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Decentralized International Exchange Author(s): Robert R. Reed and Kathleen A. Trask Source: The Canadian Journal of Economics / Revue canadienne d'Economique, Vol. 39, No. 2 (

May, 2006), pp. 516-543 Published by: on behalf of the Wiley Canadian Economics Association Stable URL: http://www.jstor.org/stable/3696167 Accessed: 09-03-2015 17:06 UTC

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Decentralized international exchange Robert R. Reed Department of Economics, University of

Kentucky Kathleen A. Trask The Services Group

Abstract. We utilize a random-matching model to examine the relationships between market frictions and international trade. In our setting, an individual may choose to search abroad where she may have a cost advantage, but is less likely to meet potential trading partners, owing to higher market frictions. Interestingly, we find that interna- tional trade may be associated with lower welfare than autarky. We show how this is due to price distortions resulting from bargaining when there are opportunities for exchange across countries. JEL classification F10, C78, D83

Echanges internationaux dicentralises. Les auteurs utilisent un modele d'arrimage alea- toire pour examiner les relations entre les coilts de transaction dans le marche et le commerce international. On postule qu'un individu peut choisir de chercher des parte- naires commerciaux dans d'autres pays oui il peut avoir un avantage de cofits mais qu'il est moins susceptible de rencontrer de tels partenaires 'a cause des cofits de transaction. II1 appert que le commerce international peut etre associei a un niveau de bien-etre plus bas que ce que genererait l'autarcie. On montre comment cela est attribuable aux distorsions de prix qui decoulent du marchandage quand il y a des opportunites d'&change entre pays.

1. Introduction

Any model of international trade asks the following: 'Why does exchange take

place between countries?' Traditional trade theory focuses on this issue by examining the determinants of comparative advantage and investigating the effects of policy on relative prices, trade volumes, and welfare. These insights,

We are grateful to Ronald B. Davies and Chris Waller for valuable discussions. We also thank Marco Castenada, Josh Ederington, David Wildasin, and two anonymous referees for important suggestions. Seminar participants at Alabama, Kentucky, Oregon, Notre Dame, Tilburg, and the Midwest International Economics Conference provided insightful comments. Email: [email protected]

Canadian Journal of Economics / Revue canadienne d'Economique, Vol. 39, No. 2 May / mai 2006. Printed in Canada / Imprime au Canada

0008-4085 / 06 / 516-543 / ? Canadian Economics Association

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Decentralized international exchange 517

however, largely avoid the question: 'How does exchange take place between countries?' Standard trade theory ignores this question by assuming that transactions (aside from transportation costs) are costless. That is, most mod- els of international trade typically specify that exchange takes place in friction- less environments, where trade is coordinated by a fictitious Walrasian auctioneer. However, what if there are frictions in exchange? Are the predic- tions and policy recommendations from traditional trade theory robust to decentralized trading environments? For example, under what conditions will free trade be associated with higher welfare from the perspective of an indivi- dual country? How does trade affect world welfare?

Moreover, available evidence suggests that such frictions act as significant barriers to exchange across countries. For example, Gould (1994) finds that immigration is associated with a higher volume of bilateral trade from immi- grants' home countries. In particular, he stresses that immigration helps to reduce market frictions inherent in international trade: 'immigrants bring with them foreign market information and contacts that can lower the transactions costs of trade.' Casella and Rauch (2002) further emphasize these aspects in their work on ethnic ties: 'Connections to local agents facilitate entry into foreign unfamiliar markets by providing "insider knowledge"... they give access to the correct distribution channels and at times supply the expertise necessary to overcome local bureaucratic hurdles.' In addition, Frankel (2000) argues that a host of frictions limit the amount of exchange across countries: 'Such differences in currencies, languages, political systems, each have their own statistically estimated trade-impeding influences, besides the remaining significant effects of distance, borders, and other geographical and trade-policy variables.'1 As a result, incomplete information about opportunities for trade in foreign markets can be either 'natural' (due to cultural or language barriers) or 'supernatural' (due to explicit trade policy). That is, governments contribute to the degree of market frictions incurred by foreign firms by promoting or limiting access to their markets.2

Therefore, traditional trade models based upon market-clearing mechan- isms fail to account for some significant features involved in the process of exchange across countries, in particular, the decentralized nature of trade. Obviously, understanding how such frictions affect the pattern and volume of trade is important for the development of optimal policy. Nevertheless, there has been relatively little work incorporating these aspects of exchange into the literature on international trade. In an attempt to fill this gap, we

1 Frankel, Stein, and Wei (1993) find that more trade takes place between countries that share the same language. Thus, language barriers may impose an additional friction in exchange between countries - a friction that renders it more difficult to obtain contacts in the foreign marketplace.

2 The 1988 Economic Report of the President, among other references, makes the following observation: 'Invisible barriers to trade can take virtually an unlimited number of forms. Examples include discriminatory access to distribution systems for foreign goods relative to domestic goods' (133).

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518 R.R. Reed and K.A. Trask

depart from standard models by explicitly accounting for information frictions associated with exchange in a two-country setting. To begin, we dispense with the idea that trade, both within and across economies, is coordinated by the Walrasian auctioneer. In contrast, as in Diamond (1982), we formally model that trade is the result of a time-consuming process. In particular, we assume that contacts take place through pairwise random matching between agents. Given the bilateral aspects of exchange, the standard notion of price-taking behaviour dictated by the auctioneer no longer applies - instead, the terms of trade in each transaction occur as a result of bargaining. Notably, each agent's alternative opportunities for exchange affect the amount they are willing to trade. In this manner, each individual has a degree of monopoly power.

Since we are interested in addressing how the decentralized aspects of exchange affect transactions across countries, we integrate incomplete infor- mation along with some traditional features of trade models. Specifically, we consider the Ricardian motivation based upon differences in labour produc- tivity and comparative advantage. In an open economy, individuals may choose to move between countries in search of trading opportunities. Although each country is characterized by search frictions, our central hypoth- esis is that agents find it more difficult to trade in the foreign market. Thus, an individual may choose to search abroad, where she may have a comparative advantage, but she is less likely to meet potential trading partners, owing to higher market frictions.

As each individual is able to influence both the amount they produce and relative prices, this leads to a pricing distortion in the economy. Interestingly, we characterize the severity of the price distortion in autarky in terms of a relative cost or matching advantage of agents. For example, if an individual finds it relatively more difficult to find alternative opportunities for exchange, his partner will effectively have more bargaining power. Consequently, he must produce more in a match and receives a lower relative price for his output.

We show that open markets permit highly beneficial trade between high- productivity agents from each country. In fact, international matches lead to efficient terms of trade. However, when exchange between countries is possible, some agents who produce for the domestic market will have greater bargaining power. Consequently, this exacerbates the pricing distortion from bargaining in domestic matches. As a result, trade may lead to an 'anti-competitive' effect in each market.3 Thus, we find that international trade may lead to greater efficiency, owing to highly beneficial exchange, but it also can generate more severe pricing distortions in domestic transactions. Importantly, through these chan- nels, we demonstrate that international trade may be associated with lower welfare than autarky. Therefore, incorporating bargaining and endogenous

3 A similar effect occurs in Markusen's (1982) model of foreign direct investment. For more discussion, see section 2 below.

