This study incorporates transport price and endogenous product differentiation in an international oligopoly. Assuming endogenous determination of transport price based on the profit maximization of the transporter and using a three-stage game, we analyze the effect of the

degree and difficulty of product differentiation on transport price. We show that both negatively affect the endogenous transport price. The intuition of this result comes from that the positive effect of a decrease in endogenous transport price on the demand for the differentiated products is greater than the negative effect on the price

Kamei, Keita

Kanehara, Daishoku

Munich Personal RePEc Archive

MPRA
Munich Personal RePEc Archive
Transport Price, Product Differentiation
and R&D in an Oligopoly
Daishoku Kanehara and Keita Kamei
7 April 2019
Online at https://mpra.ub.uni-muenchen.de/93148/
MPRA Paper No. 93148, posted 8 April 2019 03:55 UTC
Transport Price, Product Differentiation and
R&D in an Oligopoly∗
Keita Kamei† Daishoku Kanehara‡
Abstract
This study incorporates transport price and endogenous product dif-
ferentiation in an international oligopoly. Assuming endogenous determi-
nation of transport price based on the profit maximization of the trans-
porter and using a three-stage game, we analyze the effect of the degree
and difficulty of product differentiation on transport price. We show that
both negatively affect the endogenous transport price. The intuition of
this result comes from that the positive effect of a decrease in endogenous
transport price on the demand for the differentiated products is greater
than the negative effect on the price.
JEL classification: L13, L16, F12, F16, O30
Keywords: Endogenous Product Differentiation; International Trade;
Oligopoly; Product R&D; Transport Price.
1 Introduction
Transport price is generally treated as a key factor in international trade. In a
series of new trade theory, Krugman (1980) revealed that a reduction in trade
cost (including transport price) increased the volume of international trade of
differentiated goods. In fact, as Hummels (2007) mentioned, with the expansion
of world trade, time series have shown a gradual decline in the air transport price
index. Many studies on new trade theory assume trade cost as an exogenous
variable, so they do not investigate how product differentiation affects trade cost
(ef. transport price). An example of this can be seen in the fact that Maserati,
known as one of the luxury car brands, transports its latest models by air rather
than by sea1. In addition to this, Hummels, Lugovskyy, and Skiba (2009) have
∗This work has been supported by JSPS KAKENHI Grant Number 18K12761, JSPS KAK-
ENHI Grant Number 18J0063, JSPS KAKENHI Grant Number 16K21110, and the Joint
Research Program of KIER.
†Department of Economics, Seinan Gakuin University. 6-2-92, Nishijin, Sawara-ku,
Fukuoka-shi, Fukuoka 814-8511, JAPAN. E-mail: k-kamei@seinan-gu.ac.jp
‡Graduate School of Economics, Kobe University, 2-1 Rokkodai, Nada, Kobe, Japan. Re-
search Fellow of Japan Society for the Promotion of Science. E-mail: kanehara@people.kobe-
u.ac.jp
1See the following website: https://www.airbridgecargo.com/en/news/228/airbridgecargo-
provided-dedicated-lift-for-28-maserati-granturismo-cars
1
shown that transport prices are endogenously determined by transportation
firms. They reveal that the larger the degree of product differentiation, that
is, the smaller the price elasticity of (import) demand, the higher the prices
imposed by transporters.
In this article, we construct an international oligopoly model with endoge-
nous product differentiation and endogenous transport price. Our main conclu-
sion is that when product differentiation is more difficult, transportation prices
will become lower.
In recent years, there have been many studies on endogenous transport price.
Notable examples are: Francois and Wooton (2001); Andriamananjara (2004);
Behrens and Picard (2011); Takahashi (2011); Abe et. al. (2014); Forslid
and Okubo (2015); Ishikawa and Tarui (2018). In addition to this, Takauchi
(2015) incorporated cost-reducing R&D into an international oligopoly with
endogenous transport prices. Conversely, our model focuses on the product
R&D in an international oligopoly with endogenous transport prices.
