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Journal of International Economics 50 (2000) 473–495
www.elsevier.nl / locate / econbase
International trade agreements between countries of
asymmetric size
Jee-Hyeong Park*
Department of Economics, Wayne State University, Detroit, MI 48202, USA
Received 28 January 1997; received in revised form 10 October 1998; accepted 10 November 1998
Abstract
This paper analyzes how changes in the structure and environment of trade agreements
between a small and a large country affect the efficient frontier of those self-enforcing
agreements and hence, negotiation outcomes. Using the autarky punishment instead of the
interior Nash punishment may provide the small country with greater bargaining power.
Negotiating direct transfers under free trade instead of reciprocal tariff reductions improves
the worst possible negotiation outcome for the small country. The existence of irreversible
investment may strengthen (weaken) the small country’s bargaining power under the interior
Nash (autarky) punishment scheme.  2000 Elsevier Science B.V. All rights reserved.
Keywords: Trade negotiation; Asymmetric size; Bargaining power; Irreversible investment
JEL classification: F02; F13; F15
1. Introduction
The ‘new regionalism,’ characterized by rapid growth in the number and scope
of regional trade agreements since the early 1990s, has frequently taken the form
of a small country (or a few small countries) signing a free trade agreement with a
large trading partner, as in the cases of US–Canada, NAFTA, and EU association
agreements with Eastern European countries and with Mediterranean countries. In
comparison with the GATT’s negotiations that have mostly focused on reciprocal
*Tel.: 11-313-577-3345; fax: 11-313-577-0149.
E-mail address: [email protected] (J.-H. Park)
0022-1996 / 00 / $ – see front matter  2000 Elsevier Science B.V. All rights reserved.
PII: S0022-1996( 99 )00006-9
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J.-H. Park / Journal of International Economics 50 (2000) 473 – 495
tariff concessions, a significant part of negotiations for these regional trade
agreements has involved non-tariff concessions. Consequently, smaller countries
have typically agreed to enforce stricter intellectual property rights, raise environmental standards, and change other domestic policies to favor their larger
trading partner in return for attaining tariff-free access to the large country’s
market.1 Despite the increasing importance and distinct characteristics of trade
agreements between countries with large size differences, there have been
relatively few theoretical studies on the issues raised specifically by such
agreements.
Previous analyses mainly focus on two different but related features germane to
the trade relationship between different-sized countries. The first one is asymmetry
in each country’s ability to manipulate the terms of trade through tariffs. Since this
manipulative ability largely depends on the relative size of trading partners, the
terms of trade gains for a larger country from imposing tariffs can dominate the
loss from its domestic distortions caused by a tariff war with a smaller country.2
This will lead to the situation where the larger country will prefer a tariff war to
free trade with its smaller trading partner, emphasized in Mayer (1981) and
Kennan and Riezman (1988). A Pareto-improving trade agreement is still possible,
however, if the large country’s tariffs, a mechanism of transferring wealth from the
small to the large country but incurring losses from distortions, are replaced with
an efficient transfer mechanism, like direct transfers under free trade.3 McLaren
(1997) explicitly considers this possibility utilizing a Ricardian model of bilateral
trade between a small and a large country. More importantly, his analysis
illustrates the second type of asymmetry intrinsic to countries of disproportionate
size in the presence of sunk investments specific to trading partners. As the degree
of trade-related specialization (for example, ratio of exports to GDP) will be
higher for a smaller country than a larger one, free trade can generate a significant
asymmetry whereby the small country becomes more dependent on trade.
McLaren shows that irreversible specialization by the small country (in anticipation of free trade with the large country) may dramatically reduce its bargaining
1
Perroni and Whalley (1994) compare lists of concessions made by small and large trading partners
in various recent trade agreements. They argue that these seemingly unbalanced non-tariff concessions
were made by smaller countries as insurance fees to ensure their access to the large countries’ markets
in the case of a global trade war. Using a calibrated numerical general equilibrium model of world
trade, they substantiate this view by illustrating that a large country like the U.S. will lose rather than
gain from committing itself to free trade with its smaller trading partners (Canada and / or Mexico)
under a global tariff war, without such concessions by smaller countries.
2
As well known since Johnson (1953 / 54), terms-of-trade-driven incentives to use tariffs generate a
prisoner’s dilemma situation for symmetric trading partners where both countries are worse off under a
tariff war than under free trade. Thus, free trade can be a natural goal for trade negotiations for
countries with similar sizes, but this does not apply for countries with asymmetric size.
3
Although trade agreements rarely specify direct income transfers between countries, bargaining over
non-tariff concessions, which can be interpreted as a form of ‘direct’ transfer, is often a significant part
of free trade negotiations between asymmetric countries, as mentioned earlier.
J.-H. Park / Journal of International Economics 50 (2000) 473 – 495
475
power in trade negotiations to such a level that it would have been better off by
committing to a tariff war against the large country.
Using the same Ricardian model as in McLaren (1997), I will reproduce the two
asymmetries discussed above.4 However, in contrast to the prior analyses that
largely ignore the issues related to the enforcement of agreements, I analyze
self-enforcing trade agreements in a repeated relationship by focusing on subgame
perfect trade agreements where deviations are punished by a permanent reversion
to a static Nash tariff war between countries.5 This analysis, then, identifies several
factors in the structure and environment of agreements which may affect the
outcome of trade negotiations between countries of asymmetric size.
First, it shows that asymmetric countries may have conflicting interests in using
harsher punishments against defections from agreements. Specifically, using an
autarky punishment scheme (as opposed to a weaker punishment such as waging
interior Nash tariff wars) may only benefit the small country with a greater
bargaining power in trade negotiations since it expands the set of self-enforcing
trade agreements only in a direction that is favorable to the small country. This
result differs considerably from the conventional arguments for supporting
stronger punishment schemes as Pareto-improving arrangements simply on the
grounds that countries can attain a higher level of cooperation through more severe
punishments.
Second, my analysis shows that changing the focus of negotiation from one
form of concession to another kind may affect the negotiation outcome. In
particular, by negotiating the size of direct transfers under free trade instead of
negotiating the balance of reciprocal tariff concessions (which entails indirect
transfers to the large country), the small country can make a range of larger
transfers to the large country incentive incompatible, thus precluding them from
the set of possible negotiation outcomes. As explained later, this result comes from
the small country’s increased control over the execution of agreements with direct
transfers, which in turn gives the small country leverage to enhance its bargaining
position through the improved threat of not fulfilling the outcome of trade
negotiations.
Finally, regarding the role of irreversibility in trade-related investment, this
4
Thus, my analysis will focus on the trade issues for a bilateral relationship rather than a multilateral
one. Campa and Sorenson (1996) explore the issue of asymmetric country size in a multilateral trading
setting where there are many small countries and one large country, analyzing how integration of
numerous very small provinces promotes free trade by deterring the exercise of market power by a
large dominant province.
