ECONOMIC RESEARCH CENTERDISCUSSION PAPER
E-Series

No.E17-1

Determination and Harmonization of
Product Standards in a Free Trade Agreement
byAkihiko Yanase
Hiroshi Kurata

April 2017

ECONOMIC RESEARCH CENTERGRADUATE SCHOOL OF ECONOMICSNAGOYA UNIVERSITY

Determination and Harmonization of ProductStandards in a Free Trade Agreement∗
Akihiko Yanasea†, Hiroshi Kuratab‡a Graduate School of Economics, Nagoya University
b Faculty of Economics, Tohoku Gakuin University

March 31, 2017

Abstract
This study considers endogenous domestic standards on products to control negative
consumption externalities in a three-country model of international oligopoly witha possible free trade agreement (FTA). We examine how the level of standards andwelfare eﬀects of FTA are aﬀected and what is caused by harmonization of standards.
We find that if asymmetries in preference or transboundary externalities are not too
strong, an FTA makes the standards more stringent, and it may or may not makethe FTA members better oﬀ, while the non-member countries better oﬀ. We also
demonstrate that harmonization of standards between the FTA members makes the
FTA more favorable.
Keywords: Optimal tariﬀs; Standards; Free trade agreements; International oligopoly;
Harmonization
JEL classifications: F12; F13; F15; F18∗

The authors would like thank Nicola Coniglio, Marco Martorana, Minoru Kunizaki, Keisaku Higashida,
Morihiro Yomogida, Noritsugu Nakanishi, Laixun Zhao, Cheng-Hau Peng, Kazunobu Hayakawa, Toshihiro
Ichida, Taiyo Yoshimi, Jadish Dean, Kristy Buzard, Naoto Jinji, Yan Ma, and Qiang Wu for their comments
on earlier drafts.
†
Corresponding Author; Address: Graduate School of Economics, Nagoya University, Furo-cho,
Chikusa-ku, Nagoya 464-8601, Japan; E-mail: yanase@soec.nagoya-u.ac.jp‡
hkurata@mail.tohoku-gakuin.ac.jp1

1

Introduction

Regional trade agreements (RTAs) have dramatically been increased in the last two decades.
As of 8 January 2015, 604 notifications of RTAs (counting goods, services and accessions
separately) had been received by the World Trade Organization (WTO), and among them
398 were in force.1 This is more than twenty times from the corresponding number in 1990.
Under these RTAs, tariﬀs on trade in manufacturing products have been considerably reduced between its member countries. In contrast, even under the RTAs, non-tariﬀ barriers
such as domestic regulations and technical regulations still exist among the RTA member
countries. Instead of tariﬀs, non-tariﬀ barriers can now be a cause of trade disputes.
Among non-tariﬀ barriers, product standards, that is, domestic regulations to keep
safety or environmental condition for the country, become emerging issues relating to trade
agreements. Such product standards include vehicle emissions and safety standards, restrictions on pesticide residues on agricultural goods, regulations on food additives, andensuring the safety of electrical products. If these product standards are mandatory, they
will have direct impacts on international trade because the standards are generally diﬀerent
across the countries and only the products that meet standards are allowed to circulate in
the market; consequently, such diﬀerent standards may be obstacles for foreign exporters.
Moreover, if regulations and standards are set arbitrarily, they could be used as an excuse
for protectionism.2
In the recent trend, governments lower tariﬀs by contracting RTAs, while they take nontariﬀ barriers at the same time. Then, the levels of product standards must be aﬀectedby RTAs. In other words, product standards and the RTAs are strategically interacted.
Although some studies focus on product standards quite recently, such strategic interactions between product standards and RTAs have been overlooked. Fisher and Serra (2000)
point out the possibility of strategic use of standards under international oligopoly; theyshow that governments can exclude foreign firms by setting the lowest standard though
1

See WTO website: http://www.wto.org/.
In response to the concerns that standards might be a disguised form of protectionism, the WTO
has established two specific agreements that govern standards: Agreement on Technical Barriers to Trade(TBT) and Agreement on the Application of Sanitary and Phytosanitary Measures (SPS).
2

2

it increases costs of domestic firms. Costinot (2008) compares performance between two
diﬀerent agreements on product standards; one is based on a national treatment principle
applied in the WTO, and the other is based on a mutual recognition principle, which is
being employed within the EU. More recently, Takarada, et al (2016) investigate regionaland multilateral agreements on standards in a three-country oligopolistic trade model toshed light on how country-specific or region-specific regulations aﬀect multilateralism. Notice that these studies focus on standards as non-tariﬀ barriers by assuming no tariﬀ-based
protection. Furthermore, with such strategic interactions between product standards and
RTAs, are RTAs reasonable for the member or nonmember countries? This question is notstraightforward, and we believe that this question is quite important from the viewpointof economic policy.
Additionally, we have often witnessed harmonization of standards in contracting RTAs.3
For example, when the European Union (EU) forms an RTA with other countries, theagreement requests the partner country to harmonize its national standards and conformity assessment procedures with those of the EU (Stoler, 2011). What is the reason for
harmonization of product standards in RTAs?
The purpose of this paper is two-fold. The first one is to clarify how product standards
is determined in an RTA and whether the RTA with standards is preferable for member andnonmember countries. The second one is to explain the incentive to harmonize standards
in contracting RTAs. Among several forms of RTAs, this paper focuses on free trade
agreements (FTAs), where each member country chooses its external tariﬀs independently.4
More specifically, we address the following questions: Do standards become more or lessstringent under an FTA than in the absence of it? After a formation of the FTA, do member
and nonmember countries better oﬀ? Do potential FTA members have an incentive to3Harmonization is one of the approaches for removing impediments caused by diﬀerences between national standards. The approaches are (i) using the existing international standards set by international
standard bodies such as the International Organization for Standardization (ISO), and (ii) mutual recognition (MR), where a country may recognize standards imposed by another country as equivalent to its
own standards even if they diﬀer. The EU has adopted the MR principle as well as harmonization.
4
In view of the fact that most existing RTA arrangements take the form of FTAs and less than 10%
can be considered to be fully fledged customs unions, 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.

3

harmonize their standards? In a simple theoretical framework, we provide clear answers tothese questions. In contrast to the existing studies we have mentioned, we consider both
tariﬀs and non-tariﬀ barriers — standards. In this paper, therefore, we take account of theinteractions between these “traditional” and “modern” forms of trade protection.
The structure of our model is based on those in the studies on welfare eﬀects of RTAs
or the possibilities for RTAs to achieve global free trade under international oligopoly (Yi,
1996, 2000; Krishna, 1998; Freund, 2000; Orneras, 2005a,b; Saggi, 2006). We consider athree-country model of international oligopoly and incorporate an endogenous determination of standards by national governments into the model. More specifically, we consider
standards for controlling negative externalities by consumption of goods; in order to enter the importer country?fs market, foreign exporters must produce goods that meet theimport?fs standard. Assuming that governments are benevolent, without any politicalincentives to set their respective standards, we consider endogenous determination of standards as well as (external) tariﬀs.5
Among several forms of RTAs, this paper focuses on free trade agreements (FTAs),
where each member country chooses its external tariﬀs independently.6 The structure of
the model employed in this paper is based on those in the studies on welfare eﬀects of RTAs
or the possibilities for RTAs to be multilateral free trade under international oligopoly (Yi,
1996, 2000; Krishna, 1998; Freund, 2000; Orneras, 2005a, b; Saggi, 2006). We consider athree-country model of international oligopoly and incorporate an endogenous determination of standards by national governments into the model. More specifically, we consider

5

Taxation on consumption can also be as a means to control the negative externalities. Gulati and Roy(2008) point out that it is often diﬃcult to employ an emissions tax. For example, according to Fullerton
and West (2002), the technology to apply a tax per unit of automobile emissions is currently unfeasible.
It is not possible to measure each car’s emissions in a reliable and cost-eﬀective manner. Being unable
to measure and regulate emissions eﬀectively generally true for most consumption-generated pollutants,
mainly because the technology to do so does not justify the costs. In the absence of an emissions tax,
the government s next best alternative is to tax consumption instead. However, unlike an emission tax,
the consumption tax does not encourage consumers to value goods with a higher environmental standard.
Under a consumption tax, the market fails to deliver the optimal environmental standard, the government
has to regulate both the standard and the consumption tax to achieve its first best.
6
In view of the fact that most existing RTA arrangements take the form of FTAs and less than 10%
can be considered to be fully fledged customs unions, 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.

4

standards for controlling negative externalities generated by consumption of goods;7 inorder to enter the importer country’s market, foreign exporters must produce goods thatmeet the import’s standard, and thus the standard can be a nontariﬀ barrier. Assumingthat governments are benevolent, without any political incentives to set their respective
standards, we consider endogenous determination of standards as well as (external) tariﬀs.
Our main findings are as follows: Compared with the policy game in the absence of
FTAs, an FTA makes the member countries to choose more stringent standards. Regarding
the national welfare in each country, the FTA member countries may or may not be betteroﬀ under the formation of an FTA, while the nonmember country becomes better oﬀ.
By comparing the case in which FTA members independently determine their respective
national standards with the case in which the FTA member countries harmonize theirstandards within the FTA, such harmonization of standards will lead the member countries
to choose less stringent standards and make the formation of the FTA more favorable.
The rest of this paper is organized as follows. In section 2, we set up a three-country
model of international oligopoly with standard imposed by the national government. In
section 3, we derive the equilibrium of policy game in the absence of FTAs. In section 4,
we derive the equilibrium of policy game under an FTA. When governments in the member
countries determine their respective standards, they may act independently or jointly. In
section 5, we examine how a formation of the FTA aﬀects the standards chosen by themember countries and national welfare in member and nonmember countries. In section
6, we compare the outcomes under national standards with those under harmonization ofstandards within the FTA. We extend the basic model and discuss the robustness of thebasic results; in section 7, we consider an asymmetry in externality parameters, and insection 8, we introduce transboundary externalities into the basic model. In section 9, we
provide brief concluding remarks.

7

We focus on product standards related to consumption externalities because the issue will not be aneasy job when we discuss the optimal level of standards and harmonization of such standards. In thepresence of externalities, national governments have an incentive to set their own respective standards so
as to protect the residents from possible damages. In general, the resultant standards can diﬀer between
these countries, an anecdotal evidence reveals that countries dealt with the conflicts in diﬀerent manners.

