Article XXIV of the GATT: Good, Bad, or
Both?
Kamal Saggi∗ and Halis Murat Yildiz†
Preliminary draft — comments welcome.
Abstract
Article XXIV of the General Agreement on Tariffs and Trade
(GATT) provides an important exception to Article I (most favored
nation clause) by permitting countries to enter into preferential free
trade agreements (PTAs). Does the existence of Article XXIV undermine multilateral trade liberalization? Would aggregate world welfare
be higher if PTAs could not be formed? To answer these questions,
this paper endogenizes the formation of free trade agreements (FTAs)
in a three-country oligopoly model of intraindustry trade where countries are asymmetric with respect to market sizes and production costs.
Two tariff games are contrasted: one where countries have the option
to form FTAs and another where they do not. We show that free trade
is less likely to occur as an equilibrium outcome under the FTA option
game and that the FTA option lowers world welfare when countries
are relatively symmetric. Also, the country with the largest market
(and/or the highest cost) always benefits from the existence of the
FTA option.
Keywords: Multilateral Trade Liberalization, Free Trade Agreements, GATT, Intraindustry Trade, Oilgopoly. JEL Classifications:
F13, F12.
∗
Department of Economics, Southern Methodist University, Dallas, TX 75275-0496.
Phone: 214-768-3274; fax: 214-768-1821; e-mail: ksaggi@mail.smu.edu.
†
Department of Economics, Ryerson University, 350 Victoria Street, Toronto, ON,
Canada M5B 2K3. Phone: 416-979-5000 (ext 6689); fax: 416-979-5289; e-mail: hyildiz@ryerson.ca.
1
1
Introduction
By permitting member countries of the World Trade Organization (WTO)
to preferential trade agreement (PTA) wherein a group of member countries
of the WTO extend tariff concessions to each other that they do not extend
to other members, Article XXIV of the General Agreement on Tariffs and
Trade (GATT) provides an important exception to the most-favored-nation
(MFN) clause (contained in Article I of GATT). Since the notion of nondiscrimination as specified by the MFN clause is at the heart of the WTO
system, the existence of Article XXIV has not been without controversy.1
Does the option of forming PTAs adversely affect incentives for multilateral
trade liberalization on the part of member countries of the WTO? Wouldn’t
the ultimate goal of GATT (i.e. multilateral free trade) be easier to obtain if
member countries of the WTO had to strictly abide by Article I and could not
form PTAs? The present paper addresses these questions in a three-country
oligopoly model of intraindustry trade wherein countries differ with respect
to their market sizes and production costs.2 The underlying asymmetry in
the model sheds light on underlying characteristics that determine how the
PTA option affects individual countries as well as on the welfare effects of
PTAs.
That the above questions are important is evident from the fact that over
150 PTAs are in force today and almost all major countries participate in
some type of a PTA or another (WTO, 2002). The trend toward the formation of PTAs has intensified in recent years — most PTAs have been concluded
in the last 10 years or so and since 1995 over 100 such agreements have been
notified to the WTO. Prominent examples of PTAs include the North American Free Trade Agreement (NAFTA), the South American Common Market
(MERCOSUR), the Association of South East Asian Nations (ASEAN) Free
Trade Area, the Andean Pact, and the numerous agreements of the European
1
To minimize the potential harmful effects of PTAs Article XXIV article requires that:
(i ) a PTA must cover almost all trade between its members; (ii) PTA members must fully
eliminate tariffs and other trade restrictions on each other; and (iii) they should not raise
tariffs (or any other trade restrictions) on non-members.
2
These questions are related but not completely equivalent to the question posed by
Jagdish Bhagwati (1991): “Are PTAs building or stumbling blocks for multilateral trade
liberalization?” The difference is that in our approach, both preferential and multilateral
trade liberalization are endogenous and article XXIV is the underlying exogenous factor.
See Bhagwati and Panagariya (1999) and Winters (1998) for overviews of the main policy
questions in the area.
2
Union with other countries.3
Restricting attention to free trade agreements (FTAs), we evaluate the
incentives countries have for multilateral trade liberalization under two scenarios: one in which they can avail of the option to form FTAs and another
where this option does not exist. Formally, the paper compares two tariff
games. The FTA game proceeds as follows. In the first stage, each country
announces a set of countries with whom it wants to form a trade agreement.
A bilateral FTA is formed if both countries want the agreement. Similarly,
multilateral free trade emerges only when all countries want such an agreement. Next, given the constraints imposed by the policy regime in place,
countries simultaneously choose their tariffs to maximize national welfare
(defined as the sum of the local firm’s profits, consumer surplus, and tariff
revenue).4 Finally, firms compete in the product market in a Cournot fashion where individual country markets are assumed to be segmented. In the
no FTA game, in stage one, countries must choose between participating in
multilateral free trade or utilizing individually optimal tariffs (i.e. no trade
agreement at all).
From each country’s perspective, an FTA embodies the following tradeoff. On the one hand, joining an FTA implies that the domestic surplus is
lowered relative to the case where (optimally chosen) tariffs can be used. On
the other hand, being part of an FTA increases export profits of members in
each other’s markets. Since countries are asymmetric, the loss in domestic
surplus and the gain from increased market access abroad generally differ
across countries. In fact, a country’s loss in domestic surplus from an FTA
increases with own market size while the gain in export profits increases
with the partner’s market size. As a result, an FTA between the largest
and smallest countries is never stable. Furthermore, a country’s gain from
increased market access abroad decreases with own cost whereas it increases
with a partner’s cost. As a result, the country with the biggest market size
and the one with the highest cost are the most FTA desirable partners from
the viewpoint of other countries.
3
The phrase ‘regional trade agreements’ is often used to describe trade liberalization
amongst a few countries. However, the phrase ‘preferential trade liberalization’ is more apt
since such liberalization need not occur only among geographically proximate countries
(although it often does).
4
Under bilateral FTAs, a country imposes optimally chosen tariffs on non-members and
no tariffs on members. Under the multilateral trade agreement, all countries practice free
trade.
3
Our approach is similar to that of Riezman (1999) who also asks whether
the PTA option facilitates or hinders the achievement of global free trade.
However, there are important differences between the two papers. First,
our model differs substantially from Riezman (1999) who utilizes a simple
general equilibrium framework with fixed endowment levels. In his model,
trade is inter-industry in nature and countries impose tariffs to improve their
terms of trade. By contrast, in the oligopoly model presented here trade is
intraindustry in nature (as in Brander and Krugman, 1983) and countries
use tariffs to extract rents from foreign firms (as in Brander and Spencer,
1984). Second, and more importantly, our model allows us to address issues
related to asymmetries between countries; such is not the case in Riezman
(1999). For example, our model permits an assessment of whether or not
MFN facilitates multilateral free trade.5
While we ask questions related to those examined in Krishna (1998), the
conceptual approach of our paper is quite different. Using a similar underlying trade model, Krishna (1998) explores the relationship between FTAs and
multilateral trade liberalization. In his model, tariffs are exogenously given,
but FTAs are endogenous in the sense that only those FTAs that benefit
producers in member countries are considered. Krishna (1998) finds that the
formation of FTAs undermines support for multilateral trade liberalization.
The present paper supports this result because we show that FTAs reduce
the likelihood of obtaining multilateral free trade. On the other hand, we
argue that in a world in which the FTA option does not exist is not necessarily superior to one where it does exist: there are regions over which
multilateral free trade cannot be obtained but welfare improving PTAs are
feasible. Shutting out FTAs would imply that such welfare gains would have
to be foregone. Furthermore, our analysis of cost asymmetries delivers an
interesting insight that we believe is truly novel to the literature: a pattern
of FTAs where the lowest cost country forms bilateral PTAs with the other
two can be actually welfare superior to multilateral free trade.
