Strategic export decisions in international trade
Kazuhiro Takauchi
Tomomichi Mizuno
Katsufumi Fukuda)HEUXary 2024
㻌Discussion Paper No. 2401

GRADUATE SCHOOL OF ECONOMICS
KOBE UNIVERSITY㻌ROKKO, KOBE, JAPANStrategic export decisions in international trade∗
Kazuhiro Takauchi†‡Tomomichi Mizuno§

Katsufumi Fukuda¶First version: December 18, 2022
This version: February 13, 2024
Abstract
As it is well known that export markets are often oligopolistic, we build an oligopoly trade modelin which ﬁrms choose whether or not to export. We focus on the diﬀerent roles of transport andﬁxed export costs with respect to the export decision, and show that depending on the sizes ofboth transport and ﬁxed export costs, all possible trade patterns appear between two symmetriccountries. If the transport cost is large because ﬁrms behave in diﬀerent ways, “One-way trade”
appears. If the ﬁxed export cost is large because ﬁrms adopt the same behavior, situations of“No trade” and “Two-way trade” could occur.

Key words: Trade pattern; Fixed export cost; Transport cost; Oligopoly
JEL classiﬁcation: F12; L13; D43∗

This paper is a revised version of our discussion paper, Kazuhiro Takauchi and Tomomichi Mizuno, December 2022, “Strategic exporting in an international oligopoly,” Discussion Paper No. 2216, Graduate Schoolof Economics, Kobe University, Kobe, Japan. We thank Hajime Sugeta for several constructive comments onan earlier version of this paper. The usual disclaimer applies. We thank Dr Amanda Fitzgibbons from Edanz(https://jp.edanz.com/ac) for editing a draft of this manuscript.
†
Corresponding author: Kazuhiro Takauchi, Faculty of Business and Commerce, Kansai University, 3-3-35
Yamate-cho, Suita, Osaka 564-8680, Japan. E-mail: kazh.takauch@gmail.com; Tel.: +81-6-6368-1817; Fax: +816-6339-7704.
‡
Research Fellow, Graduate School of Economics, Kobe University, 2-1 Rokkodai-cho, Nada-ku, Kobe-City,
Hyogo 657-8501, Japan.
§
Graduate School of Economics, Kobe University, 2-1 Rokkodai-cho, Nada-ku, Kobe-City, Hyogo 657-8501,
Japan. E-mail: mizuno@econ.kobe-u.ac.jp.
¶
School of Global Studies, Chukyo University, 101-2 Yagoto Honmachi, Showa-ku, Nagoya 466-8666, Japan.
E-mail: chukyokatsuf@lets.chukyo-u.ac.jp.

1

Introduction

In this study, we incorporate ﬁrm options of the Melitz (2003) type regarding “whether to export
or not” into an oligopolistic competition. Then, we consider what size transport and ﬁxed export
costs result in unilateral entry to the foreign market in response to the export decision (i.e.,“One-way trade”) or a bidirectional entry to the foreign market (i.e., “Two-way trade”). We
demonstrate the following trade pattern in equilibrium: [a] When the transport cost is large andthe ﬁxed export cost is small, asymmetric equilibria in which only one country exports between
two symmetric countries, i.e., “One-way trade,” can occur. [b] When the transport cost is small
and the ﬁxed export cost is large, multiple equilibria involving “No trade” and “Two-way trade”
between the two symmetric countries can occur.
Studies on ﬁrm export activity and international trade using a Melitz-type model focus on the
productivity diﬀerences among ﬁrms as a cause of the appearance of exporting ﬁrms. However,they tend to overlook strategic interaction among ﬁrms. It is well known that many export
markets are oligopolistic and thus it is highly natural to expect that a ﬁrm’s behavior depends
on interactions with other ﬁrms in the export markets. In the real world, many export markets
are reported to be oligopolistic, including the markets for iron, lead, tin, and zinc (Zhang andLawell, 2017); rice-milling and cigarettes (Arnade et al., 1998); semiconductors and steel (Kimand Lee, 2017); automobiles (in the US) (Goldberg, 1995); and wheat (in the Caucasus region)(Gafarova et al., 2023).1 Therefore, if we consider ﬁrms’ export activity, focusing on oligopolisticcompetition is partially consistent with real-world examples.
We built an oligopoly model of the Brander and Krugman (1983) type, consisting of twosymmetric countries and two ﬁrms. Each ﬁrm has two options: export to the foreign market
and/or supply the local domestic market. If a ﬁrm exports, it pays not only transport costs but
1

In addition, studies point out that both German exporters of beer and US exporters of linerboard paper haverelatively large market power (Goldberg and Knetter, 1999).

1

also a ﬁxed export cost. The ﬁrm only supplies the domestic market if it does not export. Eachﬁrm has a quadratic cost function, and ﬁrst chooses whether to export, and subsequently decides
on quantities.2 In this situation, two kinds of multiple equilibria appear when the transport cost
and the ﬁxed export cost are at intermediate levels. [a] When the transport cost is large and theﬁxed export cost is small, an asymmetric equilibrium in which only one country exports (i.e.,“One-way trade”) appears. A ﬁrm exports if its rival decided to supply the domestic market
rather than export. This is because the ﬁrm gains market share in the foreign country if it
exports, and enjoys a monopoly in its local market. In contrast, a ﬁrm supplies the domestic
market if its rival exports. This is because exporting is not attractive when the foreign market
is relatively small and, moreover, competition in the local market is weak because entry barriers
are high. [b] When transport cost is small and the ﬁxed export cost is large, multiple equilibria
involving “No trade” and “Two-way trade” appear. A ﬁrm exports if its rival exports. Thisis because, given that import barriers are low, there is strong competition in the local market.
Furthermore, the size of the foreign market is relatively large because the transport cost is small.
A ﬁrm supplies the domestic market if its rival does so in its country. The reason for this is thatthe entry barriers to the foreign market are high, and the ﬁrms can enjoy monopoly in theirlocal markets.
In addition, we show that trade liberalization with a reduction in the transport cost cansigniﬁcantly reduce consumer welfare. If the ﬁxed export cost is relatively small, “One-way
trade” can appear. In this situation, let us consider that trade liberalization proceeds. Then, thetrade pattern can switch from “No trade” to “One-way trade.” That is, because the equilibrium
regime can switch from a “No one exports” regime to a regime in which “only the home country
becomes an exporting country,” the consumer surplus in the home country can drop sharply
when the transport cost falls below a certain level.
2

In the Discussion section, we consider both diﬀerentiated quantity and price competition. See Section 5.

2

Furthermore, we discuss how the mode of competition aﬀects the trade pattern. In diﬀerentiated quantity competition, our main result does not alter. However, in diﬀerentiated pricecompetition, because the rivalry among ﬁrms increases compared with quantity competition, theequilibrium trade pattern becomes a multiple equilibria of “No trade” and “Two-way trade.”
The three main contributions of our paper to the literature are as follows: First, we determine the trade pattern between two symmetric countries based on ﬁrms’ strategic exporting
behavior. As a result, we show that all possible trade patterns can appear according to the sizeof the transport and ﬁxed export costs. This analysis presents new insights to the trade literature. Second, our study demonstrates that trade liberalization may reduce consumer welfare
signiﬁcantly. Therefore, competition authorities that value consumer welfare [e.g., the Federal
Trade Commission (FTC) in the USA] should ensure that the governments of their countries
pay attention to the eﬀects of trade liberalization. Third, we show that each country should
become a non-exporting country rather than an exporting country if the ﬁxed export cost is
relatively large. This result oﬀers a new perspective to practitioners and policy makers, who
tend to emphasize export promotion and exports of ﬁrms.3 Thus, our result oﬀers a uniquepolicy implication.
This paper is related to the works of Melitz and others adopting Melitz-style models toinvestigate ﬁrm exporting behavior and international trade (e.g., Melitz, 2003; Demidova andRodrı́guez-Clare, 2013; Melitz and Ottaviano, 2008; and Long et al., 2011).4 To address ﬁrmheterogeneity well, Melitz (2003) incorporated a productivity distribution into a standard monopolistic competition model. Then, he showed that less-productive ﬁrms become non-exporting3
4

In fact, Van Biesebroeck et al. (2015) point out that export promotion programs are often observed.
Other studies also use Melitz-type models to focus on the relationship between labor markets and tradeliberalization (e.g., Egger and Kreickemeier, 2009; Helpman and Itskhoki, 2010; and Helpman et al., 2010). Egger
and Kreickemeier (2009) emphasize workers’ fair wage preferences. Helpman and Itskhoki (2010) consider wage
bargaining and search and matching frictions in the labor market. Helpman et al. (2010) mainly consider labormarket frictions and diﬀerences in workforce composition across ﬁrms.