5

2

Model

We consider three countries, A, B, and C, each with one firm that produces a homogeneous
product. Consumption of the product generates negative externalities, the level of which
depends on a regulatory standard imposed by the national government. We suppose a worldin which the standard should be nondiscriminatory; if the government sets a standard on
the product produced by the home firm, the same standard should be applied to imported
products. Let us denote the standard imposed in country i by si (i = A, B, C), andthe externalities per unit of consumption is thus given by bi (si ), which is assumed to be
decreasing in si . In the basic model, we assume that the externalities are purely local.
This assumption will be relaxed in the later section. There is also another homogeneous
good, which serves as the numeraire and is assumed to be freely traded and produced under
perfect competition with constant returns to scale technology, and generate no externalities.
There is a continuum of homogeneous consumers of measure one. Each consumer incountry i has the following quasi-linear preference:
U i (Qi , Yi ; si , Q̄i ) = ui (Qi ) + Yi − bi (si )Q̄i ,where Qi and Yi are his consumption of the externality-generating product and the numeraire, respectively, and Q̄i is the aggregate consumption of the product. As explained
above, bi (si )Q̄i denotes the negative externalities in this country.8 Throughout the paper,
we assume that ui (Qi ) is quadratic and hence the consumers’ utility maximization derives
the linear inverse demand function Pi (Qi ) = αi − Qi , αi > 0, i = A, B, C.
The three firms compete in quantities in each of the national markets, which are assumed to be segmented. Throughout the paper we assume that these firms have identicaltechnologies and each firm’s unit production cost is a function of standard imposed in the
country of consumption. Let us denote the unit production cost by c(si ), which is assumed
to be increasing in si . That is, it is more expensive to produce at a higher standard.98For each consumer, bi (si )Q̄i is taken as given in the utility maximization problem, the first-ordercondition of which is thus given by pi = u′i (Qi )9For example, if the use of a certain food additive is legally prohibited in a country, the firms supplying
food products in that country’s market should avoid using that material in their production process.

6This is because the firms are banned from selling goods that do not meet individual national standards, and thus the firms produce goods which exactly fulfill the requirementsof standards in each country’s market.
We also assume that the governments imposes tariﬀs on imports. Because the markets
are segmented, we can consider the Cournot–Nash equilibrium in each market separately.
Let us denote the output of the domestic firm by qii and the outputs of foreign exporters
by qij , and qik , i, j, k = A, B, C, i ̸= j ̸= k, thus Qi = qii + qij + qik . The foreign firms facea specific tariﬀ when exporting to country i. Let us denote the tariﬀ rates on imports thatthe national government in country i imposes by tij and tik , respectively. Assuming thatthe firms do not incur fixed costs, profits of the respective firms supplying to the market
in country i are given by
πii = [Pi (Qi ) − c(si )]qii = [ai (si ) − Qi ]qii ,πij = [Pi (Qi ) − c(si ) − tij ]qij = [ai (si ) − Qi − tij ]qij ,πik = [Pi (Qi ) − c(si ) − tik ]qik = [ai (si ) − Qi − tik ]qik ,where ai (si ) ≡ αi −c(si ). From the first-order conditions for profit maximization, Cournot–
Nash equilibrium output of each firm is derived as follows:qii =ai (si ) + tij + tik
,
4

qij =

ai (si ) − 3tij + tik
,
4

qik =

ai (si ) + tij − 3tik
.
4

(1)

The total output sold in country i is therefore derived as
Qi =3ai (si ) − tij − tik
.
4

(2)

These equilibrium outputs are a function of policy variables imposed by the government
in country i.
The total profit of the firm producing the externalities-generating product is the sumof profits from domestic and export sales: πi = πii + πji + πki , i, j, k = A, B, C, i ̸= j ̸=
k. National welfare in each country is defined as the sum of consumer surplus CSi =∫ Qi
Pi (x)dx − Pi (Qi )Qi , total profit πi , and tariﬀ revenue tij qij + tik qik , minus the social0
cost from negative externalities bi (si )Qi . Given the linear demand function, it holds that7

CSi = (Qi )2 /2 and πi = (qii )2 + (qji )2 + (qki )2 . In light of (1) and (2), national welfare is
therefore given byWi =[3ai (si ) − tij − tik ]2 [ai (si ) + tij + tik ]2 [aj (sj ) − 3tji + tjk ]2 [ak (sk ) − 3tki + tkj ]2
+
+
+
32
16
16
16
ai (si ) − 3tij + tikai (si ) + tij − 3tik
3ai (si ) − tij − tik
+ tij
+ tik
− bi (si )
.
(3)
4
4
4

In the following analysis, we assume that there are two standards available, sH andsL , with sH > sL . If the government chooses a low standard, firms do not incur costs,
i.e., c(sL ) = 0, but consumption generates negative externalities bi (sL ) = βi > 0. If thenational government chooses a high standard, firms incur a unit cost c(sH ) = γ > 0,
but negative externalities generated from consumption becomes smaller, i.e., bi (sH ) = θβi ,θ < 1. These simplifications of unit cost and externality functions enable us to compare
the welfare levels under diﬀerent regimes of policy games.
In our analysis, we consider the following order: in the first stage, each government
determines tariﬀs and standards, and in the second stage the firms compete in the Cournot
way. We derive the subgame perfect Nash equilibrium of this game by backward induction.
Although we implicitly consider the situation in which the governments determine thesepolicy instrument simultaneously, under our setting the same solutions are obtained even
if the governments first determine the standards, and then chooses the optimal tariﬀsthat maximizes national welfare taking the standard as given (see Appendix). We thus
formulate the governments’ behavior as if their policy games are played sequentially.

3

Policy Game without FTAs

In this section, we consider a policy game in the absence of FTAs as a benchmark. It isnatural to assume that the determination of tariﬀs follows the principle of nondiscrimination, known as the most-favored-nation (MFN) clause. That is, the government in eachcountry imposes a single nondiscriminatory tariﬀ on its trading partners and all countries
simultaneously choose their respective tariﬀs to maximize their own welfare. Substituting

8

tij = tik = ti into (3), the national welfare is rewritten as
Wi =[3ai (si ) − 2ti ]2 [ai (si ) + 2ti ]2 [aj (sj ) − 2tj ]2 [ak (sk ) − 2tk ]2
+
+
+
32
16
16
16
ai (si ) − 2ti
3ai (si ) − 2ti+ ti− bi (si )
.
2
4

(4)

Taking the tariﬀs in other countries tj and tk as given, the government in country i determines ti so as to maximize welfare (4). From the first-order condition ∂Wi /∂ti = 0, theMFN tariﬀ for a given standard is derived asti =3ai (si ) + 4bi (si )≡ tMi (si ).
10

(5)

Notice that because of the assumptions of segmented markets and a constant unit cost(for a given si ), a country’s MFN tariﬀ does not depend on the other countries’ tariﬀs.
MThis also means that the MFN tariﬀs in the trading partners are tMj (sj ) and tk (sk ). The

stringency of standards aﬀects the MFN tariﬀ rate in the following manner:tM
i (sH ) =3αi + 4βi
3(αi − γ) + 4θβi<= tMi (sL ).
10
10

(6)

Because more stringent standards lead a higher cost of compliance, which reduces outputsof both domestic and foreign firms and raises the price. In order to compensate for the
resulting losses in consumer surplus and tariﬀ revenue, the national government will reduce
the tariﬀs on imports.
We turn to the determination of standards, which are made noncooperatively in thisbenchmark situation. In light of (5), the national welfare (4) can be rewritten as WiM =MM
wiM (si ) + πji(sj ) + πki(sk ), whereMb(si )[3ai (si ) − 2tM[11ai (si ) − 10tM
i (si )]i (si )][ai (si ) + 2ti (si )]−32
44ai (si )2 − 6ai (si )bi (si ) + bi (si )2=10

wiM (si ) ≡(7)

is the domestic surplus andMπhi(sh ) ≡

2[ah (sh ) − 2tM[ah (sh ) − 2bh (sh )]2
h (sh )]
=
,
16
100

h = j, k(8)

are the export profits. Taking the standards in other countries sj and sk as given, the government in country i determines si ∈ {sL , sH } so as to maximize the national welfare WiM .
9

Since WiM is additively separable, the problem is equivalent to choose si that maximizes
the domestic surplus (7).10 A direct calculation yields that if∆wiM ≡ wiM (sH ) − wiM (sL ) =−4γ(αi − γ) + 6βi γθ + (1 − θ)βi [6αi − (1 + θ)βi ]10(9)is positive (negative), the government find it optimal to choose sH (sL ). In order to exclude
cases where governments set prohibitive tariﬀs, we restrict our attention to the parametervalues that satisfy αi > 2θβi + γ and αi > 2βi .11 Given these parameter restrictions, ∆wiM
tends to be positive if βi becomes larger whereas it tends to be negative if γ becomeslarger. Because the property on the sign of ∆wiM will be maintained for any θ < 1, we
henceforth assume that θ = 0 without loss of generality. It therefore follows that ∆wiM > 0(∆wiM < 0) holds if and only if√
γ < (>) γ̄iM (βi ) ≡ αi −3β2
αi2 − αi βi + i .
2
4

It is easily verified that γ̄iM (βi ) is increasing and convex in βi :3αi − βi
dγ̄iM
=
dβi
4

(
)−1/2
3
βi2
2
αi − αi βi +
> 0,
2
4

In addition, it holds that γ̄iM (αi /2) = (1 −d2 γ̄iM
5αi2
=
dβi2
16
√

(
)−3/2
3
βi2
2
α i − α i βi +
> 0.
2
4

5/4)αi ≈ 0.4410αi < αi . Therefore, thegovernment chooses a high standard if γ < γ̄iM (βi ), whereas it chooses a low standard if
γ > γ̄iM (βi ).
Lemma 1. Under the MFN, each government’s dominant strategy for standards is tochoose sH if 0 < γ < γ̄iM (βi ) and sL if γ̄iM (βi ) < γ < αi .
The intuition behind Lemma 1 is straightforward. In tightening standards, national
governments face a trade-oﬀ between a rise in the firms’ unit cost γ and a mitigationof negative externalities βi . If γ is relatively high compared with βi , the former eﬀect
dominates the latter, and thus the governments will choose a less stringent standard. If βi
is relatively high, the government will make an opposite choice.
10

That is, because of the additive-separability property of the welfare function indicates that a country’s
optimal standard is strategically independent of the other countries’ standards.
11
Substituting (5) into the export outputs, we obtain qij = qik = [ai (si ) − 2bi (si )]/10, which becomes
positive if αi > 2θβi + γ (in the case of high standard) and αi > 2βi (in the case of low standard).

