47-6941.

E-mail : rinri@sun.ac.jp (T. Mizuno), takauch@onomichi-u.ac.jp (K. Takauchi).
‡Corresponding author: Tel.: +81-078-7247; fax: +81-078-803-6877.

1

Introduction

Is better technology sold for higher fee? If so, this is an everyday occurrence. However, if better
technology is sold for a lower fee in a licensing contract, this appears slightly paradoxical. In
this paper, we present results to this eﬀect in the case that a highly productive technology islicensed: First, better technology is sold for lower fee. Second, similar to the ﬁrst result, boththe licenser’s and the licensee’s proﬁts decrease as the licensed technology improves. In otherwords, cost reduction reduces the proﬁt of both ﬁrms.
Recently, some theoretical studies (e.g., Kabiraj and Marjit 2003; Mukherjee 2010; Mukherjee and Pennings 2006) have focused on international technology licensing, and this ﬁeld isgradually growing. With regard to technology licensing, our study is closely related to themodel of Mukherjee and Pennings (2006) and Mukherjee (2010).1 The former focus on thewelfare eﬀects of licensing and consider the situation that licensing is done by a foreign monopolistic exporter and that a duopoly arises as an outcome of technology licensing. They show thatthe home country gains more surpluses from technology licensing (i.e., increased competition).
However, they assume that the government of the home country imposes a speciﬁc tariﬀ. Since
they do not consider the ad valorem tariﬀ, further examination of the form of tariﬀs and technology licensing is needed. Mukherjee (2010) considers the case of technology licensing from a
low-cost ﬁrm to a high-cost one and compares Cournot with Bertrand competition in a productmarket. His main ﬁnding is that social welfare may be higher under Cournot competition thanunder Bertrand competition. However, his analysis is limited to domestic competition; he does
not consider the relationship between tariﬀ policy and technology licensing.
The present paper is also related to a few works on speciﬁc and ad valorem instruments.
Although relatively few existing works on trade policies focus on the role of ad valorem tariﬀs,
some studies focus on the eﬀects of this tariﬀ, albeit in a diﬀerent model.2 For instance, Shea
1
In the context of international trade and technology transfer, a few studies focus on technology licensing, forexample, Kabiraj and Marjit (2003) and Horiuchi and Ishikawa (2009). The former show that in an international
duopoly that comprises home and foreign ﬁrms, the tariﬀ policy is more desirable than the free trade policy is,from the viewpoint of the home consumers when the foreign ﬁrm is allowed to license its technology. Horiuchi
and Ishikawa (2009) examine a North-South technology transfer through intermediate products. They show thatin a three-ﬁrm oligopolistic setting, a decrease in the tariﬀ on the ﬁnal good may induce technology transfer andthat tariﬀ reduction may enhance home welfare.
2
Several studies examine ad valorem instruments in the context of taxation. After Bishop (1968) comparedad valorem and speciﬁc taxes, a series of studies have arisen on tax forms and their welfare implications. For
instance, Delipalla and Keen (1992) compare ad valorem and speciﬁc taxes in a Cournot oligopoly with andwithout free entry. Myles (1996) discusses an optimal combination of ad valorem and speciﬁc taxation in animperfect competitive market. Moreover, Ushio (2000) examines whether a shift from a speciﬁc to an ad valorem
tax would enhance welfare.