5
As distinct from domestic matters, international agreements have no external enforcement
mechanism upon which to rely (see, for example, Dam, 1970 or Staiger, 1995, for a detailed discussion
on this point). As Dixit (1987) shows, countries can overcome this enforcement issue if they are in a
repeated relationship by agreeing to use a self-enforcing punishment scheme against the use of high
tariffs. If countries care enough about gains from future trade, then they can support free trade as a
subgame perfect equilibrium.
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J.-H. Park / Journal of International Economics 50 (2000) 473 – 495
analysis provides a contrasting result to that of McLaren (1997) by showing that
irreversibility can improve the small country’s bargaining position in trade
negotiations. The large country can take advantage of the small country’s
irreversible specialization under free trade by imposing an excessive tariff rate
when it deviates from a free trade agreement. However, as long as the specialization is not permanently irreversible as in McLaren (1997), the irreversibility also
has a positive effect on the small country’s bargaining power by making the
retaliatory action more severe against the large country’s defection from the
agreement. This positive effect dominates the negative one when countries put
high enough values on future gains from trade.
Section 2 of this paper describes a static tariff-setting game between a large and
a small country. Based on results from the static game, I investigate the issue of
trade agreements in Section 3: I describe the efficient trade agreements in Section
3.1, self-enforcing free trade agreements with direct transfers in Section 3.2, and
self-enforcing reciprocal trade liberalization without direct transfers in Section 3.3.
Section 4 investigates the effect of irreversible investment on trade agreements.
Section 5 concludes.
2. The static game
The basic set-up for the static game follows a standard Ricardian model of
bilateral trade. Consider trade between a small and a large country, where each
country has m and M ( . m) units of labor, respectively, as its only production
inputs (a capital letter will indicate a large country variable). There are two kinds
of goods, x and y, that require one unit of labor to produce one unit of them in
each country, except that producing one unit of x requires only 1 /a , 1 units of
labor in the small country. I assume that changing production from one kind of
goods to another involves no additional cost.6 For preferences, all the consumers in
the two countries have the following CES utility functions:
U(c x ,c y ) 5 (c (xs 21) / s, ,c (ys 21) / s )s / (s 21 ) ,
(1)
where c x and c y represent the consumption of the two goods, and s (.0) is the
elasticity of substitution. As long as s ,`, the autarky price of y in terms of x will
be a (.1) for the small country and 1 for the large country, implying the small
country’s comparative advantage in the production of x. Finally, I assume that the
small country is too small to accommodate the excess supply of the large country
in the event that the large country were to specialize completely in the production
6
This assumption of perfect mobility of labor across industries will be relaxed in Section 4, to
analyze the effect of trade-related sunk investment on trade agreements.
J.-H. Park / Journal of International Economics 50 (2000) 473 – 495
477
of y.7 This ensures the large country’s incomplete specialization in equilibrium,
having its local relative prices being fixed at 1.
Let px , py , Px , and Py denote the local prices of x and y in the small and the
large countries, respectively. If the countries impose ad valorem tariffs of t and T
on imports, and trade according to comparative advantage, then Px 5 (1 1 T )px
and py 5 (1 1 t)Py by the goods–market arbitrage condition. But since the large
country’s incomplete specialization fixes Py /Px at 1, the small country’s domestic
price ratio, py /px , is then equal to (1 1 t)(1 1 T ), and the terms of trade (ratio of
untaxed prices), Py /px , will be (11T ). Observe that the large country can change
the terms of trade in its favor by imposing a tariff, but the small country cannot
affect the terms of trade by its trade policy choices.
Given the set-up described above, two kinds of Nash equilibria exist in the static
game: one with trade and the other without trade. Since a detailed discussion of the
static Nash equilibria can be found in McLaren (1997), which uses the same
Ricardian model, I will only provide brief characterizations of the equilibria.
2.1. The interior Nash equilibrium
Since the small country cannot affect the terms of trade through its trade policy
choices, any non-prohibitive tariff imposed by the small country will therefore
simply introduce a local consumption distortion. As a result, in any interior Nash
equilibrium with positive trade, the small country will set t equal to 0. However,
the large country can change the terms of trade in its favor by raising its tariff rate.
It can be shown that there exists a critical level of the elasticity of substitution
(denoted by s M ) such that iff s # s M , the large country has a strong enough
incentive to push the terms of trade (Py /px ) to be equal to the small country’s
autarky price ratio (a ).8 Thus, for s # s M , all the gains from trade are transferred
to the large country with the interior Nash equilibrium tariff pair (t N , T N ) 5(0,
a 21). For s . s M , however, the small country is better off than under autarky
since (t N , T N )5(0,T(s )) with T(s )(, a 21) being a strictly decreasing function of
s.
From the world welfare point of view, there is no production distortion
associated with the large country’s positive tariffs in the interior Nash equilibrium
(uniquely defined for any given d . 0) described above. Since the small country
7
A sufficient condition for this is m,M / 2a.
s M is the unique solution for s of a s [((1 2 a ) /a )s 2 1] 5 1. The derivation of this formula can be
found in McLaren (1994); however, an intuitive explanation of this result can be provided: since Dixit
and Norman (1980), it is well known that the optimal tariff is equal to the reciprocal of export elasticity
of the other country. It is easy to understand that the small country’s export elasticity is positively
related with s, which then implies that the large country’s interior Nash tariff rate, denoted by T N , will
increase as s gets smaller. However, there is an upper bound for T N given by Py /px 5 (1 1 T N ) # a,
since the terms of trade should be less or, at most, equal to the small country’s autarky price ratio to
allow positive trade flows. At s 5 s M , T N reaches its upper bound, a 21.
8
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J.-H. Park / Journal of International Economics 50 (2000) 473 – 495
continues to be completely specialized in the production of x, the large country’s
tariff plays the role of dividing the efficient world output between the small and
the large country. However, it is important to note that the large country’s tariff
does distort the consumption decision of the small country by creating a difference
in the countries’ local price ratios.9 This inefficiency associated with the interior
Nash equilibrium creates the possibility of a mutually beneficial trade agreement
between the two countries, as discussed in the following section.
2.2. The autarky equilibria
Now, consider the set of Nash equilibria without trade. Recalling that the small
country’s domestic price ratio, py /px 5 (1 1 t)(1 1 T ) for t and T non-prohibitive,
it is easy to show that any tariff pair (t, T ) with (t, T ) . (a 2 1, a 2 1) can be
supported as a Nash equilibrium yielding an autarky state. If either country
imposes a tariff rate greater than a 21, its trading partner will be indifferent in
choosing any non-negative tariff rate, since trade will be prohibited in any event.