3

ﬁrms and productive ﬁrms become exporting ﬁrms. A transport cost reduction brings about
an export expansion through the “intensive margin” and “extensive margin.”5 Melitz showedthat this “extensive margin” causes a reallocation of resources from less-productive ﬁrms to
productive ﬁrms. Then, the country’s welfare rises because of a fall in the price index.
Demidova and Rodrı́guez-Clare (2013) focused on a welfare analysis using a Melitz (2003)type model.6 They modiﬁed the Melitz (2003) model to an asymmetric two-country modelcomposed of small and large countries with an endogenous wage rate, and demonstrated that
trade liberalization raises the country’s welfare because of reallocation eﬀects.
Melitz and Ottaviano (2008) constructed a model with an endogenous markup rate. Tradeliberalization results in higher (constant) welfare for the trade liberalizing country (the trade
partner) because of a reallocation eﬀect, including a lower markup rate in the short run; however,fewer (more) potential entrants lead to lower (higher) welfare in the long run.
These studies are central and signiﬁcant to the literature focusing on a monopolisticallycompetitive trade model with ﬁrm heterogeneity. However, as they are all based on monopolisticcompetition they do not analyze strategic interaction among ﬁrms. Therefore, the analyses do
not consider all possible trade patterns that occur according to the size of the transport andﬁxed costs.
To consider the relationship between ﬁrm process innovation (or cost-reducing R&D activity)
and trade liberalization, Long et al. (2011) incorporated Melitz-type ﬁrm exporting behavior
into an oligopolistic competition model.7 However, the main purpose of Long et al. (2011) was
5

The “intensive margin” indicates the expected value of one ﬁrm’s export volume. The “extensive margin”

refers to the number of ﬁrms exporting from a certain country to the foreign country (Antràs, 2016, p. 38).
6

Arkolakis et al. (2012) showed that the condition of gains from trade in the Melitz model depends on two

factors. One is the shape of the productivity distribution, and the other is the expenditure share for the own
country’s products in the open economy.
7

Impullitti et al. (2022) considered heterogeneous oligopolistic competition and R&D in a general equilibrium

framework. Furthermore, Edmond et al. (2015) presented a general equilibrium model in which intermediate-good4

to examine the eﬀects of trade liberalization on R&D investment and hence, the ﬁrms’ strategic
choice regarding whether to export and the decision of trade pattern are omitted in their model.
This paper is also related to the studies in which ﬁrms endogenously determine whether
to become a multiproduct producer (e.g., Basak and Mukherjee, 2018; Grossmann, 2007; andKawasaki et al., 2023). In our model, ﬁrms consider whether to become an exporter. Thissituation is similar to single-product ﬁrms becoming multiproduct ﬁrms due to paying a ﬁxed
cost and by developing new products. Basak and Mukherjee (2018) consider new productdevelopment, that is, product R&D, in a unionized duopoly model. Kawasaki et al. (2023)
examine downstream ﬁrms’ new product development and upstream ﬁrms’ cost-reducing R&D.
Moreover, Grossmann (2007) builds a model in which ﬁrms decide the number of their products.
Although these studies oﬀer interesting results, their models are limited to the domestic market
alone, and therefore, do not cover international trade.
The remainder of this paper is organized as follows. Section 2 presents the baseline model andSection 3 examines the trade patterns that arise. Section 4 presents the welfare considerations.
Section 5 discusses the case where ﬁrms engage in diﬀerentiated quantity and price competition.
Section 6 concludes.

2

Model

We consider a segmented market of the Brander and Krugman (1983) type. There are twosymmetric countries, the home country (labeled H) and the foreign country (labeled F ), andeach country has a product market and a ﬁrm, which we refer to as ﬁrms H and F , respectively.
Each ﬁrm has two options, that is, it must decide whether to export or not export, and it pays
a ﬁxed export cost k ≥ 0 if it exports. When ﬁrm i exports, its output includes both “domestic
supply” (labeled D) and “exports” (labeled E). To export one unit of product to the foreign
producers compete in Cournot fashion.

5

market, ﬁrms must pay a per unit transport cost t ≥ 0. We assume that the ﬁrms have aquadratic cost function:8 (γ/2) q 2 , where γ > 0 is the production eﬃciency of ﬁrms and q is aquantity. According to the decisions made by the ﬁrms, four trade patterns appear. Figure 1
illustrates all possible trade patterns between the Home and Foreign ﬁrms. In the baseline model,
ﬁrms engage in a homogenous quantity competition in both the Home and Foreign markets. In
the discussion in Section 5, we consider diﬀerentiated quantity and price competition.

The inverse demand of country i when all ﬁrms export is pi = a − qii − qji , i = j, i, j = H, F ,where pi is the product price, qii is the domestic supply of ﬁrm i, and qji is the export of ﬁrm j(or the imports of country i from country j). The inverse demand of country i when ﬁrm j does
not export is pi = a − qii . The consumer surplus in country i is given by CSi = Q2i /2, where
Qi is aggregate output of country i. For example, if all ﬁrms choose E, the consumer surplus incountry i becomes CSi = (qii + qji )2 /2 for i = j, i, j = H, F .
The proﬁts of the ﬁrms depend on the trade pattern realized. When all ﬁrms choose E,
two-way trade occurs. Then, ﬁrm i’s proﬁt without k (the ﬁxed export cost) is given by:
Πi ≡ (a − qii − qji )qii + (a − qjj − qij − t)qij −γ(qii + qij )2 for i = j, i, j = H, F.
2When only ﬁrm i (= j) chooses D, its proﬁt is:Πi ≡ (a − qii − qji )qii −8γ(qii )2 for i = j, i, j = H, F.
2

The production technology for manufacturing often involves decreasing returns to scale. Basu and Fernald(1997) found that a typical industry has decreasing returns to scale based on aggregate data of 34 manufacturingindustries in the US. Kee (2002) empirically found that many manufacturing industries in Singapore have decreasing returns to scale. In addition, Xu et al (1994), among others, found that decreasing returns to scale can beobserved in the transportation sector. Furthermore, a quadratic cost function is frequently adopted in theoreticalstudies of oligopoly. See, for example, Dastidar (1995), Delbono and Lambertini (2016), Goerke (2022), Mizuno
and Takauchi (2020, 2024), Mukherjee (2014, 2024), Takauchi and Mizuno (2022), and von Weizsäcker (1980).