The ‘stumbling versus building block’ question posed by Bhagwati (1991)
has also been analyzed extensively in the literature through models that allow
for repeated interaction between countries — see Riezman (1991), Bagwell and
Staiger (1997a, 1997b, and 1998a), Bond et. al. (2001), and Bond and Sy5
It is also worth noting that Riezman (1999) uses the cooperative solution concept
of the core to illustrates his results via numerical examples whereas we analyze a noncooperative game and analytically derive its sub-game perfect and coalition proof Nash
equilibria.
4
ropoulos (1996). In these models, cooperation is required to be self-enforcing
in the sense that each country balances the current benefit of deviating from
the cooperative tariff against the future losses caused by the breakdown of
multilateral cooperation that results from its defection.6 In our model, an
FTA is self-enforcing in the sense that it needs to be immune to credible
coalitional deviations by both members and non-members.
Levy (1997) focuses on political economy considerations that we abstract
from and finds that in the monopolistic competition model of intraindustry
trade in differentiated goods, PTAs can supplant multilateral trade liberalization.7 Unlike in the present paper, tariffs play virtually no role in Levy’s
analysis since only the choice between free trade (bilateral as well as multilateral) and autarky is considered. Freund (2000b) investigates how (exogenous)
multilateral trade liberalization affects incentives for preferential trade liberalization in the oligopoly trade model.8 Her main result is that multilateral
trade liberalization encourages the formation of PTAs and makes it more
likely that such agreements are non-credible.
2
Model
We develop a simple oligopoly model of trade in which each country has a
unilateral incentive to impose rent extracting tariffs on those trading partners
with whom it does not have any trade agreement. There are three countries
and two goods: x and y. Countries are asymmetric with respect to their
market size and production costs. Good x is produced by a single profitmaximizing firm in each country at a constant marginal cost in terms of the
numeraire good y.9 Preferences over the two goods are quasilinear:
Ui (xi , yi ) = u(xi ) + yi
6
(1)
The literature on PTAs is rather extensive and we only discuss closely related papers.
The reader is referred to Bhagwati et. al. (1999) for a collection of many of the important
papers in the area.
7
See also Grossman and Helpman (1995) for a political economy model of trade agreements wherein trade protection is a function of contributions made by agents to their
respective governments.
8
By contrast, in our approach, all types of trade agreements are endogenously determined.
9
The gains from trade stem from reduced market power in the domestic industry. To
this end, the monopoly assumption is not crucial but is the simplest way to represent
market power.
5
Furthermore, u(xi ) is assumed to be quadratic:
u(xi ) = αi Xi −
Xi2
2
P
where xi ≡ (xii , xji , xki ) is country i’s consumption profile, and Xi ≡ 3j=1 xji .
Note that xji is country i’s consumption of country j’s product (or denotes
the output sold by country j’s firm in country i),
Due to the quasilinear nature of the utility function, country i’s inverse
demand function is given by:
X3
xji
(2)
Pi (xi ) = αi −
j=1
where αi represents the market size of each country. Let country 1 have the
largest market for good x and country 3 the smallest:
α1 ≥ α2 ≥ α3
(3)
Consider a three stage game. In the first stage, each country announces a
set of countries with whom it wants to form an agreement. An FTA between
two countries is formed if both countries want the agreement. Similarly, multilateral free trade emerges only when all countries want such an agreement.
Next, countries simultaneously choose their tariffs given the agreement(s)
formed in the first stage. Finally, firms compete in the product market in a
Cournot fashion and markets are segmented so that each firm makes independent decisions regarding how much to sell in each market (as in Brander
and Krugman (1983) and Brander and Spencer (1984)).
In the absence of any trade agreement, firm j faces a specific tariff tji when
exporting to country i.10 Denote the vector of the tariff schedule of country
i by ti ≡ (tji , tki ).11 Since Article I of GATT forbids tariff discrimination,
in the absence of any FTAs we restrict attention to the case where tji =
tki = ti for i, j, k. In section 5, we evaluate the contribution of MFN to trade
liberalization by allowing countries to tariff discriminate even in the absence
of any FTAs.12
10
It is obvious that tii = 0 for all i .
We also assume that the countries do not impose tariffs on the numeraire good that
may be traded internationally in order to balance trade.
12
Note that, relative to discrimination, MFN treatment not only changes the optimal
tariffs in the absence of any trade agreements but also changes non-member countries’
optimal tariffs under a bilateral FTA.
11
6
Country j’s effective marginal cost of exporting to country i, denoted by
cji , equals:
cji = cj + tji
(4)
where cj denotes the marginal cost of production of country j’s firm. Let
country 1 be the lowest cost producer and country 3 the highest:
c3 ≥ c2 ≥ c1
(5)
Country j’s profit function for exports to country i, denoted by Πji , can be
written as:
Πji = xji Pi (Xi ) − cji xji
(6)
First order conditions for profit maximization yields equilibrium output
levels:13
P
αi − 3ci + j,j6=i cji
αi + ci − 3cji + cki
and xji =
, k 6= i, j.
(7)
xii =
4
4
Similarly, equilibrium price in country i is easily calculated:
P
αi + ci + j,j6=i cji
Pi =
4
(8)
Using (7) and (8), equilibrium profits are:
Πii = x2ii and Πji = x2ji
(9)
The following comparative statics are standard:
∂Πji
∂Πii
∂Πki
3xji
xii
xki
< 0,
> 0, and
> 0.
=−
=
=
∂tji
2
∂tji
2
∂tji
2
(10)
Country i’s welfare function, Wi consists of four components: domestic consumer surplus Ui (Xi ) − Xi Pi (Xi ), domestic firm’s profits in home market
(Πii ), domestic firm’s export profits (Πij , j 6= i) and tariff revenue:
X
X
Wi = Ui (Xi ) − Xi Pi (Xi ) + Πii +
Πij +
tji xji
(11)
j6=i
13
j6=i
In order to guarantee market access to all exporting firms in any country under both
MFN and tariff discrimination, we assume the following condition 3c2 > 7c3 − 1.
7
At the second stage of the FTA game, countries simultaneously choose
their tariffs in order to maximize their own welfare given the agreement(s)
formed in the first stage. Since markets are segmented and marginal costs
are constant, strategic independence of trade policies obtains. As a result,
own tariffs do not affect export profits and each country chooses an optimal
tariff schedule, ti ≡ (tji , tki ) in order to maximize:
X
tzi xzi (tji , tki )
(12)
max CSi (tji , tki ) + Πii (tji , tki ) +
z6=i
Next, we derive optimal tariffs under various FTAs and explore their
formation.
3
Formation of trade agreements
We have two motivating questions. First, does the fact that countries can
form FTAs make global free trade less likely to occur? Second, how does the
variation in market size and production cost across countries affect their incentives for forming FTAs? To address these questions, we begin by deriving
the sub-game perfect Nash equilibria (SPNE) of the two games. However,
to allow countries to deviate as a coalition, we also analyze Coalition Proof
Nash equilibria (CPNE) of the two games.
While the model permits countries to be asymmetric along two dimensions
(production costs and market size), to highlight the role played by each type
of asymmetry, we consider each in isolation.
3.1
Equilibrium FTAs: the role of market size
From here till section 4, to focus on market size asymmetries we set ci = 0
for all i. In addition, the following normalization is imposed throughout the
paper:14
α1 ≥ α2 = 1 ≥ α3
(13)
Under the status quo (i.e. no trade agreement), each country imposes its
optimal MFN tariff on others. The optimal MFN tariff for country i is found
14
Similarly, from section 4 onwards we focus on cost asymmetries and set α1 = α2 =
α3 = 1.