1and Shea (2006) use the conjectural variation approach and examine the relationship between advalorem and speciﬁc tariﬀs under international duopoly. Collie (2006) considers the eﬃciencyof ad valorem and speciﬁc trade policies (tariﬀs and subsidies) under asymmetric oligopoly.
Additionally, Miyagiwa (2009) investigates the eﬀects of a speciﬁc tariﬀ, an ad valorem tariﬀ,
and an import quota on the ﬁrm and consumers’ behavior when the production technologyof the ﬁrm is unobservable. Although the above studies examine the eﬀects of ad valorem
tariﬀ in various situations, they do not consider technology licensing. Thus, we believe that
our investigation of the relationship between the ad valorem tariﬀ and licensed technology in alicensing contract is a unique contribution to the existing literature.
Our main purpose is to investigate how a relationship arises between the ad valorem tariﬀ
and licensed technology in a licensing contract. We focus on the ad valorem tariﬀ because thistariﬀ is important in view of the following two points: First, in real international trade, an
ad valorem tariﬀ is more frequently observed than a speciﬁc tariﬀ.3 Second, in an imperfectcompetitive market, the ad valorem tariﬀ directly alters the product price; thus, this tariﬀ has
a stronger eﬀect on imports than a speciﬁc tariﬀ does.
In order to demonstrate the above ﬁndings, we study an international Cournot duopoly inwhich a high-tech foreign ﬁrm (hereafter, the foreign ﬁrm) can license its production technology.
This ﬁrm owns the production technology and exports the product to an importing country’s
market, where an ad valorem tariﬀ is imposed on the product. Once the foreign ﬁrm licenses
its technology to the importing country, a ﬁrm that has the same marginal production cost as
the foreign ﬁrm has (hereafter, the home ﬁrm) comes into existence in the importing country;
the foreign ﬁrm takes a ﬁxed licensing fee from the home ﬁrm, which competes with the foreign
ﬁrm in the home market. We commence our analysis from the situation that the production
technology has been licensed by foreign ﬁrm; hence, the home ﬁrm has already come into
existence.
Thus, our model is a two-country (home (importing) and foreign (exporting)), two-ﬁrm(home and foreign) duopolistic trade model with a licensing contract. We examine the following
three-stage game: In the ﬁrst stage, the level of the ﬁxed licensing fee is decided through Nashbargaining between the home and foreign ﬁrms. Second, the government of the home country3

See the website of Japan Customs (URL: http://www.customs.go.jp/toukei/index.htm). In particular,
see item 3: the mechanism of tariﬀs (in Japanese). Further, data from JETRO (Japan External Trade Organization) show that a similar situation exists in many countries. See the home page of JETRO (URL:
http://www.jetro.go.jp/indexj.html).

2

chooses the ad valorem tariﬀ rate. Third, the home and foreign ﬁrms compete à la Cournot in
the home market.
The logic behind our results is as follows: When a highly productive technology is licensed,
the output of the home ﬁrm decreases as the licensed technology improves. In our model, thehome government raises the tariﬀ rate as the licensed technology improves. However, if a highly
productive technology is licensed, the eﬀect of an increase in the tariﬀ rate weakens because
this rate is now suﬃciently high. Since the eﬀects of technology improvement dominate theeﬀect of the tariﬀ increase, the exports of the foreign ﬁrm increase and the output of the homeﬁrm decreases as the licensed technology improves. The output of the home ﬁrm is inverted Ushaped for the licensed technology, and this shape is a key factor behind our results. If a highly
productive technology is licensed, the foreign ﬁrm attempts to lower the license fee because an
improvement in the technology reduces both the output of the home ﬁrm and revenues from thelicense fee. Similar to the output of the home ﬁrm, the licensing fee is inverted U-shaped forthe licensed technology. Since the proﬁt of the home and foreign ﬁrms is decided by bargaining
and depends on the ﬁxed fee, each ﬁrm’s share is the same as its own bargaining power. The
proﬁt of the two ﬁrms is basically the same except for bargaining power. Hence, both ﬁrms’
proﬁts are inverted U-shaped for the licensed technology.
The remainder of this paper is organized as follows: Section 2 presents the model. Section
3 discusses the analysis of our model, and Section 4 concludes.

2

The Model

We consider a partial equilibrium trade model with a homogeneous product. A high-tech foreign
ﬁrm produces this product at a marginal cost c (0 < c ≤ 1) and exports this product to a market
in the home country. We call the foreign ﬁrm’s marginal production cost c licensed technology.
The inverse demand function in the home market is p = 1 − X, where p is the price and X isthe aggregate amount of products. In the home country, there exists a home ﬁrm that does nothave the technology to produce the product. Hence, this ﬁrm must be licensed by the foreign
ﬁrm if the former produces the product. We denote the exports of the foreign ﬁrm as xF andthe output of the home ﬁrm as xH . Then, X = xF + xH .
We assume that when the foreign ﬁrm licenses the technology, it uses a ﬁxed-fee contract
and the ﬁxed fee, f , is determined through Nash bargaining. Further, we suppose that if the3

negotiation breaks down, both ﬁrms’ proﬁts are equal to zero. We denote the proﬁts of theforeign and home ﬁrms as πF and πH respectively. Hence, the Nash bargaining solution is givenbyf = argmax α log[πF ] + (1 − α) log[πH ],f(1)