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Decentralized international exchange 519

relative prices provides some novel intuition for the effects of international trade.4

Finally, we discuss the implications of our model for world welfare and trade policy. We find that world welfare may be higher when search is suffi- ciently more difficult in the foreign market than in the home country. In these settings, some highly productive international matches take place, but the pricing distortions from differences in bargaining power are not too severe. We conclude by studying a planner's choice of foreign market participation and obtain conditions under which free trade is likely to move the world closer to the global optimum. We also examine possibilities where trade takes the world away from the global optimum.

Our paper is organized as follows. Section 2 provides a discussion of the related literature. Section 3 outlines the autarkic version of our model. This provides a useful benchmark for examining the effects of international trade in our economy. In section 4, we describe the economic environment in the open economy setting and the incentives for international trade. To begin, we discuss how differences in relative prices across economies provide motivation for exchange across countries. The section proceeds by studying agent's choices regarding market participation in the world economy.5 Section 5 examines the implications of our model for world welfare and trade policy along with the planner's choice of foreign market participation. We provide some concluding remarks in section 6.

2. Related literature

Our work complements earlier research by Casella and Rauch (2002) and Davidson, Martin, and Matusz (1987, 1991, 1999) who explore the interactions between market frictions and international trade.6 Casella and Rauch also interpret trade as a decision to enter the foreign market, but model market frictions due to uncertainty about the quality of foreign matches. We pursue an alternative notion of search frictions involving the time delay until matching occurs. In contrast to our approach, Casella and Rauch do not explicitly introduce the incentives for international trade. In their model, they assume that international matches may generate more surplus, while we motivate international trade through comparative advantage. Alternatively, Davidson,

4 Casella and Rauch (2002) also consider the links between market frictions and international trade. However, in their model production is indivisible, so that there is no notion of pricing. In contrast to our work, in which differences in relative prices provide a necessary condition for trade across countries, they assume that international matches are potentially more productive than domestic matches. Further details are described in section 2 below.

5 This is analogous to the segmented markets approach in Brander (1981) and Brander and Krugman (1983), in which Cournot duopolists determine the amount of output to ship to each country. For more discussion, see section 2 below.

6 Alessandria (2004) provides another example. He extends a model of costly consumer search to explain deviations from the law of one price.

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520 R.R. Reed and K.A. Trask

Martin, and Matusz study the effects of international trade on unemployment by incorporating search frictions in the labour market. However, the world product market is assumed to be Walrasian.

Our framework improves on these earlier models by allowing each agent to bargain over how much to produce when matched. In contrast to prior research in which the total output from matching is exogenous, both total output and relative prices in each match are endogenous. As discussed in the introduction, including this aspect of matching introduces an additional source of inefficiency, owing to differences in bargaining power between agents. However, following standard trade models, differences in autarkic relative prices act as a necessary condition for exchange across countries.

Although our approach departs from traditional trade theory by incorpor- ating incomplete information regarding opportunities for exchange, it shares similar themes that have been introduced in the new trade literature. Notably, recent contributions have introduced various aspects of imperfect competition into open economy settings. For example, Brander (1981), Brander and Krugman (1983), and Markusen (1981) consider the effects of open markets under Cournot-Nash competition between firms from different countries. Interestingly, Markusen (1981) demonstrates the potential for international trade to raise welfare even if both economies remain closed. This occurs because of the threat of increased competition from abroad. However, when countries differ in size, the small country always gains from trade, while the large country may lose.

Moreover, the segmented markets approach of Brander (1981) and Brander and Krugman (1983) also produces conflicting insights regarding the effects of international trade. On the one hand, trade has a welfare-enhancing output creation effect, owing to lower prices. Nevertheless, welfare may fall, since some domestic production is replaced by the foreign firm subject to transpor- tation costs.7 Finally, Markusen's (1982) model of multinationals illustrates similar trade-offs. Although opening markets can lead to greater technical efficiency, the multinational may decrease production, as a result of higher market power.

In contrast to the pricing distortions from imperfect competition, inefficient terms of trade arise in our framework as a result of bilateral bargaining. This notion of price determination seems appealing in our economy, given pairwise matching in decentralized trade. As individuals in each match have different opportunities for exchange, a natural notion of price discrimination will be observed. Specifically, high-productivity agents in each country will have two different markets in which they can trade. In international matches between agents from two different countries, the terms of trade will be efficient, since neither individual possesses a relative cost or matching advantage. This is

7 Clarke and Collie (2003) prove that there are always gains from trade under Bertrand competition with differentiated products.

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Decentralized international exchange 521

analogous to Brander's (1981) output creation effect. However, the terms of trade in domestic transactions will be further distorted than they would be under autarky. This occurs because high productivity agents who produce for the domestic market have both a cost and a matching advantage over low- productivity individuals.

Consequently, the welfare effects of international trade will depend on whether the gains from increased output in international matches offset the welfare losses from pricing distortions in domestic exchange. In particular, we find the net impact depends on the relative degrees of search frictions between both countries as well as the productivity differential between agents within each market. If foreign search frictions are sufficiently strong, the amount of international exchange is inefficiently low. However, if frictions in the foreign country are not too much higher than at home, the amount of foreign market participation is excessively high because of the large changes in bargaining power. In these settings, we demonstrate that international trade may be associated with lower welfare than under autarky.8 Moreover, our results provide alternative insights regarding the effects of international trade under imperfect competition. For example, Brander and Krugman (1983) find that trade will be associated with lower welfare under high transportation costs. In contrast, we show that trade may be more likely to have adverse consequences when the costs of entry into foreign markets (in terms of the delay in matching) are relatively low.

3. Autarky

In this section, we present an autarkic version of our model, in which all agents face identical search frictions. An examination of the autarkic equilibrium allows us to describe our framework in a tractable setting and, most important, sets a benchmark for evaluating the open economy equilibrium. We begin by describing the components of the physical environment and characterizing the decisions faced by agents in the economy. We then define and examine the properties of the steady-state equilibrium that emerges.

3.1. The environment We consider an economy populated by a continuum of agents of two types, types 1 and 2, where pi denotes the exogenously given proportion of type i agents. Agents of each type can produce only one of the two divisible goods in the economy. In order to provide a simple motivation for exchange, we impose

8 Krugman (1981) shows that trade may lead to lower welfare if both countries are sufficiently different in terms of the distribution of factor endowments. This occurs because of Stolper-Samuelson effects in which the scarce factors in each country lose from trade. In contrast, we show that open markets can lead to lower welfare when both countries are sufficiently similar. This takes place because too many high productivity individuals target the foreign market for production rather than the home country.

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522 R.R. Reed and K.A. Trask

that individuals cannot produce the good that they consume and therefore must enter a decentralized marketplace to search for appropriate trading partners. If an agent finds a suitable partner, they bargain over the quantities exchanged. After reaching an agreement, they immediately produce and con- sume and then exit the economy to be replaced immediately by an identical pair.9 Finally, time is continuous and p > 0 represents the discount rate.

Upon consumption, agents obtain utility u(q) such that u'(q) > 0 and

u"(q) < O. In contrast, production results in the loss of utility given by cost

ci(q) in which ci(q)

> 0 and ci'(q)

> 0. In addition, we assume that one of the inequalities on the second derivatives of the utility or cost functions strictly holds and that there exists a qi such that u(i) = ci('i). Furthermore, the marginal costs of production are such that c' (q) = c'(q) < ?'(q) = c'(q). Thus, type 1 agents produce good 1 at a lower marginal cost than type 2 individuals.

