On The Advantages of Piecemeal Integration: A model of trade with several countries where local integration benefits all

Hansen, Bodil O.; Keiding, Hans Working Paper On The Advantages of Piecemeal Integration: A model of trade with several countries where local integration benefits all Working paper, No. 4-2005 Provided in Cooperation with: Department of Economics, Copenhagen Business School (CBS) Suggested Citation: Hansen, Bodil O.; Keiding, Hans (2005) : On The Advantages of Piecemeal Integration: A model of trade with several countries where local integration benefits all, Working paper, No. 4-2005, Copenhagen Business School (CBS), Department of Economics, Frederiksberg, https://hdl.handle.net/10398/7495 This Version is available at: https://hdl.handle.net/10419/208497 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Hansen Copenhagen Business School Hans Keiding University of Copenhagen February 2005 Abstract Forthestudyofeconomicintegration,itiscostumarytouseathreecountryworld, where two of the countries may introduce forms of closer economic cooperation. In the present model, we follow this tradition but put special emphasis on the role of credit and entrepreneurship. Our model is of the standard neoclassical type, with the addition that production takes time and is subject to uncertainty. Also, firms must use thefinancial systemin ordertobuyinputs; thecost ofcreditmay differamongcountries and industries, reflecting their basic patterns of uncertainty. Following the Newbery-Stiglitz approach, we show that in such model we may exhibit cases of Pareto inferior trade and, in particular, Pareto inferior economic integration. More specifically, we show that integrating countries of very different economic size may give rise to adverse effects on welfare, whereas integration of countries with a more similar economic structure and size tends to have beneficial effects for the parties. Keywords: trade, uncertainty, Pareto inferior trade, regional integration. JEL classification: F11, F15, F34 1. Introduction In recent years, economic integration has been a main theme of both research and policy, and new instances of economic integration of countries into free trade areas or costums unions are presented each year, whether in connection with the expansion of the European Union or the formation of free trade areas in America. While initially economic integration was largely a question of abolishing or diminishing tariffs within the cooperating family of countries (see the classical contributions 1 of e.g. Viner (1953) and Vanek (1965)), the ongoing process of trade liberalization has to some extent shifted focus to other aspects of economic integration. This is supported by the experience that there is limit to what trade liberalization can do for the countries, as seen both in the unification of the two Germanies and after the formation of NAFTA. Consequently, there is a need for a better understanding of what is actually being achieved in the cause of economic integration. Some of the important aspects of economic integration, namely those related to credit and investment, have been less intensively studied than those related directly to commodity trading, and the role of the institutions which are used for these purposes (financial markets, intermediaries) have only been objects of theoretical studies in later years. Therefore, adding these features to models of international trade will often produce surprising results, such as the case of Pareto inferior trade presented by Newbery and Stiglitz (1984). In order to have financial markets in the model, it must contain a time dimension, runningoveratleasttwoperiodsoftime. Andifthecreditinstitutionsaretobeofnon-trivial nature, there should be some form of uncertainty in the first period about outcomes in the second period. This means that we need a model of international trade under uncertainty, and presumably with less than full information; as it emerges, information asymmetry is not needed to obtain the conclusions, which follow from the structural properties of the model alone. Modelsofinternationaltradeunderuncertaintyisofcoursenonovelty,theyhavebeen used actively at least since the seminal work by Helpman and Razin (1978). However, in the model to be developed the emphasis is on the financial markets and their impacts on commodity allocation. In particular, we consider situations where financial markets prevent small (in a sense to be made precise) countries from reaping benefits of economic integration. The model follows the tradition of international trade theory in dealing with a world where two commodities are produced