8
by imposing the constraint tji = tki on the above problem and it is given by15
ti (Φ) =
3αi
10
If countries i and j form the FTA (ij ), they abolish tariffs on each other
and choose their tariffs on country k’s independently. As a result, under
(ij ), the problem in (12) is subject to the constraint tji = 0. The following
optimal tariff levels are easily calculated under the different FTAs:
tji (jk) = tki (jk) = tji (Φ) =
3αi
10
(14)
and
αi
(15)
7
As might be expected, when an FTA member i reduces its tariff on the
other member j to zero, exports of the non-member k decrease. As a result,
compared to the case of no agreement (Φ), a members incentive to impose
a tariff on the non-member decreases since the non-member becomes a less
important source of rent-extraction. This result is known as the tariff complementarity effect in the literature (see Bagwell and Staiger 1997a, 1997b,
and 1998a).16
tji (ik) = tji (ki, kj ) =
3.1.1
SPNE of the FTA game
Under the FTA game, the strategy set of country i, denoted by Si , consists
of four duples of strategies (si ) that involve countries with whom i wants to
form an agreement:
Si = {{φ, φ}, {j, φ}, {φ, k}, {j, k}}
(16)
where φ represents country i announcing in favor of ‘no agreement’. In order
to conserve notation, each agreement is denoted as follows: (i) Status quo Φ
15
It turns out that even if a country is free to tariff discriminate, under market size asymmetry each country imposes a common tariff on the other two. However, the constraint
implied by MFN binds under cost asymmetry (see section 5 for further discussion).
16
A recent report by the World Bank (2000) argues that no clear evidence shows that
the formation of a PTA leads member countries to become more protectionist towards
non-member countries. While such an outcome may be a consequence of Article XXIV,
the tariff complementarity result implies that it could also be optimal for member countries
to voluntarily lower tariffs on non-members.
9
— obtains when no two announcements match or when all announce φ; (ii)
a bilateral FTA between countries i and j — (ij ) is formed iff two countries
announce each other’s names j si and i sj ; (iii) two independent FTAs in
which i is the common member — (ij, ik) is formed iff (a) j si and i sj and (b)
k si and i sk ; and (iv) free trade — (123 ) obtains iff all countries announce
each others’ names.17
As is clear from the discussion above, member of an FTA can sign an
independent FTA with the non-member without needing consent of the other
member.18 Consider the following announcements:
s1 = {2, φ}, s2 = {1, 3}, s3 = {φ, 2}
(18)
The above strategy vectors give rise to two independent FTAs: (21 ) and
(23 ) of which country 2 is the common member.
Note also that different strategy vectors may yield the same agreement(s)
when there is an asymmetry in terms of countries’ choices. To see this,
suppose the strategy vector is given by:
s1 = {2, 3}, s2 = {1, 3}, s3 = {φ, 2}
(19)
Even though country 1 announces country 3, country 3 wants to form an FTA
only with country 2.19 As a result, strategy vectors in (19) yields the same
agreements (21, 23 ) as the ones in (18). In order to eliminate redundant
announcements in the set of SPNE, it is assumed that FTA announcements
cost each country ε (where ε > 0 is arbitrarily small).
The following lemma summarizes the incentives of countries to form a
bilateral FTA:
Lemma 1: Country i’s incentive to form a bilateral FTA with country
j is increasing in the market size of country j whereas it is decreasing in its
own market size.
17
Formally, free trade obtains iff
s1 = {2, 3}, s2 = {1, 3}, s3 = {1, 2}
18
(17)
As indicated in Furusawa and Konishi (2003), this distinction creates an important
difference between an FTA and a CU and leads to a sharp contrast to Yi (1996).
19
Under the open membership rule by Yi (1996), membership is open to all countries.
However, this rule does not seem to be appealing for discussions of PTAs since the formation requires consent from both sides.
10
The above lemma implies that the smallest country (3) always has an
incentive to form an FTA with the other two countries. Similarly, the medium
size country (2) also benefits from an FTA with the largest country (1). The
trade-off underlying FTAs is as follows: From each country’s perspective,
joining an FTA is costly because its domestic surplus is lowered relative to
the case where it is free to use its optimal MFN tariff.20 On the other hand,
being part of an FTA increases export profits of members in each other’s
markets. Consequently, the size of the larger member country plays a crucial
role in determining which bilateral FTAs can arise in equilibrium.
What type of FTAs arise in equilibrium? We can show that unless country
j is too large relative to country i the bilateral FTA (ij ) is a SPNE:
√
(ij ) is SPNE for all αj s.t. 70αj ≤ 3 910αi
(20)
From the perspective of countries 2 and 3, given that they call each other’s
names, the marginal gain of gaining free access to an additional market (i.e.
that of country 1) dominates the loss in domestic surplus from having an
additional FTA. As a result, when the smaller countries (2 and 3) call each
other’s name, they also announce the name of the largest country (1) in
order to form two independent FTAs. However, the largest country (1) has
an incentive to unilaterally deviate from such a pair of bilateral FTAs (in
which it itself is not the common member). This can be explained as follows:
Since the FTA partner for country 1 is the common member country (2 or
3), country 1 does not enjoy any competitive advantage over the non-partner
country implying that increase in its export profit from the FTA is small.
Moreover, country 1 benefits from the tariff complementarity effect when it
is not a member of an FTA.
W3 (31, 32 ) ≥ W3 (23 ) but W1 (23 ) ≥ W1 (31, 32 ).
(21)
W2 (21, 23 ) ≥ W2 (23 ) but W1 (23 ) ≥ W1 (21, 23 ).
(22)
Similarly
As a result, the two smaller countries (2 and 3) cannot form two independent FTAs (unless it is global free trade) so that (31, 32 ) and (21, 23 ) are
20
Note that it is not obvious that an FTA is worse for domestic surplus relative to MFN
since even under MFN, a country is solving a constrained optimization problem in that
it must treat its trading partners the same. However, when two countries are symmetric
with respect to cost, it is optimal for the third country to not tariff discriminate so that
the optimal MFN tariff is in fact its unrestricted optimal tariff.
11
never SPNE. The only possible FTA that involves two independent bilateral
FTAs is the one in which the largest country is the common member (12,
13 ). Finally, global free trade (123 ) is a SPNE if all countries are relatively
symmetric with respect to their market size. We summarize these results in
the following proposition:
Proposition 1: FTAs (12), (13), (23), (12,13), (123) and status quo
( Φ), are all SPNE iff the degree of asymmetry between countries is not too
high (i.e. iff α3 ≥ α3 and α1 ≥ α1 ≥ α1 ). When countries are completely
symmetric with respect to market size (i.e. αi = 1 for all i), all FTAs are
SPNE except for those that involve two independent FTAs.21
Why cannot two independent FTAs such as (12,13 ) arise in equilibrium
when countries are completely symmetric? This is because each member
country that belongs to only a single FTA (i.e. both countries 2 and 3)
has an incentive to unilaterally deviate from its FTA with country 1 to take
advantage of the tariff complementarity effect — the gain from tariff reductions
a non-member enjoys comes at no cost whereas the gain of free market access
in country 1 requires granting free access in return. In effect, each country
with a single FTA prefers to free ride on the other two and is better off if
the other two form an FTA rather than be part of one itself!
Given that there exist multiple SPNE (including status quo Φ), we refine the set of multiple SPNE by deriving Coalition-Proof Nash equilibrium
(CPNE) of the FTA game. While the SPNE concept defines equilibrium only
in terms of unilateral deviations, CPNE eliminates all non-credible deviations
by every conceivable coalition.22
3.1.2
Stable FTAs
We first clarify how the notion of CPNE applies in our model and then discuss
stable FTAs.
21
Explicit formulae for these market size thresholds are reported in the appendix.
As per Bernheim et al. (1987), an FTA is defined to be coalition-proof if and only if
it is Pareto efficient among self enforcing agreements. In turn, an FTA is self enforcing if
and only if no proper subset (coalition) of countries, taking the actions of its complement
as fixed, can agree to deviate in a way that makes all of its members better off.
