ECONOMIC RESEARCH CENTERDISCUSSION PAPER
E-Series

No.E15-6

Trade Costs and Welfare-worsening
Free Trade Agreement
byAkihiko Yanase
Masafumi Tsubuku

October 2015

ECONOMIC RESEARCH CENTERGRADUATE SCHOOL OF ECONOMICSNAGOYA UNIVERSITY

Trade Costs and Welfare-worsening
Free Trade Agreement
Akihiko Yanase†

Masafumi Tsubuku‡

October 8, 2015

Abstract
This paper examines the eﬀects of concluding a free trade agreement (FTA) in the presence of international trade costs between countries. In the traditional arguments, the optimal external tariﬀs set by
the FTA members are always lower than the pre-FTA optimal tariﬀs,
which implies that there are the tariﬀ complementarity eﬀects as the
FTA forming. To reexamine this argument, we construct a simple
three-country model of imperfect competition with endogenously determined (external) tariﬀs, and demonstrate that in the presence oftrade costs, the member countries may employ the higher external
tariﬀ as they form the FTA. That is the tariﬀ complementarity effects disappear. We also find that in contrast to traditional argument,
the non-member country’s welfare may worsen even if there are tariﬀ complementarity eﬀects. Furthermore, the findings show that the
FTA is likely to result in the deterioration of the member countries’
welfare, depending on the trade costs.

JEL classification F13, F15
Keywords Trade Costs, Free Trade Agreement, Tariﬀ Complementarity
Eﬀect.

†

School of Economics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601,
Japan. Tel:+81-52-789-5111 E-mail: yanase@soec.nagoya-u.ac.jp‡
Graduate School of Economics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya
464-8601, Japan. Tel:+81-52-789-5111 E-mail: msfm.tbk@gmail.com

1

1

Introduction

Over the last 2 decades, we have observed the significant surge of regional
trade agreements (RTAs) the purpose of which is to eliminate the tradebarriers between the signatories. Among the several forms of RTAs, mostexisting arrangements take the form of free trade agreement (FTA), whileless than 10% are represented by customs unions (CUs).1 Actually, there are
now over 250 FTAs in force and a lot of negotiation is on going toward theenforcement. Given their widespread appearance, the relationship between
international trade and the FTA formation is enhanced rapidly, so that
economic analysis on FTAs provides us with a plenty insight for the world
trading system.
Indeed, many researchers have addressed issues related to the surge of
FTAs, and in particular, have argued the impact of an FTA on its member’s external tariﬀ and on multilateral trade liberalization.2 A numberof studies have highlighted the tariﬀ complementarity eﬀect that the enforcement of an FTA induces the member countries to employ the lower
tariﬀ on the non-member countries, resulting in multilateral trade liberalization(e.g., Richardson,1993; Bagwell and Staiger, 1999; Yi, 2000; Bond etal, 2004; Ornelas, 2005 and Saggi and Yildiz, 2010). An intuition behind thistrade-liberalizing property of FTAs is that the member countries have lessincentive to manipulate their terms of trade vis-à-vis non-members since an
FTA leads its member countries to import less from non-member countries.
In addition, it is more important that tariﬀ complementarity eﬀects leadto positive welfare consequences of FTAs with endogenously determined external tariﬀs (e.g., Bagwell and Staiger, 1999; Yi, 2000; Bond et al., 2004;
Ornelas, 2005). These studies have shown that the tariﬀ complementarity
eﬀect is large enough to place the external tariﬀs below the Pareto-improving
external tariﬀs, and consequently, both members and non-members of FTAs
become better oﬀ.3
Although the previous literature in international trade has explored a lot
1

Facchini et al. (2012) develop a political economy model of trade policy under imperfect competition to provide a positive explanation for the prevalence of FTAs rather
than CUs.
2
See, for example, Maggi (2014, §4) for a survey of recent developments.
3
The well-known Vanek–Ohyama–Kemp–Wan theorem (Vanek, 1965; Ohyama, 1972;
Kemp and Wan, 1976) establishes that if two or more countries form a CU by fixing their
net external trade vector through a common external tariﬀ and eliminating internal tradebarriers, the union as a whole and the rest of the world cannot be worse oﬀ than before.
Ohyama (2002) and Panagariya and Krishna (2002) extend the Vanek–Ohyama–Kemp–
Wan theorem to the case of FTAs; they show the existence of FTAs that lead to Pareto
improvements in world welfare.

2

of properties in favor of an FTA, but it has paid the less attention to all costs
except for tariﬀ incurred between countries, so that its analysis has been limited to the economy where there is no cost to trade with abroad. In view ofthe fact that economic activities are separated in some form, the trade costs
incurred from various factors must be considered beyond economic factors.
As stated by Anderson and Van Wincoop (2004), trade costs are defined as
all costs incurred in getting a good to a final user other than the marginal
cost of producing the good itself (e.g., transportation costs, policy barriers, information costs, contract enforcement costs, costs associated with theuse of diﬀerent currencies, legal and regulatory costs, and local distribution
costs).4 In addition, they roughly estimate the trade costs for industrializedcountries at 170% in terms of ad valorem tax equivalent.5 Thus, this empirical evidence that broadly-defined trade costs are considerably large leads us
to recognize the importance of incorporating trade costs into the analysis oftrade policy. Furthermore, in new trade theory or new economic geography
developed by Helpman and Krugman (1985) and Fujita et al. (1999), theanalysis on distribution of economic activities is permitted by incorporating
the trade costs between countries. The several studies in these fields havediscussed the relationship between the capital tax and the firms’ agglomeration, but not consider the tariﬀ policy (Ludema and Wooton, 2000; Baldwin
and Krugman, 2004; and Ottaviano and Van Ypersele, 2005).
The objective of this paper is to dissolve the limitation of trade costs in a
simple three-country model of imperfect competition and explore how trade
costs aﬀect the desirability of FTA formation. We treat three policy regimes:
tariﬀ discrimination, a most-favored nation (MFN) principle, and an FTA,
and we investigate the eﬀects of trade costs on the tariﬀ determined in eachregime. Although the tariﬀ discrimination regime may violate the principleof non-discrimination prescribed in the General Agreement on Tariﬀs andTrade (GATT)/World Trade Organization (WTO) rule, it allows us to understand the basic mechanism under which trade costs aﬀect a country’s
tariﬀ unconstrained by any rule.
As for the results of comparing the tariﬀ in the MFN with the external
tariﬀ in the FTA, it is found that the tariﬀ complementarity eﬀects may
disappear with the higher trade costs between the FTA member countries.
This implies that considering the trade costs in the economy, the RTA does
not always facilitate multilateral trade liberalization, which is in contrast
4

See also Hummels and Skiba (2004), Hummels (2007) and Hummels et al. (2009) for
the detail about transportation cost.
5
This ad valorem tax equivalent includes 55% local distribution costs as well as international trade costs; the latter are composed of 21% transport costs and 44% border-relatedtrade barriers (1.7 = 1.55 × 1.21 × 1.44 − 1).