where α (0 ≤ α ≤ 1) measures the bargaining power of ﬁrm F relative to that of ﬁrm H.
Given the level of the ﬁxed fee, the government of the home country chooses the level of thead valorem tariﬀ τ so as to maximize social welfare. Social welfare is equal to the summation of
consumer surplus, the home ﬁrm’s proﬁt, and tariﬀ revenue. Consumer surplus is (1/2)X 2 , andtariﬀ revenue is τ pxF . After the government’s decision, the foreign and home ﬁrms compete inquantity.
In this model, the government cannot commit its policy. This assumption is motivated by
the time-inconsistent nature of trade policy (see Mukherjee and Pennings 2006; Staiger andTabellini 1987).4 To summarize, we consider the following model.
Stage 1: The foreign ﬁrm decides the level of the ﬁxed fee through Nash bargaining.
Stage 2: The home government chooses an ad valorem tariﬀ rate τ .
Stage 3: The foreign and home ﬁrms choose their outputs xF and xH respectively.
The proﬁt of the foreign ﬁrm is
πF = ((1 − τ )p − c) xF + f.

(2)

πH = (p − c) xH − f.

(3)

The proﬁt of the home ﬁrm is

The social welfare of the home country, SW , is1
SW = (xH + xF )2 + πH + τ pxF .
2(4)

We assume complete information. The model is solved by backward induction and only
pure strategies are considered. For simplicity, this paper does not discuss incentives to license.
4

Other studies focussing on the time-inconsistent trade policy include Ishizawa (1995), who considers thecase wherein the government is not committed to a tariﬀ policy. In his model, the government may revise thetariﬀ after the production stage. Additionally, Neary and Leahy (2000) further investigate the time-inconsistentproblem of trade policies.

4However, even if we consider these incentives, our results hold under some conditions. In otherwords, the foreign ﬁrm licenses technology in the equilibrium if this ﬁrm’s bargaining power isgreater than that of the home ﬁrm. Since the foreign ﬁrm has the technology and the homeﬁrm does not, the assumption of bargaining power is natural.

3

Analysis

This section examines the eﬀects of an improvement (or a deterioration) in the licensed technology, c, on the ﬁrms’ output and proﬁt and on the ﬁxed fee.
From (2) and (3), the ﬁrst-order conditions yield the optimal outputs in stage three.

xF =1 − τ − c(1 + τ ),3(1 − τ )xH =1 − τ − c(1 − 2τ ).
3(1 − τ )(5)

In the ﬁnal stage of the game, (∂xH /∂c) < 0 if τ < 1/2, but (∂xH /∂c) ≥ 0 if τ ≥ 1/2.
Putting (5) into (4) and diﬀerentiating it with respect to τ , we obtain the ﬁrst-order condition
leading to the optimal ad valorem tariﬀ rate:√
2 + c − c(4 + 5c).
τ (c) =
2(1 + c)(6)

Diﬀerentiating (6) with respect to c, we obtain√√(2 + 3c) + c(4 + 5c)
2 + 12c + 24c2 + 15c3 + c(4 + 5c) c(4 + 5c)
dτ
d2 τ
√
=−
< 0,
=
> 0.
[
]3/2
dc
dc2
2(1 + c)2 c(4 + 5c)(1 + c)3 c(4 + 5c)
The optimal ad valorem tariﬀ (6) is decreasing and convex with respect to the licensed
technology c. Note that the convexity is in sharp contrast with the speciﬁc tariﬀ.5
First, let us verify the property of the output or export of both ﬁrms.
Proposition 1. Suppose that a highly productive technology is licensed (i.e., c ≤ c1 ≃ 0.0472136).
Then, a decrease in c reduces the output of the home firm but increases the export of the foreign
firm.

Proof. Substituting (6) into (5), we obtain the following equilibrium output of the home ﬁrm:
5

If the imposed tariﬀ is speciﬁc, then the optimal tariﬀ is linear and decreasing with respect to the marginalcost. Thus, the equilibrium outputs of the ﬁrms are also linear and decreasing with respect to the marginal cost.
See Appendix.

5

√
[
]
xH = (1/6) 2 − 5c + c(4 + 5c) . Diﬀerentiating this equation with respect to c yields√
2 + 5c − 5 c(4 + 5c)
dxH
√
=
.
dc
6 c(4 + 5c)
Solving dxH /dc ≥ 0 for c, we obtain c ≤ c1 ≃ 0.0472136.
Similarly, substituting (6) into (5), we obtain the following equilibrium export of the foreign√[]ﬁrm: xF = (1/3) 1 + 2c − c(4 + 5c) . Diﬀerentiating this equation with respect to c yields√−2 − 5c + 2 c(4 + 5c)
dxF
√
.
=
dc
3 c(4 + 5c)
From a numerical calculation, dxF /dc < 0 for all c in [0, 1]. Q.E.D.