22
12
The notion of CPNE In order to see how the concept of CPNE is applied
in our context, consider the following example:
s1 = {2, φ}, s2 = {1, φ}, s3 = {φ, φ}
(23)
Suppose now that (12 ) is a SPNE and it is immune to any conceivable
deviation except for the deviation to (23 ):23
W2 (23 ) > W2 (12 ) and W3 (23 ) > W3 (12 ).
(24)
In order for (12 ) to be a CPNE, it is necessary to check whether the joint
deviation of countries 2 and 3 from (12 ) to (23 ) is credible or not. If there is
no incentive for any coalition of countries to further deviate from (23 ), the
joint deviation from (12 ) to (23 ) would be credible and (12 ) would not be a
CPNE. But what if country 2 — a subset of the countries that deviate from
(12) to (23) — do indeed has incentive to deviate further from (23) to (21, 23)
taking country 1’s strategy as given (s1 = {2, φ} in the original agreement
(12 ))? Suppose
W2 (21, 23 ) > W2 (23 ).
(25)
Then the original deviation from (12 ) to (23 ) would be non-credible. As a
result, the FTA (12 ) would be a CPNE.
Further note that there can be multiple FTAs that are CPNE simultaneously. Consider the above example again and suppose now that (23 ) is
immune to any conceivable deviations except for the joint deviation of countries 1 and 3 to (13 ):
W1 (13 ) > W1 (23 ) and W3 (13 ) > W1 (23 )
(26)
Suppose further that country 3— a subset of the countries that deviate from
(23 ) to (13 )— has an incentive to deviate further from (13 ) to (31, 32 ), taking
country 2’s strategy s2 = {φ, 3} in the original agreement (23 ) as given:
W3 (31, 32 ) > W3 (13 )
(27)
Under such a situation, (12 ) and (23 ) are both CPNE. Finally, following Dutta and Mutuswami (1997), we call an equilibrium FTA stable if it
corresponds to a CPNE.24
23
24
It is clear that (12 ) is a SPNE since it is immune to unilateral deviations.
Furusawa and Konishi (2002) use a network formation model to endogenize free trade
13
Stable FTAs under market size asymmetry Figure 1 shows stable
FTAs in the (α3 , α1 ) space:25
––Insert figure 1 here––
As seen from figure 1, when the largest country (1) is too large relative
to other countries, it does not have an incentive to form an FTA because of
the unfavorable trade-off between loss in domestic surplus and gain in export
profits. In this situation, the only possible stable agreement is (23 ) unless
the smallest country (3) is too small relative to the medium size country (2).
Otherwise, no agreement (Φ) is a CPNE. Similarly, if the smallest country (3)
is too small, neither country 1 nor country 2 has an incentive to form an FTA
with country 3. In this case, if the size of the largest country (1) is similar to
the one of the medium size country (2), (12 ) is the stable equilibrium. The
following is immediate:
Lemma 2: A bilateral FTA between the largest and smallest countries
(13) is not stable.
It is important to note that only the bilateral FTAs that include the
similar size countries, (12 ) and (23 ), are stable. The FTA (13 ) is not stable
since 1 and 2 have incentives to deviate from (13 ) to (12, 13 ). This deviation
is not credible only within the market size parameter range over which the
deviation from (13 ) to no agreement (Φ) is credible. As a result, (13 ) is
never a CPNE. From inequalities in (21) and (??), since both (31, 32 ) and
(21, 23 ) are not SPNE, they are trivially not in the set of CPNE as well.
Moreover, (12, 13 ) is stable if countries 2 and 3 are not too small relative
to the largest country (1). Most importantly, free trade (123 ) obtains if and
only if market sizes of all countries are similar — in fact, free trade is the
unique CPNE when countries are completely symmetric.26
agreements (FTAs). Given any FTA configuration, they examine whether a pair of countries have incentives to sign another FTA, and whether a country has an incentive to
cut an existing FTA. A network that is immune to these two incentives is called pairwise
stable.
25
Throughout the paper, explicit functions used to obtain the figures can be found in
the appendix. Also we limit the range of country 1’s market size as follows while drawing
the figures for the case of market size asymmetry: 2 ≥ α1
26
A similar result is also obtained by Furusawa and Konishi (2002) and they conclude
that FTAs are building blocs for free trade. However, our approach is different from
14
3.2
Eliminating the FTA option
Under the no FTA option, bilateral agreements are not possible so countries
can either announce in favor of the status quo or in favor of free trade. The
strategy set of country i, denoted by Si , consists of two duples of strategies
(si ):
Si = {{φ, φ}, {j, k}}
(28)
Free Trade (123 ) occurs if and only if the following hold:27
W1 (123 ) > W1 (Φ), W2 (123 ) > W2 (Φ) and W3 (123 ) > W3 (Φ).
(29)
The set of CPNE of the no FTA game is represented in figure 2.
––Insert figure 2 here––
The comparison of figures 1 and 2 leads to the following proposition:
Proposition 2: Under both games, free trade (123) is found to be uniquely
stable if and only if countries are relatively symmetric with respect to market
size. However, free trade (123) is stable over a larger parameter space under
the no FTA game than under the FTA game.
As seen from figure 2, when countries do not have the option to form
FTAs, global free trade (123 ) is stable in the light and dark blue regions
while it is stable only in the dark blue region under the FTA game. As a
result, free trade is more likely to obtain under the no FTA game. Over
the light blue region, countries prefer free trade (123 ) to no agreement (Φ).
However, an FTA option provides them an intermediate opportunity to form
a trading bloc that is preferable to free trade (123 ).
Further analysis of the two games yields some subtle results regarding the
welfare implications of FTAs in an asymmetric world. Two distinct regions
need to be emphasized. In region I (12 ), (23 ), and (12, 13 ) are stable agreements under the FTA game while free trade (123 ) is the stable agreement
Furusawa and Konishi (2002) in an important way: Beside investigating whether FTA
formation continues until free trade or not, we also ask whether the option of forming
FTAs makes global free trade less likely to occur.
27
Note that the set of SPNE and CPNE are identical in the no FTA option game.
15
under the no FTA game. In region II, (12 ), (23 ), and (12, 13 ) are stable
agreements under the FTA game, whereas no agreement (Φ) is the stable
outcome under the no FTA game. Note that the former (latter) region refers
to the situation in which countries are relatively symmetric (asymmetric)
with respect to the market size. Given these two distinct regions, we explore
the following questions: Which countries benefit (suffer) the most from the
FTA option and what are the world welfare implications of FTAs?
Proposition 3: A comparison of the FTA game and the no FTA game
yields the following results: (i) over region I, the FTA option has beneficial
welfare effects for the largest country (1) but harmful effects for the smallest
country (3) as well as for the world as a whole; (ii) the welfare impact on the
medium size country (2) is ambiguous and it depends on the size distribution
of countries: if the smallest country (3) is quite small and the medium size
country (2) is similar in size to the largest country (1), the FTA option has
beneficial welfare effects for the medium sized country; however, if the largest
country (1) is too large and the medium size country (2) is similar in size
to the smallest country (3), the FTA option is harmful for the medium sized
country (2); and (iii) over region II, the FTA option has beneficial welfare
effects for all countries (and therefore for the world as a whole).
Proposition 3 implies that the largest country necessarily benefits from
the FTA option. As indicated in lemma 1, smaller countries always have
incentive to form an FTA with the largest country (1). This gives the largest
country (1) a special position in the FTA game that it ends up exploiting
in equilibrium in that stable FTAs are those that benefit the largest country
(1). On the other hand, country 3 has the weakest position in the FTA game
since it offers free access to the smallest market. This makes the no FTA
game preferable for the smallest country (3) over region I. Note also that,
over region I, if the smallest country (3) is too small relative to the medium
size country (2) and the largest country (1) is similar in size as the medium
size country (2), the stable FTAs are (12 ) or (12, 13 ) both of which are
superior for the medium size country relative to free trade (123 ). However,
if the largest country (1) is too large relative to the medium size country (2)
and the smallest country (3) has a similar size as the medium size country
(1), the resulting FTA is (23 ), which is inferior for the medium size country
(2) relative to free trade (123 ). Furthermore, from the world welfare point of
16
view, free trade is always preferable to stable FTAs over region I. However,
in region II, all forms of stable FTAs are preferable to no agreement (Φ). As
a result, when countries are relatively symmetric (asymmetric) with respect
to the market size, FTA game has harmful (beneficial) impacts on the world
welfare.