This article also relates to the context of oligopolistic competition and prod-
uct R&D. Lin and Saggi (2002) constructed an oligopolistic competition model
with both product and process R&D. They employed the utility function of Sing
and Vives (1984) and derived the equilibrium not only under the Bertrand com-
petition, but also under the Cournot competition. Bastos and Straume (2012)
evolved Lin and Saggi (2002) into an oligopolistic general equilibrium and inves-
tigated how trade liberalization has affected product R&D. They revealed that
the protection from international trade (an increase in the number of shielded
sectors) has ambiguous effects on welfare. In addition to this, Brander and
Spencer (2015) showed that additional product differentiation increases trade
benefits.
To our knowledge, there are few studies on the relationship between the
degree of product differentiation and transport price. This implies that we
do not know the mechanism how the degree of differentiation (or quality of
products) affects transport price through strategic interaction. Therefore, we
have constructed a basic framework that incorporates both product R&D and
endogenous transport price and reveals the relationship between the degree of
differentiation and transportation price.
This paper is composed of the following sections: Section 2 constructs the
basic model; Section 3 provides the main results; and Section 4 concludes.
2 The Model
We assume perfectly symmetric2 two countries (country one and country two)
in an open economy. In this economy, there are two sectors: a differentiated
product sector and a homogenous product sector. Homogenous products are
non-tradable and producers in this sector are faced with perfect competition.
In contrast, differentiated products are tradable and each country has one iden-
tical firm that produces its own variety. For simplicity, the marginal cost of
2This implies that the analysis of one country can be applied to another.
2
differentiated products is assumed to be zero. We denote the quantity of the
differentiated goods produced in country i and supplied to country j by qij .
To transport one unit of product, the exporter is required to pay a transport
price f3. To reduce competition, firms can choose varieties through their prod-
uct R&D investment di. As discussed above, the profit of a firm in country i
becomes
pii = piiqii + pijqij − fqij − c (di) , (1)
where pij is the price of firm i’s product in country j and c (di) is the cost of
R&D when investment level is di.
We also assume that consumers are perfectly symmetric. The utility function
of consumers in country i is defined by
ui = α (qii + qji)− 1
2
[
q2ii + q
2
ji
]− sqiiqji +mi, (2)
where α (> 0) is a parameter, mi is the quantity of the homogenous goods, and s
is the inverse of the degree of differentiation between two products. The budget
constraint of consumers in country i becomes
piiqii + pjiqji +mi = Ii. (3)
The utility maximization of both countries implies the following inverse demands
pii = α− qii − sqji, (4)
pij = α− qij − sqjj . (5)
These indicate that higher differentiation (i.e. s is small) implies higher prices
pii, pij .
We assume that the degree of differentiation is determined by the R&D
investment of both firms:
s := S − (d1 + d2) , (6)
where S is a measure of difficulty in differentiation4. R&D cost function c (di)
has the following characteristics5: c′ (di) > 0, c′′ (di) < 0.
Finally, we assume that the transportation cost is zero and the transporter
chooses the transport price f to maximize its profit.
2.1 Analysis
We assume that the procedure of decision-making between the transporter and
the differentiated firms is the following three-stage game: In step 1, firms decide
their R&D investment level di to maximize their profits. In step 2 the trans-
porter chooses the transport price f to maximize its profit. In step 3, based on
the above results, firms produce their differentiated products under the Cournot
competition.
3We will discuss the determination of f later in this section.
4In this article, we assume that each industry has identical difficulties in differentiation.
For example, S in the luxury car industry would be smaller than S in the Vitamin C industry.
5We will specify c (di) in Section 2.4.
3
2.2 Step 3
Based on the degree of differentiation s and the transport price f , firm i chooses
the quantities to be supplied to home qii and foreign qij in order to maximize
its profit:
pii = piiqii + pijqij − fqij − c (di) .