104

Policy Games under an FTA

Let us now suppose that countries A and B form a free trade agreement (FTA), which
reduces tariﬀs between these country to zero: tAB = tBA = 0. By definition of an FTA, themember countries set their respective external tariﬀs independently, and let us denote theexternal tariﬀ rate by tiC = ti , i = A, B. Substituting these into (3), the national welfare
of a member country is given byWi =[3ai (si ) − ti ]2 [ai (si ) + ti ]2 [aj (sj ) + tj ]2 [aC (sC ) − 2tC ]2
+
+
+
32
16
16
16
ai (si ) − 3ti
3ai (si ) − ti
+ ti
− bi (si ), i, j = A, B, j ̸= i.
4
4

(10)

Because tariﬀs are eliminated within the FTA partners, total sales and the export to the
FTA partner increase, which lead to increases in consumer surplus and export profit in the
FTA partner’s market. At the same time, the elimination of tariﬀs reduce the domestic
profit and tariﬀ revenue. In addition, the increase in the domestic consumption leads tolarger negative externalities.
Taking the external tariﬀ rate in the FTA partner tj and the tariﬀ rate in the nonmember country tC as given, the government in country i determines ti so as to maximize
welfare (10). The optimal external tariﬀ for a given standard is derived asti =3ai (si ) + 4bi (si )≡ tFi (si ),
21

(11)

which is less than the optimal tariﬀ level under the MFN, tMi (si ).
Lemma 2. For a given level of standards, the optimal external tariﬀ for member country
i under an FTA is lower than the MFN tariﬀ: tFi (si ) < tM
i (si ).
Lemma 2 is a well-known tariﬀ complementarity eﬀect (Bagwell and Staiger, 1998).
Intuitively, because of a change in competitive advantage in the member countries’ markets,a formation of FTAs reduces imports from the nonmember country, which in turn reduces
tariﬀ revenue and consumer surplus, and in order to oﬀset these negative eﬀects the member
countries encourage the import from the nonmember country by reducing external tariﬀs.

11

The government’s behavior in the nonmember country is the same as that under MFN,
and thus, for the firms in the FTA members, the export profit in the nonmember countryM
is πCi(sC ), i = A, B. Then, in light of (11), the member country’s national welfare (10)FM
can be rewritten as WiF = wiF (si ) + πji(sj ) + πCi(sC ), where

11ai (si )2 + 6ai (si )tFi (si ) − 21tFi (si )2 bi (si )[3ai (si ) − tFi (si )]−32
415ai (si )2 − 30ai (si )bi (si ) + bi (si )2=42

wiF (si ) ≡(12)

is the domestic surplus andFπji(sj ) ≡[aj (sj ) + tFj (sj )]2[6aj (sj ) + bj (sj )]2
=
16
441

(13)

is the export profit in the FTA partner’s market.
In the following sections, we consider two scenarios regarding the determination of the
FTA members’ standards. One is a “national standards” regime, where the government
in each member country independently determines the individual standard so as to maximize its own welfare. The other is a “harmonization” regime, where the governments inmember countries harmonize their standards; they jointly determine a common standard
in a cooperative manner.

5

National standards

5.1

Determination of standards

In the national-standards regime, taking the standards in other countries sj and sC as
given, the government in country i determines si ∈ {sL , sH } so as to maximize the national
welfare WiF , or equivalently, the domestic surplus wiF (si ). From (11) and (12), it holds thatwiF (sH ) = 5(αi − γ)2 /14 and wiF (sL ) = (15αi2 − 30αi βi + βi2 )/42. Therefore, the government
find it optimal to choose sH (sL ) if
∆wiF ≡ wiF (sH ) − wiF (sL ) =−30αi γ + 15γ 2 + 30αi βi − βi242is positive (negative), or equivalently, if√

γ < (>) γ̄iF (βi ) ≡ αi −12

αi2 − 2αi βi +

βi2
.
15

(14)

It is easily verified that γ̄iF (βi ) is increasing and convex in βi . As in the policy game equilib{}
rium in the absence of the FTAs, we can partition the set (βi , γ) ∈ R2+ | αi > γ, αi > 2βi
into two regions, one in which the member countries choose sH and the other in which theychoose sL .
Lemma 3. Suppose that countries A and B form an FTA. If the governments in member
countries choose their respective national standards, each government’s dominant strategy
is to choose sH if 0 < γ < γ̄iF (βi ) and sL if γ̄iF (βi ) < γ < αi .
Comparing Lemmas 1 and 3, we see that a formation of the FTA changes the regionsof optimal standards. More specifically, we obtain the following lemma.
Lemma 4. It holds that γ̄iM (βi ) < γ̄iF (βi ) ∀βi ∈ (0, αi /2).
(Proof) Comparing the slopes at the origin, we have dγ̄iM (0)/dβi = 3/4 < 1 = dγ̄iF (0)/dβi .
√In addition, it holds that γ̄iF (αi /2) = (1 − 15/30)αi ≈ 0.8709αi > γ̄iM (αi /2). Since bothγ̄iM (βi ) and γ̄iF (βi ) are increasing and convex in βi , the statement of the lemma holds. □Lemma 4 implies that the FTA further partitions the region in (βi , γ) space where thegovernment in country i choose a low standard under the MFN into two subsets. In lightof Lemmas 1 and 3, if γ̄iM (βi ) < γ < γ̄iF (βi ), the member country i changes its behavior insuch a way that it chooses a low standard under the MFN but it chooses a high standard
after the formation of the FTA. This is illustrated in Figure 1. If (βi , γ) is in region I,
the member country i chooses sL both under the MFN and FTA. If (βi , γ) is in region II,
the member country i chooses sL under the MFN but they choose sH under the FTA. If(βi , γ) is in region III, the member country i chooses sH both under the MFN and FTA.
Because there exists a set of parameters (βi , γ) in which each member country chooses a
low standard under the MFN but chooses a high standard under an FTA and each member
country does not change their standards before and after an FTA formation if (βi , γ) is not
an element of this set, we can establish the following proposition.
Proposition 1. In comparison with the MFN, an FTA makes the member countries tochoose more stringent standards.
13

Figure 1: Comparison of optimal standards before and after an FTA

The intuition behind Proposition 1 is as follows. Eliminating tariﬀs between FTA
partners increases consumption and production in the member countries, but at the sametime, the member countries suﬀer from reduced tariﬀ revenue. However, because of thetariﬀ complementarity eﬀect demonstrated in Lemma 2, the import from the nonmember
country increases, which mitigates the reduction of tariﬀ revenue. Therefore, the positiveeﬀect of the FTA dominates the negative one, and the member country will not be worseoﬀ even though it raises the unit costs of firms supplying to the market by adopting
more stringent standards. Moreover, the increase in consumption will cause expansion ofnegative externalities, and thus the member country should actually adopt more stringent
standards.

5.2

Welfare eﬀects of an FTA with national standards

We are now in a position to examine whether or not an FTA makes each country better oﬀ.
In light of Proposition 1 and Figure 1, there are nine possibilities regarding the combination14

of the member countries’ optimal standards under MFN and FTA, as shown by Table 1.
Therefore, we make comparisons of each country’s national welfare in the respective regions.

(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)(ix)(si , sj ) under MFN(sL , sL )(sL , sL )(sL , sL )(sL , sL )(sH , sL )(sH , sL )(sL , sH )(sL , sH )(sH , sH )(si , sj ) under FTA(sL , sL )(sH , sL )(sL , sH )(sH , sH )(sH , sL )(sH , sH )(sL , sH )(sH , sH )(sH , sH )Table 1: Possible combinations of the member countries’ optimal standards

Member countries We begin with the member countries. Member country i’s nationalMM
welfare is given by WiM = wiM (si ) + πji(sj ) + πCi(sC ) under the MFN and WiF = wiF (si ) +FMπji(sj ) + πCi(sC ) under the FTA, i, j = A, B, j ̸= i.12 Then, from (7), (8), (12), and (13),

we haveM
F
WiM − WiF = wiM (si ) + πji(sj ) − [wiF (si ) + πji(sj )]=

4ai (si )2 − 6ai (si )bi (si ) + bi (si )2 [ah (sh ) − 2bh (sh )]2+
1010015ai (si )2 − 30ai (si )bi (si ) + bi (si )2 [6aj (sj ) + bj (sj )]2
−
−
.
42
441

(15)

In the Appendix, we present the calculation results for cases from (i) to (ix) in Table
1, from which it is diﬃcult to judge whether each member country gains or loses fromforming an FTA. In the following analysis, we focus on some specific cases.
Let us first consider the case in which the member countries share common preference
parameters; i.e., αA = αB = α and βA = βB = β.13 In this case of symmetric member
countries, only cases (i), (iv), and (ix) in Table 1 are possible. In case (i) in Table 1, (15)12The nonmember country always chooses the MFN tariﬀ and does not change the standard before andafter the formation of FTA.
13
In this symmetric countries case, we omit the subscript indicating the country index in the functions
M
γ and γ F .

15can be rewritten as
WiM − WiF = −(423α − 1256β)(3α + 4β)
.
44100

(16)

Then, WiM > WiF (WiM < WiF ) if and only if β > (<) 423α/1256 ≈ 0.3368α.14 In case(iv) in Table 1, (15) can be rewritten as
WiM − WiF =−141α2 − 3136αβ + 686β 2 + 4300αγ − 2150γ 2
.
4900

(17)

Given the parameter restrictions α > γ and α > 2β, it can be verified that WiM > WiF(WiM < WiF ) holds if and only if
7
γ > (<) γ̃(β) ≡ α −5√

41 2 327
α − αβ + β 2 .
86
43
43
(
)
It also holds that γ̃(0) ≈ 0.0333α and γ̃(α/2) ≈ 0.4663α ∈ γ̄ M (α/2), γ̄ F (α/2) . Finally,in case (ix) in Table 1, (15) can be rewritten as
WiM − WiF = −141(α − γ)2
< 0.
4900

(18)

Therefore, the FTA achieves higher welfare than MFN for the member countries. To sum
up, we have the following lemma (see also Figure 2).
Lemma 5. Suppose that αA = αB = α and βA = βB = β. For the FTA member countries
i = A, B, the national welfare under the FTA and the national standards compared with
the MFN is as follows.
(i) If γ̄ F (β) < γ < α, WiM > WiF (WiM < WiF ) for β > (<) 423α/1256.
(ii) If γ̃(β) < γ < γ̄ F (β), WiM > WiF .
(iii) If 0 < γ < γ̃(β), WiM < WiF .
Lemma 5 can be interpreted as follows. In case (i), the member countries choose sL
both under the MFN and FTA. Because of the elimination of tariﬀs within the FTA andthe tariﬀ complementarity eﬀect, output and consumption become larger under the FTA.
Therefore, the member countries gains from the formation of the FTA unless the negative
externalities per unit of consumption indicated by the parameter β are large enough. In
14

It holds that γ̄ F (423α/1256) ≈ 0.4221α < γ̄ M (α/2).