3to the previous studies. In the absence of trade costs, tariﬀ elimination by
an FTA leads the government to reduce the tariﬀ on other country (nonmember) so as to hold balanced consumption between domestic and foreign
production, resulting in the tariﬀ complementarity eﬀects.6 An incorporation of trade costs into the model brings about diﬀerent outcomes. Whenthe model incorporates the costs to trade with a foreign country, the governments achieve balanced consumption depending on trade cost level. Then,high trade costs within the FTA mean more consumption from non-member
countries rather than from the partner country, and thus, discourage themembers to decrease the tariﬀ on the non-member country.7
We now highlight the results of welfare analysis. As opposed to previous literature, our study demonstrates that an FTA under trade costs may
worsen the welfare of member countries and the non-member country. In
the analysis of welfare eﬀects of an FTA on member countries, we first consider the case of symmetric countries in which all three countries share thesame trade costs. Under such an environment, the member countries areworse oﬀ with suﬃciently high trade costs. An FTA formation reduces thetariﬀ revenue of member countries and increases the volume of international
trade, leading an increase in the payment of trade costs. Thus, under thehigh trade costs, the serious loss of income for the payment to trade costs
induced by signing the FTA. Subsequently, we consider cases in which thecountries face asymmetric trade costs and confirm that FTA conclusion canworsen the member’s welfare even with the asymmetry in trade costs.
Our results bring about the preserve wisdom of FTA related to trade
costs. Supposing that international trade costs arise according to the distance between the countries, the formation of FTA have more beneficial
eﬀects on the countries who are located close to each other. Actually, many
FTAs are formed by neighboring countries in Americas, European countries,
or Asian countries. Although there are some exceptions such as Japan-Chile,and Japan-Mexico FTA, our analysis could explain these cases using the degree of substitutability between domestic and foreign products. As a resultof welfare analysis, FTA conclusion has more beneficial eﬀects on the member countries under the low degree of substitutability. Accordingly, since6

Under a similar environment to ours, Yi (2000) has demonstrated that the welfare
function of each country is super-modular in tariﬀs that have high welfare with a balanced
consumption level, and has shown that if an FTA is formed, the member country imposes
lower external tariﬀs in order to achieve balanced consumption.
7
Also, our result could provide the hypothesis for empirical analysis about the disappearance of tariﬀ complementarity eﬀect. Some studies empirically analyze the existenceof tariﬀ complementarity eﬀects (Limão, 2006 Estevadeordal et al, 2008, and Karacaovali
and Limão, 2008), but it is controversial yet. The knowledge provided by our analysis
helps to construct the valid hypothesis.

4the tendency of international trade between developed country (Japan) anddeveloping country (Chile or Mexico) is to exchange the very diﬀerentiatedgoods with low substitutability between each other, they have more incentive to sign the FTA even if the long distance generate the high trade costs
between them.
The remainder of this paper is organized as follows. Next section shows
the simple intra-industrial trade model composed of three countries. In section 3, we explore the optimal tariﬀ in each regime and investigate whether
there are tariﬀ complementarity eﬀects. Section 4 conducts welfare analysis
on the FTA members and non-member. Section 5 concludes this paper.

2

The economy

2.1

Settings

We construct an intra-industry trade model following Furusawa and Konishi (2007).8 There are three symmetric countries (indexed by i, j, k) in theeconomy. Each country has two sectors, the agricultural sector and manufacturing sector. Consumers in all countries have identical preferences for
agricultural and manufacturing goods. We assume that each consumer supplies one unit of labor and, thus, the population size µ in each country isequal to labor force endowment.
The agricultural sector operates under perfect competition and constantreturns to scale using only labor. To produce one unit of the agricultural
good, one unit of labor needs to be employed in this sector. Assuming that
agricultural goods are numeraire, the price and wage rates are equal to one.
The firms in the manufacturing sector produce horizontally diﬀerentiatedgoods that are imperfectly substitutable for each other. The production of
manufacturing goods operates under imperfect competition. One variety ωis produced by one manufacturing firm, which is negligibly small and does
not influence the behavior of other firms in the sector. Formally, there is acontinuum Ω of manufacturing firms in the economy. Note that the set Ω
also represents the set of all varieties of manufacturing goods in the economy.
Assuming no entry to this sector, we normalize the size of the set, |Ω| = 1.
In this study, the distribution of manufacturing firms is symmetric between
countries, so that domestic consumers own one third of the total number of
8

Furusawa and Konishi (2007) employ a network formulation game and analyze
whether global free trade is stable among n countries with an intra-industry trade model.
Unlike their study, we introduce trade costs and explore the properties of trade policy inthe presence of trade costs.

5

firms in the economy. The set of firms located in country i is denoted byΩi ⊂ Ω, whose size is one third, |Ωi | = 1/3.
To purchase one unit of the manufacturing good from abroad, consumers
have to pay the trade costs, in addition to the good’s price and the tariﬀ
imposed by the government.9 We refer to the trade costs of transportationfrom country i to country j as τij , which is independent on the direction oftransportation, that is, τij = τji . The tariﬀ rate imposed on imports fromcountry j by the government of country i is represented as tij . While thetrade costs are given exogenously, the import tariﬀ rate is determined by
the government and its revenue is distributed evenly to consumers in eachcountry.10 To simplify the analysis, agricultural goods are assumed to be
shipped without trade costs.
2.1.1

Preference

All consumers in the economy are assumed to be identical. We formulate
the preferences of consumers with a quadratic utility function as follows:u(q(ω), q0 ; ω ∈ Ω)
)2
(∫
∫
∫
1−γ
γ
2
=
q(ω)dω −q(ω) dω −q(ω)dω + q0 ,
2
2
Ω
Ω
Ω

(1)

where q(ω) (q0 ) is the amount of manufacturing (agricultural) goods consumption and γ denotes the degree of substitutability between manufacturing goods. A lower γ means that consumers recognize manufacturing goods
as more diﬀerentiated. If γ = 0, manufacturing goods are perfectly diﬀerent from one another. If γ = 1, every manufacturing good is recognized as
identical.
From the utility maximization problem, we can deduce the demand functions for manufacturing goods as follows:q(ω) =

1[1 − p̃(ω) − γ(1 − P̃ )],
1−γ

9

(2)

An assumption of tariﬀ incidence is not crucial in our model. Even if the manufacturing firms burden the tariﬀ, same outcomes can be deduced.
10
If we suppose the trade costs are compensation for transportation services suppliedby the private sector, which is perfectly competitive, transportation services are delivered
inelastically with marginal cost pricing. It is reasonable that the trade costs τ are given
exogenously as constant marginal costs in the competitive transportation sectors. Somestudies introduce the mechanism that transportation costs are determined endogenously
and explore its eﬀects on the economy (see, e.g., Takahashi, 2006; Mun and Nakagawa,
2010; Tsubuku, 2014).

6

where p̃(ω) represents the consumer price of manufacturing goods ω andP̃ is a price index. If consumers import the manufacturing goods, they
have to pay the tariﬀ and trade costs in addition to the price set by the
manufacturing firm. As an example, the consumer prices in country r isrepresented by{prr (ω)if ω ∈ Ωr ,p̃(ω) =
(3)psr (ω) + tsr + τsr if ω ∈ Ωs , r ̸= s,where prs (ω) denotes the price of manufacturing goods in country r producedin country s (r, s = i, j, k) and Ωr is the set of manufacturing firms locatedin country∫ r. The price index is defined by the sum of consumer prices thatis P̃ ≡ Ω p̃(ω)dω. Thus, based on Eq. (3), the price index for consumers incountry r, Pr , is written by∫∫Pr =prr (ω)dω +[psr (ω) + tsr + τsr ]dω.
(4)
Ωr

2.1.2

Ωs

Manufacturing sector

The manufacturing firm producing a variety of ω supplies to both the domestic country and two foreign countries. Supposing no marginal costs for
production, the operating profit πi (ω) of the firm located in country i is∑
µpir (ω)qir (ω),(5)
πi (ω) =r=i,j,kwhere qrs (ω) represents the quantity of manufacturing goods supplied tocountry s produced in country r (r, s = i, j, k) and Ωr is the set of manufacturing firms located in country r. Given the price index Pr and other firms’
behavior in the economy, each firm maximizes its own profit by setting theprice.11 According to the first-order conditions of the profit maximization
problem, all the firms in country i set their own prices as follows:1
pii = [1 + γ(1 − Pi )],2
tir + τirpir = prr −, r = j, k.
2
11

(6)
(7)

The assumption that diﬀerentiated goods in the manufacturing sector are denoted by
the continuum of manufacturing firms results in the same equilibrium being deduced regardless of price or quantity competition, so that our model excludes strategic interaction
among manufacturing firms.