By the first order conditions and inverse demand functions (4)(5), the optimal
quantities become
qii =
(2− s) a+ sf
4− s2 , qij =
(2− s) a− 2f
4− s2 . (7)
It is evident that a higher transport price f has a positive effect on domestic
supply qii and a negative effect on export qij . This is because if the transport
price f is high, it impedes export and mitigates competition between home and
foreign firms.
By (8) the effect of the degree of differentiation s to quantities is
∂qii
∂s
= −a(−2 + s)
2 + f(4 + s2)
(−4 + s2)2 < 0,
∂qij
∂s
= −a(s− 2)
2 + 4fs
(s2 − 4)2 < 0.
The higher level of differentiation (i.e. small s) makes qii and qij increase simul-
taneously through the product differentiation. Using inverse demand functions
(4) and (5), we can derive that the higher level of differentiation decreases pii
and pij .
2.3 Step 2
We assume that to export differentiated products, firms are required to pay the
unit transport price f6 to the transporter. The transporter chooses the trans-
port price f to maximize its profit. Since the marginal cost of transportation is
assumed to be zero, the profit of the transporter is
pif = f (q12 + q21) = 2f
(
(2− s) a− 2f
4− s2
)
. (8)
By the first order condition of the profit maximization, the optimal transport
price f becomes
f =
(2− s) a
4
. (9)
Thus, a higher level of differentiation implies the higher optimal transport price
through the reduction of competition.
To summarize (7) and (9), qii and qij becomes
qii =
(4 + s) (2− s) a
4 (4− s2) , qij =
(2− s) a
2 (4− s2) . (10)
6Being symmetric, the transporter will exhibit the same transport price f .
4
2.4 Step 1
Using the above discussion, firm i chooses the product R&D investment di. By
(1) and (6), the optimal R&D investment level di is
∂pi
∂di
= 0 ⇐⇒ ∂c (di)
∂di
=
di
(S − 2di + 2)3
. (11)
To make the analysis tractable and derive a closed-form solution, we specify the
R&D cost function c (di) as
c (di) :=
S − 4di + 2
8 (S − 2di + 2)2
. (12)
It is easy to verify that this specification satisfies both c′ (di) > 0 and c′′ (di) < 0.
Additionally, this c (di) and the industry specific difficulty in differentiation S
have the following relationship:
∂c (di)
∂S
=
1
8
(
2 + a2
) (
2a4 + a2 (S + 14)− 2 (S + 2))
4 (−2a2 + S + 2)3 . (13)
A sufficient condition of ∂c(di)∂S > 0 is
S > 2a2 + 18 +
32
a2 − 2 . (14)
This implies that if the industry-specific difficulty in differentiation S is suffi-
ciently high, S promotes R&D investment. Hereafter, we assume this condition.
In preparation for the analysis of the optimal product R&D investment, we re-
visit the relationship between the profit of firm i (1), qii, and qij . The first order
conditions in Step 3 are
∂pii
∂qii
+ pii = 0,
∂pii
∂qij
+ pij − f = 0. (15)
Using this and (10), the profit of firm i pii becomes
pii = q
2
ii + q
2
ij − c (di) (16)
=
[
(4 + s) (2− s) a
4 (4− s2)
]2
+
[
(2− s) a
2 (4− s2)
]2
− c (di) . (17)
Since s = S − (d1 + d2) and symmetricity, the first order condition in Step 1
becomes
−a
2 (6 + S − 2di)
4 (S − 2di + 2) =
S − 4di + 2
8 (S − 2di + 2)2
(18)
Thus, the optimal product R&D investment di is
di =
a2 (6 + S)
4 + 2a2
. (19)
5
3 Comparative Statics
Based on (19), we derive the following proposition.
Proposition 1 In an industry with high difficulty in differentiation, i.e., large
S, the optimal product R&D investment level di is also high.
The intuition of Proposition 1 comes from the positive effect of the decrease
in endogenous transport price on the demand of the differentiated product is
greater than the negative effect on the price. Proposition 1 is consistent with
previous literature including Lin and Saggi (2002). Additionally, using (9) the
optimal transport price f becomes
f =
(
4 + 8a2 − 2S) a
8 + 4a2
. (20)
Thus, the following is derived naturally:
Proposition 2 In an industry with high difficulty in differentiation, i.e., large
S, the optimal transport price f is low.
