DP2024-21

Strategic Export Decisions inInternational Trade
K a z u h i r o TA K AU C H I
To m o m i c h i M I Z U N O
K a t s u f u m i F U K U DA

July 8, 2024

Strategic export decisions in international trade∗
Kazuhiro Takauchi†‡Tomomichi Mizuno§

Katsufumi Fukuda¶

July 7, 2024
Abstract
The type of marginal cost faced by a firm is important when considering the firm’s export
behavior. However, in the literature, it is frequently assumed that firms have constantmarginal costs. By contrast, this paper considers the case in which a firm’s marginal
cost is increasing, and the firm pays a fixed cost when it exports. We show that an
asymmetric trade pattern, whereby one country exports but the other does not, appears
in a symmetric two-country two-firm setting. We also show that trade liberalization
produces a non-monotonic change in welfare because of reduced transport costs.
Key words: Increasing marginal cost; Fixed export cost; Transport cost; Trade pattern
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
School of Economics, Kobe University, Kobe, Japan. An earlier version of this paper was presented at the13th Spring Meeting of The Japan Society of International Economics on June 1, 2024. We specially thankTaiji Furusawa and the seminar participants for their useful comments. We also thank Hajime Sugeta andNoriaki Matsushima for their many constructive comments. The usual disclaimer applies. This study is
supported by JSPS KAKENHI (Grant Number 24K04904). We thank 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.: +81-6-63681817; Fax: +81-6-6339-7704.
‡
Research Fellow, Graduate School of Economics, Kobe University, 2-1 Rokkodai-cho, Nada-ku, KobeCity, 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.
§ RIEB(Research Institute for Economics and Business Administaration), Kobe University, 2-1 Rokkodai-cho,Nada-ku, Kobe-City, Hyogo 657-8501, Japan.

11Introduction

In a framework of oligopolistic intra-industry trade, that is, the Brander and Krugman (1983)-type two-way trade model, it is frequently assumed that firms have constantmarginal costs. This assumption of “constant marginal cost” is significant in simplifying
the analysis, and hence the results, of firms’ behavior and the welfare consequences. However, by assuming constant marginal costs, a significant problem tends to be overlooked,
namely the “realizing trade pattern”. This is because, if oligopolistic firms can choose
whether to export or not, the firms’ cost structure aﬀects the interaction between markets,
which can markedly alter the realizing trade pattern.
In this paper, we consider a two-way oligopolistic trade model in which a fixed cost isnecessary for a firm to export. We incorporate Melitz (2003)-type firm options regarding“whether to export or not” into an oligopolistic competition scenario. Then, we consider
what size transport and fixed export costs result in unilateral entry to the foreign market
in response to the export decision or a bidirectional entry to the foreign market. In
this environment, a firm’s marginal cost has a key role. We assume that firms haveincreasing marginal costs. Based on this cost structure, we demonstrate that the following
unprecedented trade pattern appears in the equilibrium state. [a] When the transport costis large and the 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 thetransport 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.
We built an oligopoly model of the Brander and Krugman (1983) type, consistingof two symmetric countries and two firms. Each firm has two options: export to the2foreign market and/or supply the local domestic market. If a firm exports, it pays not
only transport costs but also a fixed export cost. The firm only supplies the domestic
market if it does not export. Each firm has a quadratic cost function, and first chooses
whether to export, and subsequently decides on quantities.1 In this situation, two kindsof multiple equilibria appear when the transport cost and the fixed export cost are atintermediate levels. [a] When the transport cost is large and the fixed export cost is small,an asymmetric equilibrium in which only one country exports (i.e., “One-way trade”)
appears. There are positive and negative eﬀects when firms export. The positive eﬀect is“obtaining foreign market share” and the negative eﬀect is “an increase in the marginal
cost of domestic supply”. When the rival firm chooses not to export, the positive eﬀect isstrong because the fixed export cost is small. Thus, each firm has an incentive to choose
to export. When the rival firm chooses to export, the import barriers become higher andthe positive eﬀect becomes weaker. Thus, each firm no longer has an incentive to choose
to export. When the rival firm does not export, the positive eﬀect is dominant because
each firm’s local market is non-competitive and a new market can be enjoyed by choosing
to export. Hence, each firm exports.
[b] When transport cost is small and the fixed export cost is large, multiple equilibria
involving “No trade” and “Two-way trade” appear. When the rival firm exports, the lowtransport cost means that the positive eﬀect is dominant, so each firm chooses to export.
When the rival firm does not export, the large fixed export cost allows each firm to enjoy
a local monopoly. In this case, the negative eﬀect is relatively strong, and hence, eachfirm chooses not to export.2
1