Therefore, neither country has an incentive to deviate from any tariff pair with (t,
T ) . (a 2 1, a 2 1), satisfying the definition of a Nash equilibrium.
3. Trade agreements
In this section, I will consider the possibility of trade agreements between the
small and the large country that can correct the inefficiencies embodied in the
Nash equilibrium. I will assume that, prior to a negotiated agreement, the tariff
choices of the two countries are characterized by the interior Nash equilibrium, but
I will consider the possibility that the two countries adopt tariffs from the set of
autarky Nash equilibria as well as the possibility that they revert to the interior
Nash equilibrium as a means of punishing deviations from the trade agreements.
The analysis in the previous section illustrates that only the large country has a
terms-of-trade driven incentive to impose positive tariff rates in the interior Nash
equilibrium.10 However, due to the inefficiency associated with the large country’s
9
Note that T .0 does not cause any consumption distortion in the large country since its local price
is fixed at 1. Therefore, the large country’s optimal trade policy is to set a tariff rate that maximizes
tariff revenue.
10
This may look unrealistic in the sense that many small countries also impose positive tariff rates
prior to trade negotiations. Such policies could be accommodated by introducing non-economic
objectives into the model. However, with respect to the possibility of mutually beneficial trade
agreements as assessed by the government objectives in each country, it will still be the terms-of-trade
driven aspects of the large country’s policy that are the source of the inefficiency in the Nash
equilibrium, and the source of the mutual gains from an agreement (see Bagwell and Staiger, 1995).
Hence, I abstract from non-economic objectives in my formal modeling and focus on the pure
terms-of-trade motivations for policy.
J.-H. Park / Journal of International Economics 50 (2000) 473 – 495
479
positive tariff, it is possible to negotiate an efficient trade agreement under which
both countries are better off than in the interior Nash equilibrium. First, I will
discuss this possibility by characterizing efficient trade policy combinations. Then,
I will analyze how an arrangement that implements efficient policy combinations
can be supported as a self-enforcing trade agreement in a repeated relationship.
3.1. Efficient policy combinations
Since the inefficiency generated by trade policy intervention comes from the
difference in local price ratios across countries, it can be eliminated by using
combinations of tariff policies that equalize local price ratios. Recalling that and
Py /Px 5 1, the Pareto efficient combinations of (t, T ) can be represented by EE in
Fig. 1, satisfying (1 1 t)(1 1 T ) 5 1.11 Denote the efficient combinations of tariff
policies on EE by (t e , T e). Then, different combinations of (t e , T e) correspond to
different divisions of the efficient world outputs between the two countries.
Starting from reciprocal free trade point F 1 , a movement up and to the left along
EE in Fig. 1 corresponds to the introduction of positive import tariffs for the large
Fig. 1. Please supply caption.
11
This way of describing efficient tariff combinations was introduced by Mayer (1981).
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J.-H. Park / Journal of International Economics 50 (2000) 473 – 495
country and import subsidies for the small country. Since local price ratios in each
economy are fixed at one all along EE, the tariff / subsidy combinations along EE
to the northwest of F 1 represent a lump-sum mechanism for transferring income
from the small to the large country relative to reciprocal free trade.12
This is illustrated in Fig. 2, which plots welfare levels for the large and the
small country relative to their autarky welfare levels, W A and w A respectively.
Given the CES utility function, each country’s level of welfare (w, W ) is a linear
function of its level of income measured at local prices; thus, I can formulate
Fig. 2. Please supply caption.
12
In the presence of political motivations in trade policies, trade agreements on reciprocal tariff
concessions do not necessarily entail import subsidies by the small country since it may also have
positive tariff rates prior to trade negotiations. However, T .0 is a more stringent requirement for the
large country to benefit from any trade agreement that exclusively focuses on reciprocal tariff
concessions because all the gains from trade will accrue to the small country with T 5 0. It turns out
that T . 0 (rather than t , 0) is the crucial element for the result in the following analysis, as discussed
later in relation to Proposition 2.
J.-H. Park / Journal of International Economics 50 (2000) 473 – 495
481
utilities in the two countries as functions of their tariff rates, respectively denoted
by w(t, T ) and W(T, t), as follows:
w(t, T ) 5 w( p, i) 5 i /(1 1 p 12 s )1 / ( 12 s ) and
W(T, t) 5 W(P, I) 5 I /(1 1 P 12 s )1 / (12 s )
(2)
where i and I denote the incomes measured in units of x, with p 5 py /px 5 (1 1
t)(1 1 T ) and P 5 Py /Px 51. Now, noting that i 1 I is constant and local prices are
fixed at 1 on EE in Fig. 1, the tariff / subsidy combinations along EE from F 1
toward the northwest direction have the corresponding welfare combinations on
the line labeled F 2 F (with slope of 21) in Fig. 2, starting from F 2 (the welfare
combination under reciprocal free trade). Fig. 2 also depicts the interior Nash
welfare levels by the point labeled N for the case where s # s M . Given this point
N, it is evident that any point on the segment FF9 is preferred by both countries to
the interior Nash equilibrium, implying the possibility of mutually beneficial trade
agreements between the small and the large country.
Finally, note that if direct lump-sum international transfer mechanisms are
available, there is an alternative way for the two countries to achieve points along
the efficiency locus F 2 F in Fig. 2: the large country unilaterally gives up its
attempts to manipulate the terms of trade, thereby implementing free trade, and the
two countries then move along the locus FF9 via a direct lump-sum transfer from
the small country to the large. This suggests two possible forms that trade
negotiations between small and large countries could take: countries could either
adopt the efficient (free trade) policies that each would have adopted absent
terms-of-trade considerations and negotiate over the size of the direct lump-sum
international transfers, or they could negotiate over tariff reductions to reach both
an efficient level of trade and an acceptable distribution of the gains from the
agreement across trading partners.
In principle, these two approaches to efficient trade agreements could yield
identical outcomes for the two countries, as illustrated in Fig. 2. However, in
practice, different issues of enforcement may arise across these two kinds of
agreements that could affect the feasible outcomes of the negotiation in each case.
To explore this possibility, I will first consider the nature of self-enforcing
agreements between the two countries when reciprocal free trade is to be
implemented and the focus of negotiation is on the size of direct international
transfers. I will then characterize self-enforcing agreements when such transfers
are unavailable and the focus of negotiation is on the degree of reciprocal
liberalization.
3.2. Self-enforcing agreements with direct international transfers
As established in the previous section, the countries can achieve mutually
J.-H. Park / Journal of International Economics 50 (2000) 473 – 495
482
beneficial free trade agreements with direct transfers from the small to the large
country. Denote welfare levels for the small and large country under free trade by
w F and W F , respectively, with s representing the per-period value of direct
transfers measured in utility terms and paid each period.13 Then, noting that
W F 5 W A , I can denote the per-period welfare level of each country under the free
trade agreement with direct transfers by w F 2 s and W A 1 s, respectively.