When the difficulty in differentiation is high, the industry becomes more
competitive and, therefore, firms in this sector are less profitable. In such a
situation, because the unit-profit of the differentiated goods is lower, the trans-
port price f and the profit of the transporter are dropped. This also implies the
following Corollary 3:
Corollary 3 In an industry with low difficulty in differentiation, i.e., small S,
the optimal transport price f is high.
An example of Corollary 3 is observed in the luxury car industry, as described
in the introduction.
4 Conclusion
In this article we have constructed a symmetric international oligopoly model
with endogenous product differentiation and endogenous transport price. The
main result of this article is that, when product differentiation is more difficult,
firms in differentiated product sector increase their R&D investment and, ac-
cordingly, transporter sets transport prices lower. This result is a benchmark in
the analysis of the relationship between product differentiation and transporta-
tion costs.
An example of how this base model could be expanded to analyze an asym-
metric case where each country hasidentical R&D cost functions and trans-
portation fees. Another expansion would be to introduce cost reduction R&D
of transporter.7
7Hummels (2007) indicated that transportation costs have also declined in the second half
of the twentieth century as a result of technological change.
6
References
• Abe, Kenzo, Keisuke Hattori, and Yoshitaka Kawagoshi. ”Trade liber-
alization and environmental regulation on international transportation.”
The Japanese Economic Review 65.4 (2014): 468-482.
• Andriamananjara, Soamiely. ”Trade and International Transport Ser-
vices: an Analytical Framework.” Journal of Economic Integration (2004):
604-625.
• Bastos, Paulo, and Odd Rune Straume. ”Globalization, product differen-
tiation, and wage inequality.” Canadian Journal of Economics 45.3 (2012):
857-878.
• Behrens, Kristian, and Pierre M. Picard. ”Transportation, freight rates,
and economic geography.” Journal of International Economics 85.2 (2011):
280-291.
• Brander, James A., and Barbara J. Spencer. ”Intra-industry trade with
Bertrand and Cournot oligopoly: The role of endogenous horizontal prod-
uct differentiation.” Research in Economics 69.2 (2015): 157-165.
• Forslid, Rikard, and Toshihiro Okubo. ”Which firms are left in the pe-
riphery? Spatial sorting of heterogeneous firms with scale economies in
transportation.” Journal of Regional Science 55.1 (2015): 51-65.
• Francois, Joseph F., and Ian Wooton. ”Trade in international transport
services: the role of competition.” Review of International Economics 9.2
(2001): 249-261.
• Hummels, David. ”Transportation costs and international trade in the
second era of globalization.” Journal of Economic Perspectives 21.3 (2007):
131-154.
• Hummels, David, Volodymyr Lugovskyy, and Alexandre Skiba. ”The
trade reducing effects of market power in international shipping.” Journal
of Development Economics 89.1 (2009): 84-97.
• Ishikawa, Jota, and Nori Tarui. ”Backfiring with backhaul problems:
Trade and industrial policies with endogenous transport costs.” Journal
of International Economics 111 (2018): 81-98.
• Krugman, Paul. ”Scale economies, product differentiation, and the pat-
tern of trade.” The American Economic Review 70.5 (1980): 950-959.
• Lin, Ping, and Kamal Saggi. ”Product differentiation, process R&D,
and the nature of market competition.” European Economic Review 46.1
(2002): 201-211.
• Takahashi, Takaaki. ”Directional imbalance in transport prices and eco-
nomic geography.” Journal of Urban Economics 69.1 (2011): 92-102.
7
• Takauchi, Kazuhiro. ”Endogenous transport price and international R&D
rivalry.” Economic Modelling 46 (2015): 36-43.