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

2

If the firms’ marginal production costs are constant, multiple equilibria cannot appear because the3In addition, we show that trade liberalization with a reduction in the transport cost
can significantly 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, the trade pattern can switch from “No trade” to “One-way trade.” Thatis, 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.
We also show that trade liberalization can produce non-monotonic fluctuations in
welfare. In general, in the Brander and Krugman (1983)-type model, welfare is U-shapedwith respect to the transport cost. Hence, the area in which trade liberalization occurs
suﬀers from reduced welfare. In contrast, changes in the trade pattern create gaps inwelfare, and so trade liberalization may reduce welfare multiple times. Even if welfare
rises following trade liberalization, practitioners should pay special attention to further
trade liberalization.
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 price competition, because the rivalry among firms increases compared with quantity
competition, the equilibrium 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
strategic interactions between firms does not occur. Hence, trade patterns are “both countries export”
or “both countries do not export.”4

according to the size of 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 ensurethat 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 thanan exporting country if the fixed export cost is relatively large. This result oﬀers a newperspective to practitioners, who tend to emphasize export promotion and exports offirms.3 Thus, our result oﬀers a unique policy 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
and Rodrı́guez-Clare, 2013; Melitz and Ottaviano, 2008; and Long et al., 2011). To
address firm heterogeneity, Melitz (2003) incorporated a productivity distribution into astandard monopolistic competition model, and showed that eﬃcient firms both export
and sell domestically, whereas less-eﬃcient firms only operate in the domestic market.
This model is extended to asymmetric two-country models and is related to our paper.
Demidova and Rodrı́guez-Clare (2013) conducted a welfare analysis using a Melitz-typemodel.4 They demonstrated that trade liberalization for the home country raises thecountry’s welfare. Melitz and Ottaviano (2008) constructed a model with an endogenous
markup rate.
These studies are central and significant to the literature focusing on a monopolisti3

In fact, Van Biesebroeck et al. (2015) point out that export promotion programs are often observed.

4

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 sharefor the own country’s products in the open economy.

5

cally competitive trade model with firm heterogeneity. However, as they are all based onmonopolistic competition they do not analyze strategic interaction among firms. Therefore, the analyses do not consider all possible trade patterns that occur according to thesize of the transport and fixed costs.
To consider the relationship between firm process innovation (cost-reducing R&D activity) and trade liberalization, Long et al. (2011) incorporated Melitz-type firm exporting
behavior into an oligopolistic competition model.5 However, the main purpose of Longet al. (2011) was to examine the eﬀects of trade liberalization on R&D investment andhence, the firms’ strategic choice regarding whether to export and the decision of tradepattern 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;
and Kawasaki et al., 2023). In our model, firms consider whether to become an exporter.
This situation 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
product development, 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 thenumber 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
5

Impullitti et al. (2022) considered heterogeneous oligopolistic competition and R&D in a generalequilibrium framework. Furthermore, Edmond et al. (2015) presented a general equilibrium model inwhich intermediate-good producers compete in Cournot fashion.

6

model and Section 3 examines the trade patterns that arise. Section 4 presents thewelfare considerations. Section 5 discusses the case of diﬀerentiated goods and considers
the scenario in which firms have constant marginal costs. 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 ),and each 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 notexport, 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 market, firms must pay a per unit transport cost t ≥ 0.
We assume that the firms have a quadratic cost function:6 (γ/2) q 2 , where γ > 0 is the
production eﬃciency of firms and q is a quantity. According to the decisions made by thefirms, four trade patterns appear. 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,
6

The production technology for manufacturing often involves decreasing returns to scale. Basu andFernald (1997) found that a typical industry has decreasing returns to scale based on aggregate data of
34 manufacturing industries in the US. In addition, Xu et al (1994), among others, found that decreasing
returns to scale can be observed in the transportation sector. Furthermore, a quadratic cost function isfrequently adopted in theoretical studies of oligopoly. See, for example, Dastidar (1995), Delbono andLambertini (2016), Goerke (2022), Mizuno and Takauchi (2020, 2024), Mukherjee (2014, 2024), Takauchi
and Mizuno (2022), and von Weizsäcker (1980).