We now formalize the description of the search and bargaining process and outline the requirements for the steady-state equilibrium. We derive the equili- brium in two steps. First, taking the quantities exchanged between agents as given, we derive the expected lifetime utilities for each type of agent. Second, taking the expected lifetime utilities as given, we derive the outcome of the bargaining process that determines the quantities to be exchanged in each match. We conclude this section by characterizing the steady-state equilibrium under autarky.

3.2. Asset value functions In deriving the asset value function of a type i agent, vi, we first assume that all matches between appropriate partners result in a successful bargain with qi units of good i exchanged for qj units of good j.1 The type i agent will then receive a net instantaneous utility u(qi) -

c,(qi) and exit the economy, forfeiting vi in future

periods. Thus, the net change in utility from a match is [u(qj) - c(q,q) - vi]. Given

this outcome, the asset value functions of agents will depend on the likelihood they will find a suitable match.

In the decentralized marketplace, we normalize the flow probability of matching to one. The probability of matching with an appropriate trading partner depends additionally on the proportion of such partners in the market- place, py. The flow value of a type i agent is given by

9 Masters (1998) also assumes that agents immediately exit the market after trading. In an alternative setting, agents could remain matched for a period of time until detachment occurs. Therefore, there will be an endogenous distribution of matched and unmatched individuals. Assuming that agents immediately exit the market after matching makes the analysis more tractable, since all agents in the market are unmatched. Alternatively, we could assume that both goods are completely durable. In this case, agents would choose to permanently exit the market after trading occurs.

10 As we are concerned only with steady-state equilibria, we assume that the traded quantities and asset value functions are constant over time. We provide a formal derivation of the asset value functions in the appendix.

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Decentralized international exchange 523

PVi = pij[u(qj) - ci(qi) - vi]. (1)

Therefore, the flow value is the expected net surplus from trading with other agents in the market. With flow probability pj, agent i will meet and trade. For example, if the economy is relatively more populated with type 1 agents (pL1 > 0.5), they will incur a longer delay until matching occurs.

3.3. Bargaining In the decentralized market, agents will meet and bargain with appropriate trading partners. Agents engage in a bilateral Nash bargaining game in which an individual's threat point is his expected utility from remaining in the market and is taken as given. This problem is

max [u(q2) - Cl(ql) - vl][u(ql) - c2(q2) - v2], (2) ql,q2

subject to the participation constraints:

u(q2) - cl (ql) _ v

u(ql) - c2(q2) ? V2.

For an interior solution in which the participation constraints do not bind, the first-order conditions are

u'(ql)= c(q2)j C(ql) (3) ?u'(q2))

I

q , cq u(ql) - Vc2 2) - (4) u'(ql) =

cl'ql).u(q2)-

cl(ql) - 1 (4) -u(q2)- ci(ql) - v1

By (3), we can express q2 as a function of q1. In general, the quantities exchanged are functions of the parameters of the cost functions, as well as the agents' threat points. In particular, we observe

oqi(vi, vj) qi(vi, vj) > .

< 0 ; > 0. dvi dvi

Thus, as an agent's threat point increases, the terms of trade he receives in the match, pi = qj/qi, improves as he produces less while his partner produces more. Additionally, changes in the relative threat points of agents will also alter the total surplus received by the two agents. This is in contrast to much of the existing literature in this area, in which matched agents jointly produce an exogenous level of output while bargaining only determines the division of output (surplus from matching) (see Casella and Rauch 2002; Davidson, Martin, and Matusz 1987, 1991, 1999).

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524 R.R. Reed and K.A. Trask

3.4. Equilibrium We now combine the results of the two preceding sections and characterize the equilibrium for the autarkic economy. Restricting our attention to interior solutions in which the participation constraints, given in (2), do not bind, the autarkic steady-state equilibrium is formally defined as follows:

DEFINITION 1. The autarkic steady-state equilibrium is a list (qi, vi) for all i E {1,2} such that (qi, vi) satisfy:

(i) the returns to search, (1) (ii) the bargaining conditions, (3) and (4).

After imposing the equilibrium requirements, (1) along with (3) and (4) provide solutions for equilibrium variables. In what follows, we characterize the autarkic equilibrium that allows us to highlight the central features of our framework. In particular, we emphasize how differences in costs and propor- tions across types give rise to a pricing distortion in the economy.

3.4.1. Equilibrium quantities After imposing the equilibrium requirements, we obtain the following:

PROPOSITION 1. Assume that u(q) = q and ci(q) = ciq2. For all ci E (0, 00), the quantities exchanged in the autarkic equilibrium are uniquely determined and given by

q(cl, A) = (1/2cl)A ; q2 = (1/2c2)(1/A) (5)

where

F(ci )

(3p+ (1 I

) 1/3

c2 3p + (2 - pt)

Additionally, these quantities define the terms of trade:

Pi = q2/ql = (Cl/C2)(l/A2) = (l/P2).

By (5), qi can be decomposed into two terms. The first term, (1/2ci), provides the quantity of good i that would be produced if types were identical in costs and proportions:

cl = C2 ; Al = l2 = (1/2) = A = 1, qi = (1/2ci).

Importantly, when agents produce quantities qi = (1/2c;), they will maximize their total surplus from the match. However, if agents are not identical, the total surplus will not be maximized, since one of the agents will possess a relative advantage in bargaining. This advantage is encompassed by the second term, A, and derives from a relative cost advantage and/or a relative matching

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Decentralized international exchange 525

advantage. For A = 1, neither of the agents possesses an advantage. As A increases, the terms of trade received by type 1 agents decline. In particular, for A > 1 (A < 1), type 2 (1) agents will possess a relative advantage in bargaining.

To illustrate how the relative bargaining power is determined, we initially consider the case in which A = 1. Next, suppose there is an increase in t1. Since agents take their expected lifetime utilities as given, proportions do not have a direct effect on the quantities determined by (3). Holding the quantities constant, (1) illustrates that when Cp increases, type 2 (1) agents will find it relatively easier (more difficult) to meet potential trading partners and conse- quently v2 (v1) increases (decreases). This alters the agents' threat points in the bargain. As a result, the relative bargaining strength of type 2 agents increases. The effect on the equilibrium quantities can then be characterized as follows:

COROLLARY 1. An increase in the proportion of type i agents in the marketplace, pi, unambiguously increases qi, decreases qj, and improves the terms of trade received by type j agents, pi=qj/qi.11

Changes in the cost parameters of agents will have more complicated effects on the equilibrium quantities, since their impact will extend beyond changes in the relative bargaining power of agents. Again, starting from the case in which A = 1, consider the effect of an increase in c2. Holding the relative bargaining power, A, constant, such a change has no effect on ql. However, by increasing the marginal costs of type 2 agents, lowering (1/2c2), the increase in c2 has a negative direct productivity effect on q2 which tends to lower P2. In addition to this direct effect, as type 2 agents become less efficient, their relative bargaining strength declines. This lowers A, decreases

ql, increases q2, and lowers P2. Nevertheless, the negative direct effect dom- inates. Thus, while both ql and q2 will decrease, q2 decreases by proportion- ally more so that the net effect on P2 is positive. The following corollary summarizes these results:

COROLLARY 2. An increase in the costs of type i agents, ci, unambiguously decreases the equilibrium quantities produced by both types of agents while improving the terms of trade received by type i agents, pi=qj/qi.12

11 Corollary 1 illustrates that the current framework provides a result consistent with the Heckscher-Ohlin Theorem in that countries whose population is relatively abundant in good i producers will have a lower relative price for good i in autarky, pi. However, in the current setting the effect operates only through the effect of proportions on relative bargaining strengths, not through increasing opportunity costs.