from two inputs, using a technology which is known to everybody. However, we departslightly from traditionin allowing forentrepreneurship, even if in a very crude way: There is a given number of firms or entrepreneurs, but an entrepreneur may choose to produce either of the two commodities, and, in connection with an economic integration, to operate the firm in another country; thus the distribution of firms producing one or the other commodity is an equilibrium outcome of the model. The point of this way of introducing entrepreneurship is that the progress expected from economic integration would be that domestic firms get a larger share of world production, rather than that foreign firms establish branches in the country to exploit cheap production factors. We study equilibria under different assumptions on the rules for international cooperation. Throughout the paper, we assume that there is free international trade in commodities,whilefactorsofproductioncannotbetradedbetweencountries;asmentioned above, firms ofone countrymay however operatein anothercountry, atleast undersuitable 2 regimes of economic integration, thereby achieving results which are similar to moving the factors of production. In the definition of equilibria, we assume that consumers choose savings under assumptions on the (random) yield of bonds which are rational in the sense that they are confirmed by actual performance. The markets for bonds issued by firms of a given country play an important role, and since the performance is determined by the outcome of the firms which belong to the country, their repayment rates are expressions of the country risk which again has to do with the economic size of the country; since output shocks are independent, the variance of output produced by firms of that country will be smaller, the larger its number of firms, and the lower will be the repayment rate at which the bond will be demanded by the consumers. Thus, country risk is connected with economic size or strength, and an economic integration which allows for operation of one country’sfirms in another country, while retaining country-specific bond markets, may result in a situation where the smaller country’sfirms closedown whileitsfactors of productionareemployed in firms belonging tothe largercountry. This isthecase ofdisadvantageous integration; itdoesnotarise when the participating countries are of comparable size. The paper is organized as follows: In Section 2, we introduce the model, which is a standard simple trade model over two periods and with uncertainty. The uncertainty comes from independent and identically distributed output shocks in the firms, and it affects second period output and consumption as well as the payoff of the bonds used to finance the investment in production factors needed to produce the outcome. In the following section, we consider the special case of constant returns to scale in production; here equilibrium profits are zero, and the workings of the model become more transparent, but on the other hand it fails to illustrate the role of the entrepreneur, which does not then play anessential role. In Section4, we treatthe moregeneral caseof nonincreasing returns to scale, opening up for nonzero profits as well as a choice of industry by entrepreneurs. Having treated the basic features of the model, we may then turn to what was its purpose, namely thestudy of economicintegration, whichis donein Section5; here weshow thatin certain cases (namely such where all other, trade-related, effects of integration are netted out) integration between economically strong (in the sense of having many firms) and weak (few firms) countries will have unfavorable effects for the latter, whereas economic integration by more evenly situated countries will be welfare improving for both. Section 6 contains some concluding comments; the proof of the equilibrium existence result stated in Section 3 is given separately in an appendix. 