7

i, j = H, F , where pi is the product price, qii is the domestic supply of firm i, and qji isthe export of firm j (or the imports of country i from country j). The inverse demand ofcountry 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 in country 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 − γ2 (qii + qij )2 for i ̸= j, i, j = H, F .
When only firm i (̸= j) chooses D, its profit is: Πi ≡ (a − qii − qji )qii − γ2 (qii )2 fori ̸= j, i, j = H, F . When only firm i (̸= j) chooses E, its profit without k is: Πi ≡(a − qii )qii + (a − qjj − qij − t)qij − γ2 (qii + qij )2 for i ̸= j, i, j = H, F .
When all firms choose D, there is no trade. Then, firm i’s profit is: Πi ≡ (a − qii )qii −γ(q )2 for i = H, F .
2 ii

For simplicity, hereafter, we normalize γ at unity, i.e., γ = 1. This normalization does
not alter our main results. In the Online Appendix, we illustrate the equilibrium of ourmodel with 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 homogeneousquantity competition. The solution concept is the sub-game perfect Nash equilibrium.
The game is solved by backward induction.

8

3

Trade Patterns

In the second stage of the game, each firm i (i = H, F ) competes in Cournot fashion.
By solving the first-order conditions (FOCs) for the profit maximization of firms in eachregime, we obtain the following outputs:
a + 2ta − 3ta; qijEE∗ =; qiiDD∗ = ,553
a − 3t2a + t
ED∗
ED∗
DE∗
ED∗
qFDE∗
=
,
qHH
= qFDE∗= qHF
H =F = qHH = qF F ;7
7
where “∗” is an equilibrium value.
qiiEE∗ =(1)

To ensure a positive quantity, we set Assumption 1.
Assumption 1. t/a < 1/3.
Equation (1) yields the firms’ equilibrium profit without k:a2
8a2 − 8at + 27t2
; ΠDD∗,=i50
619a2 − 16at + 24t2
3(2a + t)2
DE∗
ED∗
ED∗
;
Π
=
Π
=
.
ΠDE∗
=
Π
=
F
H
H
F
98
98
ΠEE∗
=
i

(2)

From equation (2), we obtain Lemma 1.
Lemma 1. (i) Suppose that rival (firm j) chooses E. If φD ≡ 2(23a−104t)(a−3t)>(≤) k/a2 ,12252>(≤) k/a2 , firm
firm i chooses E (D). (ii) Suppose that rival chooses D. If φE ≡ 4(a−3t)
147
i chooses E (D).
Proof. φD ≡ ΠEE∗
− ΠDE∗= ΠEE∗− ΠED∗= 2(23a−104t)(a−3t)
and φE ≡ ΠED∗
− ΠDD∗
=
H
H
H
H
F
F
1225
2

. Q.E.D.
ΠDE∗− ΠDD∗= 4(a−3t)
F
F
147
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.
9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.
k/a2