16Figure 2: Comparison of the FTA members’ welfare in the symmetric case

case (ix), the member countries choose sH both under MFN and the FTA. In this case,the negative externalities are internalized by the imposition of a high standard, and thus
the FTA unambiguously achieves higher welfare to the member countries. In case (iv),where the member countries choose sL under MFN but they choose sH under the FTA,
the member countries face the firms’ higher compliance costs but the negative externalities
will be reduced under the FTA. If γ is relatively high, the high compliance costs harm themember countries, but if β is high, the escape from the negative externalities benefits themember countries.
We now relax the assumption that the member countries are completely symmetricby considering the case where the member countries have diﬀerent perceptions toward
consumption externalities (i.e., βA and βB can diﬀer). We focus on one specific case inwhich the member countries continue to share a common demand size, i.e., αA = αB = α,and γ is equal to γ̄ M (α/2). In this case, the standards chosen under the MFN regime areM
sM
A = sB = sL , and the standard chosen by country i (i = A, B) under the FTA with17

national standard is

{
sL
sFi =
sH

if 0 ≤ βi ≤ β∗if β∗ ≤ βi ≤ α/2,

where β∗ satisfies γ̄ F (β∗ ) = γ̄ M (α/2).15 That is, there are four cases, i.e., from (i) to(ix) in Table 1, and the equilibrium configurations of the member countries’ standards areillustrated in Figure 3.

Figure 3: Equilibrium configurations of the member countries’ standards when βi ’s diﬀer

The possibility that the member countries may choose diﬀerent standards implies thatthe welfare eﬀects of an FTA formation will be more complicated.
Case (i): (sA , sB ) = (sL , sL ) both under MFN and FTA From (15), the diﬀerence
in member country i’s welfare between MFN and FTA is
M
F
WiM − WiF = wiM (sL ) + πji(sL ) − [wiF (sL ) + πji(sL )]=(3α + 4βi )2 13(3α + 4βj )(81α − 32βj )
−
,
210
44100

(19)

which is positive (negative) if}{√
1
13(81α − 32βj )(3α + 4βj )βi > (<)− 3α ≡ β̄(βj ).
4210
It is verified that β̄ ′ > 0, β̄ ′′ < 0, and β̄(0) < β̄(β∗ ) < β∗ . That is, for a given valueof βj , country i’s welfare is smaller (larger) under the FTA than under the MFN if βi is
15

Since γ̄ M (α/2) = α(1 −√√5/4), β∗ is explicitly solved as β∗ = α(60 − 3435)/4 ≈ 0.3478α.

18higher (lower) than a critical value. It follows that both member countries will be better oﬀ
from the FTA formation if these countries’ externality parameters are not suﬃciently large
and not so diﬀerent. However, if the externality parameters are considerably diﬀerent,
only the country with a lower externality parameter will be better oﬀ. The intuition issimilar to the case of symmetric countries; since the member countries do not change theirstandards before and after the formation of an FTA, the optimal external tariﬀs of the
FTA member countries become lower than the MFN tariﬀs, as demonstrated in Lemma
2. In addition to this tariﬀ complementarity eﬀect and the elimination of mutual tariﬀsof FTA members lead to an increase in consumption and export in the member countries.
The increase in consumption, however, has a negative eﬀect on member country i’s welfare
if βi is suﬃciently large.
Case (ii): (sA , sB ) = (sL , sL ) under MFN and (sA , sB ) = (sH , sL ) under FTA The
diﬀerence in member country A’s welfare between MFN and FTA is derived asMMFF
WAM − WAF = wA(sL ) + πBA(sL ) − [wA(sH ) + πBA(sL )]=

323α2 − 672αβA + 112βA213(3α + 4βB )(81α − 32βB )
−
,
1120
44100

which is positive (negative) if√
241047α2 + 23712αβB − 13312βB2√≡ β̂(βB ).
βA < (>)3α −84 5
It is verified that β̂ ′ < 0, β̂ ′′ > 0, and β∗ < β̂(β∗ ) < β̂(0) < α/2. Therefore, for a given
value of βB , country A’s welfare is larger (smaller) under the FTA than under the MFN
if βA is higher (lower) than a critical value. Intuitively, because country A chooses more
stringent standard under the FTA than under MFN, its tariﬀ complementarity eﬀect isstrong.16 This means that the FTA formation increases country A’s domestic consumption
to a larger extent, which increases its consumer surplus. At the same time, the large
reduction in the optimal external tariﬀ reduces the profit from domestic sales and the tariﬀ
revenue. However, since the more stringent standard is chosen under the FTA, negative
consumption externalities reduce (becomes zero in the present setting), and the benefit
16

F
F
From Lemma 2 and (11), it holds that tMi (sL ) > ti (sL ) = (3α + 4βi )/21 > (α − γ)/7 = ti (sH ).

19

from the reduction in the negative externalities becomes larger if βA is larger. Therefore,
for larger values of βA , country A tends to be better oﬀ by the FTA formation.
The diﬀerence in member country B’s welfare between MFN and FTA is derived as
M
MFF
WBM − WBF = wB(sL ) + πAB(sL ) − [wB(sL ) + πAB(sH )]=

51α2 + 336αβB + 224βB2(α − 2βA )2
+
,
1120
100

which is unambiguously positive. That is, country B loses from the FTA formation. Intuitively, since Country B does not change its standard, the FTA formation generates thetariﬀ complementarity eﬀect, which increases the domestic consumption but reduces thedomestic output. Thus, there is an increase in consumer surplus, but the country also suffers from more negative externalities. In addition, the firm profit from domestic sales andtariﬀ revenue decrease. These negative welfare eﬀects dominate the increase in consumer
surplus, and therefore, country B becomes worse oﬀ by forming an FTA.
To sum up, in this case, only the country that changes its standard to a more stringent
one under the FTA can, if any, gain from the FTA formation.

Case (iii): (sA , sB ) = (sL , sL ) under MFN and (sA , sB ) = (sL , sH ) under FTA
This case is the same as case (ii) with A and B being interchanged. That is, country A
unambiguously loses from the FTA formation (WAM > WAF ), and country B becomes betteroﬀ (worse oﬀ) from the FTA formation if βB > β̂(βA ) (βB < β̂(βA )).
Case (iv): (sA , sB ) = (sL , sL ) under MFN and (sA , sB ) = (sH , sH ) under FTA From(15), the diﬀerence in member country i’s welfare between MFN and FTA isFM(sH )](sL ) − [wiF (sH ) + πji
WiM − WiF = wiM (sL ) + πji=

4α2 − 6αβi + βi2 (α − 2βj )2
215 2
+
−
α ,
10
100
1568

which is positive (negative) if√
βi < (>)3α −24583α2 + 1568αβj − 1568βj2√≡ β̃(βB ).
28 5

20

It is verified that β̃ ′ < 0, β̃ ′′ > 0, and β∗ < β̃(α/2) < β̃(β∗ ) < α/2. This means that for agiven value of βj , country i’s welfare is larger (smaller) under the FTA than under the MFN
if βi is higher (lower) than a critical value, and if βA and βB are suﬃciently large and close
to each other, both countries will gain from the FTA formation. The intuition is basicallysimilar to that of country A in case (ii). That is, since both member countries choose more
stringent standard under the FTA than under MFN, they reduce their external tariﬀs
to a larger extent. As a result, both countries enjoy higher consumption and therefore
higher consumer surplus, but the profit from domestic sales and the tariﬀ revenue under
the FTA are small than those under the MFN. However, the member countries suﬀer lessfrom negative consumption externalities under the FTA than under the MFN because they
set more stringent standards, and country i’s benefit from the reduction in the negative
externalities becomes larger if βi is larger. Therefore, for larger values of βi , the positive
welfare eﬀects of the FTA formation in country i will dominate the negative eﬀects. If
both βA and βB are suﬃciently large, both member countries tend to be better oﬀ by the
FTA formation.

From the analysis of welfare comparison in each case, we obtain the welfare eﬀects ofan FTA, as illustrated in Figure 4. This figure shows that, depending on each member
country’s externality parameter, it is possible that both member countries’ welfare will increase under the FTA compared with the MFN, that both member countries’ welfare will
decrease, or that one member country gains and the other member country loses. In particular, if the member countries’ externality parameters are suﬃciently close to each otherand if these parameters take suﬃciently small or suﬃciently large value, both members will
gain from an FTA conclusion. However, if the externality parameters take medium values,
both member countries will lose from the FTA formation. These results are consistent
with the symmetric case demonstrated in Lemma 5. In addition, if the externality parameters considerably diﬀer between the members, the welfare eﬀects of the FTA become
asymmetric.