We next compare the two games under cost asymmetry.
4
How cost asymmetry matters
As in the case of asymmetric market sizes, we investigate the following questions under cost asymmetry. First, how does a country’s incentive to form
FTAs depends upon its own cost of production relative to others? Second,
does the option of pursuing FTAs undermine incentives for multilateral trade
liberalization? We begin with the FTA game and then analyze the no FTA
game. Throughout the analysis we assume that αi = 1 for all i and we
normalize c1 = 0.
4.1
Equilibrium FTAs
As per Article I of GATT (MFN), we impose the following constraint on the
problem in (12) under no agreement (Φ):
tji = tki = ti
(30)
As a result, the optimal MFN tariff (ti (Φ)) under no agreement (Φ) is:
P
3 − j cj
(31)
ti (Φ) =
10
The following tariff levels are found under the different FTAs:
tji (jk) = tki (jk) =
6 − 2ci + 3ck − 7cj
20
and
tji (ik) = tji (ki, kj ) =
17
3 − 9cj + 7ck − ci
21
(32)
(33)
4.1.1
Multiplicity of SPNE
Recall that a country’s incentive to form an FTA is determined by two countervailing forces: an FTA increases export profits but it lowers domestic
surplus. If country i’s production cost is sufficiently lower than that of country j then country j’s loss in domestic surplus from the FTA (ij) outweighs
the beneficial effects of improved access to country i’s market and the FTA
(ij) is not a SPNE.
Lemma 3: Country i’s incentive to form an FTA with country j is increasing in country j’s cost whereas it is decreasing in own cost and that of
country k.
The above lemma implies that the low cost countries always has an incentive to form an FTA with higher cost ones and the higher their cost
the stronger is this incentive. Given the above incentives, the highest cost
country’s (3’s) decision is the crucial one in determining equilibrium FTAs.
Moreover, once country i announces country j ’s name, it has always has an
incentive to independently announce country k’s name as well. This is because an additional FTA results in an increase in the export profits due to
the better competitive position country i enjoys against each FTA partner
in the other partner’s market and this positive impact is always larger than
the additional loss in domestic surplus caused due to the second FTA:
W1 (12, 13 ) ≥ W1 (12 ) and W1 (12, 13 ) ≥ W1 (13 )
(34)
W2 (21, 23 ) ≥ W2 (12 ) and W2 (21, 23 ) ≥ W2 (23 )
(35)
W3 (31, 32 ) ≥ W3 (13 ) and W3 (31, 32 ) ≥ W3 (23 )
(36)
However, country 3 has an incentive to unilaterally deviate from an agreement that involves two independent FTAs in which the other two countries
are common members since country 3 is at a competitive advantage — it does
not gain much in its export markets while it loses a lot in its own market:
W3 (12 ) ≥ W3 (12, 13 ) and W3 (12 ) ≥ W3 (21, 23 ) for all c2 , c3
(37)
Consequently, inequalities in (34), (35), (36) and (37) together imply
that (12, 13 ) and (21, 23 ) are never SPNE. The only possible agreement
that involves two independent FTAs is the one in which the country 3 is the
common member (31, 32 ).
18
Proposition 4: FTAs (12), (13), (23), (31, 32) and (123) and status
quo ( Φ), are all SPNE iff the degree of cost asymmetry between countries is
not too high (i.e. iff c3 ≤ c3 and c2 ≥ c2 ≥ c2 ). Furthermore, if countries
are completely symmetric with respect to cost, all FTAs are SPNE except for
those that involve two independent FTAs.
Two independent FTAs cannot arise because when countries are completely symmetric, the countries that belong to only FTA have a unilateral
incentive to become a non-member: once again, the tariff complementarity
effect that these countries enjoy when they are not a member is greater than
the gain from forming an FTA. Next, we describe stable FTAs under cost
asymmetry.
4.1.2
Stable FTAs
Figure 3 shows stable FTAs under cost asymmetry in the (c3 , c2 ) space.
––Insert figure 3 here––
The following corollary is immediate:
Corollary 1: No agreement ( Φ), and FTAs (23) and (31, 32) are not
in the set of CPNE although they belong to the set of SPNE.
In other words, agreements that involve two independent FTAs are never
a CPNE. Recall that (12, 13 ) and (21, 23 ) are not even SPNE, so that
they cannot be CPNE as well. If (31, 32 ) is formed, the joint deviation
of countries 1 and 2 to free trade (123 ) is credible unless country 1 is too
efficient relative to country 2. Moreover, if the country 1 is too efficient
relative to country 2, then country (2) has an incentive to deviate form (31,
32 ) to (13 ) and this deviation is credible. Consequently, (31, 32 ) is never
a stable agreement. Furthermore, the deviations from no agreement (Φ) to
(12 ) and (23 ) are credible over the entire region so that no agreement (Φ)
is never a stable equilibrium although it is a SPNE. Finally, the deviation of
countries 1 and 2 deviate from (23 ) to (21, 23 ) is credible unless they are
almost symmetric with respect to their production costs. When all countries
have relatively similar costs, they jointly deviate from (23 ) to global free
19
trade (123 ) and this is a credible deviation since (123 ) is immune to any
conceivable deviations over this range. As a result, (23 ) is never a CPNE.
Figure 3 demonstrates that over the dark blue region, there are two
CPNE: (12 ) and (123 ). This region is determined by two non-credible deviations. First, the joint deviation of countries 1 and 3 from (12 ) to (13 )
is not credible since country 1 always has an incentive to deviate further to
(12, 13 ) (see inequality in (36)). Second, the deviation from (12 ) to (123 )
is not credible since countries 2 and 3 have incentives to deviate further to
(23 ). As a result, (12 ) is a CPNE. Finally, over the same region, the only
possible deviation from free trade (123 ) is the joint deviation of countries 2
and 3 to (23 ) but this turns out to be non-credible since country 3 has an
incentive to further deviate to (31, 32 ).
Over the green region, there are two CPNE: (12 ) and (13 ). Three credible deviations from (13 ) determine the boundaries of the green region: (i)
Countries 2 and 3 deviate to (31, 32 ), (ii) Country 3 deviates to no agreement
(Φ) and (iii) All countries deviate to free trade (123 ). The yellow region is
determined only by two credible deviations: (i) Country 2’s deviation to no
agreement (Φ) and (ii) joint deviation of all countries to free trade (123 ).28
It is important to note that the region over which free trade (123 ) is
stable is determined by the unilateral deviation of country 3 from (123 ) to
(12 ). As a result, country 3’s choice is pivotal for the stability of free trade
(123 ).
Next, we examine which agreements arise in the CP NE if countries do
not have an FTA option.
4.2
No FTA game
Figure 4 shows stable FTAs under cost asymmetry in the (c3 , c2 ) space.
––Insert figure 4 here––
A comparison of figures 3 and 4 shows that if countries can not form
FTAs, free trade is achieved in the light blue region in figure 4; while it is
not the case under the FTA option. Thus, we have the following result.
28
It is important to note that the region over which free trade (123 ) is stable is determined by the unilateral deviation of country 3 from (123 ) to (12 ). As a result, country
3’s choice is pivotal for the stability of free trade (123 ).
20
Proposition 5: Under both games (FTA and no FTA), free trade (123)
is uniquely stable if and only if the countries are relatively symmetric with
respect to their production costs. However, even under cost asymmetry, free
trade (123) is stable over a larger parameter space under the no FTA game
than under the FTA game.