Proposition 1 states that the output of the home ﬁrm is inverted U-shaped with respect to c.
Under the optimal ad valorem tariﬀ (6), the output of the home ﬁrm is written as xH (τ (c), c). To
observe the direct and indirect eﬀects of a change in c, we focus on xH (τ (c), c). Diﬀerentiating
xH (τ (c), c) with respect to c, we obtain (dxH /dc) = (∂xH /∂τ )(dτ /dc) + (∂xH /∂c). This yields
3(1 − τ (c))2 ·

dxH
dτ
= c·
dc
| {zdc}+indirect eﬀect[]− 3(1 − τ (c))(1 − 2τ (c)) .
|{z}
direct eﬀect

The indirect eﬀect (ﬁrst term on the right-hand side) is always negative, but the direct eﬀect(second term on the right-hand side) is eventually negative. If a highly productive technology
is licensed (i.e., c ≤ c1 ≃ 0.0472136), the direct eﬀect is negative and the indirect eﬀect weakens
because the tariﬀ rate is now suﬃciently high. Therefore, in that case, the output of the homeﬁrm increases as c increases.
Intuitively, we can consider the following logic: Suppose that c ≤ c1 . When c increases,from dτ /dc < 0, the optimal tariﬀ rate decreases. Since the eﬃciency of production in the homeﬁrm decreases, the incentive of the home government to protect this ﬁrm weakens. However,
the eﬀects of the deteriorating eﬃciency of production dominate the rent-shifting eﬀect fromthe home to the foreign ﬁrm that is caused by a tariﬀ reduction; the exports of the foreign ﬁrm
decrease. Then, strategic substitution in the product market works; the output of the homeﬁrm increases.
Next, we turn to the game of the ﬁrst stage. Since the ﬁxed fee is determined through Nash

6bargaining between the home and foreign ﬁrms, the ﬁrst-order condition leads to
f∗ =

]
√
√
1 [
−5c3/2 4 + 5c + c2 (11 + 4α) + c(7 − 15α) + c(4 + 5c)(3α − 1) + 2α .
18(7)Then, we obtain the following.
Proposition 2. Suppose that c < 0.0503762 and α > ᾱ(c) or that c > 0.0503762 and α < ᾱ(c).
Then, an increase in c increases the equilibrium fixed fee f ∗ , where√
2 + 5c(7 + 10c) − (7 + 22c) c(4 + 5c)√
ᾱ(c) =.
6 + 15c + (8c − 15) c(4 + 5c)

Proof. Diﬀerentiating (7) with respect to c yields[6 + 15c +
∂f ∗
=
∂c

√

c(4 + 5c)(8c − 15)]α − 2 − 5c(7 + 10c) +√18 c(4 + 5c)

For the coeﬃcient of α in the numerator, 6+15c+√√c(4 + 5c)(7 + 22c).

c(4 + 5c)(8c−15) > 0 leads to c < 0.0503762.

Hence, when c is small (c < 0.0503762), a large α makes ∂f ∗ /∂c positive. On the other hand,when c is large (c > 0.0503762), a large α makes ∂f ∗ /∂c negative. Solving (∂f ∗ /∂c) = 0 for α
leads to√2 + 5c(7 + 10c) − (7 + 22c) c(4 + 5c)√≡ ᾱ(c).
α=
6 + 15c + (8c − 15) c(4 + 5c)

Therefore, we obtain Proposition 2. Q.E.D.

Figure 1 shows the result of Proposition 2.
[Figure 1 here.]In this result, three diﬀerent types of the ﬁxed fee curve can be observed. These types arise
depending on the bargaining power of the foreign ﬁrm α. The ﬁrst type is an inverted-U curvewith respect to the licensed technology c, the second is monotonically decreasing for c, and thethird has a bottom and peak for c. When the bargaining power of the foreign ﬁrm is strong (αis suﬃciently close to 1), this ﬁrm’s proﬁt is largely accounted in the optimal ﬁxed fee. If thehome ﬁrm’s output increases because of an increase in c, the foreign ﬁrm tries to compensate
for a loss in its own proﬁt in order to set a higher fee. When the bargaining power of the foreign7