21

Figure 4: Welfare eﬀects of an FTA for member countries in an asymmetric countries case

Nonmember country In the nonmember country, the national government always
chooses the MFN tariﬀ and does not change the standard before and after the formation of FTA. Therefore, comparisons of the nonmember’s welfare are equivalent to those∑MFof its export profits: WCM − WCF = i=A,B [πiC(si ) − πiC(si )], whereFπiC(si ) =[ai (si ) − bi (si )]2[ai (si ) − 3tFi (si )]2
=
,
16
49

i = A, B

is the export profit in each member country’s market.
If the pair of parameters (βi , γ) for each member country is in either region I or region III
M
F
in Figure 1, WCM < WCF holds because πiC(sL )−πiC(sL ) = −(17αi −24βi )(3αi +4βi )/4900 <MF
0 and πiC(sH ) − πiC(sH ) = −51(αi − γ)2 /4900 < 0. If (βi , γ) is in region II, where member

country i chooses sL under the MFN and sH under the FTA, it holds thatFM(sH ) = −(sL ) − πiC
πiC(17αi − 14βi − 10γ)(3αi + 14βi − 10γ).
4900

Since αi > 2βi , it holds that 17αi − 14βi − 10γ > 10(αi − γ) > 0. Therefore, the sign of theabove expression is positive (negative) if and only if γ > (<) (3αi + 14βi )/10 holds. Region22

II is contained in the set{}(βi , γ) ∈ R2+ | γ < (3αi + 14βi )/10, αi > 2βi . Therefore, inMFregion II it holds that πiC(sL ) < πiC(sH ), which means that WCM < WCF holds as well. To

sum up, we have the following proposition.
Proposition 2. In comparison with the MFN, the nonmember country of the FTA unambiguously becomes better oﬀ under the formation of an FTA.
Intuitively, Proposition 2 can be interpreted as follows. When (βi , γ) is in region I or
region III in Figure 1 for both member countries, the nonmember’s welfare improvement
stems from the tariﬀ complementarity eﬀect shown in Lemma 2. Because the members
adopt the same standards under the FTA as under the MFN, the nonmember country will
face a lower tariﬀ rate under the FTA than under the MFN, which increases its exports
to the member countries and hence export profits of the domestic firm. If (βi , γ) is inregion II, member countries i will tighten up their standards under the FTA, which raises
the unit production cost of the firm in the nonmember country. At the same time, as wehave shown in (6) and similar result holds for the comparison of tFi (sH ) and tFi (sL ), a more
stringent standard lowers the optimal (external) tariﬀ. Therefore, in region II, the tariﬀ
rate that the nonmember country faces under the FTA becomes lower than the MFN tariﬀ
in two channels: one is the tariﬀ complementarity eﬀect and the other is a more stringent
standards chosen by the FTA member. Because the unit cost is at a “moderate” levelin region II, the reduction in the tariﬀ oﬀsets the increase in the unit cost, and thus thenonmember country can increase its export under the FTA.

6

Harmonization of standards

We now consider the second scenario regarding the determination of standards, namely“harmonization”. Suppose that the FTA member countries harmonize their standards inaddition to eliminate tariﬀs between them. More specifically, the member countries A and
B determine a common standard sA = sB = s ∈ {sL , sH }, taking the standards in thenonmember country sC as given, in a cooperative manner. As a cooperative solution, we
consider a Nash bargaining solution, in which the member countries jointly determine the
23

[
][
]
common standard s so as to maximize the Nash product WA (s) − W̄A WB (s) − W̄B
subject to the constraints WA (s) ≥ W̄A and WB (s) ≥ W̄B , where Wi (s) is country i’s
welfare under harmonization of standards and W̄i is country i’s welfare when negotiations
break down. We assume that in the case of disagreement, the member countries choose
their respective national standards, denoted by sFA and sFB , keeping the FTA. Because thenonmember country C chooses the tariﬀs and standards under the MFN regime, it holds
M M
FM(sC ) and W̄i = ω̃i (sFA , sFB ) + πCi(sC ), where ωi (s) ≡ wiF (s) + πji(s)that Wi (s) = ωi (s) + πCi
F F(sj ), i, j = A, B. Therefore, the Nash bargaining problem
and ω̃i (sFA , sFB ) ≡ wiF (sFi ) + πji

can be rewritten as follows:]][[max ωA (s) − ω̃A (sFA , sFB ) ωB (s) − ω̃B (sFA , sFB )ss.t. ωi (s) ≥ ω̃i (sFA , sFB ) for i = A, B.
(20)

6.1

Symmetric member countries

We begin with the case where the member countries share identical preference parameters.
The solution to the problem (20) is characterized by the following lemma.
Lemma 6. Suppose that countries A and B form an FTA and harmonize their standards. Assuming that αA = αB = α and βA = βB = β, it is optimal for both member
countries to choose sH if 0 < γ < γ̄¯ F (β) and sL if γ̄¯ F (β) < γ < α, where γ̄¯ F (β) ≡√23 2
αβ + 387
β .
α − α2 − 202
129(Proof) Since the countries are assumed to be symmetric, either (sFA , sFB ) = (sL , sL ) or(sFA , sFB ) = (sH , sH ) holds under national standards. Suppose that (sFA , sFB ) = (sL , sL ). In
light of (11), (12), and (13), it follows that the member countries jointly choose s = sH if
387γ 2 − 774αγ + 606αβ − 23β 2
ωi (sH ) − ωi (sL ) =
882

(21)

is positive for i = A, B.17 By straightforward calculation, it can be verified that ω(sH ) >ω(sL ) holds if and only if 387γ 2 − 774αγ + 606αβ − 23β 2 > 0, or equivalently, given the
The conditions for s = sL to be chosen are ωA (sH ) ≥ ω̃A (sL , sL ), ωB (sH ) ≥ ω̃B (sL , sL ),and [ωA (sH ) − ω̃A (sL , sL )] [ωB (sH ) − ω̃B (sL , sL )] > [ωA (sL ) − ω̃A (sL , sL )] [ωB (sL ) − ω̃B (sL , sL )]. Since
ωi (sL ) − ω̃i (sL , sL ) = 0 for i = A, B, the above three conditions hold if the sign of (21) is positive.
17

24

parameter restrictions, γ < γ̄¯ F (β). Conversely, if γ > γ̄¯ F (β), it follows that the member
countries jointly choose s = sL . In the case where (sFA , sFB ) = (sH , sH ), the same results□

are obtained.

√√
Since dγ̄¯ F (0)/dβ = 101α/129 ≈ 0.7829α and γ̄¯ F (α/2) = (1 − 359/6 43)α ≈ 0.5184α,
it follows that γ̄ M (β) < γ̄¯ F (β) < γ̄ F (β) for all β ∈ (α/2). This implies that, in light ofLemmas 3 and 6, region II in Figure 1 is further partitioned into two subregions: one inwhich sH is chosen by member countries both under national standards and harmonization(when γ̄ M (β) < γ < γ̄¯ F (β)), and the other in which sH is chosen under the national
standards but sL is chosen under harmonization (when γ̄¯ F (β) < γ < γ̄ F (β)). See also
Figure 5.

Figure 5: Harmonization of standards under the FTA in the symmetric case

Proposition 3. The FTA member countries have an incentive to choose less stringent
standards when they harmonize their standards than when they choose their respective
national standards.
25

Intuitively, Proposition 3 can be interpreted as follows. If the FTA member countries determine their respective standards independently, their objective is to maximize
the domestic surplus wiF (si ). By contrast, if the member countries harmonize their standards, they can take into account the export profit in the FTA partner’s market πijF (s) as
well as the domestic surplus wiF (s) because the FTA partner chooses the same standard(si = sj = s). Because an increase in the standard reduces the export profit in the FTA
partner’s market, compared to the national standards, each member country should adopt
less stringent standards under harmonization.18
Let us conclude this subsection by analyzing the welfare eﬀects of the FTA with harmonization of standards. For the nonmember country, it is verified that Proposition 2 remains
valid; the nonmember country unambiguously gains from a formation of FTAs. For themember countries, because γ̄ M (α/2) < γ̃(α/2) < γ̄¯ F (α/2) holds, we obtain the following
lemma.
Lemma 7. For the FTA member countries i = A, B, the national welfare under the FTA
and harmonization of standards compared with the MFN is as follows.
(i) If γ̄¯ F (β) < γ < α, WiM > WiF (WiM < WiF ) for β > (<) 423α/1256.
(ii) If γ̃(β) < γ < γ̄¯ F (β), WiM > WiF .
(iii) If 0 < γ < γ̃(β), WiM < WiF .
From Lemmas 5 and 7, we find that if β and γ are of moderate size, the member
countries’ welfare under the FTA becomes higher than the MFN level when they jointly
determine the standards even though the opposite holds when they determine their respective standards independently, as illustrated by the shaded area in Figure 6. In otherregions, such a reversal of welfare ranking between the MFN and the FTA does not occur.
The reversal of the welfare ranking implies that harmonization of standards within an FTA
makes the formation of the FTA more favorable.
Proposition 4. Suppose that the member countries have identical preferences as well as
technologies. Then, regional harmonization of standards increases the gains from an FTA
18

Notice that similar intuition and result hold under more general economic environment, as demonstrated by Takarada et al. (2016) assuming free trade in goods.

26formation in the sense that there exists a set of parameters (β, γ) in which, for i = A, B,
WiM > WiF holds when the member countries seek their national standards but WiM < WiF
holds under harmonization of standards.
Proposition 4 has the following implications. The FTA member countries prefer harmonizing their standards in addition to remove tariﬀs between them. This can explain
the recent regional and preferential economic agreements being the form of harmonizeddomestic regulations as well as tariﬀ reductions. Notice that the less stringent standards
are chosen by the members at the expense of increasing the gains from FTA.

Figure 6: Comparison of the welfare eﬀects of FTA between national standards and harmonization in the symmetric case

6.2

Asymmetric member countries

We next consider a situation in which preferences can diﬀer across member countries anddiscuss how our findings under the assumption of symmetric countries can be aﬀected.

27

As in the previous section, we focus on the case where αA = αB = α and γ is equal toγ̄ M (α/2). As noted in the previous section, there are four cases, i.e., from (i) to (ix) in
Table 1, and the equilibrium configurations of the member countries’ national standards
are illustrated in Figure 3.
Case (i): (sFA , sFB ) = (sL , sL ) under national standards In this case, if ωi (sH ) >ω̃i (sL , sL ) = ωi (sL ) for i = A, B, s = sH is the Nash bargaining solution. Otherwise,sA = sB = sL is the equilibrium outcome.19 Comparing ωi (sH ) and ωi (sL ), we haveFF
ωi (sH ) − ωi (sL ) = wiF (sH ) + πji(sH ) − wiF (sL ) − πji(sL )−336βi2 + 10080αβi − (4257α2 + 384αβj + 32βj2 )
=
.
14112

Suppose that the sign of the above equation is positive, which is possible if√
71343α2 − 384αβj − 32βj2√
βi < 15α −
.
4 21

(22)

It is easily verified that the right-hand side of (22) is increasing in βj . In addition, βi =√√√(420− 166467)α/28 ≈ 0.4284α if βj = 0 and βi = (60− 2453 + 16 3435)α/4 ≈ 0.4424α
if βj = β∗ . Both of these values for βi are strictly greater than β∗ , and thus contradicts(βA , βB ) ∈ [0, β∗ ] × [0, β∗ ]. Therefore, it must hold that ωi (sH ) < ωi (sL ) for i = A, B, andthus, we have the Nash bargaining solution s = sL .
Case (ii): (sFA , sFB ) = (sH , sL ) under national standards In this case, s = sL ischosen as a Nash bargaining solution if ωA (sL ) ≥ ω̃A (sH , sL ), ωB (sL ) ≥ ω̃B (sH , sL ), and[ωA (sL ) − ω̃A (sH , sL )][ωB (sL ) − ω̃B (sH , sL )] > [ωA (sH ) − ω̃A (sH , sL )][ωB (sH ) − ω̃B (sH , sL )].
However,FF(sH ) =(sL ) − wA
ωA (sL ) − ω̃A (sH , sL ) = wA

165α2 − 480αβA + 16βA2
672

is equal to 0 if βA = β∗ and negative for βA ∈ (β∗ , α/2). This means that country A has no
incentive to join in the bargaining. By contrast, country B has an incentive to participate
19

If ωi (sL ) > ω̃i (sH , sH ) = ωi (sH ) for i = A, B, s = sL is the Nash bargaining solution. If ωi (sH ) <ωi (sL ) but ωj (sH ) > ωj (sL ), i ̸= j, the member countries fail to reach an agreement. In this case, theseFcountries implement national standards, which are sF
A = sL and sB = sL .