12 This effect is consistent with Ricardian trade theory in that, all else equal, an increase in the cost of producing good i should raise its autarkic relative price.

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526 R.R. Reed and K.A. Trask

,c2

c2

FIGURE 1 Welfare under autarky

3.4.2. Equilibrium welfare To complete our analysis of the autarkic equilibrium, we consider aggregate welfare in the steady state: W = PIv + (1 - Pl)V2. Using the analysis above, aggregate welfare may be expressed as the product of the expected number of matches, Pu(1 - p1), and the present discounted utility received in such matches:

W(ch,c2,, ,A) = 11(1-I1)

?q2(C2,A)-Cl(ql(Cl,A))2+

+ ql(Cl,A)- C2(q2(2(C2, ))2 (6) P+ (0- PI) P+P1

From (6), changes in costs and/or proportions will have two distinct effects on aggregate welfare in equilibrium: a direct effect and an indirect effect caused by changes in the relative bargaining power of agents, A.

Using the benchmark case in which A = 1, consider the impact of an increase in c2. Holding A constant, with less efficient agents total welfare achieved by the economy declines. Figure 1 illustrates this result for a simple numerical case in which p = 1/6, p1 = 0.5, and cl = 0.5. The horizontal axis consists of alternative values of the cost parameter for type 2 agents. The locus W"* represents the maximum welfare available in the economy for each value of c2. Although potential welfare falls with less efficient agents, equilibrium welfare falls even more. This occurs because the increase in c2 improves the relative bargaining power of type 1 agents (as can be seen from the higher value of A). Since the terms of trade are determined inefficiently, production of good 2 does not fall as much as it should. Consequently, the market equilibrium is inefficient in that it does not maximize aggregate welfare when one of the agents possesses a relative advantage in bargaining.13

13 An identical analysis can be derived for changes in p1. Holding A constant, an increase in p1 will directly decrease aggregate welfare by raising the amount of time it takes for type 1 agents to match. By increasing the relative bargaining power of type 2 agents, welfare is further reduced.

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Decentralized international exchange 527

In this manner, the welfare analysis serves to highlight the key differences between our framework and other random-matching models. In a labour market context, Mortensen (1982) and Pissarides (2000) determine how the degree of unemployment results from a matching process between workers and firms. However, our model departs from the Mortensen-Pissarides set-up in significant ways. To begin, in our autarky benchmark, we study matching between two groups of individuals who separately produce and consume. In addition, the population of each type of agent is exogenous. In standard search models of the labour market, the equilibrium number of job vacancies is determined by a free-entry condition in which firms continue to enter the market until expected profits are exhausted.

Moreover, in our framework, bargaining power affects both the total sur- plus (as a result of the output produced by each agent in a match) and the division of the surplus (which pins down relative prices). In the typical Mortensen-Pissarides model, matches jointly produce an exogenous level of output, while bargaining only determines the division of surplus (which is split through wages).'1415 As a result of these distinctions, our work provides additional insights regarding the interactions between market frictions and international trade. For example, Davidson, Martin, and Matusz (1987, 1991, 1999) extend the Mortensen-Pissarides model to study the effects of international trade on unemployment. Since matched agents always jointly produce an exogenous level of output, the effects on welfare would be limited to the W* locus. By contrast, in our framework, changes in the relative bargaining power of agents alters not only the division of surplus between agents but also the total surplus available.

Finally, in labour market search models, the degree of inefficiency may be relieved when the number of firms is endogenous. For a fixed number of vacancies (analogous to the autarky economy), employers may possess higher bargaining power than workers. As a result, wages will be inefficiently low, so that firms can expect to earn positive profits. Under free entry, firms would have an incentive to create additional job vacancies, which renders it more difficult for them to hire workers. Consequently, wages increase and the degree of inefficiency falls. In our benchmark model under autarky, the total number of each type of agent is fixed. As demonstrated above, differences in produc- tivity and matching ability generate pricing distortions. Interestingly, as we show in section 5, opportunities for exchange across countries (endogenous market participation) can exacerbate the pricing distortions under autarky.

14 The total amount of output can be endogenized by incorporating capital. In the standard model, firms rent capital, which implies that a hold-up problem does not occur. As a result, the introduction of capital does not affect bargaining. See Pissarides (2000).

15 Trejos and Wright (1995) construct a random-matching model of money in which prices are determined by Nash bargaining. However, in their model, all agents incur the same disutility of production and the population of each is symmetric. As a result, barter exchange will feature efficient relative prices, since both individuals have the same opportunities for trade.

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528 R.R. Reed and K.A. Trask

4. International exchange

Having characterized the autarkic equilibrium, we now turn to the case of open economies. We consider a world comprising of two countries, home (h) and foreign (f), each of which is represented as a geographically distinct market- place. Both countries are endowed with a population of two types of agents. In each country, the population mass of each type of agent is equal to 1. In particular, agents may choose to search outside of their domestic market if they perceive the possibility of improved trading opportunities abroad. However, a central feature of our framework is that search is more difficult abroad, and thus individuals must weigh any potential benefit against the greater difficulties of searching.

We proceed with a formal description of the world economy. There are four types of agent differentiated by the type of good they produce and their country of origin. We refer to an agent of type ij E { lh, 2h, If, 2f} as one who produces good i E {1, 2} and is from country j E {h, f}. When a type 1 agent and a type 2 agent from any country are matched, a double coincidence of wants occurs and there are opportunities for mutually beneficial exchange. Production results in the loss of utility given by cost ci,{q) in which c'(q) > 0 and c.(q)> O0. Furthermore, we assume that the marginal costs of production across types and countries are symmetric such that

Clh(q) = Cf(q) =

c(q) < (q) = C2h(q) = c$q). Thus, type lh agents produce good 1 at a lower marginal cost than If individuals. Similarly, type 2 agents in the foreign market produce good 2 at a lower cost than at home. In this sense, the home country has a comparative advantage in good 1, while foreign has a comparative advantage in good 2.

4.1. Asset value functions In this section, we determine the expected returns to search for each type of agent in each market. As described above, each individual has a country of origin, and the populations of each type are the same initially in each country. In addition, the marginal costs of lh and 2f agents are equal. Similarly, 2h and If agents produce at the same marginal cost. Moreover, since lh and 2f individuals have higher productivity than 2h and If agents, they potentially may obtain better terms of trade and higher surplus from searching abroad. Thus, there is a large degree of symmetry in the world economy. In particular, both lh and 2f agents can have the same incentives to seek trading opportunities in their alternative market. Therefore, we choose to study a symmetric equilibrium in which the same number of lh and 2f individuals search abroad. In particular, we exploit the symmetry in our economy by studying activity from the perspective of agents from the home country.