However, the agreement must be constructed so that neither country has any
incentive to deviate. I assume that countries choose their actions simultaneously in
each period: thus, the large country chooses T while the small country chooses t
and s. Then, the small country may deviate from the agreement by not providing
the transfers, realizing w F instead of w F 2 s. The large country can attain
W(T N ,0) 1 s (. W A 1 s) from its defection by imposing its interior Nash tariff rate
T N (its best response to t50). Given that any deviation from the free trade
agreement will be punished by permanently reverting to the static Nash tariff war
(the interior Nash or the autarky equilibrium) defined in Section 2, the incentive
constraints for the small and the large country, which I denote by ICS and ICL , are
given by
1
d
(ICS ) ]] (w F 2 s) $ w F 1 ]] w p
12d
12d
1
d
(ICL ) ]] (W A 1 s) $ W(T N , 0) 1 s 1 ]] W P
12d
12d
where w P and W P represent the countries’ per-period levels of welfare under the
punishment phase, with d [ (0,1) denoting the discount factor between periods.14
To sustain the free trade agreement, the discounted payoffs from keeping the
agreement for the small and the large country (the left sides of ICS and ICL ,
respectively) should be greater than the payoffs from defections (the right sides of
ICS and ICL , respectively). Finally, it is useful to rewrite these incentive
constraints as
(ICS )
s # d (w F 2 w P ),
N
A
P
(1 2 d )W(T , 0) 2 W 1 d W
(ICL ) s # ]]]]]]]]]
d
(3)
The general incentive constraints in (3) can be used to evaluate the range of
incentive compatible transfers with which countries can support free trade under
s 5 d /(1 1 p ( 12 s ))1 / ( 12 s ) 5 d /(2)1 / ( 12 s ) , where d is the level of transfers in units of x and
p 5 px /py .
14
This simple trigger-strategy punishment scheme is adopted to simplify my analysis, but the insights
developed in the analysis should also be valid under more general punishment schemes.
13
J.-H. Park / Journal of International Economics 50 (2000) 473 – 495
483
various punishment schemes. I will begin by considering the range of agreements
(as characterized by the range of direct transfers) that can be supported by the
interior Nash punishment scheme. Denoting each country’s level of welfare under
the interior Nash equilibrium by w N and W N , and noting that w N 5 w A (with
s # s M ), I then have w P 5 w N 5 w A and W P 5 W N under the interior Nash
punishment scheme. I can now rewrite the incentive constraints in (3) as follows:
(W N 2 W A)
]]]] # s # d (w F 2 w A)
d
(4)
]]]]]]]
Define dI ;œ(W N 2 W A) /(w F 2 w A), which equates both sides of inequalities in
(4). Using the fact that W A 5 W F and w A 5 w N , it is direct that dI , 1 iff
W N 1 w N , W F 1 w F . Therefore, as long as the interior Nash equilibrium is
inefficient, dI , 1, it is obvious from (4) that countries can support a mutually
beneficial free trade agreement with direct transfers and the threat of interior Nash
reversion over the range of discount factors d [ [dI ,1].
I now consider how the range of incentive compatible agreements would be
altered if countries adopted the more severe autarky punishment scheme. With
w P 5 w A and W P 5 W A , the incentive constraints in (3) become:
12d
]] (W N 2 W A) # s # d (w F 2 w A).
d
(5)
In an analogy to the case of interior Nash punishments, let dA denote the critical
value of d above which countries can support free trade with transfers under the
threat of autarky punishments. From a comparison of (4) and (5), I can easily
show that dA , dI . This reflects that it is easier to sustain trade agreements with the
autarky (more severe) punishment scheme than with the interior Nash punishment.
Note, however, that the large country can only lose in agreeing to the more
severe autarky punishment rather than the interior Nash punishment as a
mechanism for enforcing the free trade agreement, provided that d $ dI . That is, as
a comparison of (4) and (5) reveals, the autarky punishment simply reduces the
minimum transfer under which a free trade agreement would be incentive
compatible. In this way, the more severe punishment simply opens up a range of
possible outcomes to the free trade negotiations that are less (more) favorable for
the large (small) country. This is summarized in the following proposition:
Proposition 1. Given d $ dI and s # s M , a reliance on autarky punishments as
opposed to interior Nash punishments expands the set of transfers under which a
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J.-H. Park / Journal of International Economics 50 (2000) 473 – 495
free trade agreement is incentive compatible in a way that is unfavorable
( favorable) to the large (small) country.15
Proposition 1 reflects the fact that, owing to its strong incentive to manipulate
the terms of trade, the large country is very effective in using the threat of high
tariffs to induce the small country to uphold its transfer obligations under the
agreement, and it is able to inflict maximal punishments on the small country
(autarky utility forever) even in the interior Nash equilibrium, if s # s M . Hence,
the large country cannot increase the maximum transfer possible under the
agreement beyond that which is incentive compatible under the interior Nash
punishment.
The small country, however, because it has no ability to manipulate the terms of
trade, should rely more heavily on non-tariff measures to punish the large country
in the event of a deviation from the agreement. When the interior Nash punishment
is adopted, the small country must rely completely on the threat of terminating
transfer payments as a means of inducing the large country to fulfill its tariff
obligations under the agreement. This constraint is relaxed somewhat when the
autarky punishment is employed, permitting a range of lower transfers to become
feasible outcomes of the bargaining process without violating incentive compatibility. In this way, it is in the small country’s interest but against the interest of
the large country to facilitate harsher punishments.
As Proposition 1 illustrates, asymmetric countries may differ from symmetric
15
The effect of using different punishment schemes on countries’ relative bargaining power can be
more directly illustrated by comparing bargaining solutions under a specific bargaining model. For this
purpose, I will apply the bargaining solution concept proposed by Kalai and Smorodinsky (1975),
hereafter to be called K&S, that substitutes the axiom of independence of irrelevant alternatives used in
the bargaining solution of Nash (1950) with the ‘axiom of monotonicity.’ In contrast to the insensitivity
of the Nash bargaining solution to changes in the set of feasible bargaining outcomes when the
constrained maximization problem of the Nash bargaining does not lead to a corner solution, the
alternative axiomatic approach of K&S yields a unique bargaining solution which can reflect such
changes as well as the changes in the threat points of bargaining (payoffs for the bargaining parties
when they fail to reach an agreement). By defining the set of feasible bargaining outcomes to be the
countries’ welfare levels under self-enforceable free trade agreements with direct transfers as
characterized in (3), the K&S bargaining solution with the interior Nash equilibrium serving as the
threat point and also as the punishment against defections from bargaining outcomes, denoted by s NR , is
equal to [d (w F 2 w A)2 2 (W N 2 W A)2 /d ] / [(1 1 d )(w F 2 w A) 2 (1 1 d )(W N 2 W A) /d ] given that d $ dI
and s # s M as in Proposition 1. Let s AR denote the K&S solution under the autarky punishment with
the interior Nash equilibrium serving as the threat point, then s AR 5 [d (w F 2 w A)2 2 (1 2 d )(W N 2
W A)2 /d ] / [(1 1 d )(w F 2 w A) 2 (W N 2 W A) /d ]. Now, it is easy to show that s NR . s AR if d . (W N 2
W A) /(w F 2 w A) ( , dI ). Thus, the small country will have a more favorable bargaining solution under
the autarky punishment than under the interior Nash punishment, confirming Proposition 1. I am
grateful to a referee and Robert Staiger, respectively for suggesting that I check the result using a
specific bargaining solution and informing me about the K&S bargaining solution concept.