DD & EE
0.035

DD

0.030
0.025
0.020

φE

0.015
0.010

DE & ED
0.005

0.00

EE
0.05

0.10

0.15

0.20

0.25

0.30

t
a

Figure 1: Four areas

The equilibrium trade pattern depends on the sizes of both the transport cost t and thefixed export cost k. (See Figure 1.) Independent of the rival’s strategy, firm i exports if k
is small and does not export if k is large. Whether the rival exports or not is dependent of
the thresholds φD and φE to which firms are indiﬀerent between choosing E and choosing
D.
To consider the mechanism of Proposition 1, let us explain why (i) φD > φE for t = 0
and (ii) ∂φD /∂t < ∂φE /∂t < 0. We first consider the case where φE (≡ ΠED∗
− ΠDD∗=iH
ΠDE∗− ΠDD∗) = k/a2 . In this case, the rival chooses D. There are positive and negativeiF
eﬀects when firms export. The positive eﬀect is “obtaining foreign market share”. The
negative eﬀect is “an increase in the marginal cost of domestic supply”. If φE = k/a2 ,the positive and negative eﬀects are equal.
10Suppose that the rival switches its strategy from D to E. It is then easier for each firm
to obtain the foreign market share required to start exporting. This is because the rival’s
marginal cost increases, so the competition in the destination market becomes weaker.
This raises the benefit of exporting. Further, the eﬀects of “an increase in the marginal
cost of domestic supply” become weak. This is because the rival is already exporting
before firm i begins to export, so the domestic supply is small and the profit reduction
caused by an increase in the firm’s marginal cost eases. This illustrates the benefit of firm
i exporting. From these two factors, when “φE = k/a2 for t = 0”, firm i has a greater
incentive to export in the case where the rival chooses E compared with the case where
the rival chooses D. Hence, firm i chooses E. This implies that when the rival chooses E,
the value of k at which firm i is indiﬀerent between E and D (i.e., k/a2 = φD ) is greaterthan k/a2 = φE .
We now show that (ii) “∂φD /∂t < ∂φE /∂t < 0”. Note that exports decrease as tincreases. We first consider the slope of φD . When the rival chooses E, a rise in t weakens
the eﬀects of “obtaining the foreign market”. Furthermore, the local firm’s domestic
supply increases because of the reduction in the exports of the foreign rival, so the eﬀectof the increased marginal cost in the domestic supply by starting to export becomesstronger. These eﬀects combine to reduce the benefit of exporting. Hence, if t rises in
the case where the rival chooses E, a significant decrease in k is required to make firm iindiﬀerent between choosing E and choosing D.
We next consider the slope of φE . If the rival chooses D, its exports are zero and the
expansion in domestic supply caused by a rise in t partly disappears. Hence, the reduction
in export benefit that appears when the rival chooses E becomes weaker. When t rises inthis situation, it is not necessary for a significant reduction in k to make firm i indiﬀerent
11between choosing E and choosing D.
From the above arguments, “φD > φE for t = 0”. Because “∂φD /∂t < ∂φE /∂t < 0”,
φD = φE holds at a certain level of t. If t exceeds this level, φD < φE holds.
As a result, within some range where the value of t is small, “strategic complementary
equilibrium” (i.e., [b] “No trade” and “Two-way trade”) appears if k is of intermediate
magnitude. By contrast, within some range where the value of t is large, “strategic substitutes equilibrium” (i.e., [a] “One-way trade”) appears if k is of intermediate magnitude.7
We showed that, in a symmetric two-country model, depending on the transport andfixed export costs, “all possible trade patterns” appear. This is our contribution. Overall,
it is significant that “One-way trade” (asymmetry) occurs from a symmetric two-country
scenario (symmetry). In general, studies based on Brander and Krugman’s (1983) model
frequently assume that firms have constant marginal costs. However, under this assumption of constant marginal costs, asymmetric results cannot occur from a symmetric twocountry setting. Hence, when we consider the trade pattern, we must pay special attention
to the production technology of firms. Our analysis indicates this point. Thus, we believethat our results make a significant contribution to the literature.

7

It is well-known that some firms will continue exporting but others will stop exporting and behave

inside the country. In reality, for example, Onkelinx et al. (2016) report that many Belgian small andmedium-sized enterprises (SMEs) stopped exporting and continued activities domestically. “More thanhalf (2,786 or 53%) of the 5,283 SMEs that were exporting in 1998 had stopped exporting by 2008. ...Theremaining 1,866 firms are still active in the domestic market.” (Onkelinx et al., 2016, p. 54.) In Estonia,
a similar situation is found by Vissak and Masso (2015).

12

4Welfare Considerations

As illustrated in Figure 1, the welfare in each country can vary drastically because thesize of transport cost t alters the trade pattern. Therefore, we now consider the eﬀects ofa change in the transport cost on the welfare in each country.

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., a reduction in the transport cost t) aﬀects the consumer surplus.
From equation (1), the consumer surplus in each equilibrium regime is:
CSiEE∗ =a2(3a − 2t)2
(2a + t)2
(2a − t)2
DE∗
ED∗
; CSiDD∗ = ; CSH
=
; CSH
=
,
50
18
98
98

(3)

ED∗
DE∗
= CSFDE∗ .
= CSFED∗ and CSH
where CSH

Equation (3) and Proposition 1 yield Proposition 2.
Proposition 2. Suppose that k/a2 < 25/2187. Then, trade liberalization involving a reduction in the transport cost, t, may suddenly lower the consumer surplus of the exporting
country.