We begin our analysis by assuming that a fraction of type 1 agents from home, 7, search in the foreign market. In addition, the same fraction of

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Decentralized international exchange 529

type 2 agents from foreign seek trading opportunities in the home country. In deriving the value functions, we take the quantities exchanged between agents as given. For simplicity, we use lower case letters to denote the returns to search and quantities in the home country. For the foreign market, we use upper case letters. Specifically, let vii represent the expected lifetime utility of a type ij agent from searching in the home market, while

Vi. denotes the expected surplus from searching in the foreign market.

Next, we assume that qlh and q2h are the quantities of good 1 and good 2 produced in a match between two agents from the home country in the home marketplace. Similarly, qlf (q2f) is the quantity of good 1(2) produced by a home (foreign) agent in a match with a foreign (domestic) producer of good 2(1) in the home market. In contrast, let Qif and Q2f denote the quantities of good 1 and good 2 produced by a type lh agent and a type 2f agent in the foreign market.

To begin, we derive the returns to search for a type 1 h individual. In the decentralized marketplace of each country, agents randomly encounter poten- tial trading partners. Type 1 h agents who choose to remain at home may trade with either domestic producers or foreign producers of good 2. For agents from the home country who search in their own market, we continue to normalize the Poisson flow probability of matching with any agent to 1. The flow value of a type 1 agent from home who chooses to remain in the home market is

rvlh = [u(q2h) - Clh(qlh) - Vlh] + Y[U(q2f) - Clh(qlf) - Vlh], (7)

where r = 2p. Thus, the flow value is the sum of the expected net surplus obtained from trading with others in the home market.16 With flow probability (1/2), type lh agents meet producers of good 2 from home. If agents agree to trade, the net gains involve the net utility received from production and consumption. If trade does not occur, the lh agent could continue searching in the home market. Thus, the net surplus from trading with a domestic producer of good 2 is the net utility from production and consumption offset by the expected utility an individual could obtain from continuing to search. Alternatively, with flow probability (y/2), the agent will meet and trade with foreign producers of good 2.

In contrast to the home country, search in the foreign market is more difficult for home agents. Therefore, the flow probability of matching is lower, / < 1. For type 1 agents from the home country who choose to search in the foreign market, individuals have the opportunity of potentially obtaining better terms

16 Under the assumption that the fraction, 7, of type lh agents chooses to search in the foreign market and type 2f agents choose to search in home, the population masses of the three types of individuals searching in the home market will not in general be the same. The population mass of type lh agents is (1 - 7), while the mass of type 2f agents is equal to y. All of the type 2h agents are assumed to remain at home. Under these population masses, the fraction of type 2h agents in home is equal to 1/2, while the fraction of 2f individuals is -y/2.

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530 R.R. Reed and K.A. Trask

of trade and more surplus, but will wait longer for matches to occur17 Consider the flow value of type lh agents in the foreign market:

rV1h = 0(1 - -)[u(Q2f) - Clh(Qlf) - Vlh]l (8)

Thus, lh individuals will incur a longer delay until matching occurs. This happens not only because of the inherent difficulties for search in the foreign market, but because there are fewer type 2 individuals in the foreign country than at home.

For type 2h agents, we also have

rv2h = (1 - )[u(qlh) - C2h(q2h) - V2h]. (9) In contrast to type 1 agents who remain in their domestic market, it takes longer for type 2 agents searching at home to find matches. This occurs because of foreign market participation under open markets. When there is more foreign market participation, there are fewer type 1 agents available to trade with in the home market and there is more demand, since foreign type 2 agents will also be seeking trading opportunities at home. Thus, the higher the degree of foreign market participation (for given quantities), the lower the expected lifetime utilities of type 2h agents. As a final note, given the symmetric environment, individuals from the foreign country will have a similar set of value functions. For example, the asset value function for a type 2 agent from the foreign country who remains in that market will be the same as (7). Thus, the value functions for agents from the foreign country are omitted.

4.2. Bargaining In the home market, type lh agents will meet and bargain with either home or foreign producers of good 2. As a useful reference we write the bargaining problem for matches in the home country:

max [u(q2j) - Clh(qlj) - vlh][u(qlj) - c2j(q2j) - v2j], (10)

qlj,q2j

subject to the participation constraints:

u(q2j) - Clh(qlj) > Vlh

17 Note that we continue to assume that all matches are only temporary. However, as pointed out by a referee, it is also reasonable to consider that there are long-term relationships between trading partners. In contrast to the current version of the model, we could follow Laing, Palivos, and Wang (1995) by asserting that all matches lead to permanent relationships. Once matches occur, agents exit the market forever. If there is a flow rate of new entrants over time, the population of unmatched agents would remain constant. As in Kiyotaki and Wright (1993), owing to constant returns to scale of the matching technology, the matching rate does not depend on the number of individuals engaged in search activity in each country. One could also follow standard labour search models by assuming that agents remain matched until detachment occurs. This would affect only the returns to search in each market, but not our main results. The important aspect of our framework is that it is more difficult to establish matches in the foreign market than in the home country.

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Decentralized international exchange 531

u(qlj) - c2j(q2j) > V2j, where j {h f}. For an interior solution in which the participation constraints do not bind, the first-order conditions may be expressed as

u'(q1j) = (q2) c(qlj) (11)

u(qlj)=ch(qlj) [u(qlj) -

c2j(q2j) - v2j

(12) [u(q2j)

- Clh(qlj) - VlhJ

By (11), we can describe the outcome of the bargaining process for each match entirely in terms of q1j. In addition, as we will demonstrate below, open markets will affect agents' outside opportunities, total production, and relative prices in each match.

4.3. International equilibrium Using the intuition outlined above, we now endogenize the degree of foreign market participation. We begin by characterizing the motivations for trade from autarky, where 7 = 0. Provided that international search frictions are not too severe, lh and 2fagents will have an incentive to search in their respective foreign markets to take advantage of the possibility of meeting with more efficient partners. However, no such incentive will exist for If and 2h agents who could only find less efficient partners abroad in addition to facing higher search frictions. Thus, as a result of the symmetry in the model, we consider a particular international equilibrium in which only types lh and 2f seek trading opportunities outside of their home countries. In contrast, 2h and lf agents choose to remain in their domestic markets.

Having described the equilibrium within each marketplace, we now consider how the distribution of agents across economies will be determined by their market participation choices. To illustrate, consider the decision of a type lh agent. The individual takes the returns to search in each country as given. Letting 7ih denote the probability that a type ih agent searches in the foreign market, the agent selects yih in order to

max Tih Vih + (1 - Yih)Vih. (13) 'Tih

If Vih > Vih, type ih agents will always remain in the domestic market. Similarly, if vih < Vih, then the returns to search in the foreign market are greater than at home and therefore

"Yih = 1. However, if Vih = Vih, any Yih E

[0, 1] would solve the problem. We note that yf solves

max yifvif + (1 - Yif) V. (14)

Combining with the earlier results and the symmetry in our model, we may define the equilibrium conditions from the perspective of the home country.

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532 R.R. Reed and K.A. Trask

Restricting our attention to interior solutions in which the participation con- straints, given in (10), do not bind, the steady-state equilibrium is formally defined as follows:

DEFINITION 2. The symmetric steady-state international equilibrium is a list:

(qij, QIf, Vih, Vlh, Yih, Tif)

for all i E {1, 2} andj E {h, f} such that (qij, Qlf, vih, V1h, Yih, 'Yif) satisfy (i) the returns to search, (7)-(9) (ii) the bargaining conditions, (11) and (12)

(iii) yih solves (13) and 7yifsolves (14) (iv) 7 Y1h = 2f C [O, 1]; 72h = f = 0.