The analysis of figure 3 and figure 4 provides additional results regarding the welfare implications of FTAs. Before doing that, it is important to
note again that (12 ) and (13 ) are the stable agreements under the FTA option over the yellow region and the theory offers no guidance as to which
agreement ((12 ) or (13 )) might actually be observed. We suppose that the
‘natural’ trading block (12 ) is the one that obtains as the stable agreement.29
Two distinct regions should be examined: region I: (12 ) is the stable agreements under the FTA option while free trade (123 ) is achieved as the stable
agreement under the no FTA option, region II: (12 ) is the stable agreement
under the FTA option whereas no agreement (Φ) is the stable outcome under
the no FTA option. Given these distinct regions, we explore the following
questions: Do the efficient or inefficient countries benefit from the FTA option and what are the world welfare implications of having an FTA option?
Proposition 6: A comparison of the FTA game and the no FTA game
yields the following results: (i) over region I, the option to form FTAs has
beneficial welfare effects for the highest cost country (3) but harmful welfare
effects for the other two countries as well as the world as a whole. (ii) over
region II, the FTA option has beneficial welfare effects for all countries (and
therefore the world as a whole).
Proposition 6 implies that the highest cost country always benefits from
the FTA option. This result reflects the fact that market access to the highest
cost country does not come at too high a price for the lower cost countries who
are at a competitive advantage. However, this stronger incentive of low cost
countries actually turns into an advantage for the high cost country who ends
up exploiting it in equilibrium. In fact, for the least efficient country, (12 )
29
If the stable agreement we observe over yellow region is (13 ), we have three distinct
regions: region I: (13 ) is the stable agreement under the FTA game while free trade (123 )
is achieved as the stable agreement under the no FTA game, region II: (12 ) is the stable
agreement under the FTA option while free trade (123 ) is the stable one under the no
FTA option, and region III: (12 ) is the stable agreement under the FTA option whereas
no agreement (Φ) is the stable outcome under the no FTA option.
21
is always preferable to the stable agreements (123 ) and (Φ) under the FTA
option and no FTA option respectively. However, over region I, countries 1
and 2 prefer free trade (123 ) that is not stable under the FTA option. As a
result, these countries are worse off with the FTA option over region I and it is
the lowest cost country that loses the most from the FTA option. Over Region
II, when (12 ) is a CPNE, since there is no unilateral deviation of countries
1 and 2 to Φ, they prefer (12 ) to Φ. Because of the tariff complementarity
effect, 3 also prefers (12 ) to Φ. Consequently, world welfare is higher under
(12 ) than under Φ.
Next, we examine the role of the most favored nation (MFN) principle in
the formation of trade agreements.
5
Role of MFN in trade agreements
If Article I (MFN) were not applicable, the problem in (12) under no agreement (Φ) is no longer subject to the symmetric treatment constraint in (31)
and countries are free to tariff discriminate. The following optimal discriminatory tariff (tji (Φ)) is obtained under no agreement (Φ):
tji (Φ) =
6 − 2ci + 3ck − 7cj
20
It is important to note that inefficient (efficient) exporters benefit (suffer)
from tariff discrimination relative to MFN:
ck − cj
(38)
tji (Φ) − ti (Φ) =
> 0 iff ck > cj
4
It is straightforward to argue that a non-member country’s welfare under a
bilateral FTA is higher when its trade policy is not constrained by MFN.
The following lemma explains the role of MFN in the two games:
Lemma 4: A country’s incentive to deviate from any agreement to no
agreement ( Φ) or to the ones in which it is a non-member is higher under
tariff discrimination relative to MFN.
The above lemma argues that the region over which the agreements that
are stable under MFN treatment changes. Figure 5 shows stable agreements
under the FTA option when countries are free to discriminate.
22
––Insert figure 5 here––
Similarly, stable agreements under the no FTA option are represented in
figure 6.
––Insert figure 6 here––
A Comparison of figures 3-6 yields the following result:
Proposition 7: MFN contributes to trade liberalization in two ways: (i)
Under both games, the region over which free trade (123) is stable is larger
under MFN than under tariff discrimination; (ii) under the FTA game, over
the region where free trade is not stable, (12) and (13) are stable over a larger
cost parameter space under MFN relative to tariff discrimination.
Since country 3 is pivotal and its welfare under (12 ) is higher under
discrimination than under MFN, the region over which free trade (123 ) is
stable is larger under MFN treatment. The same argument is valid for the
no FTA option as well since the deviation of country 3 from free trade (123 )
to (Φ) determines the region over which free trade (123 ) is stable. Over the
region where free trade is not stable, since the deviations of the less efficient
member countries (2 and 3) from (12 ) and (13 ) to no agreement (Φ) are
binding for the stability of these bilateral FTAs, the region over which they
are stable is larger under MFN relative to tariff discrimination.
The following insight emerges from the above analysis: Article I (MFN
treatment) facilitates the achievement of global free trade independent of the
role of Article XXIV. However, when countries are not allowed to practice
Article XXIV (no FTA option), the impact of MFN on the stability of free
trade is relatively larger.
6
Concluding remarks
This paper contributes to the long-standing debate regarding the effect of
FTAs on multilateral trade liberalization by analyzing two games: one where
countries have the choice to pursue both FTAs and global free trade and
another where they cannot form FTAs. We find that the option to pursue
23
FTAs does lower the likelihood of achieving global free trade. In this sense,
the exception made available by Article XXIV is in conflict with the GATT’s
main goal of achieving global free trade. However, since both types of trade
liberalization is endogenous in our model, we also find that the option to form
FTAs leads to welfare improving trade liberalization when global free trade
cannot be achieved. In this sense, Article XXIV supports GATT’s main
goal — it can be better to have some preferential trade when multilateral
liberalization is infeasible. In fact, the underlying asymmetry in our model
delivers a surprising insight: the option to pursue FTAs can actually lead
to an outcome that is welfare preferred to free trade when the FTAs formed
favor low cost producers relative to high cost ones.
Our analysis further sharpens the stumbling block versus building block
debate by highlighting conditions under which the answer goes one way or
another. When the underlying asymmetry between countries is relatively
small, the option to pursue FTAs does more harm than good. On the other
hand, when countries are quite asymmetric, multilateral free trade is harder
to obtain and the FTAs are actually be desirable from a world welfare perspective.
Finally, we show that Article I (MFN treatment) facilitates the achievement of global free trade independent of the role of Article XXIV. However,
when countries are not allowed to practice Article XXIV (no FTA option),
the impact of MFN on the stability of free trade is relatively larger.
7
Appendix
All supporting calculations and proofs not provided in the text are given
below.
Market Size Asymmetry
First, we report the welfare levels of countries under different types of
agreements for the general case:
Wi (Φ) =
40α2i + α2j + α2k
100
35α2i + 8α2j
40α2k α2i + α2j
α2k
Wi (ij ) =
+
, Wk (ij ) =
+
98
100
100
49
2
2
2
2
4(αj + αk )
5α2j α2k
11αi
α
+
, Wj (ij ), (ik) = i +
+
Wi (ij ), (ik) =
32
49
16
14
49
24
(39)
(40)
11α2i + 2(α2j + α2k )
(41)
Wi (ijk) =
32
In the following proofs, the critical α1 and α3 levels can be found following
the proof of proposition 3.
Lemma 1
Ii (ij ) is defined as the incentive of a country i to form an FTA with a
larger country j : Accordingly, the following is immediate:
Ii (ij ) = Wi (ij ) − Wi (Φ) =
As a result:
351α2j − 210α2i
4900
(42)
∂Ii (ij )
∂Ii (ij )
> 0 and
<0
∂αj
∂αi
Proposition 1
Part (i): When countries are asymmetric (α1 > α2 = 1 > α3 ):
(12 ) is SPNE for all α1 s.t. α1 ≤ αa1
(13 ) is SPNE for all α1 s.t. α1 ≤ αa1 α3
(23 ) is SPNE for all α3 s.t. α3 ≥ αa3
(12, 13 ) is SPNE if
a-) αc3 ≥ α3 ≥ αf3 for all α1 s.t. αe1 ≥ α1 ≥ αh1
and
b-) α3 ≥ αc3 for all α1 s.t. αd1 ≥ α1 ≥ αh1
and finally,
(123 ) is SPNE if α3 ≥ αe3 for all α1 s.t. α1 ≤ αb1 .