28

in the bargaining sinceFFωB (sL ) − ω̃B (sH , sL ) = πAB(sL ) − πAB(sH ) =

99α2 + 48αβA + 4βA2
> 0.
1764

Suppose, then, country B makes an international transfer to compensate country A’s welfare loss. Now the question is whether [ωA (sL ) − ω̃A (sH , sL )][ωB (sL ) − ω̃B (sH , sL )] >F
[ωA (sH ) − ω̃A (sH , sL )][ωB (sH ) − ω̃B (sH , sL )] holds, or equivalently, whether [wA(sL ) −
F
F
F
F
F
F
F
(sH )][πAB(sL )−πAB(sH )]−[πBA(sH )−πBA(sL )][wB(sH )−wB(sL )] is positive. A straightwAforward calculation yields
F
F
F
F
F
F
F
F
(sH ) − wB(sL )](sL )][wB(sL ) − πAB(sH )] − [πBA(sH ) − πBA(sH )][πAB[wA(sL ) − wA=

α(βA − βB )(−660α2 + 32βA βB + 11α(βA + βB ),14112

which unambiguously negative since we are considering the case of βA > βB and it holds
that −660α2 + 32βA βB + 11α(βA + βB ) < 0. Therefore, even though the transfer fromcountry B to country A is made, s = sL cannot be a Nash bargaining solution.
We next consider the possibility that s = sH is chosen as a bargaining solution, which
occurs if ωA (sH ) ≥ ω̃A (sH , sL ), ωB (sH ) ≥ ω̃B (sH , sL ), and [ωA (sH ) − ω̃A (sH , sL )][ωB (sH ) −ω̃B (sH , sL )] > [ωA (sL ) − ω̃A (sH , sL )][ωB (sL ) − ω̃B (sH , sL )]. However, sinceFFωA (sH ) − ω̃A (sH , sL ) = πBA(sH ) − πBA(sL ) = −99α2 + 48αβA + 4βA2
<0
1764

and
F
F
ωB (sH ) − ω̃B (sH , sL ) = wB
(sH ) − wB(sL ) = −165α2 − 480αβB + 16βB2
672

is nonpositive if βB ≤ β∗ , both countries have no incentive to join in the bargaining.
To sum up, the bargaining for harmonization breaks down in this case.
Case (iii): (sFA , sFB ) = (sL , sH ) under national standards This case is the same ascase (ii) with A and B being interchanged. That is, the member countries fail to achieve
the harmonization of standards.
Case (iv): (sFA , sFB ) = (sH , sH ) under national standards In this case, if ωi (sL ) >ω̃i (sH , sH ) = ωi (sH ) for i = A, B, s = sL is the Nash bargaining solution. Otherwise,29

sA = sB = sH is the equilibrium outcome.20 As demonstrated in the analysis of case (i),ωi (sH ) > ωi (sL ) holds if the parameters satisfy (22). The right-hand side of this inequality√√
is shown to be increasing and convex, and it holds that βi = (60− 2453 + 16 3435)α/4 ≈√0.4424α > β∗ if βj = β∗ and βi = (60 − 71143/21)α/4 ≈ 0.4489α ∈ (β∗ , α/2) if βj = α/2.
Therefore, if (βA , βB ) is in the area northeast of ωA (sH ) = ωA (sL ) curves and ωB (sH ) =ωB (sL ) in Figure 7, the member countries harmonize their standards and choose s = sH .
By contrast, if (βA , βB ) is in the area southwest of these curves, they jointly choose s = sL .
In other areas, the member countries fail to achieve harmonization of standards, and thus,
individually choose sH .

Figure 7: Harmonization of standards under an FTA in an asymmetric countries caseTo sum up the above discussion, we obtain the outcome of negotiation over harmonization of standards, as illustrated in Figure 7. The member countries will agree on
harmonizing their standards only if the pair of parameters (βA , βB ) is in the shaded area;
if there is a considerable asymmetry in the externality parameter, the member countries
20

If ωi (sH ) > ωi (sL ) for i = A, B, s = sH is the Nash bargaining solution. If the signs of ωA (sH )−ωA (sL )and ωB (sH ) − ωB (sL ) diﬀer, the member countries fail to reach an agreement and thus, these countries
F
implement national standards, i.e., sF
A = sB = sH .

30

fail to achieve harmonization. In addition, if βA and βB are of intermediate values (darkshaded area in Figure 7), the member countries will choose s = sL under harmonizationeven though they individually choose sH under national standards. That is, we can confirm
that Proposition 3 remains valid in the presence of an asymmetry considered here.
We conclude this subsection by discussing whether harmonization of standards increases
the gains from an FTA formation. We are interested in the case where the member countries
will choose less stringent standards when they harmonize their standards than when theychoose their respective national standards, i.e., the dark-shaded area in Figure 7. In thiscase, under national standards, WiM > WiF holds for both member countries i = A, B,
as shown in Figure 4. However, under harmonization, the comparison of WiM and WiF
follows (19), and it was shown that WiM > WiF if βi > β̄(βj ) and vice versa. It can be√verified that β̄(α/2) = ( 887250−630)α/840 ≈ 0.3714α > β∗ , which means that the curve
βi = β̄(βj ) goes through the dark-shaded area, as illustrated in Figure 8. It follows thatif βi ∈ (β∗ , β̄(βj )), WiM < WiF and WjM > WjF hold for i, j = A, B, j ̸= i. That is, oneof the member countries can gain from an FTA formation when these countries harmonize
their standards even though they both lose from the FTA formation in the absence ofharmonization.21

7

Transboundary Externalities

In this section, we extend our basic model by incorporating transboundary consumption
externalities. A typical example of standards related to transboundary externalities is
the regulation to limit automotive exhaust emissions. For analytical tractability, we focus
on the situation in which all countries are symmetric in terms of preferences as well as
technologies.
Let us denote the degree of transboundary externalities by δ ∈ [0, 1]. Then, the representative consumer’s utility function is rewritten as U (Qi , Yi ; si , Q̄i ) = u(Qi )+Yi −b(si )Q̄i −21

In this example, only one country can gain from an FTA formation under harmonization. This isbecause we set γ = γ̄ M (α/2). If we assume a case where γ is suﬃciently lower than γ̄ M (α/2), Figure 6
infers that there can be the case where harmonization of standards facilitates an improvement in member
countries’ welfare under an FTA.

31

Figure 8: Welfare eﬀects of an FTA with harmonization of standards in an asymmetriccountries case∑22and hence the national welfare (3) is rewritten asj̸=i δb(sj )Q̄j ,Wi =[3a(si ) − tij − tik ]2 [a(si ) + tij + tik ]2 [a(sj ) − 3tji + tjk ]2 [a(sk ) − 3tki + tkj ]2
+
+
+
32
16
16
16
a(si ) + tij − 3tik
3a(si ) − tij − tika(si ) − 3tij + tik+ tik− b(si )
+ tij
4
4
4
[
]
3a(sj ) − tji − tjk
3a(sk ) − tki − tkj− δ b(sj )+ b(sk )
.
(23)
4
4

The above expression implies that the presence of transboundary externalities does not
aﬀect the first-order conditions for optimal unilateral tariﬀs. Therefore, the optimal tariﬀ
formulas, i.e., (5) under the MFN and (11) under an FTA, are still valid when transboundary externalities exist.

7.1

MFN

In the presence of transboundary externalities, the national welfare under the MFN canMM(sj ) + ηki(sk ), where the domestic surplus wiM (si )now be rewritten as WiM = wiM (si ) + ηji

is defined by (7) andηliM (sl ) ≡ πliM (sl ) − δb(sl )Ql=[a(sl ) − 2tM (sl )]23a(sl ) − 2tM (sl )− δb(sl )
,
16
4

22

l = j, k(24)

Because of the symmetry assumption, we omit the subscripts in the subutility function u and the
per-unit externality function b.

32

is the net export profits deducted the costs of transboundary externalities.
Notice that because the optimal standards depend on the comparison between wiM (sH )and wiM (sL ), the replacement of πliM (sl ) by ηliM (sl ) due to the presence of transboundary
externalities does not aﬀect the condition under which whether sH or sL is chosen. In otherwords, Lemma 1 is still valid.