Condition (iii) simply states that all individuals will choose a probability of foreign market participation that maximizes their expected surplus from trade. In contrast, condition (iv) imposes a symmetry condition upon the choice of market participation. Under the symmetry condition, the most productive agents make the same choice about searching abroad, and the least productive agents choose to remain in their home markets.

From the perspective of the home country, there is a total of six endogenous variables to solve for: (i) the quantities traded in domestic matches, (ii) the quantities traded in international matches, and (iii) the endogenous market participation decisions of type 1 and 2 agents.'8 Our algorithm for proving the existence and uniqueness of the symmetric equilibrium begins by solving for the quantities traded in international matches.

For clarity, we focus on proving the results using the functional forms from proposition 1. Therefore, we have Clh(q) = C2fq) cq2 < cq2 c2h(q) = Clf(q). As a first step, under open markets, type lh agents who choose to remain at home will have the same expected surplus as type lh agents who search in the foreign market. By symmetry, 2f individuals seeking trading opportunities in the home market will obtain the same expected surplus as lh agents who choose to search in the home country. Thus, in a match between types lh and 2f, the threat points of the two partners will be identical. As they have the same cost functions, neither agent will possess an advantage in the bargaining process. Equations (11) and (12) yield

qf = qlf = q2f = (1/2c).

18 Under our equilibrium concept, agents choose a probability of searching in the alternative marketplace. With a continuum of agents, the law of large numbers implies that y also represents the fraction of agents who seek trading opportunities abroad. Alternatively, one could interpret that agents choose pure strategies so that entry in the foreign market occurs until expected utility is the same as in the home country.

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Decentralized international exchange 533

--qBR . .qP (betalow)

qP(betahigh)

7

FIGURE 2 International equilibrium

Therefore, we only have four remaining endogenous variables to obtain. By the bargaining condition, we have already shown that q2h q2h(qlh), SO that there are three remaining endogenous variables in the system.

We proceed by proving that there are unique values of 7 and qlh that satisfy the equilibrium conditions. In the final step, we provide conditions under which type 2h agents choose to remain at home, so that -Y2h = 0. Given the outcome of the match between lh and 2fagents, the market participation condition that vlh = V1h can be expressed in terms of / and the remaining endogenous variables 7 and qlh:

Vlh(7, qlh)= Vlh(Q; P). (15)

Hereafter, we refer to this condition as the 'participation condition.' The combi- nations of y and qlh that satisfy it make up the participation locus. Thus, we denote qP(y; /) as the value of qh where type lh agents who remain at home achieve the same level of expected lifetime utility as type 1 h agents searching in the foreign market. Please refer to figure 2, where the participation locus is depicted. The properties of qP(y; P) are easily derived in the appendix. First, the participa- tion locus is upward sloping. Holding / constant, as - increases, type lh agents find it easier to meet partners in the home market than in foreign markets. As a result, Vlh increases relative to Vlh. In order for agents to remain indifferent between search in the home market and abroad, qlh must rise to lower vlh to the level of Vlh. Second, qP(y; /) is decreasing in /3. Holding - constant, as /3 increases, search in foreign markets becomes easier and V2h must increase. In order to maintain the equality, type lh agents who remain at home must be compensated by improved terms of trade in domestic matches and qlh must fall.

We next consider the bargaining game between two domestic agents. The outcome of the bargaining process will be determined by the threat points of the two partners. It can then be characterized by

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534 R.R. Reed and K.A. Trask

qlh = lh(Vlh(Y, qlh), V2h( Y, qlh)) that solves (12) and strictly satisfies the bargaining participation conditions in (10).

For any -, let qBR(y) denote the value of q1h that solves the above condition. We refer to this condition as the 'bargaining condition' and refer to combina- tions of -y and qlh that satisfy it as the bargaining locus. We illustrate a specific example in figure 2.19 It is easily shown that the bargaining locus is downward sloping. As y increases, the resulting change in proportions in the market causes Vlh to rise and V2h to fall for any qlh. The increase in the threat point of type lh agents improves the terms of trade that agents receive in a match. As a result, qBR must fall which means that the bargaining locus is downwards sloping.

Using these results, an international equilibrium will then require: qBR(_)= qP(Q; P). Guaranteeing the existence of an interior equilibrium in which y e (0, 1) and the 2h and if agents choose to remain in their domestic markets requires additional restrictions on costs and /. Based on our analysis, we have the following proposition:

PROPOSITION 2. Provided that/3 E (0, ), as defined in the appendix, there exists a unique equilibrium in which

(i) qf = (1/2c) (ii)

,y(/) E

(0,1), Y'(O) > 0

(iii) q'lhh()

< 0.

Proof. See appendix.

In order to establish the existence of an equilibrium in which only the lh agents choose to search in the foreign market, we need two important condi- tions. First, we need sufficient incentives for the lh individuals to seek trading opportunities in the foreign country. Depending on the degree of cost differ- ences between lh and 2h agents, lh individuals will search abroad if search frictions are sufficiently low (/ > /, where / is an increasing function of (c/T)). If c is not much lower than c (/ higher), then there is little benefit from matching with foreign trading partners. Thus, if / > /3, existence of the equili- brium is guaranteed by the fact that

qBR(y = 0) > qP(7 = 0; 3).

This relationship captures that starting from autarky, lh individuals could obtain higher utility from searching in the foreign market than at home.20 At higher values of y, lh individuals will have more bargaining power than in autarky, since there are fewer potential trading opportunities available to

19 Unless otherwise stated, we use the following benchmark set of parameters: p = 1/6, c=.5, and T=1.

20 Note that qBR (_y = 0) is simply the autarkic quantity of good 1 produced in home.

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Decentralized international exchange 535

domestic producers of good 2. Eventually, the gains from search in the foreign market will be the same as the returns to search at home. The second condi- tion, /3 < establishes that only the productive agents search in the foreign market for trading opportunities. Since foreign search is guaranteed to be sufficiently difficult, 2h agents will choose to remain at home rather than look abroad. We therefore have that a symmetric international equilibrium exists and is unique.21

Figure 2 also demonstrates the effect of an increase in 3 on equilibrium outcomes. As discussed above, while the qBR locus will remain unchanged, the qP(-y; /) locus will shift downwards. As illustrated, qlh will decrease while 7 will increase. The intuition is straightforward. When search in foreign markets is easier, more agents will seek trading opportunities abroad. Consequently, the domestic terms of trade favour lh agents, since it takes less time for them to find matches than 2h individuals.

5. Welfare and trade policy

We now turn to a consideration of aggregate welfare. In particular, we are interested in examining how welfare varies with the level of foreign search frictions, 3, and the corresponding implications for trade policy. Using the symmetry properties, global welfare may be expressed as W = [(1 - ')Vlh + 7V1h + V2h]. Imposing the equilibrium requirement that

vlh = Vlh provides

W(3) = Vlh(/3) + V2h(0). (16)

Consider how an increase in / affects equilibrium welfare

OW OVlh OV+2h

As argued in the preceding section, the effects of the increase on the individual types of agents are unambiguous:

OVlh/la > 0 > Ov2h/0/. This result is certainly not unique. In any standard model of trade, a movement from autarky to trade will increase the welfare of exporters and harm import competing sectors. However, unlike the situation of standard models, the net effect on welfare will not necessarily be positive. The increase in /3 will have

21 It may be possible that other asymmetric equilibria exist in which only some types from each country choose to search in the foreign market. For example, it is plausible that a large number of type lh agents would choose to search in the foreign market, while only a small group of type 2f agents seek trading opportunities in the home country. We chose to focus our attention on a symmetric equilibrium because we believe it is the most robust and the most tractable. Furthermore, we only claim that the equilibrium we study is unique among the class of symmetric equilibria.