7Regardless of the variety of diﬀerentiated goods, manufacturing goods are
symmetrically priced by firms. Thus, hereafter, we omit an expression of
the variety of ω. The export price set by the firms is cheaper than thedomestic price, but the consumer price including the trade costs and tariﬀ
pir + tir + τir exceeds the domestic price, so that there is no arbitration
between countries. In addition, we find half of the trade costs and tariﬀ
absorbed by manufacturing firms. From (6) and (7), the diﬀerence between
the prices faced by domestic and foreign consumers is (pir + tir + τir ) −pii = (tir + τir )/2., which is smaller than the trade costs and tariﬀ paid byconsumers.
Substituting (6) and (7) into the definition of price index P̃ , equilibrium
prices are determined as follows:
]
1 [
γ
pii =
1 − γ + (t̄i + τ̄i ) ,
(8)
2−γ
2
] t +τ
1 [
γ
ir
ir
pir =
(9)
1 − γ + (t̄r + τ̄r ) −, r = j, k.
2−γ
22where t̄i , (τ̄i ) is defined by the weighted average of tariﬀs (trade costs) as
τ̄i ≡

1 ∑
τri ,
3 r=j,k

t̄i ≡

1 ∑
tri .
3 r=j,kWe can obtain the equilibrium quantities from the relationship, prs = (1 −γ)qrs , which can be provided by the firm’s first-order condition.

2.2

Welfare decomposition

We now characterize the welfare of each country that has symmetric economic structure, consumer’s preference, firm behavior, and the sizes of population and manufacturing firms, except for the trade costs and tariﬀs facedby them. Because of the symmetric assumption, only the welfare of country
i is shown. Per capita income in country i is constituted by the total of
the wage rate, wi (= 1), rents of manufacturing production activities, anddistributed tax revenue:
1 πr 1 ∑yr = 1 ++(10)
tri qri ,3µ3 r=j,kwhere the third term represents tariﬀ revenue distributed by the government. Based on the budget constraint of consumers, the demand function
for agricultural goods can be represented by manufacturing demand as fol8

lows:
q0[]∑
1= yr −
pii qii +(pri + tri + τri )qri
3
r=j,k
∑
∑
= 1+
(pri + τri )qri +pir qir .
r=j,i

(11)

r=j,i

Assuming τ i = (τji , τki ) and ti = (tji , tki ) as the vector of trade costs andtariﬀs, respectively, we can decompose the welfare in equilibrium, that is
Vi (ti , tj , tk , τ i , τ j , τ k )= Ui (ti , τ i ) − IMi (ti , τ i ) + EXi (tj , tk , τ j , τ k ),(12)

where Ui (ti , τ i ) refers to gross utility and EXi (tj , tk , τ j , τ k ) (IMi (ti , τ i ))denotes the total value of exports (imports) of country i. Each term isdefined by]]2[[1−γ ∑ 2
γ ∑
1 ∑
qir −
qir −
qir + 1,Ui (ti , τ i ) ≡(13)
3 r=i,j,k6
18 r=i,j,kr=i,j,k∑1∑
IMri (ti , τ i ) =(pri + τri )qri ,IMi (ti , τ i ) ≡(14)
3 r̸=ir̸=i∑1∑EXri (tr , τ r ) =EXi (tj , tk , τ j , τ k ) ≡pir qir ,
(15)
3
r̸=i
r̸=i
where the productions and prices are evaluated at the equilibrium value,
which depends on trade costs and tariﬀs, so that the diﬀerence in the welfare
level of each country is characterized by trade costs and tariﬀs paid byconsumers.
It is worth referring to the impacts of trade costs and tariﬀs on Eqs. (13),(14), and (15). First, consider gross utility, which depends on the consumption level of domestic production and the imports from two foreign countries.
The eﬀects of a decrease in trade costs or tariﬀs on gross utility, Ui (ti , τ i ),is ambiguous owing to the substitution eﬀect caused by the reduction. For
example, high trade costs τji raise the domestic and import demands fromcountry k at the expense of imports produced in country j. Due to thissubstitution eﬀect, it is not necessary that gross utility is improved by trade
cost reduction.
Second, we consider the response of import value IMi (ti , τ i ) to trade
costs and tariﬀs. For a similar reason to the case of gross utility, it is obscure9whether a high tariﬀ leads consumers to decrease payments for imports
from abroad. An increase in the tariﬀ imposed on imports from country j
induces consumers to decrease the import value from country j, IMji (ti , τ i )and to increase imports from country k, IMki (ti , τ i ). These import values
consist of two factors; the payment for imported goods and internationaltransportation. If the trade costs increase, it directly increases the latter.
In addition, the increase in trade costs reduces the former.
Third, the export value of country i is always lowered by high trade costs
and tariﬀs since export values supplied to each foreign country, EXji (tj , τ j )and EXki (tk , τ k ), are independent of each other with regard to trade costs
and tariﬀs.

3

Trade costs and tariﬀ policy in three regimes

Here, we explore the relationship between trade costs and optimal tariﬀs determined by government under three regimes; a tariﬀ discrimination regime,
the MFN principle, and an FTA. These optimal tariﬀs are reduced to maximize national welfare depending on trade costs emerging between countries.
In this section, the eﬀect of trade costs on optimal tariﬀs is investigatedand it is shown that the tariﬀ complementarity eﬀects do not appear undercertain conditions of trade costs.

3.1

Tariﬀ discrimination regime

In order to make clear the incentive to set tariﬀs, we analyze the tariﬀ
discrimination regime as a benchmark case. In this subsection, each government can choose the tariﬀ rate on each import independently. It follows
that the maximization problem for each government is
max Vi .

tji ,tki

From, Eqs. (13), (14), and (15), the first-order conditions can be written as∂Ui ∂IMki ∂IMji−−= 0, r = j, k.
∂tri
∂tri
∂tri

(16)

The first term on the left-hand side of Eq. (16) shows tariﬀ eﬀects on grossutility, of which the sign is ambiguous, as mentioned at the end of previous
section. The second and third terms are the eﬀect on imports from two10

foreign countries. We can identify the signs of the second and third terms.
Considering the eﬀects of tji , ∂IMji /∂tji is negative and ∂IMki /∂tji is positive. From Eq. (16), we find that the tariﬀ level imposed by the government
does not depend on the tariﬀ level imposed by the other government, and so,
there is no strategic interdependence, as shown in Yi (1996). The discriminatory tariﬀ imposed by country i on imports from country j is denoted astD
ji . Superscript D means the discrimination regime. Solving Eq. (16) for
tariﬀs, we obtain country i’s optimal discriminatory tariﬀs on each foreigncountry as follows:tD
ji =36(1 − γ)(3 − 2γ) − (61γ 2 − 168γ + 108)τji + 4γ(3 − 2γ)τki. (17)
159γ 2 − 468γ + 324

From Eq. (17), it is easy to derive tD
ki owing to the assumption of a symmetric country. The discriminatory tariﬀs are always positive as long as
international trade is feasible. Comparing two discriminatory tariﬀs, it isfound thatDtD
ji > tki ⇔ τji < τki .