6

Two-way trade
ﬁrm H
qHH

ﬁrm F
qF H

qHF

qF F

ForeignHome

One-way trade
ﬁrm H
qHH

ﬁrm F
qHF

ﬁrm H

qF F

qHH

Foreign

Home

ﬁrm F
qF H

Home

qF F

Foreign

No trade
ﬁrm H

ﬁrm F
qF F

qHH

Home

Foreign

Figure 1: Trade patterns
When only ﬁrm i (= j) chooses E, its proﬁt without k is:Πi ≡ (a − qii )qii + (a − qjj − qij − t)qij −γ(qii + qij )2 for i = j, i, j = H, F.
2When all ﬁrms choose D, there is no trade. Then, ﬁrm i’s proﬁt is:Πi ≡ (a − qii )qii −γ(qii )2 for i = H, F.
2For simplicity, hereafter, we normalize γ at unity, i.e., γ = 1. This normalization does notalter our main results. In the Online Appendix, we illustrate the equilibrium of our model with7

parameter γ. (Refer to the Online Appendix for further details.)
We consider the following two-stage game. In the ﬁrst stage, each ﬁrm chooses either E or
D. If a ﬁrm chooses E, it pays k. In the second stage, each ﬁrm enters a homogeneous quantity
competition. The solution concept is the sub-game perfect Nash equilibrium. The game is solved
by backward induction.

3

Trade Patterns

In the second stage of the game, each ﬁrm i (i = H, F ) competes in Cournot fashion. Hence, theﬁrst-order conditions (FOCs) for the proﬁt maximization of ﬁrms in each regime are as follows.
In the EE regime (where all ﬁrms choose E): 0 = a−qji −qij −3qii and 0 = a−qjj −3qij −qii −t
for i = j; i, j = H, F .
In the DE regime (where ﬁrm H chooses D and ﬁrm F chooses E): 0 = a − qF H − 3qHH ,0 = a − 3qF F − qF H , and 0 = a − qF F − 3qF H − qHH − t.
In the ED regime (where ﬁrm H chooses E and ﬁrm F chooses D): 0 = a − qHF − 3qHH ,0 = a − qF F − 3qHF − qHH − t, and 0 = a − 3qF F − qHF .
In the DD regime (where all ﬁrms choose D): 0 = a − 3qii for i = H, F .
By solving the above FOCs in each regime, we obtain the following outputs:
a + 2ta − 3t
EE∗
; qij
,
=
5
5
2a + t
ED∗
DE∗
ED∗
qHH
= qFDE∗=F = qHH = qF F ;7
aqiiDD∗ = ,3
qiiEE∗ =where “∗” is an equilibrium value.
To ensure a positive quantity, we set Assumption 1.
Assumption 1.

t
1
< .
a
3

8

qFDE∗
H =

a − 3t
ED∗
= qHF
,
7

(1)

Equation (1) yields the ﬁrms’ equilibrium proﬁt without k:
8a2 − 8at + 27t2,
50
3(2a + t)2
ED∗
,
ΠDE∗
=
Π
=
H
F
98
19a2 − 16at + 24t2
ΠDE∗,
= ΠED∗
=
F
H
98
a2
ΠDD∗
.
=
i
6
=
ΠEE∗
i

(2)

From equation (2), we obtain Lemma 1.
2(23a − 104t)(a − 3t)>(≤) k/a2 ,1225
4(a − 3t)2>(≤) k/a2 , ﬁrm i
ﬁrm i chooses E (D). (ii) Suppose that rival chooses D. If ϕE ≡147

Lemma 1. (i) Suppose that rival (ﬁrm j) chooses E. If ϕD ≡chooses D (E).
− ΠDE∗= ΠEE∗− ΠED∗=
Proof. ϕD ≡ ΠEE∗
H
H
F
F
− ΠDD∗=
ΠDE∗F
F

4(a − 3t)2
. Q.E.D.
147

2(23a − 104t)(a − 3t)and ϕE ≡ ΠED∗
− ΠDD∗=H
H
1225

From Lemma 1, we establish Proposition 1.

Proposition 1. I. Suppose that t/a ≤ 19/162. (i) If k/a2 < ϕE , then EE occurs. (ii) If
ϕE ≤ k/a2 ≤ ϕD , then DD&EE can arise. (iii) If k/a2 > ϕD , then DD occurs.
II. Suppose that 19/162 < t/a < 23/104. (i) If k/a2 < ϕD , then EE emerges. (ii) If ϕD ≤k/a2 ≤ ϕE , then DE&ED can occur. (iii) If k/a2 > ϕD , then DD occurs.
III. Suppose that 23/104 ≤ t/a < 1/3. (i) If k/a2 ≤ ϕE , then DE&ED can occur. (ii) If
k/a2 > ϕE , then DD occurs.

The equilibrium trade pattern depends on the sizes of both the transport cost t and the ﬁxed
export cost k. (See Figure 2.) If both transport and ﬁxed export costs are suﬃciently high,exporting becomes too expensive and domestic supply (D) becomes the dominant strategy, andno ﬁrm chooses to export. Hence, the DD regime occurs. Conversely, if both transport and

9

ka

DD & EE



DD





E







DE & ED

EE












t
a

Figure 2: Four areas

ﬁxed export costs are suﬃciently small, exporting becomes the dominant strategy, and all ﬁrms
export. Therefore, the EE regime occurs. If both transport and ﬁxed export costs are at anintermediate level, there is no dominant strategy, and two kinds of multiple equilibria, DE&ED
and DD&EE, can occur.
We ﬁrst consider [a] DE&ED, i.e., the “One-way trade,” and then [b] DD&EE, i.e., “No
trade” and “Two-way trade.” [a] When the transport cost is high and the ﬁxed export cost issmall, DE&ED can emerge. If a foreign rival chooses D, the local market is a monopoly. Then,because a ﬁrm can gain a larger market share in the foreign country if it exports, despite the factthat its marginal costs increase, the ﬁrm chooses E. Conversely, suppose that the foreign rivalchooses E. Now, the foreign market is relatively small; hence, the beneﬁt of exporting is small.
In this case, as the transport cost is relatively high and the import barriers are also high, thelocal market competition is weak. Furthermore, the ﬁrm’s marginal cost increases if it chooses
E. Hence, the ﬁrms choose D.
[b] When the transport cost is small and the ﬁxed export cost is high, DD&EE can occur.

10

First, suppose that a foreign rival exports. Now, because the ﬁxed export cost is large, thebeneﬁt of exporting is small. However, the transport cost is low, and domestic competition isstrong. Although choosing to export increases the ﬁrm’s own marginal costs, it experiences alarge reduction in proﬁts when the foreign rival enters into the local market. Therefore, theﬁrm chooses E. Second, suppose that the foreign rival chooses D. In this case, the ﬁxed export
cost is large. The ﬁrm enjoys a local monopoly, the entry barriers into the foreign market are
high, and new entry into the foreign market raises the ﬁrm’s marginal cost. Therefore, the ﬁrm
chooses D.
Our result on the trade patterns provides a new insight into ﬁrm export behavior and international trade. Following the pioneering study of Melitz (2003), many studies have conductedanalyses based on Melitz-type models. [See, for example, Demidova and Rodrı́quez-Clare (2013)
and Melitz and Ottaviano (2008).] As pointed out by Head and Spencer (2017), the mainstream
practice in recent studies on international trade has been to adopt a monopolistic competition
model or a monopolistic competition model with ﬁrm heterogeneity. However, in the monopolistic competition model, strategic interactions among ﬁrms are omitted and hence, multiple
equilibria in which one country exports but the other country does not do not appear between
symmetric countries. By contrast, our study—although it has the limitation of a being a partial
equilibrium study—shows that by directly handling the strategic interactions among ﬁrms inoligopoly industries, all possible trade patterns can emerge with two symmetric countries. We
believe that our results make a signiﬁcant contribution to the literature.

4

Welfare Considerations

As illustrated in Figure 2, the welfare in each country can vary drastically because the size oftransport cost t alters the trade pattern. Therefore, we now consider the eﬀects of a change inthe transport cost on the welfare in each country.