2. The model We consider a model of trade based on the classical Heckscher-Ohlin-Samuelson model with two produced commodities and two productive factors. We shall assume that 3 there are three (and not two, as is usual in trade models) countries, since we shall consider a situation where two countries integrate while leaving the third outside. The countries are assumed to be identical with respect to producers’and consumers’characteristics but they may differ in size. Although our model is deliberately kept simple, it still contains several specific details, which are introduced below, where we proceed from producers over consumers to a description of the financial institutions in each country. Production. Each commodity yi,i=1,2, is produced separately in a constantreturns-to-scale technology using the two production factors z1and z2as inputs; the technology of a firm producing commodity i(available to producers in all countries) is given by production functions yi=τifi(z1i,z 2i); here τiis a random variable which for simplicity is assumed to take only two values, namely τi=1(“success”)orτi=0(“failure”). The production functions fiare assumed to satisfy the usual conditions of monotonicity, continuity and quasi-concavity. We assume that there is a continuum of firms in each country. The firms choosing to operate in industry iare connected in chunks or “conglomerates”of size 1, for which the random variables are perfectly correlated, whereas the random shocks are uncorrelated between conglomerates. We may think of the conglomerates as industrial centers which are subject to the same random disturbance; the construction is made to allow for choice of technique without introducing nonconvexities which may prevent existence of equilibria. The size of the productive sector in country his nh∈N,h=1,2,3, representing the endowment with entrepreneurial skills of this country; individual firms are indiced by the letter ν. Production is assumed to be time-consuming, so that inputs are chosen at time t=0, while output is obtained at time t=1. Firms are owned by consumer-entrepreneurs in the country who hold no other endowments, so that the purchase of inputs at t=0has to be financed by credits, to which we return shortly. We assume that the choice of the entrepreneur also involves the industry in which to produce; thus, in our model, firms may engage in production of any of the two commodities; however, the total number of firms in the country, nh, is assumed fixed, determined by the availability of entrepreneurial skills in the country. Consumption. Consumers that are not entrepreneurs will be referred to in the sequel as “factor owners”; they have an endowment ω=(ω1,ω 2)(the same for all) of factors of production. Consumption takes place only at t=1, so consumers sell their endowment to the firms at t=0and save the income using the available financial institutions. We assume that all consumers (entrepreneurs as well as factor owners) have identical von Neumann-Morgenstern utility functions u(x1,x 2)depending on the consumption of the twocommodities(att=1),andhomogeneousofdegreeone. Att=1,consumersdispose of their incomes, which are either derived from profits of firms or are repayments of the 4 savings, in order to buy the two commodities at (state dependent) prices (p1,p 2)which are the same in all countries (free trade of commodities is assumed throughout). Since factorownersin anycountry differonly inendowments, andsince they have homogeneous utility functions, by a classical aggregation result, the aggregate behavior is the same as if there was only one factor owner in each country, which we assume in the sequel. Financial intermediation. In order to link consumer savings with firms’borrowing, we need a financial intermediary. We assume that these financial intermediaries take the form of coalitions of borrowers (firms), issuing bonds at repayment rate Rh i, depending on country hand industry i; thus, bonds can be distinguished only by these characteristics, not by the individual debtors. Since we deal with a model where production is subject to random shocks, the individual borrower may at t=1be unable to fulfill the obligations contracted at t=0. Since werestrict ourselves toa two-periodmodel, where the financialintermediaries cease to exist at t=1, we assume that the shocks are reflected in the payoffs to the holders of bonds, so that if only a fraction eh iof the total number of firms in country h, industry i, succeed in producing nonzero output, then the return on the bond is eh iRh i. This feature makes the bonds of our model look somewhat unusual, but basically we are only taking into account the possibility of default on bonds. Equilibrium. Wehavenowoutlinedourmodelandmayproceedtodescribeequilibria in this model. The equilibrium conditions must specify individual optimizing behaviour by consumers and firms (or, equivalently, by factor owners and entrepreneurs), together with clearing of markets for factors, commodities, and bonds; finally, there is an additional condition related to the number of firms in any industry and country. We start with a more informal description of the details and then give the precise definition. By the nature of the uncertainty in our model, there is a finite set of possible states of natureatt=0, characterizedby thevalue