DE∗>
Proof. First, DE&ED can appear if k/a2 < 25/2187. Second, ∀t/a < 1/3, CSH
ED∗
CSiEE∗ > CSiDD∗ > CSH. Hence, ∀k/a2 < 25/2187, consumer surplus can drop if t

decreases. Q.E.D.
Proposition 2 can be explained by ranking consumer surplus. (Figure 2 illustrates therelationship between consumer surplus and the transport cost.) In the regime in which
only the foreign firm exports, the marginal cost of the home firm is small because it does
13

0.09
0.08

CSEE*
/a2
i
2
CSDE*
H /a

0.07
0.06

CSDD*
/a2
i

0.05
0.04
0.00

2
CSED*
H /a

t/a
0.05

0.10

0.15

0.20

0.25

0.30

Figure 2: Eﬀect of trade liberalization on consumer surplus (k = 0.005)

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 costis 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 noimports, the aggregate output in this regime is smaller than that 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 2 have important implications. As illustrated in Figure 2,
trade liberalization with a reduction of transport costs can suddenly lower the consumer

14

surplus in the exporting country. The reason is that the trade pattern switches from “Notrade” to “One-way trade” (where the home country exports, and the foreign country
does not) through the reduction in the transport cost. This switching in the trade patternmakes the home country’s total output equal to firm H’s domestic supply only (given thehome 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, 2022).8 Marjit and Mukherjee (2015) and Takauchi and Mizuno (2022) indicated that a reduction of 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 situation of technology licensing, an increase in the tariﬀ ratein the country receiving the technology licensing causes a technology licensing from thesuperior foreign firm, which leads to a sudden rise in consumer surplus.9 Hence, a decreasein 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 the conclusions 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
8

Moreover, although they focus on diﬀerent situations, studies have examined international trade andconsumer welfare. Mukherjee and Sinha (2019) showed that an export cartel between exporting firms canincrease 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.
9

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.

15

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.,10 believea 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 havestrong incentives to pressure their governments to avoid a non-negligible reduction in the
consumer surplus. Therefore, a meaningful policy implication of our study is that the
government may need to pay particular attention to the eﬀects of the trade liberalization.

4.2

Total Surplus

We show that trade liberalization may decrease total surplus. Total surplus in each regime
is as follows:2(3a2 − 3at + 7t2 )2a2− k; T SiDD∗ =,25
93a2 + t2
23a2 − 12at + 25t2
DE∗ED∗
− k; T SH= T SFED∗ =.
T SH= T SFDE∗ =98
14
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 thetotal surplus of the non-exporting country. (ii-b) Without changing the trade regime, thetotal surplus of 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
10

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

16

as a function of transport costs in the figures below. In Figure 3, 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 4.

0.230
0.225

TSEE*
/a2
i

TSDD*
/a2
i

0.220
2
TSDE*
H /a

0.215

2
TSED*
H /a

0.05

0.10

0.15

t/a
0.20

Figure 3: Eﬀect of trade liberalization on total surplus (k/a2 = 0.008)

Figure 4 illustrates the total surpluses of the exporting country under the EE andED&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 4, the shaded areas represent the case in which tradeliberalization has a negative impact on total surplus. Figure 4 illustrates a significant
policy implication. In our model, unlike that of Brander and Krugman (1983), there are
two areas in which trade liberalization reduces welfare. Hence, if a policymaker considers
the increase in national welfare generated by trade liberalization and further proceeds withthe trade liberalization, the national welfare may fall. This implies that a trap related to
trade liberalization can appear.
The intuition behind Proposition 3 is as follows: As trade liberalization (a decrease int) progresses, the exporting firm’s supply shifts from the domestic market to foreign markets. As a result, the domestic firm’s profit increases and the domestic consumer surplus
decreases. Which of these eﬀects is larger determines whether total surplus increases. If t

17

0.240
0.235
0.230
0.225

TSEE*
/a2
i

0.220
0.215
0.00 0.05 0.10 0.15 0.20 0.25 0.30
t/aFigure 4: Welfare decreasing trade liberalization (k/a2 = 0)

is large, the supply to the foreign market is small and the supply to the domestic market
is large. In this case, a decrease in t significantly changes the supply to the domestic
market such that the dominant eﬀect of trade liberalization is the reduction in consumer
surplus. Thus, in each regime, trade liberalization reduces the aggregate surplus in theregion 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 profit-decreasing eﬀect dominates; hence, the total surplus of the nonexporting country decreases with trade liberalization: (ii-a) in Proposition 3.
Next, the same intuition applies when a decrease in t changes the trade regime. Whena slight decrease in t changes the trade regime, the profit of the firm that begins toexport changes little. However, the total surplus of the country in which firms begin toexport falls because the supply to that country is significantly reduced. Furthermore,because trade liberalization intensifies competition among firms, the profits of the firms

18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∗
DE∗
Comparing T SH
with T SH, we establish Proposition 4.