11

4.1

Consumer Surplus

Competition authorities often focus on consumer surplus compared with total surplus (e.g.,Albæk, 2013; Viscusi et al., 2018); hence, we ﬁrst consider how trade liberalization (i.e., areduction in the transport cost t) aﬀects the consumer surplus.
From equation (1), the consumer surplus in each equilibrium regime is:
CSiEE∗ =(2a − t)2a2
(3a − 2t)2
(2a + t)2
DE∗
ED∗
; CSiDD∗ = ; CSH
; CSH
,
=
=
50
18
98
98

(3)

DE∗ = CS ED∗ and CS ED∗ = CS DE∗ .
where CSH
F
H
F

Equation (3) and Proposition 1 yield Proposition 2.
Proposition 2. Suppose that k/a2 < 25/2187. Then, trade liberalization involving a reductionin the transport cost, t, may suddenly lower the consumer surplus of the exporting country.
DE∗ > CS EE∗ >Proof. First, DE&ED can appear if k/a2 < 25/2187. Second, ∀t/a < 1/3, CSH
iED∗ . Hence, ∀k/a2 < 25/2187, consumer surplus can drop if t decreases. Q.E.D.
CSiDD∗ > CSH

Proposition 2 can be explained by ranking consumer surplus. (Figure 3 illustrates the relationship between consumer surplus and the transport cost.) In the regime in which only theforeign ﬁrm exports, the marginal cost of the home ﬁrm is small because it does not export.
Hence, its domestic supply increases. In addition, imports exist and hence, aggregate outputs
are the largest among all other regimes. Thus, the consumer surplus is also at its largest. In
the regime in which everyone exports, each ﬁrm’s marginal cost is large. Furthermore, because
strategic substitutes exist in markets, the domestic ﬁrm’s domestic supply decreases because of
the rival’s exports entering its market. Hence, the aggregate output in this regime is smaller
than that in the regime in which only the foreign ﬁrm exports. In the regime in which no one
exports, because there are no imports, the aggregate output in this regime is smaller than that

12





a
i


H a





a
i







H a



 

 





 

ta

Figure 3: Eﬀect of trade liberalization on consumer surplus (k = 0.005)

in the regime in which everyone exports. Finally, in the regime in which only the domestic ﬁrm
exports, because the domestic ﬁrm supplies two markets, its marginal cost increases. Hence,its domestic supply decreases. In this case, there are no imports; hence, the aggregate output
equals the domestic supply. As a result, the consumer surplus is at its smallest among all theregimes.
Proposition 2 and Figure 3 have important implications. As illustrated in Figure 3, tradeliberalization with a reduction of transport costs can suddenly lower the consumer surplus in
the exporting country. The reason is that the trade pattern switches from “No trade” to “Oneway trade” (where the home country exports, and the foreign country does not) through the
reduction in the transport cost. This switching in the trade pattern makes the home country’s
total output equal to ﬁrm H’s domestic supply only (given the home country does not receive
any imports).
Some studies in the literature have pointed out that trade liberalization can reduce consumer
welfare (e.g., Kabiraj and Marjit, 2003; Marjit and Mukherjee, 2015; Takauchi and Mizuno,

132022).9 Marjit and Mukherjee (2015) and Takauchi and Mizuno (2022) indicated that a reductionof trade costs (including tariﬀs and transport costs) may decrease consumer surplus in various
vertical market structures. Furthermore, Kabiraj and Marjit (2003) showed that in a situationof technology licensing, an increase in the tariﬀ rate in the country receiving the technology
licensing causes a technology licensing from the superior foreign ﬁrm, which leads to a sudden
rise in consumer surplus.10 Hence, a decrease in the tariﬀ rate sharply reduces consumer surplus.
In contrast, our study reveals that trade liberalization can lead to a sudden decline in consumer surplus through an alteration in the trade pattern. This substantially diﬀers from theconclusions of the literature and therefore, our study provides new insights into trade liberalization.
Furthermore, the negative eﬀects of trade liberalization on the consumer surplus may not
be considered desirable by the government even if it can improve the domestic total surplus.
This is because competition authorities, such as the FTC in the US.,11 believe a sharp decline
in the consumer surplus should be avoided because the consumer surplus is the standard used
to measure welfare. Thus, the competition authorities will have strong incentives to pressure
their governments to avoid a non-negligible reduction in the consumer surplus. Therefore, ameaningful policy implication of our study is that the government may need to pay particularattention to the eﬀects of the trade liberalization.

9

Moreover, although they focus on diﬀerent situations, studies have examined international trade and consumer

welfare. Mukherjee and Sinha (2019) showed that an export cartel between exporting ﬁrms can increase consumer
surplus in the importing country under a third-market model. Mizuno and Takauchi (2018) demonstrated that
if the initial level of the tariﬀ is high, a tariﬀ reduction by the ﬁnal-good importing country in a free trade area
decreases consumer surplus in that country.
10

Similarly, Takauchi and Mizuno (2020) demonstrated that relatively high transport costs maximize consumer

surplus in a two-country, two-way trade model with product innovation.
11

In the US., the consumer welfare standard is adopted in practice (e.g., Viscusi et al., 2018, p. 97).

14

4.2

Total Surplus

We show that trade liberalization may decrease total surplus. Total surplus in each regime is asfollows:2(3a2 − 3at + 7t2 )− k,25
23a2 − 12at + 25t2
ED∗
T SH
− k,
= T SFDE∗ =98
3a2 + t2DE∗,
T SH
= T SFED∗ =14
2a2
T SiDD∗ =.
9
T SiEE∗ =By comparing these total surpluses, we obtain Proposition 3.
Proposition 3. (i) If trade liberalization changes the trade regime, it always reduces total surplus. (ii-a) Without changing the trade regime, trade liberalization always reduces the total
surplus of the non-exporting country. (ii-b) Without changing the trade regime, the total surplusof the exporting country decreases if 3/14 < t/a < 23/104 and k/a2 < ϕD in the EE regime,
and if 6/25 < t/a < 1/3 and k/a2 < ϕE in the ED regime.
Proof. See the Appendix.

To conﬁrm that trade liberalization reduces total surplus, we illustrate total surplus as afunction of transport costs in the ﬁgures below. In Figure 4, trade liberalization with a changing
trade regime reduces total surplus. In addition, the total surplus of the non-exporting country
in the DE or ED regimes decreases with t. Thus, we conﬁrm results (i) and (ii-a) in Figure 5.
Figure 5 illustrates the total surpluses of the exporting country under the EE and ED&DE
regimes at k/a2 = 0. Note that from Proposition 1, either the EE or ED&DE regimes occur
at k/a2 = 0. In Figure 5, the shaded areas represent the case in which trade liberalization has
a negative impact on total surplus.