8


Transport Price, Product Differentiation and R&D in an Oligopoly

Munich RePEc Personal Archive

Munich Personal RePEc ArchiveTransport Price, Product Differentiationand RD in an OligopolyKanehara, Daishoku and Kamei, Keita7 April 2019Online at https://mpra.ub.uni-muenchen.de/93148/MPRA Paper No. 93148, posted 08 Apr 2019 03:55 UTCTransport Price, Product Differentiation andR&D in an Oligopoly∗Keita Kamei†Daishoku Kanehara‡AbstractThis study incorporates transport price and endogenous product dif-ferentiation in an international oligopoly. Assuming endogenous determi-nation of transport price based on the profit maximization of the trans-porter and using a three-stage game, we analyze the effect of the degreeand difficulty of product differentiation on transport price. We show thatboth negatively affect the endogenous transport price. The intuition ofthis result comes from that the positive effect of a decrease in endogenoustransport price on the demand for the differentiated products is greaterthan the negative effect on the price.JEL classification: L13, L16, F12, F16, O30Keywords: Endogenous Product Differentiation; International Trade;Oligopoly; Product R&D; Transport Price.1 IntroductionTransport price is generally treated as a key factor in international trade. In aseries of new trade theory, Krugman (1980) revealed that a reduction in tradecost (including transport price) increased the volume of international trade ofdifferentiated goods. In fact, as Hummels (2007) mentioned, with the expansionof world trade, time series have shown a gradual decline in the air transport priceindex. Many studies on new trade theory assume trade cost as an exogenousvariable, so they do not investigate how product differentiation affects trade cost(ef. transport price). An example of this can be seen in the fact that Maserati,known as one of the luxury car brands, transports its latest models by air ratherthan by sea1. In addition to this, Hummels, Lugovskyy, and Skiba (2009) have∗This work has been supported by JSPS KAKENHI Grant Number 18K12761, JSPS KAK-ENHI Grant Number 18J0063, JSPS KAKENHI Grant Number 16K21110, and the JointResearch Program of KIER.†Department of Economics, Seinan Gakuin University. 6-2-92, Nishijin, Sawara-ku,Fukuoka-shi, Fukuoka 814-8511, JAPAN. E-mail: k-kamei@seinan-gu.ac.jp‡Graduate School of Economics, Kobe University, 2-1 Rokkodai, Nada, Kobe, Japan. Re-search Fellow of Japan Society for the Promotion of Science. E-mail: kanehara@people.kobe-u.ac.jp1See the following website: https://www.airbridgecargo.com/en/news/228/airbridgecargo-provided-dedicated-lift-for-28-maserati-granturismo-cars1shown that transport prices are endogenously determined by transportationfirms. They reveal that the larger the degree of product differentiation, thatis, the smaller the price elasticity of (import) demand, the higher the pricesimposed by transporters.In this article, we construct an international oligopoly model with endoge-nous product differentiation and endogenous transport price. Our main conclu-sion is that when product differentiation is more difficult, transportation priceswill become lower.In recent years, there have been many studies on endogenous transport price.Notable examples are: Francois and Wooton (2001); Andriamananjara (2004);Behrens and Picard (2011); Takahashi (2011); Abe et. al. (2014); Forslidand Okubo (2015); Ishikawa and Tarui (2018). In addition to this, Takauchi(2015) incorporated cost-reducing R&D into an international oligopoly withendogenous transport prices. Conversely, our model focuses on the productR&D in an international oligopoly with endogenous transport prices.This article also relates to the context of oligopolistic competition and prod-uct R&D. Lin and Saggi (2002) constructed an oligopolistic competition modelwith both product and process R&D. They employed the utility function of Singand Vives (1984) and derived the equilibrium not only under the Bertrand com-petition, but also under the Cournot competition. Bastos and Straume (2012)evolved Lin and Saggi (2002) into an oligopolistic general equilibrium and inves-tigated how trade liberalization has affected product R&D. They revealed thatthe protection from international trade (an increase in the number of shieldedsectors) has ambiguous effects on welfare. In addition to this, Brander andSpencer (2015) showed that additional product