As a result, (Φ), (12 ), (13 ), (23 ), (12, 13 ) and (123 ) are SPNE simultaneously if α3 ≥ α3 and α1 ≥ α1 ≥ α1 and this condition is restated as the
following combination:
a-) αg3 ≥ α3 ≥ αa3 αh1 for all α1 s.t. α1 ≤ αa1 α3
25
and
b-) α3 ≥ αg3 for all α1 s.t. αb1 ≥ α1 ≥ αh1 .
Part (ii): When countries are completely symmetric (α1 = α2 = α3 = 1);
(ij) is a SPNE since no member has an incentive to deviate unilaterally:
Wi (ij ) − Wi (Φ) = Wj (ij ) − Wj (Φ) =
141
>0
4900
(123) is a SPNE since no country has an incentive to deviate unilaterally:
Wi (123 ) − Wi (Φ) =
39
>0
800
Figure 1
Figure 1 represents the following set of CPNE:30
(i) Φ is a CPNE if α3 ≤ αa3 for all α1 s.t. α1 ≥ αa1 .
(ii) (12 ) is a CPNE if α3 ≤ αb3 for all α1 s.t. α1 ≤ αa1 .
(iii) (23 ) is a CPNE if α3 ≥ αa3 for all α1 s.t. α1 ≥ αb1 .
(iv) (12, 13 ) is a CPNE if (a) αc3 ≥ α3 ≥ αb3 for all α1 s.t. α1 ≤ αc1 and
(b) αd3 ≥ α3 ≥ αc3 for all α1 s.t. α1 ≤ αd1 .
(v) (123 ) is a CPNE if α3 ≥ αe3 for all α1 s.t. α1 ≤ αb1 .
Lemma 2
Given 2 ≥ α1 ≥ α2 = 1 ≥ α3 :
(13 )−→(1 and 2)−→(12, 13 ): 1 and 2 always deviate:
W1 (12 , 13 ) − W1 (13 ) ≥ 0, W2 (12 , 13 ) − W2 (13 ) ≥ 0
and 2 has no incentives to deviate further but 1 has an incentive to deviate
further to Φ if α1 ≥ αd1 and to (12 ) if α1 ≥ αe1 .
Consequently, the initial deviation of countries 1 and 2 from (13 ) to (12,
13 ) is not self enforcing if (a) α3 < αc3 and α1 ≥ αe1 and (b) α3 ≥ αc3 and
α1 ≥ αd1 . However, over this region 1 deviates from (13 ) to Φ if α1 > αa1 and
it is self-enforcing. As a result, (13 ) is never a CPNE.
Figure 2
30
Detailed derivations are available upon request.
26
(i) Φ −→(1, 2 and 3 )−→(123 ): 3 always deviates, 2 deviates if α1 > αf1
and 1 deviates α1 > αg1 . As a result Φ is a CPNE if α1 > αg1 .
(ii) (123 )−→(1 or 2 or 3 )−→ Φ: 3 never deviates, 1 deviates if α1 < αf1
and 2 deviates if α1 > αg1 . As a result, F T is a CPNE if α1 ≤ αg1 .
Proposition 2
It is immediate from figures 1 and 2.
Proposition 3
Over region I:
When (12 ) is a CPNE (if α3 ≤ αb3 for all α1 s.t. α1 ≤ αa1 ):
W1 (12 ) − W1 (123 ) =
15
21α23
3α21
+
−
>0
224 784
400
15α21 21α23
3
+
−
>0
224
784
400
9α2 33(1 + α21 )
W3 (12 ) − W3 (123 ) = 3 −
<0
160
784
15(1 + A21 ) 39A23
W W (123 ) − W W (12 ) =
+
>0
1568
800
When (23 ) is a CPNE (if α3 ≥ αa3 for all α1 s.t. α1 ≥ αb1 ):
W2 (12 ) − W2 (123 ) =
W1 (23 ) − W1 (123 ) =
9α21 33(1 + α23 )
−
>0
160
784
15α23 21α21
3
+
−
<0
224
784
400
15
21α21
3α2
W3 (23 ) − W3 (123 ) = 3 +
−
<0
224 784
400
15(1 + α23 ) 39α21
W W (123 ) − W W (23 ) =
+
>0
1568
800
When (12, 13 ) is a CPNE (if (a) αc3 ≥ α3 ≥ αb3 for all α1 s.t. α1 ≤ αc1 and
(b) αd3 ≥ α3 ≥ αc3 for all α1 s.t. α1 ≤ αd1 ):
W2 (23 ) − W2 (123 ) =
W1 (12 , 13 ) − W1 (123 ) =
27
3α21 33α23
−
>0
224
784
15(1 + α23 )
>0
784
33
3A23
W3 (12 , 13 ) − W3 (123 ) =
−
<0
224 784
15(1 + A23 )
W W (123 ) − W W (12 , 13 ) =
>0
1568
W2 (12 , 13 ) − W2 (123 ) =
Over region II:
When (12 ) is a CPNE, since there is no unilateral deviation of countries
1 and 2 to Φ, they prefer (12 ) to Φ. Because of the tariff complementarity
effect, 3 also prefers (12 ) to Φ.
When (23 ) is a CPNE, since there is no unilateral deviation of countries
2 and 3 to Φ, they prefer (23 ) to Φ. Because of the tariff complementarity
effect, 1 also prefers (23 ) to Φ.
When (12, 13 ) is a CPNE, since there is no unilateral deviation of country
1 to Φ, it prefers (12, 13 ) to Φ, and the following holds:
21α21 51α23
3
+
−
>0
400
4900 70
21α21
51
3α2
W3 (12 , 13 ) − W3 (Φ) =
+
− 3 >0
400
4900
70
It is trivial that since the welfare of all countries rises, world welfare increases
as well.
W2 (12 , 13 ) − W2 (Φ) =
Critical α1 and α3 levels:
p
p
√
√
330 + 330α23
3 910 b
6 182 d 2 390 + 390α23
a
c
α1 =
, α1 =
, α1 =
, α1 =
70
21
35
35
p
p
√
√
210 − 196α23
210 + 210α23 h 2 770
6 182α3
f
g
e
α1 =
, α1 =
, α1 =
, α1 =
35
14
15
55
√
√
√
√
910 b 5 182 c
5 d
154
αa3 =
, α3 =
, α3 =
, α3 =
39
156
4
22
r
√
√ √
4070 f
770 182 g
11
αe3 =
, α3 =
, α3 = 10
110
858
1357
Lemma 3
28
Given that 15 ≥ ck ≥ cj ≥ ci = 0 and 3cj > 7ck − 1, when Ii (ij ) =
Wi (ij ) − Wi (Φ),
Ii (ij )
−768 + 218cj + 669ck
< 0,
=
∂ci
3150
Ii (ij )
3882 + 1471cj − 6879ck
=
>0
∂cj
22050
and
−156 − 2293cj + 657ck
Ii (ij )
< 0.
=
∂ck
7350
For the following proofs, the critical c2 and c3 levels can be found at the
end of the appendix.
Proposition 4
The proof of part (ii) is the same as the proof of part (ii) of the proposition
2.