15 

a
i




a
i




H a

 



H a



 

 

ta


Figure 4: Eﬀect of trade liberalization on total surplus (k/a2 = 0.008)

 
 
 



a
i



       taFigure 5: Welfare decreasing trade liberalization (k/a2 = 0)

The intuition behind Proposition 3 is as follows: As trade liberalization (a decrease in t)
progresses, the exporting ﬁrm’s supply shifts from the domestic market to foreign markets. As aresult, the domestic ﬁrm’s proﬁt increases and the domestic consumer surplus decreases. Whichof these eﬀects is larger determines whether total surplus increases. If t is large, the supply to theforeign market is small and the supply to the domestic market is large. In this case, a decrease int signiﬁcantly changes the supply to the domestic market such that the dominant eﬀect of tradeliberalization is the reduction in consumer surplus. Thus, in each regime, trade liberalization

16

reduces the aggregate surplus in the region in which t is large: see (ii-b) in Proposition 3.
When the foreign ﬁrm trades and the domestic ﬁrm does not, trade liberalization increases
the domestic consumer surplus but reduces the domestic ﬁrm’s proﬁt. In our model, this proﬁtdecreasing eﬀect dominates; hence, the total surplus of the non-exporting country decreases withtrade liberalization: (ii-a) in Proposition 3.
Next, the same intuition applies when a decrease in t changes the trade regime. When aslight decrease in t changes the trade regime, the proﬁt of the ﬁrm that begins to export changes
little. However, the total surplus of the country in which ﬁrms begin to export falls because
the supply to that country is signiﬁcantly reduced. Furthermore, because trade liberalization
intensiﬁes competition among ﬁrms, the proﬁts of the ﬁrms that do not change their export
decisions also decline. Although consumer surplus in the country increases, the total surplus of
the country falls because this proﬁt-lowering eﬀect dominates: (i) in Proposition 3.
Finally, we consider a characteristic implication of the total surplus in the “One-way trade”
situation.
ED∗ with T S DE∗ , we establish Proposition 4.
Comparing T SH
H

Proposition 4. In the “One-way trade” situation, the welfare level of an importing country islarger than that of an exporting country if and only if the ﬁxed export cost is relatively large.
ED∗ ≤ T S DE∗ if and only if 25a2 /2187 > k ≥ (a − 3t)2 /49.
Formally, T SH
H

Proof. See the Appendix.

The result of Proposition 4 is illustrated in Figure 4. The logic behind Proposition 4 is
intuitive. When the transport cost t is large, “One-way trade” holds (see Figure 2). A larger
transport cost means that the increase in proﬁt caused by choosing to export is smaller. In
contrast, if ﬁrm i chooses D, country i can import from the foreign rival. The imports from theforeign rival raise the aggregate outputs, so the product price falls. Then, the consumer surplus

17

increases. If the ﬁxed export cost is large, the dominant eﬀect is the increase in the consumer
surplus and thus the total surplus in the importing country is larger than that in the exporting
country.
Proposition 4 indicates that in a situation of intra-industry trade, when ﬁrms can decide
whether to export, the country can enhance its welfare if it becomes a net importer. This oﬀers
a new perspective to practitioners and policy makers who tend to emphasize that ﬁrms shouldchoose to export. Thus, our welfare analysis oﬀers a new insight into the context of international
trade.

5

Discussion: Trade Patterns in Diﬀerentiated Products

In this section, we consider how the equilibrium trade pattern is aﬀected by diﬀerentiated quantity and price competition.

5.1

Diﬀerentiated Quantity Competition

First, we consider diﬀerentiated quantity competition in both the Home and Foreign markets.
In the EE regime, the inverse demand functions of country i (i = H, F ) are pii = a − qii − bqji
and pij = a − qij − bqjj for i = j, i, j = H, F . Note that b ∈ [0, 1) is a measure of the degree of
product diﬀerentiation between the Home and Foreign products. By adopting a similar method
to that of the previous section, we obtain the following exports, q̂ij , and domestic supply, q̂ii , ineach regime.
q̂iiEE∗ =a(2 − b) + (1 + b)ta(2 − b) − 3tEE∗
; q̂ij,=(2 − b)(4 + b)
(2 − b)(4 + b)

DE∗
q̂HH
=

2a(4 − b) + 3bt
a(3 − b)(2 + b) + 3t
DE∗ED∗
= q̂FED∗= q̂HH,F ; q̂F F =23(8 − b )3(8 − b2 )q̂FDE∗H =a(2 − b) − 3tED∗
= q̂HF.
8 − b218

In the DD regime, all ﬁrms supply only the domestic market, and thus their demand is irrelevantto the parameter b. Hence, q̂iiDD∗ = a/3 = qiiDD∗ holds. (See equation (1).)
To ensure positive quantities, in this part we assume that τ ≡ t/a < τmax ≡ (2 − b)/3.
The above outputs yield the equilibrium ﬁrms’ proﬁts without k.
πiEE∗ =

8a(2 − b)2 (a − t) + 3(8 + b2 )t2,2(2 − b)2 (4 + b)2DE∗πH= πFED∗ =[2a(4 − b) + 3bt]2,
6(8 − b2 )2ED∗= πFDE∗ =πH

a2 (b4 − 8b2 − 32b + 96) − 48a(2 − b)t + 72t2,
6(8 − b2 )2(4)

where πiDD∗ = a2 /6 = ΠDD∗in the DD regime. (See equation (2).)
i
From equation (4), the diﬀerence in proﬁts without the ﬁxed export cost k is given by:
⎫
EE∗
DE∗
− πH
= πFEE∗ − πFED∗ > 0, ⎪Δ E ≡ πH
⎬
(5)

⎪

⎭
ED∗
DD∗
Δ D ≡ πH
− πH
= πFDE∗ − πFDD∗ > 0.
From equation (5), we establish Proposition 5.

Proposition 5. I. Suppose that τ < τδ (b). Then, ΔD < ΔE . (i) If k < ΔD , EE occurs. (ii)
If ΔD ≤ k ≤ ΔE , EE&DD can emerge. (iii) If ΔE < k, DD occurs.
II. Suppose that τ > τδ (b). Then, ΔE < ΔD . (i) If k < ΔE , EE occurs. (ii) If ΔE ≤ k ≤ ΔD ,
2

3

+3b )
.
DE&ED can occur. (iii) If ΔD < k, DD emerges. Here, τδ (b) ≡ (2−b)(64−40b−8b3(8+b2 )(8−b−b2 )Proof. See the Appendix.
The intuition for this result is equivalent to that for Proposition 1.

5.2

Diﬀerentiated Price Competition

Next, we consider diﬀerentiated price competition.
In the EE regime, the demand functions are:qii =(1 − b)a − pii + bpji
(1 − b)a − pij + bpjj
; qij =
for i = j, i, j = H, F.
1 − b2
1 − b219

Here, note that b ∈ [0, 1) again.
In the ED regime, the demand functions are:qHH = a − pHH ; qHF =(1 − b)a − pHF + bpF F(1 − b)a − pF F + bpHF
; qF F =.
1 − b2
1 − b2In the DE regime, the demand functions are:qHH =(1 − b)a − pHH + bpF H(1 − b)a − pF H + bpHH
; qF H =; q F F = a − pF F .
21−b
1 − b2In the DD regime, the demand function is qii = a − pii for i = H, F .
By adopting a similar method to that of the previous section,12 we obtain the following
equilibrium ﬁrm proﬁts without k.
π̄iEE∗ =4a(1 − b)(2 − b2 )(b + 2)2 (a − t) + (2b5 + 2b4 − 11b3 − 9b2 + 24b + 24)t2,
2(1 − b)(b + 2)2 (b2 − b − 4)2DE∗= π̄FED∗ =π̄H(3 − 2b2 ) [a(b + 2)(3b − 4) − 3bt]2,
2(3b4 − 20b2 + 24)2ED∗
π̄FDE∗ = π̄H=
3b8 − 48b6 − 24b5 + 222b4 + 104b3 − 432b2 − 96b + 288 a2
2(3b4 − 20b2 + 24)2+2a(b2 − 3)(2b2 + 3b − 6)(3b2 − 4)t 3(b2 − 3)2 (3b2 − 4)t2−,
(3b4 − 20b2 + 24)2
(3b4 − 20b2 + 24)2

where π̄iDD∗ = a2 /6 = ΠDD∗.
i
The above proﬁts without the ﬁxed export cost k yield the following:
⎫
EE∗
DE∗
− π̄H
= π̄FEE∗ − π̄FED∗ > 0, ⎪BD ≡ π̄H
⎬
⎪

⎭
ED∗
DD∗
BE ≡ π̄H− π̄H= π̄FDE∗ − π̄FDD∗ > 0.