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536 R.R. Reed and K.A. Trask

a) CD

tP

FIGURE 3 Effects of foreign search frictions on welfare

two distinct effects: a terms of trade effect, q'lh(/) < 0, as well as an effect on the composition of the market, -y'(3) > 0:

OW Ovlh +92h 91+ Vh OV2h < - qh(0) h Oqlh+

/() - >0.

Figure 3 illustrates the net impact. For initially low 0 and correspondingly small y, welfare is improving as the economy benefits from trade with the efficient type 2f agents. As the proportion of agents who move between countries is small, there is little impact on the composition of the market or the relative bargaining strengths. However, as 3 increases, the changes in the proportions of agents in the market result in increasing gains to the bargaining strength of the type lh agents. The negative welfare effects from the price distortion begin to dominate the positive effects of more efficient matches, so that welfare eventually declines. For sufficiently high values of 3, welfare is lower under international trade than under autarky.

Nevertheless, this finding will not always occur. The net result depends on the relative magnitudes of the bargaining power effect (an anti-competitive effect) and the traditional gains from trade coming from the efficiency of foreign matches (an output creation effect). When cost differences between agents are large under autarky, open markets will cause relatively large move- ments of agents between countries. Consequently, the pricing distortions become more severe, since large changes in relative bargaining power occur. In this manner, for low levels of foreign search frictions, welfare reductions are more likely with large cost differences. Figure 4 illustrates this result.

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Decentralized international exchange 537

c> 0< co c2low

(rr b -?.-c2high

cu

FIGURE 4 Welfare gains from foreign matching

The degree of relative search frictions in the foreign market may be inter- preted in a number of ways. One might infer that 3 reflects differences in languages or cultural barriers to trade. In that sense, 3 is somewhat arbitrary and cannot be relevant for the discussion of trade policy. However, many difficulties encountered by agents in international markets can be seen as explicit policy decisions. For example, they may represent different types of non-tariff barriers. In particular, these policies restrict information about trading opportunities. Since we demonstrate that trade may be welfare reducing, govern- ments have incentives to restrict trade through increasing market frictions.

We next examine the globally optimal volume of trade flows between coun- tries by studying the planner's choice of foreign market participation. In our setting, the planner must take the degree of search frictions in each country as fixed, but is able to choose 7 to maximize global welfare. Using the symmetry properties, global welfare may be expressed as W = [(1 -

•y)v•h + ~yVlh + V2h.

Importantly, owing to the highly decentralized notion of exchange, the planner is able to choose the degree of foreign market participation, but the quantities traded in each match result from bargaining. Essentially, the planner chooses y as opposed to the case in section 3 where it results from individuals' decisions.22

In this manner, we can compare the planner's solution with the equilibrium degree of foreign market participation. If the planner's choice is higher than in equilibrium, trade takes the world closer to the global optimum. Alternatively, if the equilibrium degree of market participation is significantly larger than what the planner obtains, trade can actually move the world farther away from the global optimum.

22 Another alternative would be to allow the planner to choose both the degree of market participation and the quantities in each match. If the planner could choose the quantities traded, he could also act as a Walrasian auctioneer. This would imply that the planner is not subject to the trading frictions in the economy. However, we intend to study international trade from the perspective of a matching process. Therefore, we focus on the case where the planner is constrained by the results of bargaining in the economy.

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538 R.R. Reed and K.A. Trask

Equilibrium Planner Autarky

FIGURE 5 Planner's choice of market participation (clow = .5)

In our framework, trade will generally be socially inefficient. When the most productive individuals in each country choose whether or not to search in the alter- native market, they affect the frequency of matching and relative prices in each country. On the one hand, if more of the productive individuals choose to search in the alternative market, social welfare is improved, since international matches provide the highest surplus to type lh and 2fagents. On the other hand, the low productivity agents in each country are worse off, since it becomes more difficult for them to trade and their bargaining power falls. Simulation results provide the following insights:

1. If foreign search frictions are sufficiently severe, it is likely the planner would choose more foreign market participation than in equilibrium. In this case, open markets lead to some foreign market participation, and international trade moves the world closer to the global optimum.

2. If search frictions are not much higher in the foreign market than in the home country and cost differences between agents are relatively large ((c/l) is low), international trade moves the world away from the global optimum.

We illustrate these results in figures 5 and 6. In figure 5, we use the same set of parameters as in our earlier calculations. In particular, we assume that (c/-) = 0.5. When search frictions in the foreign market are much higher than at home, the planner's degree of foreign market participation is higher than in equilibrium. In this case, individuals do not take into account that searching in the foreign market would increase the number of matches with foreigners in the other country. In contrast, when the expected returns from search in the foreign market are higher (0 closer to 1), agents who leave their home countries do not take into account that the remaining low productivity agents find it much more difficult to trade and have much lower bargaining power. Consequently, the equilibrium degree of market participation may

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Decentralized international exchange 539

Equilibrium Planner

...... Autark

• , • ..: _ __ ...,._ _• •. • : ........... -•:'•:•

FIGURE 6 Planner's choice of market participation (clow = .75)

become significantly higher than the planner would want. In fact, trade may be more inefficient than autarky so that open markets move the world farther away from the global optimum. Figure 6 illustrates an alternative setting where cost differences are lower, (c/p) = 0.75. As the figure shows, trade is much more likely to move the world closer to the global optimum when c is closer to c.

At this juncture, we can compare the effects of policy that emerge from our model. On the one hand, 0 may be an explicit policy variable such as non-tariff barriers. In this sense, such policies would be designed to limit the amount of foreign market participation indirectly through the degree of search frictions. Alternatively, the planner's choice of

"y could be viewed as describing the impact of a different

policy instrument, the degree of market entry. In this setting, the level of search frictions incurred by foreign firms is exogenous and beyond the scope of government intervention. The planner's solution could be the result of policy coordination on export restraints or the amount of foreign direct investment. In either case, our results do not suggest that countries should prohibit trade entirely - instead, we show that global welfare could be improved upon through policy coordination to determine the appropriate degree of market access across countries.

We conclude by discussing the role of policy in our framework compared with previous work in international trade. As in the new trade literature, the justifica- tion for trade policy stems from imperfections in the domestic economy. Under open markets, the low-productivity agents face less favourable opportunities for exchange. Consequently, they encounter a weaker bargaining position in matches. For these reasons, we illustrate that trade policy can be welfare enhan- cing. However, this may be a second-best tool for dealing with the domestic distortion.23 A direct method of intervention may be more efficient. In contrast to

23 See Helpman and Krugman (1994). As an example, tariffs can raise welfare in the segmented markets approach of Brander and Krugman (1983). Nevertheless, a production subsidy would be a better instrument for alleviating the pricing distortion from imperfect competition.