J.-H. Park / Journal of International Economics 50 (2000) 473 – 495
485
countries regarding the choice of punishment schemes. It is often argued that
developing a common understanding of autarky as part of the punishment phase
benefits trading partners since they can raise the level of cooperation through
harsher punishments.16 Even though the autarky punishment can still be more
effective in discouraging defections from the agreement between countries of
asymmetric size (observe dA , dI ), it strengthens the punishment power of the
small country disproportionately, thus, improving the small country’s bargaining
position as opposed to that of the large one.
3.3. Self-enforcing agreements without direct international transfers
As discussed earlier, an alternative way of achieving a trade agreement is
through reciprocal tariff reductions, where the focus of negotiation is on achieving
a balance of tariff concessions which both achieves efficiency and gives each
country sufficient incentives to honor its obligations. Since I will focus on
mutually beneficial and efficient agreements, the levels of tariff rates under
agreements continue to be denoted by (t e , T e) as in Section 3.1 with (1 1 t e)(1 1
T e) 5 1, 0 , T e , T N , and 2 1 , t e , 0; the large country imposes some positive
tariff rate which is less than its interior Nash tariff rates, and the small country
provides some level of import subsidies in trade agreements. However, countries
can deviate from an agreement unless the agreement is self-enforcing. The large
country can deviate by imposing its optimal tariff rate T D(t e) given t e , and the
small country can also deviate by imposing its optimal tariff rate t D(T e) given T e ;
t D(T e) 5 0 for any T e , since t50 is the dominant strategy for the small country.
Thus, negotiations amount to choosing tariff / subsidy combinations on the
efficiency locus which entails indirect transfers from the small to the large country
to keep the agreement incentive compatible.
Again, the analysis will focus on self-enforcing trade agreements in a repeated
relationship, where any deviation from the agreement is penalized by permanent
reversion to the static Nash tariff war. Then, the incentive constraints for the small
and the large countries to support the agreement become:
16
Dixit (1987) provides a detailed discussion on this point. Ludema (1990) shows that the possibility
of renegotiation may deter countries from using autarky as a part of the punishment and force countries
to end up with inefficient outcomes in trade negotiations, implying that dispute settlement procedures of
various trade agreements (facilitating renegotiations) may reduce the welfare levels of countries in the
trade agreements by disabling them to use stronger punishments against defections. Given that autarky
punishment is likely to be more vulnerable to renegotiation than the interior Nash punishment,
however, Proposition 1 implies that such procedures may actually serve the interests of the large
countries at the expense of the small countries, contrary to what is typically thought.
J.-H. Park / Journal of International Economics 50 (2000) 473 – 495
486
d
w(0, T e) 2 w(t e , T e) # ]]] [w(t e , T e) 2 w P ],
(1 2 d )
d
(ICL ) W(T D(t e), t e) 2 W(T e , t e) # ]]] [W(T e , t e) 2 W P ].
(1 2 d )
(ICS )
(6)
To sustain the free trade agreement, the gain in deviating from the agreement
(the left sides of the above inequalities) should be less than the cost of defecting
from the agreement (the right sides of the above inequalities) for both countries.
As in the case where direct transfers are part of the agreement, countries can
support a mutually beneficial trade agreement as long as the discount factor is high
enough.
However, I am interested in comparing the range of efficient agreements that
can be supported when countries negotiate over direct transfers (as in the previous
section) with those that can be supported when countries negotiate over transfers
indirectly through the balance of tariff concessions. For this comparison, I will
rewrite the incentive compatibility conditions in (6) in a way that makes it more
directly comparable with (4) of the previous section; I will focus on the interior
Nash punishment scheme, but an analogous comparison could be made with the
autarky punishment. Since W(T e , t e) 1 w(t e , T e) 5 W A 1 w F from my focus on the
efficient agreement, I can define s(T e , t e) ; W(T e , t e) 2 W A ; w F 2 w(t e , T e).
Observe that s(T e , t e) gives a corresponding level of transfer from the small to the
large country that, if offered under a free trade agreement, would give each
country the level of welfare it would enjoy under the efficient tariffs t e and T e in
the absence of direct transfer. Now, using the relations and definitions described
above, I can rewrite the incentive compatibility conditions in (6) in a form
comparable with (4) as follows:
(W N 2 W A)
]]]] 1 (1 2 d )Y(t e) # s(T e ,t e) # d (w F 2 w N ) 1 (1 2 d )Z(T e),
d
(7)
where
Y(t e) 5fW(T D(t e), t e) 2 W Ng 2sW N 2 W Ad /d, Z(T e) ; w F 2 w(0, T e).
In an analogy to (4), (7) gives the range of indirect transfers from the small to
the large country that are consistent with incentive compatible choices of t e and
T e . Observe that Z(T e) . 0 for T e . 0. Hence, a comparison of the right side of (7)
with the right side of (4) yields the following:
J.-H. Park / Journal of International Economics 50 (2000) 473 – 495
487
Proposition 2. For d [ [dI , 1), the maximum transfer payable by the small
country to the large under an incentive compatible efficient trade agreement will
be smaller if the countries adopt free trade and negotiate over the size of the
direct transfers than if they negotiate only over tariff concessions.17
To understand this result, consider the maximum (indirect) transfers that would
be incentive compatible under (7) for d [ [dI , 1). Why is this transfer not incentive
compatible if it is accomplished directly? The reason centers on who is in control
of the means by which the transfer is accomplished. When the transfer is
accomplished directly, the small country has complete control over whether or not
to provide it in any period, and this gives the small country a relatively large
one-time payoff from defecting (not paying the transfer). However, when the
transfer is accomplished indirectly through the choice of efficient tariff concessions, both countries are involved in carrying out the transfer: the transfer is
accomplished with a small country tariff less than zero and a large country tariff
greater than zero.18 Hence, the small country has less ability to stop paying the
transfer (it would only defect to t 5 0, leaving transfer payments s(T e , t 5 0) still
in place) and consequently less incentive to defect. Because of this reduced
temptation to defect, the small country could pay higher indirect transfers to the
17
To analyze how changes in the focus of trade negotiations affect countries’ relative bargaining
power, one may again use the K&S bargaining solution as in footnote 15, with the interior Nash
equilibrium serving as the threat point of bargaining as well as the punishment against defections from
the agreed solution. If the minimum level of self-enforceable transfers (left sides of the inequalities in
(7) and (4)) does not increase as countries switch their focus of bargaining from the indirect transfers
through reciprocal tariff concessions to the direct transfers under free trade, such a switch of focus will
lead to a more favorable bargaining outcome for the small country under the K&S solution with d $ dI .