ofτiateachchunk[0,1],]1,2],...,]nh−1,n h] of potential enterprises in industry iof country h,i=1,2,h=1,2,3. The actual distribution of enterprises among industries is denoted n=(nh 1,n h 2)3 h=1. Given this structure, the factor owner faces the problem of choosing an optimal portfolio of bonds, so that expected utility of the bundles bought using the bond yield is maximal. If factor prices at t=0are (qh 1,qh 2)and commodity prices at t=1and in state sare (p1(s),p 2(s)), then the problem to be solved by the factor owner in country his to choose consumption bundles (x1(s),x 2(s)), for all s∈S, portfolio weights θh ifor bonds of type (h, i), and savings shsuch that maxEu(xh 1(s),x h 2(s)) subject to p1(s)x1(s)+p2(s)x2(s)≤sh 3  h=1 2  i=1 θh i[eh i(s)Rh i],s∈S, sh≤qh 1ωh 1+qh 2ωh 2. (1) 5 For the entrepreneur, the problem to be solved is similar to (1), only here the income used for buying commodities at t=1and in state sis obtained not from bond yields but from the profits of operating the firm. Thus, the entrepreneur operating firm νof industry iin country hhas to choose inputs (zh i1,zh i2)at time t=0and consumption bundles (xh i1(s),x h i2(s)) solving maxEu(xh i1(s),x h i2(s)) subject to p1(s)xi1(s)+p2(s)xi2(s)≤ max{0,τ iν fi(zh i1,zh i2)−Rh i(qh 1zh i1+qh 2zh i2)}, (2.i) where the numbering (2.i) has been used to stress that the problem described relates to industry i. It should be noticed that the problem to be solved is the same for all firms in industry iand the solution is therefore independent of ν; we denote by Uh ithe optimal value of the objective function in (2.i). Given factor supply in each country as described by (1), commodity demand at t=1 and s∈Sas defined by (1) and (2), and commodity supply as determined by factor inputs and randomshocks, there isequilibrium if (a)supply equalsdemand in eachmarket(factor markets at t=0and commodity markets at t=1,s∈S), and, furthermore if (b) the industry chosen by each firm is the best possible, that is the one which gives the maximal expected utility of final consumption as described in (2.i). Now we may summarize the above discussion in the following definition. Definition 1. An array (n, (xh(s))s∈S,(zh i,(xh i(s))s∈S)2 i=1,qh,πh)3 h=1,(p(s))s∈S) is an equilibrium if the following conditions are fulfilled: (1) for the factor owner of country h,(xh(s))s∈Ssolves the problem (1), (2) for each entrepreneur in industry iof country h,(zh i,(xh i(s))s∈S)solves the problem (2.i), yielding the optimal value Uh i, (3) for each country h, 2  i=1 nh izh i=ωh and for each state s∈S, 3  h=1 [xh i(s)+nh ixh i(s)] = 3  h=1 nh i 0 τiν fi(zh i)dν, i =1,2, (4) for each h,(nh 1,n h 2)maximizes λ1Uh 1+λ2Uh 2over all (λ1,λ 2)∈R2 +with λ1+λ2=nh. 6 Since the equilibrium even in this model, even with our simple structure of identical consumers and producers, is quite complex, the existence problem is nontrivial and needs to be addressed. We present the existence result below; its proof is given in an appendix to the paper. Theorem 1. Assume that in the model introduced above, the following assumptions are satisfied: (1) the common von Neumann-Morgenstern utility function uis continuous, monotonous, quasi-concave, and homogeneous of degree one, (2) the production functions fiare continuous, monotonous, and concave. Then there exists an equilibrium. Moreover, if both industries operate in each country, then their bond repayment rates are equal. The proof of Theorem 1 is given in the appendix. Since the model is constructed using standard assumptions, the crucial assumptions are those which take care of the particular features introduced, in particular the perfect foresight of future prices, which to be meaningful presupposes uniqueness of equilibrium prices in each period 2 state, which also figures among our assumptions. Since bond repayment rates depend only on countries and not on industries, we may suppress reference to industry in the sequel. We pause briefly at this point to consider the case of constant returns to scale in production. In that case, expected profits are 0 in equilibrium, and as a consequence the structure of trade will resemble that of the classical Heckscher-Ohlin model. 