(6)

Further, from equation (6), we obtain: BD > BE .13
The equation (6) and the relation “BD > BE ” yield Proposition 6.
Proposition 6. (i) If k < BE , EE occurs. (ii) If BE ≤ k ≤ BD , EE&DD can arise. (iii) If
BD < k, DD emerges.
1213

The equilibrium outputs and prices are reported in the Online Appendix.
The derivation of BD > BE is reported in the Online Appendix.

20In diﬀerentiated price competition, rivalry among the ﬁrms is stronger than under quantity
competition. Consequently, when ﬁrms engage in diﬀerentiated price competition, “One-way
trade” does not occur, but the multiple equilibria comprising “No trade” and “Two-way trade”
emerge.
The intuition for Proposition 6 can be explained as follows. Let ﬁrm i choose E if its rivalchooses D. Because ﬁrm i newly enters the overseas market, its outputs increase and its marginal
cost discontinuously jumps upwards. In the case of price competition, the rivalry among ﬁrms isstrong and hence this dramatic rise in the marginal cost drastically reduces the competitivenessof ﬁrm i in its local market. Because this can lead to a proﬁt reduction for ﬁrm i, it does notchoose E.
In contrast, consider the situation where ﬁrm i chooses D if its rival chooses E. In the local
market of ﬁrm i, competition is strong. Hence, new entry by a rival ﬁrm increases aggregate
outputs and lowers product prices, which decreases ﬁrm i’s proﬁt. Therefore, like its rival, ﬁrm
i chooses E, and enters the foreign market. From the above arguments, in the situation of
diﬀerentiated price competition, the ﬁrms’ responses are strategic complements and therefore
the multiple equilibria emerge in which ﬁrms conduct the same strategy as their rivals.

6

Conclusion

This paper constructs a symmetric two-country homogeneous Cournot oligopolistic trade modelà la Brander and Krugman (1983) to examine the eﬀects of the sizes of both transport and ﬁxed
export costs on realizable trade patterns and the welfare level of each country.
Our main ﬁndings are summarized as follows: (i) Firms’ exporting choices and trade patterns
depend on transport and ﬁxed export costs. When the sizes of both transport and ﬁxed export
costs are at an intermediate level, two kinds of multiple equilibria can appear. These two
multiple equilibria involve characteristic trade patterns. One brings endogenous asymmetry,21

that is, only one country becomes an exporter, creating “One-way trade.” The other is basedon strategic complements, and so causes both “No trade” and “Two-way trade.” (ii) Tradeliberalization, that is, a reduction in transport costs, changes consumer surplus and total surplus
nonmonotonically and discontinuously through changes in the trade patterns. For example,
trade liberalization switches the trade pattern from “No trade” to “One-way trade.” If one
country becomes an exporter, it does not import from overseas (because the other country does
not export), that country’s aggregate output is equal only to the local ﬁrm’s domestic supply.
Hence, the product price rises and the consumer surplus of that country experiences a sudden
fall.
Moreover, we consider the cases in which the ﬁrms engage in diﬀerentiated quantity and pricecompetition. Although the diﬀerentiated quantity competition does not alter the equilibrium
trade pattern, the diﬀerentiated price competition can do so because competition is stronger
compared with the quantity competition.
Furthermore, we derive a policy implication concerning trade liberalization. We ﬁnd that
trade liberalization may lower consumer surplus and total surplus as a result of the changes
in trade patterns. Although practitioners and policymakers tend to believe trade liberalization
always increases welfare, we caution that this may not always be the case.
Finally, we consider directions for future work. We used a partial equilibrium oligopoly
model in this paper to examine the eﬀects of trade liberalization on trade patterns and welfare.
However, topics analyzed in a partial oligopoly model have been reexamined using a generalequilibrium model since Neary (2003a, b) built a general oligopolistic equilibrium model. Extending the analysis in this paper using the general oligopolistic equilibrium model to analyze
the general equilibrium eﬀect would be a worthwhile endeavor. As it exceeds the scope of thispaper, we leave this endeavor for future research.

22

Appendix
Proof of Proposition 3.

We distinguish two scenarios in which trade liberalization reduces

total surplus: (i) trade liberalization with a changing trade regime and (ii) trade liberalization
without a changing trade regime.
We consider case (i). From Proposition 1, the trade regime change occurs at k/a2 = ϕDor k/a2 = ϕE . From Proposition 1, for t/a ≤ 19/162, we compare T SiDD∗ with T SiEE∗ at
k/a2 = ϕD or k/a2 = ϕE :2(a − 3t)(109a + 93t)
> 0,
T SiDD∗ − T SiEE∗ k=ϕ a2 =
D
11025
 DD∗

2(a − 3t)(52a + 579t)
T Si
> 0.
− T SiEE∗ k=ϕ a2 =
E
11025



Hence, for t/a ≤ 19/162, trade liberalization reduces the total surplus of both countries.
ED∗ at k/a2 = ϕ ,Next, we consider case (i) with t/a > 19/162. By evaluating T SiDD∗ − T SH
E

we obtain the following equation:(a − 3t)(13a + 3t)
ED∗
> 0.
=
T SiDD∗ − T SH
k=ϕE a2
882

DE∗ and T S ED∗ − T S EE∗ are as follows:In addition, T SiDD∗ − T SH
i
H
DE∗
=
T SiDD∗ − T SH

(a − 3t)(a + 3t)
> 0;
126

ED∗
T SH
− T SiEE∗ =(249t − 13a)(a − 3t)
> 0.
2450

DE∗ − T S EE∗ , we obtain:
Substituting k/a2 = ϕD into T SHi
(29a − 17t)(a − 3t)
DE∗− T SiEE∗ k=ϕ a2 =
> 0.
T SH
D
2450

Therefore, trade liberalization with a changing trade regime always reduces the total surplus.
Now, we consider case (ii): trade liberalization without a changing trade regime. By diﬀerentiating the total surplus in each trade regime with respect to t, we obtain the following:ED∗DE∗
2(3a − 14t) ∂T SH
6a − 25t ∂T SH
t∂T SiDD∗∂T SiEE∗
=−
=
−
;
=
>
0;
= 0.
;
∂t
25a2
∂t
49
∂t
7
∂t

Hence, if the trade regime is ED or DE, trade liberalization always reduces the total surplus of23

the non-exporting country. In addition, without an exporting country, trade liberalization has
no eﬀect on total surplus.
Because ∂T SiEE∗ /∂t > 0 if t/a > 3/14, trade liberalization reduces the total surplus if
ED∗ /∂t > 0 if t/a > 6/25, trade
3/14 < t/a < 23/104 and k/a2 < ϕD . Next, because ∂T SH

liberalization reduces the total surplus if 6/25 < t/a < 1/3 and k/a2 < ϕE .
Summarizing the above results, we obtain Proposition 3. Q.E.D.

Proof of Proposition 4.

ED∗ − T S DE∗ = (a − 3t)2 /49 − k. Hence, k ≥First, we obtain T SH
HED∗ ≤ T S DE∗ . Second, we check that (a − 3t)2 /49 does not exceed the(a − 3t)2 /49 ⇒ T SH
Hlevel of k that brings about “One-way trade.” Solving ϕE − ϕD = 0 with respect to t, we havet = 19a/162. Thus, ϕE | t=19a/162 = ϕD | t=19a/162 = 25a2 /2187 holds. Simple algebra yields:(a − 3t)2−962a2 + 13122at − 19683t2
19a a
25a2
−
=
> 0 ∀t ∈,2187
49107163162 3.

This implies Proposition 4. Q.E.D.

Proof of Proposition 5. From equation (5), simple algebra yields:
ΔE − Δ D=

2b(ab − 2a + 3t)(3ab4 − 14ab3 − 24ab2 + 144ab − 128a − 3b4 t − 3b3 t − 24bt + 192t)3(b − 2)2 (b + 4)2 (b2 − 8)2.