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

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 1).
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 the foreign rival raise the aggregate outputs, so the product price falls.
Then, the consumer surplus increases. If the fixed export cost is large, the dominanteﬀect 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 candecide 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 emphasizethat firms should choose to export. Thus, our welfare analysis oﬀers a new insight into
the context of international trade.
19

5Discussions

5.1

Trade Patterns in Diﬀerentiated Products

Here, we consider how the equilibrium trade pattern is aﬀected by diﬀerentiated quantityand price competition.

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 theprevious section, we obtain the following the equilibrium firms’ profits without k.11
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 )2

a2 (b4 − 8b2 − 32b + 96) − 48a(2 − b)t + 72t2
ED∗,
πH
= πFDE∗ =2 2(4)6(8 − b )where πiDD∗ = a2 /6 = ΠiDD∗ in the DD regime. (See equation (2).)
From equation (4), the diﬀerence in profits without k is given by:

EE∗
DE∗
∆E ≡ πH− πH= πFEE∗ − πFED∗ > 0, 

ED∗
DD∗
∆D ≡ πH− πH= πFDE∗ − πFDD∗ > 0.




(5)

From equation (5), we establish Proposition 5.
Proposition 5. I. Suppose that τ < τδ (b). Then, ∆D < ∆E . (i) If k < ∆D , EE occurs.
(ii) If ∆D ≤ k ≤ ∆E , EE&DD can emerge. (iii) If ∆E < k, DD occurs.
II. Suppose that τ > τδ (b). Then, ∆E < ∆D . (i) If k < ∆E , EE occurs. (ii) If ∆E ≤ k ≤11

To ensure positive quantities, in this part we assume that τ ≡ t/a < τmax ≡ (2 − b)/3.

20

2

3

+3b )
∆D , DE&ED can occur. (iii) If ∆D < k, DD emerges. Here, τδ (b) ≡ (2−b)(64−40b−8b.
3(8+b2 )(8−b−b2 )Proof. See the Appendix.
Because the two threshold curves ∆E and ∆D intersect, the result of Proposition 5 isessentially the same as that of Proposition 1.

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.
2
1−b
1 − b2

Here, note that b ∈ [0, 1) again.
In the ED regime, the demand functions are:qHH = a − pHH ; qHF =(1 − b)a − pF F + bpHF
(1 − b)a − pHF + bpF F
;
q
=
.
F
F
1 − b2
1 − b2In the DE regime, the demand functions are:qHH =(1 − b)a − pF H + bpHH
(1 − b)a − pHH + bpF H; 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)2(3 − 2b2 ) [a(b + 2)(3b − 4) − 3bt]2DE∗ED∗
π̄H = π̄F =,42
22(3b − 20b + 24)

12

The equilibrium outputs and prices are reported in the Online Appendix.

21

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 = ΠiDD∗ .
The above profits without the fixed export cost k yield the following:

DE∗
EE∗
= π̄FEE∗ − π̄FED∗ > 0, 
− π̄HBD ≡ π̄H




DD∗
ED∗
− π̄H
= π̄FDE∗ − π̄FDD∗ > 0.
BE ≡ π̄H(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.
The market competition becomes keener because the competition mode changes fromquantity to price. The two threshold curves BD and BE do not intersect because of thistougher competition between firms (i.e., BD > BE ). Consequently, only the multiple
equilibria comprising “No trade” and “Two-way trade” emerge.

5.2

Constant Marginal Cost

To compare the case of a quadratic cost function, we consider the scenario in which firms
have the cost function cq, where c ≥ 0; a > c, and q is a quantity. Note that c is aconstant marginal cost. All other conditions are the same as in the previous section. If
each firm has a constant marginal cost c, because the threshold is equivalent, there is only
13

The derivation of BD > BE is reported in the Online Appendix.