(18)This result is summarized as the following Proposition 1.
Proposition 1 (Tariﬀ discrimination) Each country under a tariﬀ discrimination regime imposes higher tariﬀs on foreign goods imported withlower trade costs.
To explain this result, we provide the following intuition. Under low trade
costs incurred in the process of trading with country j, consumers in country
i demand more imports from country j. This implies that imposing tariﬀ
on the imports from country j rather than country k have more beneficial
eﬀect by protecting the domestic firms, so that the government of country i
imposes a higher tariﬀ on imports from country j. On the other hand, when
the trade costs between countries i and j are low, imports from country k
are small owing to substitution eﬀect. In order to encourage imports fromcountry k, governments have incentive to reduce tariﬀs imposed on thatcountry.
In addition, we find that the change in trade costs between a certain
two countries out of the three have two eﬀects on tariﬀ policy. For example, the reduction of trade costs between countries i and j increases imports
from country j, and at the same time decreases import from country k since11consumers substitute imports.12 Under the tariﬀ discriminatory regime,
governments can respond to these eﬀects independently and, thus, the disD
criminatory tariﬀs, tD
ji and tki , are aﬀected oppositely by the same trade
costs.

3.2

Most-favored nation principle

In this subsection, we explore the tariﬀ determined by complying with the
MFN principle, where each government imposes the same tariﬀ on the othercountries. The maximization problem of country i under the MFN principle
is defined as
max

Vi

s.t.

tji = tkitji ,tki

According to the first-order condition of this problem, the MFN tariﬀ satisfies the following condition.
∑ ( ∂Ui ∂IMki ∂IMji )
−
−
=0
∂tri
∂tri
∂tri
r=j,k
(

(
)
) (
)
∂Ui ∂Ui∂IMji ∂IMji∂IMki ∂IMki⇔−−= 0. (19)+++∂tji ∂tki
∂tji
∂tki
∂tki
∂tji
{z
} |
{z
}|
{z
}
|
- : Loss of the utility ⃝⃝+ : The income gain
+ :The income gain⃝

This condition, Eq. (19), reveals that when the government increases tji andtki simultaneously, its net benefit should be equal to zero and consist of threeparts: the loss of utility owing to decreased consumption, and two income
gains caused by decreased import payments to foreign countries. The MFN
tariﬀ rate imposed by country i is obtained as follows:
FN
tM
=
i

24(1 − γ)(3 − 2γ) − (23γ 2 − 60γ + 36) (τji + τki ).
106γ 2 − 312γ + 216(20)

Based on the assumption that international trade is feasible, the MFN tariﬀ
rate can be shown to be positive. Eq. (20) shows that what matters is thesum of trade costs, τji + τki , not each level of trade costs, since the three
countries are symmetric. Compared with the discrimination regime, the12This unilateral reduction in trade costs is induced by the establishment of transport
infrastructure that is accessed mainly by the firms in those countries, for example, openingof a highway or railway.

12

linear demand functions yield the MFN tariﬀ in the middle point between
two discriminatory tariﬀs, as shown in Saggi (2009).
Consider the impacts of trade costs on the MFN tariﬀ. The MFN tariﬀ
depends on only the sum of trade costs, and a shift in each trade cost is indifferent to the MFN tariﬀ. However, the eﬀect is ambiguous and characterized
by the degree of substitutability γ as
FN
√ )
dtM
6 (
i
≷0⇔γ≷
5 − 2 ≈ 0.935,dτri
23

and, thus, we obtain Proposition 2.
Proposition 2 (Most-favored nation tariﬀ ) When the substitutability
between domestic and foreign products is suﬃciently high, then trade cost
reduction fosters the elimination of tariﬀ.
The intuition behind Proposition 2 is that large γ amplifies the marginal
benefits of imposing tariﬀs, which is the domestic income gains induced bysubstituting imports for domestic products, so that the MFN tariﬀ increases
as trade costs rise. In our model, a reduction in trade costs, for instance τji ,
causes the reduction in import demand from country j as well as the expansion of demand for domestic production and import from country k throughthe substitution eﬀects. When the manufacturing goods is suﬃciently substitutable, the indirect eﬀects like increasing the domestic demands lead thegovernment to increase the MFN tariﬀ as trade costs increase.
Setting the single tariﬀ rate on two countries under the MFN principle,
each government is required to take into account the eﬀects on both tariﬀs, tji
and tki , together. Increasing trade costs τji have negative (positive) eﬀects onimports from country j (country k), which provides the incentive to reduce(raise) the tariﬀ on imports from country j (country k). Such conflicting
incentives yielded by change in trade costs keep the eﬀects of trade costs on
the MFN tariﬀs unclear and it is dependent on the degree of substitutability
between the products.

3.3

Free trade agreement

Supposing that countries i and j enforce the FTA and impose a zero tariﬀ
rate on each other, we investigate the external tariﬀ imposed by them on
the non-member country (country k).13 The FTA member governments
13

The maximization problem of the non-member country is equivalent to the case of
the tariﬀ discrimination regime or the MFN principle owing to the independence of thegovernment’s policy strategy.

13eliminate the tariﬀ barrier within the member countries and set the external
tariﬀ on the non-member country in order to maximize their own national
welfare. As stated in Articles XXIV of GATT/WTO, the countries signing
an FTA are required not to raise the tariﬀ on countries that are not membersof the FTA. Thus, the maximization problem is given as
max

Vi

s.t.

tji = tij = 0

tki

FNtki ≤ tMi

In this maximization problem, the third constraint reflecting the requirementof GATT/WTO’s Articles XXIV forces the government of member country
to employ the same or lower tariﬀ on the non-member country.
First, we consider the case of inner solution in which the equality condiFN. If the optimal external tariﬀ set bytion holds strictly, that is, tki < tMithe member is lower than the MFN tariﬀ, the first-order condition can be
represented by
∂Ui
∂tki

−
tji =tij =0

∂IMki
∂tki

−
tji =tij =0

∂IMji
∂tki

= 0.