This yields the following.
⎧(2 − b)(64 − 40b − 8b2 + 3b3 )⎪⎪,⎨ ≥ ΔD if τ ≤ τδ (b) ≡3(8 + b2 )(8 − b − b2 )ΔE⎪⎪⎩
< ΔD if τ > τδ (b),where τδ (b) < τmax holds. From the above formula and the deﬁnitions of ΔE and ΔD , we obtain
Proposition 5. Q.E.D.

24

References[1] Albæk, S. (2013). Consumer welfare in EU competition policy. Aims and Values in Competition Law, 67-88.
[2] Antràs, P. (2016). Global production: Firms, contracts, and trade structure. Princeton University Press.
[3] Arkolakis, C., A. Costinot, and A. Rodrı́guez-Clare (2012). New trade models, same oldgains?. American Economic Review, 102(1), 94-130.
[4] Arnade, C., D. Pick, and M. Gopinath, M. (1998). Testing oligopoly power in domestic andexport markets. Applied Economics, 30(6), 753-760.
[5] Basak, D. and A. Mukherjee (2018). Labour unionisation structure and product innovation.
International Review of Economics & Finance, 55, 98-110.
[6] Basu, S. and J. G. Fernald (1997). Returns to scale in U.S. production: Estimates andimplications. Journal of Political Economy, 105(2), 249-283.
[7] Brander, J. A. and P. R. Krugman (1983). A ‘reciprocal dumping’ model of international
trade. Journal of International Economics, 15(3-4), 313-321.
[8] Dastidar, K. G. (1995). On the existence of pure strategy Bertrand equilibrium. Economic
Theory, 5, 19-32.
[9] Delbono, F. and L. Lambertini (2016). Bertrand versus Cournot with convex variable costs.
Economic Theory Bulletin, 4, 73-83.
[10] Demidova, S. and A. Rodrı́guez-Clare (2013). The simple analytics of the Melitz model ina small economy. Journal of International Economics, 90(2), 266-272.

25

[11] Edmond, C., V. Midrigan, and D. Y. Xu (2015). Competition, markups, and the gains frominternational trade. American Economic Review, 105(10), 3183-3221.
[12] Egger, H. and U. Kreickemeier (2009). Firm heterogeneity and the labor market eﬀects oftrade liberalization. International Economic Review, 50(1), 187-216.
[13] Gafarova, G., O. Perekhozhuk, and T. Glauben (2023). The oligopolistic behavior of Kazakh
and Russian wheat exporters in the south caucasus: Evidence from a residual demand elasticity analysis. Journal of Industry, Competition and Trade, 23, 1-32.
[14] Goerke, L. (2022). Partisan competition authorities, Cournot-oligopoly, and endogenous
market structure. Southern Economic Journal, 89(1), 238-270.
[15] Goldberg, P. K. (1995). Product diﬀerentiation and oligopoly in international markets: Thecase of the US automobile industry. Econometrica, 63(4), 891-951.
[16] Goldberg, P. K. and M. M. Knetter (1999). Measuring the intensity of competition in export
markets. Journal of International Economics, 47(1), 27-60.
[17] Grossmann, V. (2007). Firm size and diversiﬁcation: Multiproduct ﬁrms in asymmetricoligopoly. International Journal of Industrial Organization, 25(1), 51-67.
[18] Head, K. and Spencer, B. J. (2017). Oligopoly in international trade: Rise, fall and resurgence. Canadian Journal of Economics, 50(5), 1414-1444.
[19] Helpman, E. and O. Itskhoki (2010). Labour market rigidities, trade and unemployment.
The Review of Economic Studies, 77(3), 1100-1137.
[20] Helpman, E., O. Itskhoki, and S. Redding (2010). Inequality and unemployment in a global
economy. Econometrica, 78(4), 1239-1283.
[21] Impullitti, G., O. Licandro, and P. Rendahl (2022). Technology, market structure and thegains from trade. Journal of International Economics, 135, 103557.
26

[22] Kabiraj, T. and S. Marjit (2003). Protecting consumers through protection: The role oftariﬀ-induced technology transfer. European Economic Review, 47(1), 113-124.
[23] Kawasaki, A., T. Mizuno, and K. Takauchi (2023). Downstream new product development
and upstream process innovation. Journal of Economics, 140(3), 209-231.
[24] Kee, H. L. (2002). Markup, returns to scale, and productivity: A case study of Singapore’s
manufacturing sector. Policy Research Working Paper 2857, The World Bank (June 2002).
[25] Kim, H. and H. Lee (2017). Does the traditional exchange rate fully explain ﬁrms’ exposure?
Applied Economics Letters, 24(1), 8-13.
[26] Long, N. V., H. Raﬀ, and F. Stähler (2011). Innovation and trade with heterogeneous ﬁrms.
Journal of International Economics, 84(2), 149-159.
[27] Marjit, S. and A. Mukherjee (2015). Endogenous market structure, trade cost reduction,
and welfare. Journal of Institutional and Theoretical Economics, 171(3), 493-511.
[28] Melitz, M. J. (2003). The impact of trade on intra-industry reallocations and aggregate
industry productivity. Econometrica, 71(6), 1695-1725.
[29] Melitz, M. J. and G. I. Ottaviano (2008). Market size, trade, and productivity. Review of
Economic Studies, 75(1), 295-316.
[30] Mizuno, T. and K. Takauchi (2018). Rules of origin and uncertain compliance cost. AsiaPaciﬁc Journal of Accounting & Economics, 25(5), 515-532.
[31] Mizuno, T. and K. Takauchi (2020). Optimal export policy with upstream price competition.
The Manchester School, 88(2), 324-348.
[32] Mizuno, T. and K. Takauchi (2024). Bertrand competition in vertically related markets.
Applied Economics Letters, 31(6), 524-529.

27

[33] Mukherjee, A. (2014). Licensing under convex costs. Journal of Economics, 111(3), 289-299.
[34] Mukherjee, A. (2024). Cooperative R&D for a new product under convex production costs.
forthcoming in Journal of Institutional and Theoretical Economics.
[35] Mukherjee, A. and U. B. Sinha (2019). Export cartel and consumer welfare. Review ofInternational Economics, 27(1), 91-105.
[36] Neary, J. P. (2003a). Globalization and market structure. Journal of the European Economic
Association, 1(2-3), 245-271.
[37] Neary, J. P. (2003b). The road less travelled: Oligopoly and competition policy in generalequilibrium. in Arnott, R., B. Greenwald, R. Kanbur and B. Nalebuﬀ (eds.) Economics for
an Imperfect World: Essays in Honor of Joseph E. Stiglitz, Cambridge, MA, MIT Press,
485-500.
[38] Takauchi, K. and Mizuno, T. (2020). Consumer-beneﬁting transport cost: The role ofproduct innovation in a vertical structure. Graduate School of Economics, Kobe University,
Discussion Paper No. 2017.
[39] Takauchi, K. and Mizuno, T. (2022). Endogenous transport price, R&D spillovers, andtrade. The World Economy, 45(5), 1477-1500.
[40] Van Biesebroeck, J., E. Yu, and S. Chen (2015). The impact of trade promotion services
on Canadian exporter performance. Canadian Journal of Economics, 48(4), 1481-1512.
[41] Viscusi, W. K., J. E. Harrington Jr., and D. E. Sappington (2018). Economics of Regulation
and Antitrust, MIT press.
[42] von Weizsäcker, C. C. (1980). A welfare analysis of barriers to entry. The Bell Journal of
Economics, 11(2), 399-420.

28

[43] Xu, K., R. Windle, C. Grimm, and T. Corsi (1994). Re-evaluating returns to scale intransport. Journal of Transport Economics and Policy, 28(3), 275-286.
[44] Zhang, W. and C. Y. C. L. Lawell (2017). Market power in nonrenewable resource markets:
An empirical dynamic model. Land Economics, 93(1), 74-86.