Part (i): When countries are asymmetric ( 15 ≥ c3 ≥ c2 ≥ c1 = 0 and
3c2 > 7c3 − 1):
(12 ) is SPNE for all c2 s.t. c2 ≤ ca2
(13 ) is SPNE for all c2 s.t. c2 ≥ cb2
(23 ) is SPNE for all c2 s.t. c2 ≥ cc2
(31, 32 ) is SPNE for all c2 s.t. c2 ≤ cd2
and finally,
(123 ) is SPNE for all c2 s.t. c2 ≥ ce2 .
As a result, (Φ), (12 ), (13 ), (23 ), (12, 13 ) and (123 ) are SPNE simultaneously if c3 ≤ c3 ∼
= 0.095 and cd2 ≥ c2 ≥ ce2 .
Figure 3
Figure 3 represents the following set of CPNE:31
a-) (12 ) is a CPNE if (i) c2 ≥ ce2 and c2 ≥ cf2 and (ii) c2 ≤ ce2 and c2 ≤ ca2 .
b-) (13 ) is a CPNE if c2 ≤ ce2 , c2 ≥ cb2 and c2 ≥ cd2 .
31
Detailed derivations are available upon request.
29
c-) (123 ) is a CPNE if c2 ≥ ce2 .
Corollary 1
(i) Φ −→(1 and 2)−→(12 ): 1 always deviates, 2 deviates if c2 < ca2 . As
a result, the deviation happens if c2 < ca2 and it is self-enforcing. Similarly,
Φ −→(2 and 3)−→(23 ): 2 always deviates, 3 deviates if c2 > cc2 . As a result,
the deviation happens if c2 > cc2 and it is self-enforcing. These two conditions
(c2 < ca2 , c2 > cc2 ) cover entire region so that Φ is never a CPNE.
(ii) (23 )−→(1 and 2)−→(21, 23 ): 2 always deviates, 1 deviates if c2 >
g
c2 . As a result, the deviation happens if c2 > cg2 and it is self-enforcing.
Furthermore, if c2 < cg2 , all countries deviate from (23 ) to free trade (123 )
and it is a self-enforcing deviation since free trade is strong Nash when
c2 < cg2 . Consequently, (23 ) is never a CPNE.
(iii) (31, 32 )−→(1 and 2)−→(123 ): 1 always deviates, 2 deviates if c2 <
h
c2 . As a result, the deviation happens if c2 > ch2 and it is self-enforcing when
c2 < ch2 . Note also that when c2 > ch2 , it is not even a SPNE. Consequently,
(31, 32 ) is never a CPNE.
Figure 4
(i) Φ −→(1, 2 and 3 )−→(123 ): 1 and 2 always deviate, 3 deviates if
c2 > 111c493 −13 . As a result Φ is a CPNE if c2 ≤ 111c493 −13 .
(ii) (123 )−→(1 or 2 or 3 )−→ Φ: 1 and 2 never deviate, 3 deviates if
c2 < 111c493 −13 . As a result, (123 ) is a CPNE if c2 ≥ 111c493 −13 .
Proposition 5
It is immediate from figures 3 and 4.
Proposition 6
Region I refers to the region over which c2 ≤ ce2 and c2 ≤ ca2 and (12 ) is
a CPNE under FTA option while free trade (123 ) is a CPNE under no FTA
option. Region II refers to the region over which c2 ≤ 111c493 −13 and (12 ) is a
CPNE under FTA option while no agreement (Φ) is a CPNE under no FTA
option. The following welfare comparison is immediate:
Over Region I:
W1 (123 ) > W1 (12 ) for all c2 and c3
W2 (123 ) > W2 (12 ) for all c2 and c3
W3 (123 ) < W3 (12 ) iff c2 ≤ ce2
30
and
W W (123 ) > W W (12 ) for all c2 and c3 .
Over Region II, when (12 ) is a CPNE, since there is no unilateral deviation
of countries 1 and 2 to Φ, they prefer (12 ) to Φ. Because of the tariff
complementarity effect, 3 also prefers (12 ) to Φ. Since welfare of all countries
are higher under (12 ) than under Φ, so is the world welfare.
Lemma 4
It is obvious that welfare of the non-member country under a bilateral
FTA and also the welfare of countries under no agreement (Φ) is lower under MFN relative to discrimination since they are constrained to treat their
importers symmetrically. The proof immediately follows this fact.
Figure 5
The CPNE condition for (123 ) is determined by the deviation of the least
efficient country (3) to (12 ). Since MFN only changes the welfare under Φ,
we obtain the same condition for (123 ) to be a CPNE:
(123 ) is a CPNE if c2 ≥ cj2 .
On the other hand,
(12 ) is a CPNE if (a) c2 ≥ cj2 and c2 ≥ ck2 , (b) c2 ≤ cj2 and c2 ≤ cm
2 .
(13 ) is a CPNE if (a) c2 ≤ cj2 , c2 ≥ cn2 and c2 ≥ cp2 .
Figure 6
Under discrimination:
(i) Φ −→(1, 2 and 3 )−→(123 ): 1 always deviates, 2 deviates if c2 ≤ cq2
and 3 deviates if c2 ≥ cr2 . As a result Φ is a CPNE if c2 < cr2 .
(ii) (123 )−→(1 or 2 or 3)−→ Φ: 1 never deviates, 2 deviates if c2 > cq2 ,
and 3 deviates if c2 < cr2 . As a result, (123 ) is a CPNE if c2 ≥ cr2 .
Proposition 7
It is immediate from the comparisons of both figure 3 with figure 5 and
figure 4 with figure 6.
Critical c2 and c3 levels:
p
−
4683
+
15
109984 − 233016c3 + 147889c23
5376c
3
ca2 =
2219
31
p
+
5
−10143 + 59682c3 + 147889c23
156
−
1792c
3
cb2 =
657
p
−1526c3 − 3882 + 15 58681 + 113890c3 + 24857c23
cc2 =
1471
p
1317 + 961c3 − 4 110880 − 305340c3 − 95970c23
cd2 =
4399
p
−807 + 2029c3 + 16 2295 − 8625c3 + 9385c23
ce2 =
291
p
38829 − 1463c3 − 120 72058 + 6090c3 + 154756c23
cf2 =
66703
p
−843 + 441c3 + 4 44730 − 80220c3 − 60480c23
g
c2 =
559
p
573 + 833c3 − 8 1386 + 6762c3 + 12201c23
ch2 =
1775
p
807 − 2029c3 − 2 200535 − 1450170c3 + 2043935c23
cj2 =
689
p
47649 + 64687c3 − 15 4824862 + 16471560c3 + 20470744c23
ck2 =
168133
√
3(3857 − 5 359086)
m
(2 + c3 ).
c2 =
41839
√
(3857c3 − 5 359086c3 )
n
c2 = −2 +
423
p
1317 + 961c3 − 1774080 − 4885440c3 + 4931010c23
cp2 =
4399
p
213 + 179c3 − 5 924 − 924c3 + 3086c23
cq1 =
571
p
87 − 179c3 − 5 426 − 2592c3 + 3086c23
cr1 =
79
32
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35
α1
No Agreement
(23)
(12)
(12, 13)
Free Trade
α3
Figure 1: Equilibrium FTAs under Market Size Asymmetry
α1
No Agreement
Free Trade under
only no FTA option
Free Trade under both scenarios
α3
Figure 2: Free Trade under Market Size Asymmetry
c2
(12)
(13)
Free Trade
Lower threshold of c2
c3
Figure 3: Equilibrium FTAs under Cost Asymmetry and MFN
c2
Free Trade under only no FTA option
Free Trade under both scenarios
No Agreement
Lower threshold of c2
c3
Figure 4: Free Trade under Cost Asymmetry and MFN
c2
(12)
(13)
Free Trade
Lower threshold of c2
c3
Figure 5: Equilibrium FTAs under Cost Asymmetry and discrimination
c2
Free Trade under
only no FTA option
Free Trade under both scenarios
No Agreement
Lower threshold of c2
c3
Figure 6: Free Trade under Cost Asymmetry and discrimination