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540 R.R. Reed and K.A. Trask

trade restrictions, the government could attempt to give the disadvantaged agents higher bargaining power. In this manner, domestic policy would correct for the enhanced monopoly power of high-productivity individuals.24

6. Conclusions

This paper studies the impact of incomplete information on international trade. Specifically, we depart from traditional market clearing models by considering that exchange results from a search and matching process. Given the bilateral aspects of exchange between agents, the standard notion of price-taking behav- iour no longer applies. In this manner, our approach complements the recent trade literature, which emphasizes pricing distortions from imperfect competi- tion. In particular, in our framework, pricing distortions naturally arise, owing to the decentralized aspects of exchange; each individual in a match has a degree of monopoly power, since the terms of trade are determined by bilateral bargaining. Interestingly, through these channels, we provide conditions under which a movement from autarky to open markets may lower global welfare. In contrast to the existing trade literature, we also illustrate how the degree of information frictions and comparative advantage affect optimal trade policy through deter- mining the appropriate degree of market access across countries. Future work that explicitly accounts for tariffs and other trade policies will provide further insights into the role of information frictions for international trade.

Appendix

A.1 We derive the asset value functions in the autarkic economy. In describing the evolution of the expected lifetime utility of a type i agent, we let vi,t denote the asset value function for a type i agent at date t, given a time path for the quantities exchanged between agents, ql,t and q2,t. Following Trejos and Wright (1995), we initially consider time in discrete units with length 0 > 0. During such a period, the probability that a producer of good i meets exactly one good j producer is approximately p10.

When such a match occurs, the type i agent receives net utility

ri,ti (qj,t+O -

ciqt+) , and immediately following

consumption the agent exits the economy and is replaced by an identical agent. The probability that he will meet more than one good j producer will be given by o(0), where limooa(O)/O = 0. Finally, the probability that he does not meet an appropriate trading partner is then approximately (1 - Aj0), in which case the agent continues on to the next period with an expected lifetime utility of

24 This idea follows from Hosios (1990). In a labour market context, he shows that a decentralized equilibrium can be efficient if the worker's share of bargaining power is equal to the elasticity of the matching function. See also Pissarides (2000).

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Decentralized international exchange 541

vi,,+o. We may thus define the asset value function for a type i agent at time t, given a time path for ql,t and q2,t as

1 vit =

p (•jOUi, t+O (1 - pjO)vi,t+ + U(0)}, (Al)

where p > 0 is a time discount parameter identical for both types of agent. The expression for the asset value function in the steady-state equilibrium shown in (1) is then obtained by collecting terms in (Al) and taking the limit of both sides of as 0 -+ 0.

A.2 In this section, we provide an explicit derivation of the symmetric economy equilibrium conditions. We begin by deriving the properties of qP(y; /3) and qBR(7). First, note that by (11), we may write both q2j and Q2f as functions of

qlj and Qlf. Next, define: 61h = 1/[r + (1 + 7)]; 61f = 7/[r + (1 + 7)]; Alh = 3(1 - y)/[r + 3(1 - -y)]. Also, let ulh(qlh) = 2h(qlh) - Clh(qlh)2;

Uif(qlf)= -- qqlf)- Clh(qlf)2. The functions Ulh and U2h are defined in a similar manner. Next, define Ql as the quantity of good 1 produced by a type if agent in the foreign market in a match with a type 2h agent. Finally, equilibrium requires

vlh(7, qlh, qlf) = V1h(7, Qf; P) (A2)

V2h (7, Qf; ) < V2h(7, qh). (A3)

Next, we derive the properties of qP(-y; /) and qBR(y). Since q I f Q = (1/2c), (A2) defines qP(7; P):

6lh(Y) [q2h(qP (y; 0)) - c(qP(2y; 3))2] +

6lf(~Y)U1f = Alh(Y; )Ulf (A4)

qP (Y; /30)

(1 (q2h(l_( Alh)AM

-+=3 qlhh J61h + ( > 0, (A5)

7y 8c2 q3 3h 61h

where - = (1/2c)(c/)1/3. The effects of/3 can be derived in a similar manner. Similarly, imposing qlf = q2f = (1/2c), (12) defines the implicit function qBR(y) as

qBR 1) -

- 61h7Y))U1h (BR) _ If7) i1f 2c)

[ (I -

62h(7))l2h(qBR '

Differentiation demonstrates that qBR(7) is decreasing in y.

A.3 We derive the results of proposition 2. We first assume an interior equilibrium exists. Equilibrium requires qP(Qy; /3) = qBR(7); using the properties of qP and qBR provides

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542 R.R. Reed and K.A. Trask

()

qP FqP (qBR 0-1

OqBR 07y qP fy 9qP q'(B)

_

6 > 0.

We now derive restrictions on 3 that guarantee the existence of an equilibrium in which y E (0, 1/2) and 2h individuals choose to remain at home. Denote 3 as the value of 3 where y = 0 is an equilibrium. Impose -y = 0 on (A2) and (12). Then (12), evaluated at 7 - 0, provides qlh - q such that Ulh(() = cq2. Using this result and evaluating at y = 0, (A2) yields 6lh(7 = O)ilh(q) + 6f(7y = 0)

Ulf =

Alh(7 = 0; /3)ui. We then have:/3 r(c/-)23/[r + (1 - (c/-)2/3)], where

(c/ )2/3 e (0,1). To demonstrate that ~ < 1/2, we can express (A4) as:

UIA(q)- {[Alh(Y; 3) - 61f(7)]/61h(7y)}1f. Using this expression, (10) requires:

Ulh(qlh) - Vlh (r//3){[3(1 - 7) - ]/l[r + 3(1 - 7)]}iuf > 0. Thus, we need 7 < [3/(3 + 1)]. Evaluating at 3 = 1 implies -y < 1/2. Furthermore, as we restrict /3 such that 3 < 1 we have y < 1/2.

Finally, we place an upper bound on / to ensure that types 2h and if do not choose to search abroad in equilibrium, which requires from (A3) that V2h 7 Qlf;i3) V2h(7, qlh). Thus, for 3 -/, the restriction is satisfied. However, as p increases, proposition 2 provides that y is increasing, while q1h decreases. Both of these effects lower V2h. For sufficiently high 3, type 2h agents would have an incentive to move between markets because (i) foreign search is easier and (ii) as increases in /3 also increase -, their potential bargaining strength in the foreign market must be increasing as the proportion of good 2 producers in the foreign marketplace is decreasing and the proportion of potential partners in the marketplace is increasing. Although analytical results are intractable, we can define an upper bound on 3 as follows. Using the equilibrium results, we may express the asset value functions and traded quantities as functions of /3 and the cost parameters. We can define 03(c, -) as a function of the cost parameters such that in equilibrium: V2h(/3, , c) = V2h(C, C); Vh(Y, C, -) = V1h(P, C,) with 7 E (0,1/2) and 2h agents remain at home. One set of parameters that will solve this condition is /3 = 1 and c = c. In this case, y = 0 in equilibrium, since all agents will be identical and have the same trading opportunities. Under higher values of T, all agents will have lower expected lifetime utility, but the asset values of the efficient agents will fall more. However, as /3 = 1, 2h agents would also begin to move to offset any differences in their expected lifetime utilities. Such movements could be deterred if /3 were lower. Thus, given costs, we can define 3 as the value of / which in equilibrium solves V2h (3, C, -) = V2h (C, -), and the above arguments guarantee that there exists such a p < 1.

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Decentralized international exchange 543

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