3. The case of constant returns to scale in production If production functions exhibit constant returns to scale, then the producers’choices of optimal levels of inputs –and hence of credits –becomes somewhat simpler to analyze. It seems natural that this case is used as a starting point, even if –as it will emerge from the analysis –the conclusions are not as immediately appealing as with the decreasing returns to scale. The key to the results which we obtain under this assumption on the technologies is given by the following simple observation, formulated as a lemma. Lemma 1. Assume that the production functions f1,f 2are positively homogeneous of degree one. Then in equilibrium, ex ante expected profits are 0 for all active firms (that is all firms choosing nonzero input levels). Proof: Clearly negative expected profit implies negative expected utility, so that the firm would prefer inaction to production. Assume that ex ante profits were positive in a firm 7 affecting the production of both commodities in the same way, and with consumers having utility functions that are symmetric in the consumption of the two goods. We consider an economic integration between countries 1 and 3; this means that firms of both countries can establish production in any of the two countries. By Proposition 1 we obtain that country 3 firms must be inactive, so that all incomes in country 3 are derived from sale of factor endowment. Whether country 3 as a whole has become better off as a result of the arrangement depends therefore on the increase in factor prices. We can check what happens in our simple model; here we assume a very specific functional form of v, namely v(r)=min{a+br, cr}, where a, b, c > 0,b<1,c>1, and a< 1 10 α(here αis the parameter used in Examples 2 and 3). Thus, the concave transformation vis the minimum of two affine functions, having a kink at the value ¯r=(c−b)/a. Since the two commodities enter the utility function in symmetrical way and their production is open to the same kind of random shocks, the allocation of factors of production will be the same as with no uncertainty, with the difference that there are now 10 firms operating in each country (all of which have their origin in country 1). Each of these produce v1 10 αof the relevant commodity; if ¯ris small enough, more specifically if ¯r≤1 10 α, then marginal products and hence factor prices remain constant at input levels equal to and above those of the equilibrium, including the level corresponding to pre-integration production in the firms of country 3. Consequently, factor remuneration does not change, whereas entrepreneurial profits disappear in country 3 after integration, and it follows that the country has become worse off. While in our examples disadvantageous integration occurs due to differences in country risk, we may similarly encounter cases of advantageous integration when country risk is of comparable size. Example 4. To give an example of advantageous integration, we modify the previous example by setting the number of firms of each type to 1, so that countries 2 and 3 become absolutely identical. However, integration makes specialization possible: Each country may specialize in a particular industry, in the sense that its firms produce only one commodity, with one of them operating in the other country in order to use the factor endowmentsefficiently. Thiswillreducecountryriskineachindustry,allowingforcheaper credit, larger production, and a greater profit share in both countries. Summing up, in the model considered the preconditions for successful integration (where integration is considered as free choice of localization of the firms of the countries involved) is that the partners must not be too unequal, since the economically stronger part –where strength is measured as availability of entrepreneurial skills –will reap the 14 benefits while the weaker part may suffer a loss. On the other hand, integration of the small countries may be beneficial to all countries involved. If the final goal is a fully integrated world economy, it may be argued that the path towards this goal, whether achieved through integrating weak countries with the strong country one by one or integrating the weak countries first and then proceed to the final full integration, must be of minor importance, and indeed this is the case in our model, where the equilibria in the fully integrated economy are independent of the way in which the integration was achieved. On the other hand, only small changes are needed for this path tomakeadifference: Ifweassumethatfirmswhichdonotproducecannotbeopenedagain, then indeed the approach to world integration will matter very much, giving preference to the integration of countries of equal economic development rather than of countries with differing economic potential. A full treatment of a model where the number of firms in each country is subject to change is however beyond the scope of this paper. 