(21)

tji =tij =0

In contrast to the MFN principle, the FTA member governments can choose
the external tariﬀ tki independently since the tariﬀs between the member
countries, tij and tji , is zero. In this case, the external tariﬀ determined by
the member governments is written by
tFkiT A =12(1 − γ)(3 − 2γ) + (12 − 7γ)γτji − 4(3 − 2γ)2 τki.
4(3 − 2γ)(9 − 5γ)(22)

In addition, this tariﬀ is positive under the feasibility of international trade.
From Eq.(22), we can show the eﬀects of trade costs on the external tariﬀ,
dtFkiT A /dτki < 0 and dtFkiT A /dτji > 0, which is summarized in Proposition 3
as follows:
Proposition 3 (External tariﬀ in FTA) The external tariﬀ is increasedby the higher trade costs between the FTA member countries as well as thelower trade costs between the member and non-member countries.
We here explain the intuition behind Proposition 3. The high trade
costs τji yield more trade between the members and non-member due tothe substitution eﬀects, leading the member country to protect the domes14

tic manufacturing firms from competition with firms in the non-member
country. Therefore, under high τji , the member governments increase theexternal tariﬀ in order to avoid competition with firms in the non-member
country and to increase domestic firms’ profit. Another intuition of this result is that imports from the member country are lowered as trade costs τji
increase, and thus, the FTA member governments increase the external tariﬀ
in order to foster import demand from the member country at the expenseof the non-member country. On the other hand, we can provide similar
intuitions regarding the trade cost between the member and non-member
countries. Lower trade costs, τki , induce the government under the FTA to
impose a higher external tariﬀ due to intense competition with firms in the
non-member country.
The case of inner solution is that under the FTA, the member has no
incentive to set the higher tariﬀ than the MFN tariﬀ. If the optimal external
tariﬀ lies at a higher level than the MFN tariﬀ, then the inequality condition
FN
holds with equality, that is, tki = tM
. This means that the externalitariﬀ under the FTA is equivalent to the MFN tariﬀ, implying the tariﬀ
complementarity eﬀects disappear. If the following condition is satisfied,then the government of the member country does not decrease the external
tariﬀ after the FTA formed.
∂Ui
∂IMki
∂IMji
−
−
>0
∂tki tji =tij =0,∂tki tji =tij =0,∂tki tji =tij =0,
FN
tki =tMi

FN
tki =tMi⇔ τji > τ̃i (τki ) .

FNtki =tMi(23)

where τ̃i is the upper bound of τji achieving the equilibrium in which themember, country i, imposes a lower tariﬀ than under the MFN principle. If
the trade costs between members exceed this thresholds τ̃i , then the members
keep the external tariﬀ rate at the same level as the MFN tariﬀ. Thisimplies that tariﬀ complementarity eﬀects do not occur when condition Eq.
(23) is satisfied. In the absence of trade costs, the external tariﬀ always
declines by FTA formation relative to under the MFN principle. Thus,
when international trade is not costless, the FTA formation provides the
incentive to raise the external tariﬀ.
See the disappearance of tariﬀ complementarity eﬀects about both member countries in a graphic form. From the equilibrium quantities, the requirement for trade costs that assume the feasibility of international trade can

15

τ̄ji

τji

τ̃i

τ̃j

τ̄ki

τ̄kj

Non tariﬀ complementarity
for country i
Non tariﬀ complementarity
for country j

τkj

0

τki

Figure 1: Trade costs and tariﬀ complementarity eﬀects

be represented as
MF N
FTAmin{qji(τ i ), qji(τ i )} ≥ 0 ⇔ τji ≤ τ̄ji (τki ),

(24)

MF N
FTA
min{qki(τ i ), qki(τ i )} ≥ 0 ⇔ τki ≤ τ̄ki (τji ).

(25)

Based on Eqs.(23), (24) and (25), we can illustrate Figure 1 regarding thetariﬀ complementarity eﬀects when international trade is feasible. Figure 1
shows the two cases of each member, countries i and j, in the first and second
quadrant, respectively.14 The dotted lines represent the upper bounds at
which international trade is feasible, τ̄ji and τ̄ki .
In the shaded area in Figure 1, the condition Eqs.(23), (24), and (25)are satisfied and, thus, the tariﬀ complementarity eﬀect does not appear ineach country.
Proposition 4 (Disappearance of complementarity eﬀects) Under thelarger trade costs between the FTA member countries and the smaller trade
costs between the member and non-member countries, the external tariﬀ rate
remains under the MFN principle.
Proposition 4 shows the possibility that tariﬀ complementarity eﬀects
disappear, once we focus on the economy with trade costs occurring in international trade. Under the MFN principle, governments face the constraintof setting the same tariﬀ on the two countries and cannot adjust tariﬀs,
14

Each threshold for country j is developed in the same way as country i.

16tji and tki , to trade costs shifting independently. By contrast, governments
concluding an FTA choose the external tariﬀ without such a constraint, andthus, they can employ the tariﬀ policy corresponding to each trade cost independently. Thus, when τji and τki satisfy Eq. (23), then the governments
signing an FTA have an incentive to raise the tariﬀ from that under the
MFN. Despite such incentive of the members existing, they are restricted toraise the tariﬀ on the non-member country and thus and set it at the samelevel as the MFN tariﬀ, resulting in no tariﬀ complementarity eﬀect.

4

Welfare analysis

At first glance, the formation of an FTA improves all countries’ welfare because international trade is fostered as tariﬀ barriers are eliminated by eachgovernment. However, if trade costs occur in the process of international
trade, FTA formation is likely to worsen the welfare of member countries
under certain conditions. In this section, we explore the eﬀects of the conclusion of an FTA on welfare in the presence of trade costs. Once we focus
on the economy in which trade costs exist, perfect market integration cannot
be achieved by FTA conclusion in contrast to the previous literature. Without loss of generality, we analyze the case in which countries i and j agree
to eliminate tariﬀs on each other (tji = tij = 0 ). Let tF T A (tM F N ) represent the tariﬀ schedules set by each government in the FTA (MFN) regime,FN
F N MF N MF N
that is, tF T A = (tFi T A , tFj T A , tM
) and tM F N = (tM
, tj
, tk
). As
i
k
discussed above, these tariﬀ rates depend on trade costs, so that the welfare
impact of FTA conclusion is also influenced through the tariﬀ change causedby trade costs.

4.1

Non-member

Here, we consider the welfare of the non-member country aﬀected by the
FTA conclusion. In our setting, there is no strategic relationship between
governments when they determine the tariﬀ rate. Accordingly, country k(non-member country) retains the tariﬀ rates under the MFN principle,
even if countries i and j form an FTA and eliminate the tariﬀ on each other.
Thus, the FTA formation aﬀects the non-member’s welfare only through thechange in tariﬀ rate set by the member countries. In fact, the non-member’s

17

τji
Non tariﬀ complementarity
of country i and j

Non-member country’s
welfare worseningτkj = τki
Figure 2: Welfare eﬀects on non-member country

welfare eﬀects induced by the FTA can be denoted as follows:∆Vk (τ i , τ j , τ k ) ≡ Vk (tF T A , τ i , τ j , τ k ) − Vk (tM F N , τ i , τ j , τ k )F N MF N= EXk (tFi T A , tFj T A , τ i , τ j ) − EXk (tM, tj, τ i , τ j ),i(26)

where ∆Vk is the diﬀerence between the FTA welfare and MFN welfare ofcountry k, which consists of export values in each state. Eq. (26) shows thata change in tariﬀ schedules of the members only matters for non-member
country’s welfare since the non-member does not change the tariﬀ policy asa response to the FTA formation. In other words, if exports from country
k to countries i and j are expanded as they conclude the FTA, the nonmember’s welfare is suﬃciently improved. As Eq. (26) shows, the welfare
eﬀects are dependent on the tariﬀ schedule of member countries, so thatthey are closely related to the tariﬀ complementarity eﬀects. If the tariﬀ
complementarity eﬀects disappear when the non-member trades with both
members, then the non-member’s welfare always declines owing to decreases
in exports to both members from the non-member.
Supposing the two trade costs faced by the non-member, τki and τkj , arethe same level, we can illustrate Figure 2 based on Figure 1. Figure 2 depicts
the thresholds for the tariﬀ complementarity eﬀects and the FTA worsening
the non-member’s welfare. If the tariﬀ complementarity eﬀects disappear,18

which the member countries do not change the external tariﬀ after the FTA
concludes, then the exports from non-member country are not influenced by
FTA formation. Thus, in the absence of tariﬀ complementarity, the FTA
conclusion does not aﬀect the welfare of non-member country. However,the non-member country could be worse oﬀ even if tariﬀ complementarity
eﬀects appear. This is because it is not necessary that exports from thenon-member country increase even though the FTA formation induces thefirms in the non-member country to face a lower external tariﬀ. As the FTA
is formed, consumers in both member countries substitute imports from thenon-member with those from each other, so that the non-member’s exports
could decrease even under the tariﬀ complementarity eﬀects. Provided thepair of trade costs bringing suﬃciently strong tariﬀ complementarity eﬀects,
e.g., perfectly symmetric trade costs, τji = τki = τkj = τ , then non-member
country’s welfare is improved by the FTA formation.