ﬁrm is strong, the optimal ﬁxed fee is single peaked with respect to c.
When the foreign ﬁrm’s bargaining power is intermediate, the inverted-U property of theoutput of the home ﬁrm weakens. This is because the proﬁts of both the home and foreignﬁrms are equally accounted in the licensing fee decision. Thus, the optimal fee monotonicallydecreases as c increases.
If the foreign ﬁrm’s bargaining power is weak, the optimal licensing fee has a bottom andpeak with respect to c.6 In this case, the home ﬁrm has almost all decisiveness on the decisionof the license fee. This case is depicted in Figure 2.
[Figure 2 here.]
Let us explain this case according to three segmented intervals in the ﬁxed fee curve.
(i) From zero to the bottom: When a highly productive technology is licensed (c is suﬃciently
small), an increase in c increases the output of the home ﬁrm. In the license fee decision, thehome ﬁrm tries to considerably decrease the optimal ﬁxed fee in order to increase its own proﬁt.
(ii) From the bottom to the peak: The market share obtained by the foreign ﬁrm relatively
recovers because the optimal ad valorem tariﬀ decreases owing to an increase in c. Thus, theforeign ﬁrm gains a larger proﬁt compared to the case of a smaller c. In the bargaining process,the foreign ﬁrm’s wish is slightly accounted in the license fee decision. Thus, the ﬁxed fee curve
gradually increases as c increases.
(iii) Over the peak: In this interval, both ﬁrms’ productivities are suﬃciently low because cis suﬃciently large. Then, the decrease in the optimal ad valorem tariﬀ caused by an increase in
c is not large and the volume of exports of the foreign ﬁrm is suﬃciently small. Thus, the market
share obtained by the home ﬁrm is large and the home ﬁrm’s wish is strongly accounted in thedecision of optimal license fee; hence, the ﬁxed fee curve gradually decreases as c increases.
Finally, we consider the proﬁts of both ﬁrms. Putting (5), (6), and (7) into (2) and (3)yields the proﬁts of the home and foreign ﬁrms.
]√
1 [2 + c(−15 + 4c) + 3 c(4 + 5c) α,
18
]
√
1 [
∗
πH
=
2 + c(−15 + 4c) + 3 c(4 + 5c) (1 − α).
18
πF∗ =

(8)
(9)

For example, when α = 0.08, the bottom of the licensing fee curve f ∗ is at c ≃ 0.0939195 and the peak is atc ≃ 0.335814.
6

8

The equations (8) and (9) yield the following result.
Proposition 3. Suppose that a highly productive technology is licensed (i.e., c ≤ c2 ≃ 0.0504).
Then, a decrease in c reduces the profit of the home and foreign firms.

∗ with respect to c, we obtain
Proof. Diﬀerentiating (1/α) πF∗ and [1/(1 − α)] πH√∗ /(1 − α)3(2 + 5c) − (15 − 8c) c(4 + 5c)∂πF∗ /α∂πH√==≤ 0 ⇔ c ≤ c2 ≃ 0.0504.
∂c∂c
18 c(4 + 5c)
Thus, Proposition 2 holds. Q.E.D.

Figure 3 shows the result of Proposition 3.
[Figure 3 here.]

Surprisingly, Proposition 3 states that a cost reduction reduces the proﬁts of all ﬁrms if ahighly productive technology is licensed. In other words, the home and foreign ﬁrms’ proﬁts areinverted U-shaped with respect to c. The inverted-U property does not depend on the bargaining
power of each ﬁrm. In the Nash bargaining process, an optimal ﬁxed fee is decided in order tomaximize the aggregate proﬁt of the home and foreign ﬁrms. The maximized aggregate proﬁt
is shared between the home and foreign ﬁrms according to each ﬁrm’s bargaining power; thus,
the shape of the equilibrium proﬁt is similar to that of the optimal ﬁxed fee curve.
Since an increase in c raises the proﬁt of the home ﬁrm for the range of 0 < c ≤ c2 (c2 ≃0.0504), one may think that social welfare in the home country also increases with c. However,
we cannot obtain this result because the negative eﬀect of production ineﬃciency dominates
the positive eﬀect of an increase in the proﬁt of the home ﬁrm. This result (∂SW/∂c < 0) canbe shown by a numerical calculation.