differentiation increases tradebenefits.To our knowledge, there are few studies on the relationship between thedegree of product differentiation and transport price. This implies that wedo not know the mechanism how the degree of differentiation (or quality ofproducts) affects transport price through strategic interaction. Therefore, wehave constructed a basic framework that incorporates both product R&D andendogenous transport price and reveals the relationship between the degree ofdifferentiation and transportation price.This paper is composed of the following sections: Section 2 constructs thebasic model; Section 3 provides the main results; and Section 4 concludes.2 The ModelWe assume perfectly symmetric2 two countries (country one and country two)in an open economy. In this economy, there are two sectors: a differentiatedproduct sector and a homogenous product sector. Homogenous products arenon-tradable and producers in this sector are faced with perfect competition.In contrast, differentiated products are tradable and each country has one iden-tical firm that produces its own variety. For simplicity, the marginal cost of2This implies that the analysis of one country can be applied to another.2differentiated products is assumed to be zero. We denote the quantity of thedifferentiated goods produced in country i and supplied to country j by qij .To transport one unit of product, the exporter is required to pay a transportprice f3. To reduce competition, firms can choose varieties through their prod-uct R&D investment di. As discussed above, the profit of a firm in country ibecomesπi = piiqii + pijqij − fqij − c (di) , (1)where pij is the price of firm i’s product in country j and c (di) is the cost ofR&D when investment level is di.We also assume that consumers are perfectly symmetric. The utility functionof consumers in country i is defined byui = α (qii + qji)−12[q2ii + q2ji]− sqiiqji +mi, (2)where α (> 0) is a parameter, mi is the quantity of the homogenous goods, and sis the inverse of the degree of differentiation between two products. The budgetconstraint of consumers in country i becomespiiqii + pjiqji +mi = Ii. (3)The utility maximization of both countries implies the following inverse demandspii = α− qii − sqji, (4)pij = α− qij − sqjj . (5)These indicate that higher differentiation (i.e. s is small) implies higher pricespii, pij .We assume that the degree of differentiation is determined by the R&Dinvestment of both firms:s := S − (d1 + d2) , (6)where S is a measure of difficulty in differentiation4. R&D cost function c (di)has the following characteristics5: c′ (di) > 0, c′′ (di) < 0.Finally, we assume that the transportation cost is zero and the transporterchooses the transport price f to maximize its profit.2.1 AnalysisWe assume that the procedure of decision-making between the transporter andthe differentiated firms is the following three-stage game: In step 1, firms decidetheir R&D investment level di to maximize their profits. In step 2 the trans-porter chooses the transport price f to maximize its profit. In step 3, based onthe above results, firms produce their differentiated products under the Cournotcompetition.3We will discuss the determination of f later in this section.4In this article, we assume that each industry has identical difficulties in differentiation.For example, S in the luxury car industry would be smaller than S in the Vitamin C industry.5We will specify c (di) in Section 2.4.32.2 Step 3Based on the degree of differentiation s and the transport price f , firm i choosesthe quantities to be supplied to home qii and foreign qij in order to maximizeits profit:πi = piiqii + pijqij − fqij − c (di) .By the first order conditions and inverse demand functions (4)(5), the optimalquantities becomeqii =(2− s) a+ sf4− s2, qij =(2− s) a− 2f4− s2. (7)It is evident that a higher transport price f has a positive effect on domesticsupply qii and a negative effect on export qij . This is because if the transportprice f is high, it impedes export and mitigates competition between home andforeign firms.By (8) the effect of the degree of differentiation s to quantities is∂qii∂s= −a(−2 + s)2 + f(4 + s2)(−4 + s2)2< 0,∂qij∂s= −a(s− 2)2 + 4fs(s2 − 4)2 < 0.The higher level of differentiation (i.e. small s) makes qii and qij increase simul-taneously through the product differentiation. Using inverse demand functions(4) and (5), we can derive that the higher level of differentiation decreases piiand pij .2.3 Step 2We assume that to export differentiated products, firms are required to pay theunit transport price f6 to the transporter. The transporter chooses the trans-port price f to maximize its profit. Since the marginal cost of transportation isassumed to be zero, the profit of the transporter isπf = f (q12 + q21) = 2f((2− s) a− 2f4− s2). (8)By the first order condition of the profit maximization, the optimal transportprice f becomesf =(2− s) a4. (9)Thus, a higher level of differentiation implies the higher optimal transport pricethrough the reduction of competition.To summarize (7) and (9), qii and qij becomesqii =(4 + s) (2− s) a4 (4− s2), qij =(2− s) a2 (4− s2). (10)6Being symmetric, the transporter will exhibit the same transport price f .42.4 Step 1Using the above discussion, firm i chooses the product R&D investment di. By(1) and (6), the optimal R&D investment level di is∂π∂di= 0 ⇐⇒∂c (di)∂di=di(S − 2di + 2)3 . (11)To make the analysis tractable and derive a closed-form solution, we specify theR&D cost function c (di) asc (di) :=S − 4di + 28 (S − 2di + 2)2 . (12)It is easy to verify that this specification satisfies both c′ (di) > 0 and c′′ (di) < 0.Additionally, this c (di) and the industry specific difficulty in differentiation Shave the following relationship:∂c (di)∂S=18(2 + a2) (2a4 + a2 (S + 14)− 2 (S + 2))4 (−2a2 + S + 2)3 . (13)A sufficient condition of ∂c(di)∂S> 0 isS > 2a2 + 18 +32a2 − 2. (14)This implies that if the industry-specific difficulty in differentiation S is suffi-ciently high, S promotes R&D investment. Hereafter, we assume this condition.In preparation for the analysis of the optimal product R&D investment, we re-visit the relationship between the profit of firm i (1), qii, and qij . The first orderconditions in Step 3 are∂pii∂qii+ pii = 0,∂pii∂qij+ pij − f = 0. (15)Using this and (10), the profit of firm i πi becomesπi = q2ii + q2ij − c (di) (16)=[(4 + s) (2− s) a4 (4− s2)]2+[(2− s) a2 (4− s2)]2− c (di) . (17)Since s = S − (d1 + d2) and symmetricity, the first order condition in Step 1becomes−a2 (6 + S − 2di)4 (S − 2di + 2)=S − 4di + 28 (S − 2di + 2)2 (18)Thus, the optimal product R&D investment di isdi =a2 (6 + S)4 + 2a2. (19)53 Comparative StaticsBased on (19), we derive the following proposition.Proposition 1 In an industry with high difficulty in differentiation, i.e., largeS, the optimal product R&D investment level di is also high.The intuition of Proposition 1 comes from the positive effect of the decreasein endogenous transport price on the demand of the differentiated product isgreater than the negative effect on the price. Proposition 1 is consistent withprevious literature including Lin and Saggi (2002). Additionally, using (9) theoptimal transport price f becomesf =(4 + 8a2 − 2S)a8 + 4a2. (20)Thus, the following is derived naturally:Proposition 2 In an industry with high difficulty in differentiation, i.e., largeS, the optimal transport price f is low.When the difficulty in differentiation is high, the industry becomes morecompetitive and, therefore, firms in this sector are less profitable. In such asituation, because the unit-profit of the differentiated goods is lower, the trans-port price f and the profit of the transporter are dropped. This also implies thefollowing Corollary 3:Corollary 3 In an industry with low difficulty in differentiation, i.e., small S,the optimal transport price f is high.An example of Corollary 3 is observed in the luxury car industry, as describedin the introduction.4 ConclusionIn this article we have constructed a symmetric international oligopoly modelwith endogenous product differentiation and endogenous transport price. Themain result of this article is that, when product differentiation is more difficult,firms in differentiated product sector increase their R&D investment and, ac-cordingly, transporter sets transport prices lower. This result is a benchmark inthe analysis of the relationship between product differentiation and transporta-tion costs.An example of how this base model could be expanded to analyze an asym-metric case where each country hasidentical R&D cost functions and trans-portation fees. 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Transport Price, Product Differentiation and R&D in an Oligopoly

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