4.2

FTA members

In this subsection, we explore the welfare eﬀects on the member countries
induced by FTA formation. The diﬀerence between welfare under the FTA
and MFN for the member country (country i) is∆Vi (τ i , τ j , τ k ) ≡ Vi (tF T A , τ i , τ j , τ k ) − Vi (tM F N , τ i , τ j , τ k )= ∆Ui (τ i ) + ∆N Eij (τ i , τ j )]τji [ F T A
MF N−∆IMki (τ i ) −qji (τ i ) − qji(τ i ) , (27)3where ∆Ui and ∆IMki are the diﬀerences between gross utility and thevalues of imports from country k in each regime and are defined as
FN∆Ui (τ i ) ≡ Ui (tFi T A , τ i ) − Ui (tM, τ i ),
i

(28)

FN
∆IMki (τ i ) ≡ IMki (tFi T A , τ i ) − IMki (tM, τ i ).
i(29)

Moreover, the welfare eﬀects of member countries depend on the change intrade surplus between them and is represented by ∆N Eij (τ i , τ j ), which is]1{ [ FTAFTA∆N Ei (τ i , τ j ) ≡pij (τ j )qijF T A (τ j ) − pFjiT A (τ i )qji
(τ i )
3]}[ MF N
MF N
FN
.
(τ
)
(τ
)q
− pij (τ j )qijM F N (τ j ) − pM
i
i ji
ji

(30)

In addition, Furusawa and Konishi (2007) demonstrate that the welfare
19

eﬀects by the FTA conclusion can be divided into gross utility eﬀects (∆Ui ),a direct surplus eﬀect (∆N Ei ), and third-country eﬀects (∆IMki ) like Eq.
(27). However, supposing that it costs to trade with foreign countries, weshould consider
eﬀect caused] by) FTA conclusion, namely, a trade( [ anotherFTA
MF N
cost eﬀect τji qji (τ i ) − qji(τ i ) /3 . This eﬀect could be negative forthe country to conclude an FTA. With the formation of an FTA between
countries i and j, an increase in imports from country j induces the amountof consumers’ payment for importing goods as well as the trade costs. Thus,
the consumers in member countries should pay the additional trade costs
under the FTA, which is called by the trade cost eﬀect.
4.2.1

Symmetric caseIn this subsection, we show that even in the absence of asymmetry in trade
costs, FTA conclusion is likely to worsen the member countries’ welfare.
We assume that the trade costs between any two countries are symmetric,
τji = τki = τkj = τ .15
Consider a condition for the feasibility of international trade in thepresent case. Under the assumption of symmetric trade costs, there arealways tariﬀ complementarity eﬀects from Figure 1, so that the volume ofinternational trade between any two of the three countries is smaller under
the MFN principle than the FTA. Considering the trade volume is the samelevel for any country under the MFN, the condition for the feasibility ofinternational trade is deduced as
FNqji (tM,τ) ≥ 0 ⇔ τ ≤i36 − 69γ + 33γ 2≡ τ̄ .
(6 − 5γ)2(31)

Welfare under the MFN principle is supposed to be Vr (tM F N , τ ) for ∀r in
which three vectors of trade costs are summarized to one since each trade cost
vector is symmetric. The MFN principle with symmetric trade costs urges
FN
FN
FN
all countries to set the same tariﬀ rate, tM
= tM
= tM
, so that eachijkcountry obtains the same level of welfare. On the other hand, when countries
i and j conclude the FTA, the member countries (countries i and j) and nonmember country (country k) oﬀers diﬀerent tariﬀ schedules. We obtain thewelfare of member countries, Vr (tF T A , τ ) for r = i, j. Under symmetric trade
costs, the direct trade surplus eﬀects disappear since τ j = τ i , so that themember’s welfare eﬀects induced by the FTA conclusion can be represented
15

The symmetric trade costs induce the same tariﬀ rate regardless of the tariﬀ discrimination regime or MFN principle since all countries have perfectly symmetric structure,including the trade costs they face.

20

as follows:∆Vi (τ ) ≡ Vi (tF T A , τ ) − Vi (tM F N , τ )]τ [ FTA
MF N= ∆Ui (τ ) − ∆IMki (τ ) −qji (τ ) − qji(τ ) .
3(32)

The tariﬀ elimination between member countries and tariﬀ complementarity
induce country i to undertake more trading with both the partner and nonmember. Hence, the gross utility eﬀects ∆Ui are positive on the welfare ofmembers while the third-country eﬀects ∆IMki are negative. By comparing
Eqs. (28) and (29), we can show that gross utility increases more than importvalue from the non-member country as the FTA is forming, ∆Ui − ∆IMki >0, which leads to the FTA improving( country
However,[ F T A i’s welfare.
] ) the third
MF N
term in Eq. (32), trade cost eﬀects τji qji (τ i ) − qji (τ i ) /3 , work as
the FTA conclusion decreases the welfare of country i. It follows that thewelfare of the member country can be undermined when the third term islarge enough to dominate the positive eﬀects. The threshold of trade costs
at which the FTA improves the member’s welfare can be deduced as∆Vi (τ ) ≥ 0 ⇔ τ ≤ τ̂ .

(33)

We show such τ̂ is smaller than τ̄ , as depicted in Figure 3, and obtain thefollowing result:
Proposition 5 (Welfare-worsening free trade agreement) Under higher
symmetric trade costs between countries, the conclusion of an FTA worsens
the welfare of member countries.
Proposition 5 indicates that higher trade costs lead the FTA formation
to undermine its member countries’ welfare, although the non-member country’s welfare increases. An intuition behind Proposition 5 is stated below.
Tariﬀ reduction by the conclusion of the FTA encourages its members totrade with each other as well as the non-member country. Although the
expansion of international trade under the FTA improves the welfare ofmember countries, it also generates the loss of their welfare in the economy
in which trade costs exist. The payment of trade costs by each member
country is more expensive under the FTA than the MFN principle. Such
payment is loss for firms’ rent and has the eﬀect of reducing welfare. Therefore, if higher trade costs per unit τ create a larger loss in the process of
trade between member countries, then the welfare loss induced from trade
costs exceeds that gains induced by trade expansion.
This discussion is reflected in Figure 3. Actually, for each γ, the member’s
21