7.2

FTA with national standards

After the formation of an FTA between countries A and B, each member country’s nationalFM(sC ), i = A, B, where the domestic
welfare can be rewritten as WiF = wiF (si ) + ηji(sj ) + ηCi

surplus wiF (si ) is the same as (12) andFFηji(sj ) ≡ πji(sj ) − δb(sj )Qj=[a(sj ) + tF (sj )]2
3a(sj ) − tF (sj )− δb(sj )
16
4

(25)

is the export profits net of transboundary externality costs associated with the FTA member country.
Again, the presence of transboundary externalities does not aﬀect the optimal choiceof standards characterized in Lemma 3. Therefore, Lemma 4 also holds, and so does
Proposition 1. That is, in comparison with the MFN, an FTA makes the member countries
to choose more stringent standards.
The welfare eﬀects of the FTA compared with the MFN are obtained by a comparison
between WiM and WiF , as implemented in section 5. Given the components of national welfare explained above, the welfare eﬀects can be dependent on the degree of transboundary
externalities, δ, as well as the other parameters β and γ.
Let us begin with the welfare comparison in the member countries. As in the casewithout transboundary externalities, there are three possibilities, i.e., the case where themember countries choose sL both under the MFN and FTA (region I in Figure 1), the casewhere the member countries choose sL under the MFN but they choose sH under the FTA(region II), and the case where the member countries choose sH both under the MFN and
FTA (region III), depending on the values of β and γ. In region I, the diﬀerence between
33

WiM and WiF is
M
F
WiM − WiF = wiM (sL ) + ηji(sL ) − [wiF (sL ) + ηji(sL )]=−(3α + 4β)[423α − 8(157 + 210δ)],
44100

from which it holds that WiM > WiF (WiM < WiF ) if and only if β > (<) 423α/[8(157 +210δ)]. The cutoﬀ value for β becomes smaller if δ becomes higher, implying that thetransboundary externalities make the formation of an FTA less beneficial for the member
countries when these countries choose a low standard both under the MFN and FTA.
In region II, the diﬀerence between WiM and WiF is
M
F
WiM − WiF = wiM (sL ) + ηji(sL ) − [wiF (sH ) + ηji(sH )]=−2150γ 2 + 4300αγ − 141α2 − 196(16 + 15δ)αβ + 98(7 + 10δ)β 2,4900

which becomes positive (negative) if and only if√
7 41 2 32 + 30δ
7 + 10δ 2
γ > (<) γ̃(β, δ) ≡ α −
α −
αβ +
β .
5 86
43
43
Note that γ̃(β, δ) is increasing in δ:∂γ̃(β, δ)7β(3α − β)
= √
> 0.
∂δ
43 41 α2 − 32+30δ αβ + 7+10δ β 2
86

43

43

In other words, an increase in the degree of transboundary externalities make the formationof an FTA more beneficial for the member countries in the case where the member countries
choose more stringent standard under the FTA than under the MFN. Finally, in region
III, all countries choose sH both under the MFN and FTA and the analysis in the absenceof transboundary externalities remains valid since b(sH ) = 0 in the present model.
While transboundary externalities narrow the region in which WiM < WiF holds forthe member countries when these countries choose the low standard both under the MFN
and FTA, the region with WiM < WiF expands when the member countries choose more
stringent standard under the FTA than under the MFN. Intuitively, these findings can beinterpreted as follows. A formation of an FTA increases consumption in member countries, and so does the consumption externalities for a given standard. In the presence of34

transboundary externalities, the social costs of externalities become higher if the member
countries choose the same standard both under the MFN and FTA. Because of this, transboundary externalities will have a pressure to reduce welfare under the FTA in region I. In
region II, however, the member countries choose more stringent standards under the FTA
than the MFN equilibrium, and in this particular model, b(sH ) = 0 and hence the social
costs of externalities disappear completely under the FTA. Therefore, the advantage of the
FTA in terms of the social costs of externalities increases as δ becomes higher.
Let us proceed to the nonmember country’s welfare. Comparisons of the nonmember’s welfare are now equivalent to those of its export profits net of the social costs ofMFtransboundary externalities since WCM − WCF = 2[ηiC(si ) − ηiC(si )], i = A, B, where[a(si ) − 3tFηiC(si ) =

F(si )]216

3a(si ) − tF (si )− δb(si ).
4

If member countries choose sL both before and after the formation of the FTA (i.e.,
region I in Figure 1), it holds thatMFηiC(sL ) − ηiC(sL ) = −(3α + 4β)[51α − 8(9 + 70δ)β].
14700

As shown in section 5, given the condition α > 2β, the sign of the above equation is unambiguously negative if δ = 0. However, even if the condition α > 2β is satisfied, the signof the above equation can be positive when δ > (51α − 72β)/560β. The intuition behind
this result is similar to the narrowing of the region in which WiM < WiF holds in region
I for the member countries: since an FTA increases consumption in member countries,
the consumption externalities in these countries become larger, and if the degree of transboundary externalities is suﬃciently high, the social costs of transboundary externalities
may outweigh the benefit of the FTA which the nonmember country can earn.
In the case where the member countries choose sL under the MFN and sH under the
FTA (i.e., region II), it follows thatFM(sH ) = −(sL ) − ηiC
ηiC(17α − 14β − 10γ)(3α + 14β − 10γ) + 980δβ(3α − β),4900

the sign of which is, in view of the discussion in section 5, unambiguously negative forany δ ∈ [0, 1]. Therefore, as in the case of no transboundary externalities, the nonmember
35

country becomes better oﬀ under the FTA. Finally, if the member countries choose sH
MF
both under the MFN and FTA, πiC(sH ) − πiC(sH ) = −51(α − γ)2 /4900 < 0 holds, as in

the case of no transboundary externalities, because b(sH ) = 0.
Proposition 5. In comparison with the MFN, the nonmember country of the FTA may
be worse oﬀ under the formation of an FTA if γ̄ F (β) < γ < α and if the degree oftransboundary externalities is suﬃciently high.

7.3

FTA with harmonization of standards

As examined in section 6, the FTA member countries jointly determine a common standard
sA = sB = s by means of a Nash bargaining. In the presence of transboundary externalities,
the problem is equivalent to[][]˜ A (sFA , sFB ) ω̂B (s) − ω̃˜ B (sFA , sFB )max ω̂A (s) − ω̃s˜ i (sFA , sFB ) for i = A, B,
s.t. ω̂i (s) ≥ ω̃
(26)

F
F F
˜ i (sFA , sFB ) ≡ wiF (sFi ) + ηji
where ω̂i (s) ≡ wiF (s) + ηji(s) and ω̃(sj ), i.j = A, B. It is verifiedthatδb(sL )[3a(sL ) − tF (sL )]42387γ − 774αγ + (606 + 630δ)αβ − (23 + 42δ)β 2=,882ω̂i (sH ) − ω̂i (sL ) = ωi (sH ) − ωi (sL ) +i = A, B,(27)

F
where ωi (s) = wiF (s)+πji(s) as is defined in section 6. Therefore, as in the proof of Lemma

6, it can be verified that there exists a cutoﬀ value for γ given by√
202 + 210δ
23 + 42δ 2Fαβ +βγ̄¯ (β, δ) ≡ α − α2 −129387
and that if γ is higher than this value, the member countries jointly choose sL , while
the member countries choose sH if γ is lower than the cutoﬀ value. It is easily verified
that this cutoﬀ value is increasing in δ. This implies that, as expected, the existence oftransboundary externalities motivates the FTA member countries to choose more stringent
standards if they harmonize their standards.

36Compared with the cutoﬀ value in the case of national standards under the FTA, it
follows thatγ̄ F (β) − γ̄¯ F (β, δ)
√
√
202
+
210δ
23
+
42δ
β2
= α2 −αβ +β 2 − α2 − 2αβ +
129
387
15
> 0 (< 0)⇔

15α(4 − 15δ) − β(1 − 15δ) > 0 (< 0).

Therefore, in contrast to the case without transboundary externalities, γ̄¯ F (β, δ) can belarger than γ̄ F (β) if the degree of transboundary externalities satisfies23
60α − β387α2 − 606αβ + 23β 2<δ<.
15(15α − β)42(15α − β)βThat is, for suﬃciently high values of δ, there can exist a set of parameters (β, γ) in
which the member countries choose sH under harmonization but choose sL under thenational standards, or in other words, Proposition 3 may not hold. The possibility thatγ̄¯ F (β, δ) can be larger than γ̄ F (β) implies that the ranking of welfare gains from an FTA
between national standards and harmonization, illustrated in Figure 6, can be reversed; ifγ̄¯ F (β, δ) > γ̄ F (β), there exists a set of parameters (β, γ) in which, for i = A, B, WiM < WiF
holds under national standards but WiM > WiF holds under harmonization.
Proposition 6. If the degree of transboundary externalities is suﬃciently high, regional
harmonization of standards may induce the FTA member countries to choose more stringent
standards than those under national standards and may reduce the gains from an FTA
formation.

8

Concluding Remarks

In this paper, we have considered both product standard and FTA to show how these
new and traditional policy tools are strategically interacted. Constructing a three-country
model of international oligopoly with endogenous determination of tariﬀs and standards on
products that cause negative consumption externalities in the presence of possible FTA, we
The left-hand side of this inequality comes from 15α(4 − 15δ) − β(1 − 15δ) < 0. The right-hand sidecomes from the constraint that γ̄¯ F (β, δ) should be a real number for given parameter values. Notice that
if β < α/2, it holds that 0 < (60α − β)/[15(15α − β)] < 1.
23

37

examine the level of standards and welfare levels of FTA member/nonmember countries.
Furthermore, we clarify the eﬀect of harmonization of standards on these two items.
The main results that we obtained are as follows: (i) Compared with the MFN, andFTA makes the member countries to choose more stringent standards; (ii) Compared with
the MFN, the FTA member countries may or may not be better oﬀ under the formation of
an FTA, while the nonmember country becomes better oﬀ; and (iii) Harmonization of standards within an FTA will lead the member countries to choose less stringent standards thannational standards case and make the formation of the FTA more favorable. We verified
the robustness of the results. As long as the asymmetries in preferences or transboundary
externalities are not so large, these results hold. These results will have implications forthe recent movement towards regionalism that takes harmonization of domestic policies
into consideration as well as liberalizing trade in goods.
Throughout this paper we focused on FTAs as a form of preferential trade agreement,
and have not considered the case of a customs union (CU), where member countries set
a common external tariﬀ, harmonizing their external trade policy. Our next task is to
examine the eﬀects of CU with endogenous determination of standards. Of another interestis the analysis of dynamic time-path problem that considers whether regional standards
are stumbling blocks or building blocks toward multilateral harmonization. There are also
a number of possible extensions of the basic model such as diﬀerence in technologies among
countries, generalization of demand functions, introduction of quality improving R&D, andsequential determination of trade and domestic policies.