29

Online Appendix of“Strategic export decisions in international trade”(Not for Publication)by Kazuhiro Takauchi, Tomomichi Mizuno, and Katsufumi Fukuda

I. Trade Patterns with γ
In the body of the paper, for simplicity of the analysis, we normalize γ (coeﬃcient of thequadratic cost function of ﬁrms) to unity. As mentioned in the paper, this normalization does
not change our result; we only illustrate the equilibrium of the model with γ here.
To ensure positive quantities, we ﬁrst assume the following.
Assumption A1. t <

a
.
γ+2

A similar computation as in the body of the paper yields the following equilibrium outcomes.
4a(γ + 1)(a − t) + (γ + 2)(4γ + 5)t2
, i = H, F,
2(2γ + 3)2[a(4γ + 2) + (γ + 2)t]2
ED
(γ)
=
Π
(γ)
=
,
ΠDE
H
F
2(γ + 2)(4γ + 3)2
a2 [4γ(4γ + 7) + 13] − 8a(γ + 1)(γ + 2)t + 4(γ + 1)(γ + 2)2 t2
ED
(γ)
=
Π
(γ)
=
,
ΠDE
F
H
2(γ + 2)(4γ + 3)2
a2
.
(γ) =
ΠDD
i
2(γ + 2)
ΠEEi (γ) =

(A01)
(A02)
(A03)
(A04)

From (A01)–(A04), we obtain the following.
DE[ΠEE
H (γ) − k] − ΠH (γ)
2(−a+γt+2t) −8aγ 3 −25aγ 2 −27aγ−9a+16γ 4 t+75γ 3 t+122γ 2 t+81γt+18t−k.
=(γ + 2)(2γ + 3)2 (4γ + 3)2



(A05)

≡ϕD (γ)DE
Note that ϕD (γ) ≡ ΠEE
H (γ) − ΠH (γ).

DD
[ΠED
H (γ) − k] − ΠH (γ) =2(γ + 1)(a − γt − 2t)2−k.
(γ + 2)(4γ + 3)2
≡ϕE (γ)

i

(A06)

DD
Note that ϕE (γ) ≡ ΠED
H (γ) − ΠH (γ).

Thus, we obtain the best response of ﬁrm i from (A05) and (A06).
• Suppose that the rival (ﬁrm j, j = i) chooses E. Then,ϕD (γ) ≤ k ⇒ ﬁrm i chooses D;
ϕD (γ) > k ⇒ ﬁrm i chooses E.
• Suppose that the rival (ﬁrm j, j = i) chooses D. Then,ϕE (γ) ≥ k ⇒ ﬁrm i chooses E;
ϕE (γ) < k ⇒ ﬁrm i chooses D.
By taking the diﬀerence between ϕE (γ) and ϕD (γ), we ﬁnd the following.
Case I.

t≤a(4γ 2 + 9γ + 6)
3(γ + 1)(γ + 2)(4γ + 5)

⇒ ϕE (γ) ≥ ϕD (γ).
(A07)

Case II. t >a(4γ 2 + 9γ + 6)
3(γ + 1)(γ + 2)(4γ + 5)

⇒ ϕE (γ) < ϕD (γ).

From the above arguments and (A07), we establish the following result.
Proposition A1.
2

a(4γ +9γ+6). Then, ϕE (γ) ≥ ϕD (γ).
I. Suppose t ≤ 3(γ+1)(γ+2)(4γ+5)(i) If k < ϕD (γ), EE appears. (ii) If ϕD (γ) ≤ k ≤ ϕD (γ), ED&DE can appear. (iii) If
ϕE (γ) < k, DD appears.
2a(4γ +9γ+6). Then, ϕE (γ) < ϕD (γ).
II. Suppose t > 3(γ+1)(γ+2)(4γ+5)(i) If k < ϕE (γ), EE appears. (ii) If ϕE (γ) ≤ k ≤ ϕD (γ), EE&DD can appear. (iii) If
ϕD (γ) < k, DD appears.

iiII. Diﬀerentiated Price Competition
i. Equilibrium Output and Price in Each Regime
In this part, we present the equilibrium output and price of ﬁrms.
To ensure positive quantities, here, we set the following assumption.
Assumption A2.

6 − 3b − 2b2t<.
a3(3 − b2 )

 In a “two-way trade” situation (i.e., the EE regime), the equilibrium outputs of ﬁrms areq̄iiEE∗ =a(1 − b)(b + 2) + (b + 1)ta(1 − b)(b + 2) − (3 − b2 )t
EE∗
;
q̄
.
=
ij
(b − 1)(b + 2) (b2 − b − 4)(b − 1)(b + 2) (b2 − b − 4)

The equilibrium prices are
p̄EE∗
=
ii

a(b + 2)(b2 − 3) − (b2 + b − 1)ta(b + 2)(b2 − 3) − (2b + 3)t
EE∗
;
p̄
.
=
ij
(b + 2)(b2 − b − 4)(b + 2)(b2 − b − 4)

 In a “one-way trade” situation (i.e., both DE and ED regimes), the equilibrium outputs ofﬁrms area(−b − 2)(3b − 4) + 3bt
a(−2b2 − 3b + 6) + 3(b2 − 3)t
DE∗
ED∗
;
q̄
,
=
q̄
=
FH
HF
3b4 − 20b2 + 24
3b4 − 20b2 + 24a(b − 2)(b + 1)(b2 + b − 3) − (b2 − 3)tED∗q̄FDE∗
.
=
q̄
=
F
HH
3b4 − 20b2 + 24
DE∗q̄HH
= q̄FED∗F =The equilibrium prices of ﬁrms are(b2 − 2)[a(b + 2)(3b − 4) − 3bt],
3b4 − 20b2 + 24a(2b4 − 14b2 − b + 18) + (b2 − 3)t
ED∗
p̄DE∗
,
=
p̄
=
FF
HH
3b4 − 20b2 + 24a(3b4 + 3b3 − 16b2 − 5b + 18) + (9 − 6b2 )t
ED∗
p̄DE∗
.
F H = p̄HF =3b4 − 20b2 + 24

ED∗
p̄DE∗
HH = p̄F F = In a “no trade” situation (i.e., the DD regime), the equilibrium output of ﬁrms is q̄iiDD∗ =a/3 = qiiDD∗ . (See equation (1) on page 8 of the body of the paper.)= (2a)/3.
The equilibrium price of ﬁrms is p̄DD∗
ii

iii

ii. Derivation of BD > BE
Both BD and BE have a strictly positive value. The diﬀerence between BD and BE is given by
BE − BD =a2 bJ16(b − 1)(b + 2)2 (b2 − b − 4)2 (3b4 − 20b2 + 24)2
abJ2 t+6(b − 1)(b + 2)2 (b2 − b − 4)2 (3b4 − 20b2 + 24)2bJ3 t2+< 0.
6(b − 1)(b + 2)2 (b2 − b − 4)2 (3b4 − 20b2 + 24)2Here,J1 ≡ 30b12 + 102b11 − 319b10 − 1123b9 + 1537b8 + 4421b7 − 6216b6 − 9568b5+ 15728b4 + 11536b3 − 19584b2 − 5760b + 9216,
J2 ≡ − 36b12 − 36b11 + 480b10 − 6b9 − 3498b8 + 2658b7 + 17898b6 − 9948b5− 48840b4 + 11376b3 + 61056b2 − 3456b − 27648,
J3 ≡ 27b10 + 297b9 − 3b8 − 3603b7 − 2679b6 + 15237b5 + 14760b4 − 27972b3− 30240b2 + 18144b + 20736.
As long as Assumption A2 holds, BD > BE .

iv