22

one threshold curve. That is,Π̂DE∗− (Π̂EE∗− k) = −Hi(a − c − 2t)2
+ k = Π̂DD∗− (Π̂ED∗
− k),
H
i
9

where Π̂DE∗= Π̂FED∗ and Π̂ED∗= Π̂DE∗. Here, “ ˆ ” denotes the case in which each firm’sH
HF
cost function is cq. There is only one threshold curve in the plane of the transportation cost
and the fixed export cost. Therefore, because no multiple equilibria exist, the equilibrium
is EE or DD. See Figure 5.
k/(a-c)2

0.15

DD

0.10

0.05

EE
t/(a-c)
0.0

0.1

0.2

0.3

0.4

Figure 5: Trade patterns of constant marginal cost (a − c = 1)

6

Conclusion

This paper constructed a symmetric two-country two-firm homogenous Cournot trademodel to examine the eﬀect of the technology employed by firms, that is, the role of anincreasing marginal cost faced by the firms, on realizable trade patterns. In our setting,when firms choose to export, they must pay not only the transport cost, but also a fixedexport cost.
Our main findings are summarized as follows: (i) The firms’ exporting choices and23

trade patterns largely depend on the marginal costs of the firms. When the sizes of bothtransport 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, that is, only one country becomes an exporter, creating“One-way trade.” The other is based on strategic complements, and so causes both “Notrade” and “Two-way trade.” These multiple equilibria do not appear when the firms
have constant marginal costs. (See section 5.2.) (ii) Trade liberalization, that is, a reduction in transport costs, changes consumer surplus and total surplus nonmonotonically anddiscontinuously 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 quantityand price competition. 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 findthat trade liberalization may lower consumer surplus and total surplus as a result of thechanges in trade patterns. Although practitioners tend to believe trade liberalization
always increases welfare, we caution that this may not always be the case.

Appendix24

Proof of Proposition 3.

We distinguish two scenarios in which trade liberalization re-duces total surplus: (i) trade liberalization with a changing trade regime and (ii) tradeliberalization 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 :
(

)
( DD∗
)
EE∗
T SiDD∗ −T SiEE∗ k=φ a2 = 2(a−3t)(109a+93t)
>0;
T
S
−T
S
= 2(a−3t)(52a+579t)
>0.
i
i
11025
11025
k=φ a2D

E

Hence, for t/a ≤ 19/162, trade liberalization reduces the total surplus of both countries.
ED∗
Next, we consider case (i) with t/a > 19/162. By evaluating T SiDD∗ − T SH
atED∗
)k=φE a2 = (a−3t)(13a+3t)
k/a2 = φE , we obtain the following equation: (T SiDD∗ −T SH
> 0.
882
ED∗
DE∗
− T SiEE∗ are as follows:
and T SHIn addition, T SiDD∗ − T SH

DE∗
T SiDD∗ − T SH
= (a−3t)(a+3t)
> 0;
126

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

DE∗
DE∗
Substituting k/a2 = φD into T SH
− T SiEE∗ , we obtain: (T SH− T SiEE∗ )k=φD a2 =(29a−17t)(a−3t)
2450> 0. 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 thefollowing:DE∗ED∗
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 of the non-exporting country. In addition, without an exporting country, tradeliberalization has no eﬀect on total surplus.

25

Because ∂T SiEE∗ /∂t > 0 if t/a > 3/14, trade liberalization reduces the total surplus if
ED∗
3/14 < t/a < 23/104 and k/a2 < φD . Next, because ∂T SH/∂t > 0 if t/a > 6/25, tradeliberalization 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∗
DE∗First, we obtain T SH
− T SH= (a − 3t)2 /49 − k. Hence,ED∗DE∗k ≥ (a − 3t)2 /49 ⇒ T SH
≤ T SH. Second, we check that (a − 3t)2 /49 does not exceed

the level of k that brings about “One-way trade.” Solving φE − φD = 0 with respect tot, we have t = 19a/162. Thus, φE | t=19a/162 = φD | t=19a/162 = 25a2 /2187 holds. Simple
algebra yields:
[
)
19a a
−962a2 + 13122at − 19683t2
25a2 (a − 3t)2−=
> 0 ∀t ∈
,
.
2187
49
107163162 3This implies Proposition 4. Q.E.D.

Proof of Proposition 5. From equation (5), simple algebra yields:∆E −∆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)2This yields the following.
(2 − b)(64 − 40b − 8b2 + 3b3 ), ≥ ∆D if τ ≤ τδ (b) ≡3(8 + b2 )(8 − b − b2 )∆E< ∆D if τ > τδ (b),where τδ (b) < τmax holds. From the above formula and the definitions of ∆E and ∆D , weobtain Proposition 5. Q.E.D.

26

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