4

Conclusion

In this paper, we consider the relationship between an ad valorem tariﬀ and ﬁxed fee in aninternational licensing contract. A simple duopoly model with a ﬁxed-fee licensing contract
yields two interesting results in the case that a highly productive technology is licensed: First,

9better technology is sold for a lower fee. Second, similar to the ﬁrst result, the proﬁts of thehome and foreign ﬁrms decrease as the licensed technology improves.
One may think that technology licensing creates a new ﬁrm (licensee) and gives the licenser
revenues from the license fee, and hence, that technology licensing beneﬁts both the licensee
and licenser. However, our ﬁndings indicate that caution must be exercised in this regard. If
the ad valorem tariﬀ that is optimally chosen by an importing country and licenser (i.e., theforeign ﬁrm) is too eﬃcient, the ﬁxed-fee licensing contract induces a lower proﬁt rather thanthat of a lower licensed technology.

Appendix
Speciﬁc tariﬀ:

If the imposed tariﬀ is a speciﬁc one (labeled τ S ), the outputs of both ﬁrms

in the ﬁnal stage are given by xF = (1/3)(1 − 2τ S − c) and xH = (1/3)(1 + τ S − c). The social
welfare of the home country is
1
SW = (xH + xF )2 + [1 − (xH + xF ) − c] xH − f + τ S xF .
2
Solving the ﬁrst-order condition for the welfare maximization with respect to τ S , we obtain thefollowing optimal speciﬁc tariﬀ: τ S = (1/3)(1−c). The equilibrium outputs are xF = (1/9)(1−c)
and xH = (4/9)(1 − c). Thus, if the speciﬁc tariﬀ is imposed, an improvement in the licensed
technology always increases the outputs of the two ﬁrms.

Acknowledgments
We are grateful to Takashi Kamihigashi and Eiichi Miyagawa for their helpful comments. Needless to say, all remaining errors are ours.

References[1] Bishop RL (1968) The eﬀects of speciﬁc and ad valorem taxes. Q J Econ 82:198-218[2] Collie DR (2006) Tariﬀs and subsidies under asymmetric oligopoly: Ad valorem versus
speciﬁc instruments. Manch Sch 74:314-333

10

[3] Delipalla S, Keen M (1992) The comparison between ad valorem and speciﬁc taxation underimperfect competition. J Public Econ 49:351-367[4] Horiuchi E, Ishikawa J (2009) Tariﬀs and technology transfer through an intermediate product. Rev Int Econ 17:310-326[5] Ishizawa S (1995) Tariﬀ protection, imperfect competition, and time consistency. In: Chang
WW and Katayama S (eds) Imperfect competition in international trade, Kluwer Academic
Publishers, Boston, pp 143-158[6] Kabiraj T, Marjit S (2003) Protecting consumers through protection: The role of tariﬀinduced technology transfer. Eur Econ Rev 47:113-124[7] Miyagiwa K (2009) Saving dolphins: Boycotts, trade sanctions, and unobservable technology.
Int Econ Rev 51:883-902[8] Mukherjee A (2010) Competition and welfare: The implications of licensing. Manch Sch
78:20-40[9] Mukherjee A, Pennings E (2006) Tariﬀs, licensing and market structure. Eur Econ Rev
50:1699-1707[10] Myles GD (1996) Imperfect competition and the optimal combination of ad valorem andspeciﬁc taxation. Int Tax Public Finance 3:29-44[11] Neary JP, Leahy D (2000) Strategic trade and industrial policy towards dynamic oligopolies.
Econ J 110:484-508[12] Shea KL, Shea EYP (2006) On the equivalence of ad valorem tariﬀs and speciﬁc tariﬀs
under duopoly. Rev Int Econ 14:445-451[13] Staiger R, Tabellini G (1987) Discretionary trade policy and excessive protection. Amer
Econ Rev 77:823-837[14] Ushio Y (2000) Welfare eﬀects of commodity taxation in Cournot oligopoly. Jpn Econ Rev
51:268-273

11Figure 1: Increasing the ﬁxed fee with less eﬃcient technology.

α
1
0.8
∂f ∗
<0
∂c

0.6
∂f ∗
>0
∂c

0.4
0.2

ᾱ(c)

0

0.2

0.4

0.6

0.0504

12

0.8

1

c

Figure 2: The equilibrium ﬁxed fee with a bottom: α = 0.08

f∗
0.002
0.005
0.001
0.0005

0

0.2

0.4

13

0.6

0.8

1

c

Figure 3: Increasing the proﬁts with less eﬃcient technology.

πF∗
α

π∗

H
and 1‑α

0.14
0.12
0.1
0.08
0.06
0.04
0.02
0.2

0.4

0.6

0.0504140.8

1c