τ
1

τ̄
∆Vi (τ ) < 0∆Vi (τ ) > 0

0

τ̂

1

γ

Figure 3: Trade costs and FTA formation

welfare is worse oﬀ with high symmetric trade costs in the figure. Figure 3
also shows that low γ tends to improve the member’s welfare as the FTA
formation even if the symmetric trade costs are high. Since manufacturing
products under low γ are recognized as more diﬀerentiated goods rather thanunder high γ, the tariﬀ elimination by FTA signing induces the consumers
to substitute less imports product for domestic one. This leads to save an
increase in the loss of transportation payments. Thus, the FTA formation
is likely to aﬀect the welfare of the members beneficially under the lower
substitutable manufacturing goods.
4.2.2

Asymmetric cases

Here, we relax the assumption that trade costs in each country are symmetric. In particular, focusing on the threshold representing the equivalence
between the FTA and MFN welfare, τ̂ in Eq. (33), we explore how thethreshold value changes response to an asymmetric small change in trade
costs. Assuming that each trade cost is set as τij = τ + em , τjk = τ + ej andτki = τ + ei , the threshold under asymmetry is defined implicitly as follows:∆Vi (τ i , τ j , τ k ) ≥ 0 ⇔ τ ≤ τ̂asy (em , ei , ej ),(34)

In Eq. (34), if the trade costs are symmetric, em = ei = ej = 0, then τ̂asy
is equal to τ̂ , as shown in Eq. (33). Consider three cases of trade costs: (i)em = e, ei = −e and ej = 0, (ii) em = e, ei = 0 and ej = −e and, (iii) em = 0,22ei = e and ej = −e. We diﬀerentiate τ̂asy with respect to e in each case andevaluate its derivative values at e = 0, implying the introduction of small
asymmetries on trade costs into symmetric equilibrium (em = ei = ej = 0).
In general, change in e does not always yield the asymmetry in trade costs,
but supposing the symmetric equilibrium as a benchmark, this calculation
represents the eﬀects of expanding asymmetry among trade costs on thethreshold τ̂ . Since the τ̂ is defined as the upper level of trade costs thatFTA formation improves the member country’s welfare, an increase in τ̂
is to spread the such range and means that the benefit of FTA conclusion
expanding. Therefore, such calculation allows us to understand how thebenefit of FTA conclusion is aﬀected by the addition of asymmetry in trade
costs as compared with symmetric case.
(i) em = e, ei = −e and ej = 0.
First, we investigate the eﬀects cased by a small decrease in trade costs
between country i and country k, and a small increase in trade costs between
country i and country j from the perfect symmetric trade costs. This case isthat the member country (country i) faces the smaller trade costs for tradingwith the partner country (country j) rather than the non-member country(country k). From Eq. (27), the eﬀects of change in e is represented bydτ̂asy (e, −e, 0)
< 0.
de
e=0

(35)

This implies that a decrease in e induces increases in τ̂asy and, thus, the range
in which the FTA improves the member’s welfare expands as the trade costs
shift in opposite direction. Therefore, the benefit of concluding the FTA
is amplified as the trade costs decline between the member countries andincrease between the member and non-member countries. The trade costeﬀect in Eq. (27) induced by the FTA formation plays an important role inthis case.
When the trade costs between countries i and j reduce and those between countries i and k increase, such as shown in Eq. (35), imports fromthe member country increase and those from the non-member decrease. In
addition, its eﬀects are larger under the MFN principle than the FTA since
the reduction of e in this case induces the external tariﬀ to decrease in order
to increase imports from the non-member country while the MFN tariﬀ isconstant. Given these shifts of trade structure for country i, we consider
the eﬀects of trade costs on the benefits of the FTA. Such changes increase
payment of trade costs under the MFN relative to the FTA, which improve
benefits of FTA formation. Thus, the threshold τ̂asy increases as the trade23costs decline between members and increase between the member and nonmember countries.
However, there are some channels in which benefits are not improved.
The third-country eﬀects (∆IMki ) change to become discouraging from concluding the FTA since the member country reduces the external tariﬀ and,thus, the payment to the non-member country under the FTA is more expensive than under the MFN. Furthermore, the gross utility eﬀects (∆Ui )and the direct trade surplus eﬀects (∆N Ei ) are ambiguous for the benefitsof the FTA and depend on the degree of substitutability between the manufacturing goods. Provided the small γ, there are small substitution eﬀects,
so that an increase of country i’s import from the partner country (countryj) caused by the reduction in trade costs between country i and the nonmember country (country k) is suppressed. Thus, the decrease in e tends
to shrink the gross utility eﬀect (∆Ui ) and expand the direct trade surplus
eﬀects (∆N Ei ) under the small γ. Despite such negative eﬀects on the FTA
benefits, the trade cost eﬀects that positively influence the FTA dominate
the other negative eﬀects under an environment of demand linearity andquasi-linear utility.
(ii) em = e, ei = 0 and ej = −e.
Second, we consider the eﬀects of a decrease in trade costs between member
countries (countries i and j) and an increase in trade costs between thepartner country (country j) and the non-member country (country k), whichis induced by small reduction in e. Thus, in this case, the member country(country i) faces the small trade costs for trading with the partner country(country j) while the trade costs between own country and the non-member
country (country k) are constant. In addition to this, the partner country(country j) faces the large trade costs for trading with the non-member
country (country k) in this case. We obtain the following equation in asimilar way to the previous case.
dτ̂asy (e, 0, −e)
< 0.
de
e=0

(36)

Eq. (36) shows that reduction in trade costs between members (countries
i and j) and increases in trade costs between the partner and non-member
country (country j and k) induce the threshold, τ̂asy , to shift upward. Thismeans that such trade cost change represented by e amplifies the benefits ofconcluding the FTA between countries i and j.
In contrast to case (i), the trade costs between the member (countryi) and non-member (country k) are constant, so that the tariﬀ rate set by24

country i is influenced only by the trade costs between members. Thus,
the external tariﬀ on the non-member country is induced to decrease by the
reduction in e, but it is ambiguous for the MFN tariﬀ. Such a change intariﬀ rates aﬀects country i’s imports from both counties. The reductionin the external tariﬀ causes imports from the non-member to increase, andthus, an increase of imports under the FTA is larger compared with thesituation under the MFN principle. This is because the tariﬀ imposed bycountry i on country k has a greater response to change in e under the FTA
FN/de < 0. On the other hand,than the MFN, that is, dtFkiT A /de < dtM
iimports from the partner country lead to a decrease by trade cost reduction
between them under both regimes. Due to the ambiguity of the trade costeﬀects on the MFN tariﬀ, it is not clear in which regime imports from thepartner country decrease more than the other.
Given such shifts in the trade structure caused by trade costs between
members and the tariﬀ set by country i, [it is found that Eq. (36)] is not exFTA
MF N
plained only by the trade cost eﬀects (τji qji(τ i ) − qji(τ i ) /3). Whenthe trade costs τ are suﬃciently large, the expenditure for trade costs increases by reducing trade costs between members. However, we can understand this[case by considering the] gross utility eﬀect (∆Ui ) and trade cost
FTA
MF N
eﬀect (τji qji (τ i ) − qji (τ i ) /3) simultaneously. Actually, under hightrade costs τ , the gross utility eﬀects work to improve the FTA benefits forcountry i and exceed the negative trade cost eﬀects. On the other hand, thelow trade costs τ indicate the trade cost eﬀects enhance the FTA benefits.
Although the gross utility eﬀect could decline as the trade costs between
members decrease owing to substitution eﬀects, positive trade cost eﬀects
outweigh that. These eﬀects, the gross utility eﬀect and trade cost eﬀect,
create positive eﬀects for the FTA benefits when trade costs between members decline and when trade costs between the partner and non-member
increase from symmetric equilibrium.
Furthermore, in this case, the eﬀects cause FTA benefits to decline. Dueto the higher tariﬀ on the non-member country employed in the FTA thanunder the MFN, country i has larger imports than the non-member when
the FTA is formed. Hence, the third-country eﬀect (∆IMki (τ i )) in thiscase shifts negatively with an increase in the payment to the non-member
country. In addition, country i’s trade structure is aﬀected by the change
in trade costs between the partner and non-member countries. An increasein those trade costs induces the partner country to substitute imports fromthe non-member country for those from country i, by which exports fromcountry i to country j are expanded. Thus, the direct trade surplus eﬀects(∆N Eij (τ i , τ j )) are likely to strengthen the benefits of country i forming the
FTA with country j. However, as mentioned above, country i’s payments
25