This result is mainly due to the decrease in the highest sustainable transfers (described in Proposition 2)
which changes the set of feasible bargaining outcomes favorably to the small country. But, if the lowest
incentive compatible transfer does increase in response to such a change in the focus of negotiation,
then the associated effect on the set of feasible bargaining outcomes is not necessarily favorable to the
small country and the level of transfers under the K&S bargaining solution may either increase or
decrease. As discussed in footnote 19, however, the effect of changes in the negotiation focus on the
minimum self-enforcing transfers is indeterminate.
18
Note that the crucial factor for the small country’s lower incentive to defect under the trade
agreement through tariff concessions is not the small country’s import subsidies but the existence of
positive tariffs of the large country since T . 0 gives the large country control over a certain part of
transfers to be made under the agreement regardless of the small country’s actions. Recalling that T . 0
(rather than t , 0) is a necessary condition for the large country to benefit from any trade negotiation
focusing on reciprocal tariff concessions as discussed in footnote 12, the point made in Proposition 2
should be valid even for the case where the trade agreements focusing on reciprocal tariff concessions
do not necessarily entail the small country’s import subsidies due to some non-economic concerns of
governments.
488
J.-H. Park / Journal of International Economics 50 (2000) 473 – 495
large country when the two negotiate over tariff concessions alone than would be
incentive compatible under a free trade agreement with direct transfers.19
The main issues of a trade negotiation can be categorized into three parts: how
to divide the increased total surplus from cooperation on trade policies between
trading partners; how to execute the division; and how to enforce the execution of
agreements. Most prior analyses on trade agreements have focused either on the
first or the third issue (or their relationship as in Proposition 1), but Proposition 2
stresses the role of choosing different measures to execute the agreement in
determining the outcome of a trade negotiation. Specifically, it illustrates how an
increased control over the execution of the division of gains from freer trade for a
country can change the set of sustainable negotiation outcomes (thus, possibly the
outcome itself as discussed in footnote 17) more favorably to the country.
Compared to the GATT’s negotiations, which have largely focused on reciprocal
tariff concessions, therefore, the flexibility of recent regional trade agreements
toward non-tariff commitments like enforcing stricter intellectual property rights or
stronger environmental laws (which can be interpreted as direct transfers) as
possible forms of concessions by smaller countries may have been a factor that
strengthened their bargaining positions rather than weakened them, especially
against the worst possible negotiation outcomes.
4. Policy commitment with respect to investment decisions
Thus far, I have focused on the character of trade agreements between small and
large countries when terms-of-trade driven policies of the large country are the
source of the inefficiency that the agreement is designed to address. I now turn to a
second possibility: trade agreements may help governments commit to trade
policies that their private sectors would not find credible in the absence of an
agreement. I focus in particular on the commitment issues faced by governments
with respect to the investment decisions of private producers. I do this by
assuming now that in each period, labor’s allocation decision is an irreversible
investment that must be made prior to the tariff decisions of governments.
19
As for a comparison of the large country’s incentive constraints across the two kinds of agreements
(the left sides of (4) and (7)), two opposing forces are at work in determining whether Y(t e) $ 0 or
Y(t e) # 0. On the one hand, a free trade agreement has the large country contemplating defection from a
lower tariff (T 5 0) than would be the case in the efficient agreements without direct transfers, making
deviation from a free trade agreement more tempting for the large country. On the other hand, the small
country’s tariff is higher under the free trade agreement (t 5 0) than it would be in the efficient
agreement without direct transfers; this gives the large country less incentive to deviate from a free
trade agreement. Hence, the lowest incentive compatible transfers may either rise or fall if countries opt
to negotiate a free trade agreement with direct transfers rather than negotiate over reciprocal tariff
concessions.
J.-H. Park / Journal of International Economics 50 (2000) 473 – 495
489
4.1. The static model
The basic set-up remains the same Ricardian model of bilateral trade defined in
Section 2. Following McLaren (1997), I incorporate irreversibility in trade-related
investments into the static model by introducing the following two-stage game:
workers in each country must choose a particular sector in the first stage; then, in
the second stage, each country’s government simultaneously sets its tariff on
imports, given goods produced in the first stage. Since the production takes place
prior to the tariff setting decisions, the property of the perfectly small and large
country character (only the large country affecting the terms of trade) will
disappear when m /M . 0. Thus, a simplifying assumption of m /M → 0 is
introduced to have P ( 5 Py /Px ) 5 1, Py /px 5 (1 1 T ), and p ( 5 py /px ) 5 (1 1
t)(1 1 T ).20 Then, again, there exist two kinds of Nash equilibria in the static
game: one with trade and one without. However, since the private sector in the
small country is now vulnerable to the large country’s use of excessive tariffs after
its irreversible specialization, the private sector in the small country may decide
not to specialize completely in the production of x. This concern about underinvestment toward trade (production distortion) turns out to be a relevant one for
the interior Nash equilibrium. Referring to McLaren (1997) for a detailed analysis
of the static game, I will simply characterize the Nash equilibria.
4.1.1. The interior Nash equilibrium
For s , s M , there is a unique interior Nash equilibrium where the small country
is incompletely specialized in the production of x with its domestic price ratio
p 5 (1 1 T N ) 5 a and t N 5 0. The small country’s zero tariff stems directly from
the assumption of m /M → 0, and the result of the incomplete specialization with
p 5 (1 1 T N ) 5 a can be explained as follows; on the one hand, if it were
irreversibly specialized in x, the large country would raise its tariffs higher than
(a 21) given s , s M , which makes the investment to y sector a better decision in
the first stage since p ( 5 1 1 T ) will be higher than a.21 On the other hand, if it
were completely specialized in y, the large country would impose tariffs on its
import of y, yielding p , 1 , a, which in turn makes the investment to x sector a
better choice in the first stage. In the subgame perfect Nash equilibrium of this
two-stage game, thus, the small country’s specialization will be only to the degree
that it gives the large country an incentive to raise its tariffs equal to (a 2 1),
having p 5 a.