38Appendix
A.1

Simultaneous determination of tariﬀs and standards

In this Appendix, we show that when the governments simultaneously determine theirtariﬀs and standards, the optimal policy mix is the same as that under the sequential
policy choice.
Let us consider the policy game under MFN. The government in country i chooses ti
and si so as to maximize (4). If si = sH , (4) is rewritten asWi =[3(αi − γ) − 2ti ]2 (αi − γ + 2ti )2
αi − γ − 2ti3(αi − γ) − 2ti
+
+ ti
− θβi
+ Π−i
32
16
2
4

≡ WiH ,

(A.1)

whereas it is rewritten as
Wi =αi − 2ti
3αi − 2ti
(3αi − 2ti )2 (αi + 2ti )2
+
+ ti
−β
+ Π−i ≡ WiL
32
16
2
4

(A.2)

if si = sL , where Π−i ≡ {[aj (sj ) − 2tj ]2 + [ak (sk ) − 2tk ]2 }/16. A direct comparison between(A.1) and (A.2) reveals that it is optimal for country i to choose sH (sL ) if and only ifti < (>)

24βi [αi (1 − θ) + θγ] − 11γ(2αi − γ)
≡ t̂i .
4[4(1 − θ)βi + 3γ](A.3)

From (A.1) and (A.2), the local maxima of WiH and WiL are attained at ti = [3(αi − γ) +4θβi ]/10 and ti = (3αi + 4βi )/10, respectively. In light of (A.1), (A.2), (A.3), and theinequality that [3(αi − γ) + 4θβi ]/10 < (3αi + 4βi )/10, the relationship between Wi and ti
is derived as

{
WiH
Wi =
WiL

if ti ≤ t̂i ,if ti ≥ t̂i .

(A.4)

Depending on the parameter values, there are three possibilities: (i) [3(αi − γ) +4θβi ]/10 < t̂i < (3αi + 4βi )/10, (ii) t̂i < [3(αi − γ) + 4θβi ]/10 < (3αi + 4βi )/10, and(iii) [3(αi − γ) + 4θβi ]/10 < (3αi + 4βi )/10 < t̂i . See also Figure A.1.24

24

Notice that t̂i is uniquely determined.

39

(a)

(b)

(c)

Figure A.1: Relationship between ti and Wi

Let us begin with case (i) where [3(αi − γ) + 4θβi ]/10 < t̂i < (3αi + 4βi )/10 holds. In
this case, the relation between ti and Wi can typically be illustrated as a curve with twin
peaks, as illustrated in Figure A.1 (a). From (A.1), (A.2), and (A.4), the local maxima()( 3αi +4βi)
3(αi −γ)+4θβi
are attained at (ti , si ) =
,
s
and
(t
,
s
)
=
,
s
. Substituting these
H
i
i
L
10
10
optimal pairs of (ti , si ) into (A.4), it follows that4(αi − γ)2 − 6βi θ(γ − αi ) + βi2 θ2


+ Π−i

10
max Wi =4α2 − 6αi βi + βi2


+ Π−i
 i
10

(

)
3(αi − γ) + 4θβi
if (ti , si ) =, sH ,10 )(3αi + 4βi
if (ti , si ) =, sL .
10(A.5)

Assuming that θ = 0 without loss of generality, it is clear from (A.5) and Figure A.1 (a)that if −8αi γ + 4γ 2 + 6αi βi − βi2 is positive (negative), sH (sL ) achieves the maximum
level of Wi . This means that the optimal policy mix, which is the dominant strategy,
√
(
)
β2
i −γ)
for each country under MFN is (ti , si ) = 3(α10, sH if γ < αi − αi2 − 32 αi βi + 4i and
40

√
βi2
3
2
(ti , si ) =
,
s
if
γ
>
α
−
α
−
α
β
+
. However, the condition whether γ
L
i
i
i
i
10
2
4
√
2
β
is higher or lower than αi − αi2 − 23 αi βi + 4i is equivalent to the condition imposed in( 3αi +4βi)

Lemma 1.
Let us consider case (ii) where t̂i < 3(αi − γ)/10 < (3αi + 4βi )/10 holds. In this case,( +4βi)Figure A.1 (b) reveals that Wi is maximized at (ti , si ) = 3αi10, sL . Finally, in case (iii)
where 3(αi − γ)/10 < (3αi + 4βi )/10 < t̂i holds, it is clear from Figure A.1 (c) that Wi is
(
)
i −γ)
maximized at (ti , si ) = 3(α10, sH .
To sum up, we can conclude that the timing of the determination of the two policy
instrument, tariﬀs and standards, does not matter. The above-mentioned equivalence between the simultaneous determination of policy instruments and sequential determinationof these policies also holds in the policy games under an FTA between countries A and B.

A.2

Welfare eﬀects of an FTA for member countries

In this Appendix, we present the calculation results of (15) for cases from (i) to (ix) in
Table 1.

Case (i): (sL , sL ) under MFN and (sL , sL ) under FTA In this case, (15) is rewrittenas
M
F
WiM − WiF = wiM (sL ) + πji(sL ) − [wiF (sL ) + πji(sL )]=(3αi + 4βi )2 13(3αj + 4βj )(81αj − 32βj )
−
.
210
44100

(A.6)

If αi = αj = α and βi = βj = β, the above equation can be simplified to (16).
Case (ii): (sL , sL ) under MFN and (sH , sL ) under FTA In this case, (15) is rewrittenas
M
F
WiM − WiF = wiM (sL ) + πji(sL ) − [wiF (sH ) + πji(sL )]

3αi2 − 42αi βi + 7βi2 + 50αi γ − 25γ 2 13(3αj + 4βj )(81αj − 32βj )=−. (A.7)
70
44100

41

Case (iii): (sL , sL ) under MFN and (sL , sH ) under FTA In this case, (15) is rewritten as
MF
WiM − WiF = wiM (sL ) + πji(sL ) − [wiF (sL ) + πji(sH )]=(3αi + 4βi )2 (27αj − 14βj − 20γ)(13αj + 14βj − 20γ)
−
.
210
4900

(A.8)

Case (iv): (sL , sL ) under MFN and (sH , sH ) under FTA In this case, (15) is rewritten as
MF
WiM − WiF = wiM (sL ) + πji(sL ) − [wiF (sH ) + πji(sH )]=

3αi2 − 42αi βi + 7βi2 + 50αi γ − 25γ 2 (27αj − 14βj − 20γ)(13αj + 14βj − 20γ)
−
.
70
4900
(A.9)

If αi = αj = α and βi = βj = β, the above equation can be simplified to (17).
Case (v): (sH , sL ) under MFN and (sH , sL ) under FTA In this case, (15) is rewrittenas
M
F
WiM − WiF = wiM (sH ) + πji(sL ) − [wiF (sH ) + πji(sL )]=3(αi − γ)2 13(3αj + 4βj )(81αj − 32βj )
−
.
70
44100

(A.10)

Case (vi): (sH , sL ) under MFN and (sH , sH ) under FTA In this case, (15) is rewritten as
MF
WiM − WiF = wiM (sH ) + πji(sL ) − [wiF (sH ) + πji(sH )]=3(αi − γ)2 (27αj − 14βj − 20γ)(13αj + 14βj − 20γ)
−
.
70
4900

(A.11)

Case (vii): (sL , sH ) under MFN and (sL , sH ) under FTA In this case, (15) isrewritten asFM(sH )](sL ) − [wiF (sL ) + πji
WiM − WiF = wiM (sL ) + πji=(3αi + 4βi )2 351(αj − γ)2
−
.
210
4900

42

(A.12)

Case (viii): (sL , sH ) under MFN and (sH , sH ) under FTA In this case, (15) isrewritten as
MF
WiM − WiF = wiM (sL ) + πji(sH ) − [wiF (sH ) + πji(sH )]=

3αi2 − 42αi βi + 7βi2 + 50αi γ − 25γ 2 351(αj − γ)2
−
.
70
4900

(A.13)

Case (ix): (sH , sH ) under MFN and (sH , sH ) under FTA In this case, (15) isrewritten as
MF
WiM − WiF = wiM (sL ) + πji(sH ) − [wiF (sH ) + πji(sH )]=3(αi − γ)2 351(αj − γ)2
−
.
70
4900

If αi = αj = α and βi = βj = β, the above equation can be simplified to (18).

43(A.14)

References[1] Baghdadi, L., I. Martinez-Zarzoso, and H. Zitouna, Are RTA agreements with environmental provisions reducing emissions? Journal of International Economics 90(2013), 378–390.
[2] Bagwell, K. and R. Staiger, Regionalism and Multilateral Tariﬀ Cooperation, in J. Pigott and A. Woodland (eds.), International Trade Policy and the Pacific Rim, London,
Macmillan, 1998.
[3] Costinot, A., A Comparative Institutional Analysis of Agreements on Product Standards, Journal of International Economics 75 (2008), 197–213.
[4] Facchini, G., P. Silva, and G. Willmann, The customs union issue: Why do we observe
so few of them? Journal of International Economics, forthcoming.
[5] Fischer, R. and P. Serra, Standards and Protection, Journal of International Economics 52 (2000), 377–400.
[6] Fullerton, D. and S.E. West, Can Taxes on Cars and on Gasoline Mimic an Unavailable
Tax on Emissions? Journal of Environmental Economics and Management 43 (2002),
135–157.
[7] Freund, C., Multilateralism and the Endogenous Formation of Preferential Trade
Agreements, Journal of International Economics 52 (2000), 359–376.
[8] Gulati, S. and D. Roy, National Treatment and the Optimal Regulation of Environmental Externalities, Canadian Journal of Economics 41 (2008), 1445–1471.
[9] Krishna, P., Regionalism and Multilateralism: A Political Economy Approach, Quarterly Journal of Economics 113 (1998), 227–51.
[10] Naiki, Y., Treatment of Technical Standards in Regional Trade Agreements — Some
Lessons for Mutual Recognition Arrangements, RIETI Discussion Paper Series 06-J042, 2006, Research Institute of Economy, Trade & Industry.
44

[11] Ornelas, E., Trade Creating Free Trade Areas and the Undermining of Multilateralism,
European Economic Review 49 (2005a), 1717–1735.
[12] Ornelas, E., Endogenous Free Trade Agreements and the Multilateral Trading System,
Journal of International Economics 67 (2005b), 471–497.
[13] Saggi, K., Preferential Trade Agreements And Multilateral Tariﬀ Cooperation, International Economic Review 47 (2006), 29–57.
[14] Stoler, A.L., TBT and SPS Measures in Practice, in J.-P. Chauﬀour and J.C. Maur
(eds.), Preferential Trade Agreement Policies for Development: A Handbook, 2011,
World Bank.
[15] Takarada, Y., Y. Kawabata, A. Yanase, and H. Kurata, Standards and trade: Multilateralism versus regionalism, unpublished manuscript (2016).
[16] Yi, S.-S., Endogenous Formation of Customs Unions under Imperfect Competition:
Open Regionalism is Good, Journal of International Economics 41 (1996), 153–177.
[17] Yi, S.-S., Free-Trade Areas and Welfare: An Equilibrium Analysis, Review of International Economics 8 (2000), 336–47.

45