for imports from country j (the partner for country i) could also increase as
the trade costs between members decline. Two such conflicting directionaleﬀects about trade between members make it ambiguous whether the direct
trade surplus eﬀects (∆N Eij (τ i , τ j )) are encouraging for forming the FTA.
However, supposing demand linearity and quasi-linear utility, these eﬀects
that could be negative are dominated[ by positive eﬀects, the] gross utility
FTA
MF N
eﬀect (∆Ui ) and trade cost eﬀect (τji qji (τ i ) − qji (τ i ) /3).
(iii) em = 0, ei = e and ej = −e.
Third, we consider the eﬀects of reducing the trade costs between the member country (country i) and non-member country (country k), and raising
the trade costs between the partner country (country j) and non-ember
country (country k). This case shows the situation as below. The member country (country i) faces the lower costs for trading with non-member
country (country k) while the trade costs between own country and thepartner country (country k) remain. Additionally, there are large trade
costs between the partner country (country j) and the non-member country(country k). Unfortunately, it is not clear whether the FTA benefit improves with the change in e, unlike in the other two cases. In this case, thetrade
between members[ Fcosts] remain constant, so that the trade cost eﬀects
TA
MF N(τji qji(τ i ) − qji(τ i ) /3) are influenced indirectly from the trade costswith the non-member country. Thus, the influence from the non-member
are mitigated relative to the previous two cases, resulting in the eﬀect oftrade cost reduction on the FTA benefits remaining unclear.
Given the reduction of costs for trading with country k, the external
tariﬀ imposed by country i on country k (non-member country) increases
while the eﬀects on the MFN tariﬀ are obscured. The decrease in trade
costs between country i and k enhances their trading and, by contrast,
country i could employ the higher tariﬀ in both regimes so as to prevent
such enhanced trade and to save payments to the non-member. The changeof the external tariﬀ is large enough to dominate the MFN tariﬀ’s change,
but both tariﬀ changes are not as large as the trade cost reduction. This
indicates that country i, under the MFN, increases imports from country kmore than under the FTA formation. On the other hand, the trade structure
between members is aﬀected from two aspects: the change in the trade costs
between country i and k, and between country j and k. When the imports
from the non-member country (country k) increase with the reduction intrade costs between countries i and k, this leads consumers in country i tosubstitute imports from country k for those from country j in both regimes.
In addition, the consumers in country j are induced by an increase in trade
costs between country j and k to substitute imports from country k for those26

from country i, which brings about an increase in exports of manufacturingfirms in country i.
From the changes of trade structure caused by the reduction in trade
costs between country i and k, we explain the eﬀects on FTA benefits in
respect of gross utility[eﬀects (∆Ui ), third-country
eﬀects (∆IMki (τ i )), and
]
FTA
MF N
trade cost eﬀects (τji qji(τ i ) − qji(τ i ) /3). As trade costs decrease
between country i and k, the gross utility eﬀects (∆Ui ) is negative on the
FTA benefits since country i under the MFN can achieve unbiased consumption relative to the FTA. Considering the third-market eﬀects (∆IMki (τ i )),an increase in country i’s import value from country k caused by their trade
costs declining is larger under the MFN than under an FTA. Thus, in thiscase, the third-country eﬀects (∆IMki[(τ i )) work to enhance]the FTA. Next,
FTA
MF N
we consider the trade cost eﬀect (τji qji(τ i ) − qji(τ i ) /3). The large
γ induces the large increase in external tariﬀ as e declines and, thus, country
i under the MFN can save payments for trade costs more than when country
i forms the FTA with country j. Consequently, a reduction in trade costs
generating the substitution eﬀects increases payments of trade costs under
the FTA relative to the MFN and, thus, does not improve the FTA benefit
in this case.
In order to show the intuition about the direct trade surplus eﬀects(∆N Eij (τ i , τ j )), we need to focus on the eﬀects on trade structure between members yielded by the trade costs faced by each member countries
via trading with the non-member country. Based on the shift of trade structure as mentioned above, a reduction in e causes the two opposing eﬀects
to country i’s trade surplus with country j. Hence, it is unclear whether
the direct trade surplus eﬀects (∆N Eij (τ i , τ j )) work on the FTA benefit
because of the change in trade costs denoted by e in this case.
In the previous two cases, the FTA benefits are improved with reduced
trade costs, even if there are ambiguous or negative eﬀects. However, thechange in e has ambiguous eﬀects on the FTA benefits in the case that we
focus on the trade costs faced by the members when they trade with thenon-member country. This is because trade costs are not aﬀected between
the member countries. Keeping
betweenthe members constant,[ F T A trade Mcosts](τ i ) − qji F N (τ i ) /3) is aﬀected by the substithe trade cost eﬀect (τji qji
tution eﬀects only indirectly and works to mitigate the benefit of forming the
FTA relative to the case of reducing the trade costs between the members.
Totally, we summarize these discussions in each case as Proposition 6
Proposition 6 (Asymmetric trade costs and welfare) As compared withthe symmetric equilibrium, the FTA benefit for member countries is amplified
by the introduction in trade costs if it is like ensuring the lower trade costs
27between member countries rather than any other trade costs. Otherwise, theFTA formation could not have an advantage relative to the symmetric case.

5

Conclusion

In this study, we construct a simple intra-industrial trade model in the presence of international trade costs, and reveal the relationship between trade
costs and tariﬀs, determined according to three scenarios: tariﬀ discrimination, the MFN principle, and the FTA. Many economists state that FTA
formation has beneficial eﬀects for member countries as well as non-member
countries owing to tariﬀ complementarity eﬀects. In contrast to previous
literature, the present analysis shows that tariﬀ complementarity eﬀects arelikely to disappear with higher trade costs between countries forming theFTA. Furthermore, welfare analysis sheds light on the negative aspects ofan FTA, which may lower FTA members’ welfare when each trade cost between countries is significantly large. Despite trade expansion by the FTA
formation, it also increases the payment of trade costs, which leads to adecrease in national welfare. Thus, higher trade costs, especially between
member countries, bring about welfare worsening under the FTA for its
members.
In the closing, we suggest the possibility of trade costs being the factor
that can influence conservative results, so that we are required to implement further analysis on FTAs in the presence of trade costs. For example,
there is a puzzle in this field whether an FTA yields “building blocks” or“stumbling blocks” (Bhagwati, 1993). To approach this issue, our model
should be extended to incorporate an endogenous decision about FTA formation, analyzing the relationship between the structure of trade costs andthe incentive to conclude the FTA.

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