20
However, the basic results in the following analysis do not specifically depend on this simplifying
assumption.
21
Recall from Section 2.1 that the large country’s reason for not raising its tariff higher than (a 2 1)
given s , s M and the small country’s complete specialization is to avoid autarky. However, there will
still be positive trade flows with T . (a 2 1) if the small country is irreversibly specialized in the
production of x.
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J.-H. Park / Journal of International Economics 50 (2000) 473 – 495
In the presence of irreversible investment, therefore, the large country’s
government faces a commitment problem with respect to the small country’s
private agents’ resource allocation, causing incomplete specialization by the small
country. However, it is important to note that the cost of this commitment problem
is borne solely by the large country in the interior Nash equilibrium. The small
country will have the same autarky level of welfare as in the case where all
investments are reversible since its price ratio after trade is the same as the autarky
price ratio. The large country will collect lower tariff revenue when investments
are irreversible than when they are reversible. It imposes the same tariff rate
T 5 (a 2 1), but the volume of trade is decreased due to the small country’s
incomplete specialization. Therefore, if the large country can commit to setting
tariffs on x which are low enough to make complete specialization a profitable
option for the small country’s workers, the large country will enjoy higher gains
from trade. In the following section, I explore the possibility of a mutually
beneficial trade agreement which might serve as this commitment device.
For s $ s M , it can be shown that the large country’s optimal tariff is lower than
(a 2 1) and the small country completely specializes in the production of x.22 This
implies that irreversible investment is no longer a binding constraint, if s $ s M ;
thus I will focus on the case with s , s M from now on.
4.1.2. The autarky equilibria
Similar to the case without irreversibility in investment, equilibria with (t,
T ) . (a 2 1, a 2 1) can be supported as autarky equilibria of the two-stage game.
Again, the autarky equilibria will be considered as a possible form of punishment
against defections from agreements.
4.2. Free trade agreement with direct international transfers
Now, I consider the possibility of mutually beneficial trade agreements.
Analogous to the case of reversible investments in Section 2, consumption
distortion occurs in the small country due to the large country’s positive tariff rate
in the interior Nash equilibrium. Furthermore, with irreversible investment, the
large country government’s commitment problem with respect to the small
country’s private sector causes production distortion in the small country (incomplete specialization). Therefore, there clearly exists room for mutually beneficial
arrangements eliminating the inefficiencies caused by these distortions.
As discussed in Section 3.1, Pareto-efficient arrangements can be achieved
either through free trade agreements with direct transfers or through trade
agreements without direct transfers. In this section, I will focus on free trade
agreements with direct transfers from the small to the large country in analogy to
22
See McLaren (1997) for the derivation of this result.
J.-H. Park / Journal of International Economics 50 (2000) 473 – 495
491
Section 3.2. Again, I analyze subgame perfect free trade agreements in a repeated
relationship, where any defection from agreements is penalized by permanent
reversion to the static Nash tariff war.
In constructing the incentive constraints for the self-enforcing free trade
agreement, I use the same assumptions as in Section 3.2. The small country may
deviate from the agreement by not providing the transfers to the large country,
realizing w F instead of w F 2 s. Similarly, the large country may deviate from the
agreement by imposing its optimal tariff rate T D given the small country’s
irreversible investment, realizing W(T D, 0) 1 s instead of W A 1 s. Since the small
country specializes completely in the production of x under free trade agreements,
T D .(a21) for s , s M .
Then, the incentive constraints for the small and the large countries to support
the agreement (as a subgame perfect equilibrium in a repeated relationship) are:
d
s # ]] (w F 2 s 2 w P ),
12d
d
(ICL ) W(T D, 0) 2 W F # ]] (W F 1 s 2 W P ),
12d
(ICS )
(8)
where (w P,W P ) represent the levels of welfare under the punishment phase, with
d [ (0,1) denoting the discount factor between periods.
Finally, I assume that irreversibility does not carry over between periods;
investment is only temporarily irreversible. Then, under the punishment phase,
countries will play the static Nash equilibrium defined in Section 4.1. This can
either be the interior Nash equilibrium or the autarky equilibrium.
Case 1. The Interior Nash Punishment. First, consider the case of using the
interior Nash punishment scheme. As discussed in Section 4.1, the small country’s
welfare level in the interior Nash equilibrium when investments are irreversible
will be the same as in the case of reversible investments. Hence, w P 5 w N 5 w A .
However, denoting the large country’s welfare in the interior Nash equilibrium in
the presence of irreversibility by W NI , then W NI , W N since the large country
collects less tariff revenue in the interior Nash equilibrium when investments are
irreversible because of the small country’s incomplete specialization. Then, based
on the fact that the large country obtains the autarky level of welfare under free
trade (W F 5 W A), we can rewrite the incentive constraints in (8) as follows:
W N 2 W A s1 2 ddfW(T D,0) 2 W NIg 2 (W N 2 W NI )
]]] 1 ]]]]]]]]]]] # s # dsw F 2 w Ad.
d
d
(9)
As long as d is sufficiently high, again, countries can support a mutually beneficial
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J.-H. Park / Journal of International Economics 50 (2000) 473 – 495
free trade agreement with direct transfers even in the presence of irreversible
investments.
Noting that W(T D, 0) . W NI and recalling that W NI , W N , a comparison of (9)
with (4) illustrates the impact of investment irreversibility on the range of
incentive compatible free trade agreements. It is clear from the right sides of (9)
and (4) that the existence of irreversibility has no impact on the maximum transfer
from the small to the large country sustainable under the agreement, but a
comparison of the left sides of (9) and (4) reveals two opposing effects that work
toward altering the minimum sustainable transfer under the agreement in the
presence of irreversibility: The large country has extra incentive to defect and
surprise private producers in the small country (W(T D, 0) 2 W NI . 0), but in doing
so, the large country sacrifices the small country’s production efficiency and
thereby a portion of its tariff revenue (W N 2 W NI . 0) in the future. If d is
sufficiently high, this second effect dominates. Thus, a comparison of the left sides
of (9) and (4) yields:
Proposition 3. Under the interior Nash punishment scheme, and provided that the
discount factor is high enough, the existence of irreversible investment can only
expand the range of incentive compatible free trade agreements in a way that is
favorable to the small country.23
Proposition 3 implies that the existence of irreversibility in trade-related
investments can improve the small country’s bargaining position in a free trade
agreement with the large country. This contrasts with McLaren’s (1997) results
where the existence of irreversibility in investments dramatically reduces the small
country’s bargaining power in a free trade negotiation. Since the investment is
permanently irreversible in McLaren (1997), the private sector’s irreversible
specialization in anticipating free trade as an outcome of trade negotiation with the
large country works only against the small country’s bargaining power. However,
if the investment is only temporarily irreversible as assumed here, the irreversibility may work in the opposite direction by strengthening the punishment power of
23
Denote the level of transfers under the K&S bargaining solution (with the interior Nash equilibrium
serving as the threat point and as the punishment) by s NI , then s NI 5 [d (w F 2 w A)2 2 (W NI 2 W A)2 2
(1 2 d )(W(T D,0) 2 W A)(W NI 2 W A) /d ] / [(1 1 d )(w F 2 w A) 2 2(W NI 2 W A) 2 (1 2 d )(W(T D,0) 2 W A) /
d ]. Given that the discount factor d is high enough to have the lowest incentive compatible transfer
with irreversible investments be lower than the one with reversible investments as assumed in
Proposition 3, I can show that s NI , s NR 5 [d (w F 2 w A)2 2 (W N 2 W A)2 /d ] / [(1 1 d )(w F 2 w A) 2 (1 1
d )(W N 2 W A) /d ], which implies a more favorable bargaining outcome for the small country with
irreversible investments than without them. This result comes not only from the small country’s
increased effectiveness in discouraging the large country’s defections (with high values for d ) but also
from the small country’s stronger threat point with irreversibility (which does not depend on d ). Thus,
we may still have s NI , s NR for lower values of d than the minimum d to ensure the result in
Proposition 3.
J.-H. Park / Journal of International Economics 50 (2000) 473 – 495
493
the small country against the large country’s opportunistic defections from the
agreement.24
Finally, note that it is not any active policy by the small country’s government
but the private sector’s rational resource allocation decision that raises the small
country’s bargaining power. In the punishment phase, the small country’s tariff
will still be zero, but the private sector will allocate its resources away from trade
in anticipation of tariff wars, strengthening the small country’s bargaining position
in the trade negotiation.
Case 2. The Autarky Punishment. Now I consider the case where any deviation
from the free trade agreement is punished by permanently reverting to the autarky
equilibrium. Then, the incentive constraints for the small and the large countries to
support the agreement become:
D
A
s1 2 ddfW(T , 0) 2 W g
]]]]]]] # s # d (w F 2 w A).
d
(10)
A comparison of (10) with (9) reveals that the autarky punishment simply
makes incentive compatible a range of low transfers from the small to the large
country that would not be incentive compatible under the interior Nash punishment
scheme. This follows from the fact that W NI . W A . Therefore, in analogy to the
case with reversible investments, using the autarky punishment may only benefit
the small country by expanding the set of incentive compatible free trade
agreements in a direction that is only favorable to the small country.
Since W(T D, 0) . W N , however, a comparison of the left side of (10) with left
side of (5) provides a contrasting result to Proposition 3, with regard to the effect
of irreversible investment on the small country’s bargaining power in the free trade
negotiation:
Proposition 4. Under the autarky punishment scheme, the existence of irreversible
investment can only reduce the range of incentive compatible free trade
agreements in a way that is favorable to the large country.25
24
However, it is important to note that the irreversibility may have a negative effect on the small
country’s bargaining position unless the discount factor is high enough. For example, if d is close to 0,
then the small country’s bargaining position becomes similar to that of McLaren (1997) since the large
country no longer cares about the loss from decreased trade volume in the future compared with current
gains from using excessive tariff rates given the small country’s irreversible specialization.
25
Let s AI denote the level of transfers as the K&S bargaining solution with the interior Nash
equilibrium being the threat point and the autarky serving as the punishment, then s AI 5 [d (w F 2 w A)2 2
(1 2 d )(W(T D, 0) 2 W A)(W NI 2 W A) /d ] / [(1 1 d )(w F 2 w A) 2 (W NI 2 W A) 2 (1 2 d )(W(T D,0) 2 W A) /
d ]. Now, two factors work in opposite directions in determining the effect of irreversibility in
investments on the bargaining outcome: the increased effectiveness in the large country’s defection
stressed in Proposition 4 works against the small country’s bargaining position, but the strengthened
threat point (the interior Nash equilibrium) of the small country with irreversible investments enhances
the small country’s bargaining power. Thus, we may have either s AI . s AR or s AI , s AR , depending on
the relative magnitudes of these two counter-acting effects.
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J.-H. Park / Journal of International Economics 50 (2000) 473 – 495
When autarky is used as punishment, then the small country is already inflicting
the strongest possible punishment on the large country. Thus, the irreversible
investment no longer plays the role of strengthening the small country’s punishment power (as it does in the interior Nash punishment case) but only provides
more incentives for the large country to defect, raising the minimum level of
incentive compatible transfers under a free trade agreement. The effect of
irreversible investment on the relative bargaining power of countries in a free trade
negotiation, therefore, largely depends on the punishment to be used in supporting
the agreement.
5. Concluding remarks
This paper has analyzed self-enforcing trade agreements between a small and a
large country and has revealed several issues specific to trade agreements between
countries of asymmetric size. First, imposing a harsher punishment against
defections from agreements (for example, the autarky punishment instead of the
interior Nash punishment) may not be a common interest for countries with
significant asymmetry in size. Asymmetric countries may also have conflicting
interests in choosing the focus of trade negotiations (such as whether to focus on
the size of direct transfers under free trade or on the levels of reciprocal tariff
reductions). Finally, the analysis shows that the existence of irreversible investment may strengthen the small country’s bargaining power instead of weakening it
in a trade negotiation, in contrast to the result of McLaren (1997).
These results on factors affecting the relative bargaining power of differentsized countries should be valid for more general models of trade, as far as there
exists a large enough difference in the size of countries in trade negotiations.
However, distinctive characteristics of various regional trade agreements rapidly
forming across significantly heterogeneous countries generate a demand for more
structures in modeling. For example, Bond and Park (1998) have developed a
model of non-stationary bilateral trade agreements between countries of asymmetric size, which interprets the gradual liberalization process (embodied in many
recent trade agreements) as a means of relaxing countries’ incentive constraints to
achieve Pareto-efficient agreements. The simple model developed in this paper can
be a useful starting point for possible extensions, such as introducing additional
small countries, allowing trade agreements to vary over time, or incorporating
political economy considerations into the model.
Acknowledgements
I would like to thank seminar participants at the University of Wisconsin–
Madison, Pennsylvania State University, and Oregon State University for their
J.-H. Park / Journal of International Economics 50 (2000) 473 – 495
495
helpful comments and discussions, with special thanks to Robert Baldwin, Michael
Baye, Eric Bond, Yeon-Koo Che, Raymond Deneckere, and Kala Krishna. I am
especially grateful to Robert Staiger for his constant help and encouragement. I
also would like to express my gratitude to two anonymous referees and the editor
for their detailed comments and constructive suggestions. I gratefully acknowledge
financial support for this research provided by Cheonwoo Express Co. Ltd.
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