6. Concluding comments In the model considered in the previous sections, we have analyzed the patterns of trade and the results of economic integration in a simple world with three countries producing two commodities from two factors. The initial situation was one of liberalized commoditytrade. This doesnothowevermean thatthereisnoscope forfurtherintegration of economic activity. Once we add uncertainty, even in its simplest possible form, namely as an output shock acting independently on each firm, we may consider more or less liberalized regimes of investment financing, and we may consider the possibility of a firm operatinginanothercountry,thelatterbeingoneofthemostwidespreadrealworldfeatures of economic integration, encountered in the movement of several industries from North to South in the European Union as well as the maquiladores industries in Mexico following after the NAFTA agreement. The paper sets out to analyze the workings of this type of integration in a context of standard trade theory, minimally extended so that questions of financing investment and change of localization of firms make sense. It should of course. Also, an underlying assumption is that all investment must be financed via the bond market, with no possibility of state-dependent contracting. Given these shortcomings, it is however worth noticing that the results of the models arequitedifferentfromthoseofstandardtradetheory,sincewelfaregainsaretobeexpected when countries are not too different and losses, at least for the weaker part, in the case where the countries are very different. This may be reassuring in view of the stylized facts about trade which seems to be flourishing more between equals than between very different countries, cf. the early contribution by Burenstam Linder (1961), but it should be remembered that we are considering gains and losses relative to a situation of perfectly 15 liberalized commodity trade. The impacts for current international economic cooperation would be that this should be encouraged particularly for similar countries, while there is reason for some scepticism as to the benefits of integration between unequal partners. Whether this recommendation is validin amoregeneral, and thereforemore realisticsetting, is howeversomething which has yet to be investigated. 7. Mathematical appendix: Proof of Theorem 1 In this section, we give a proof of the existence of equilibria in our basic model, as stated in Theorem 1. Proof of Theorem 1: Let Nbe the set of all arrays n=(nh 1,n h 2)3 h=1 with nh i∈Z+ and nh 1+nh 2=nh. The set of allocations (xh(s))s∈S,(zh i,(xh i(s))s∈S)2 i=1)which may occur in an equilibrium is bounded, so performing a standard truncation operation on feasible sets we may assume that each factor owner chooses final consumption from the setX1= ([0,M]2)SandeachentrepreneurchoosesfromX2= ([0,M]2×X1. Wedenote byΘthesetofallportfolioweights(θh 1,θh 2)3 h=1. Weconstructafamilyofcorrespondences as follows: For each country h, the demand correspondence of the factor owner ξh 0:R2 +× [0,M]6×(R2 +)S→X1×Θassigns to each array (qh,(Rh 1,R h 2)3 h=1,(p(s))s∈S)of factor prices, bond rates, and state-dependent commodity prices the solution to the consumer’s problem (1). This correspondence is upper hemicontinuous with nonempty, compact and convex values. Foreachcountryhandindustryiwesimilarlydefinethedemandcorrespondenceξh ij : R2 +×[0,M]6×(R2 +)S→X2by assigning to each array (qh,(Rh 1,R h 2)3 h=1,(p(s))s∈S) the solution of problem (2.i). Again, each φh iis upper hemicontinuous with compact and convex values. To obtain market clearing prices, we define price correspondences ψhfor each country hand commodity price correspondences ψ[s]for each state sas follows: For each allocation ξ=((xh(s))s∈S,(zh i,(xh i(s))s∈S)2 i=1)3 h=1, let ψ(ξ)=((˜qh)3 h=1,˜p(s)s∈S)∈R6 +×(R2 +)S˜qh· 2  i=1 nh izh i−ωh>0,h=1,2,3, ˜p(s)· 3  h=1 xh+(nh 1xh 1,n h 2xh 2)−nh 1 0 τ1νf1(zh 1)dν, nh 2 0 τ2νf2(zh 2)dν>0,s∈S, 3  i=1 (˜qh 1+˜qh 2)+ s∈S (p1(s)+p2(s)) = 1, 16 then ψhas open graph and convex (possibly empty) values. The next correspondence serves to set the repayment rates Rh i;define αas the correspondence taking portfolio weights θ=(θh i)and allocations into possible bond repayments, α(ξ,θ)=(˜ Rh 1,˜ Rh 2)3 h=1  3  h=1 2  i=1 ˜ Rh i[θh ish−qh·(nh 1zh 1,n h 2zh 2)] >0. Again, αhas open graph and convex, possibly empty values. The final correspondence is used for obtaining the equilibrium choice of n: For each allocation ξ, denote by Uh 1(ξ)and Uh 2(ξ)the expected utility of the factor owner and the entrepreneur in country h, and let βh(n, ξ)be given by βh(n, ξ)={(λh 1,λ h 2)∈R3 +|λh 1Uh 1+λh 2Uh 2>n h 1Uh 1+nh 2Uh 2,λ h 1+λh 2=nh}. As before, βhas open graph and convex, possibly empty values. Nowwecollectalltheabovecorrespondencesintoonecorrespondenceψwhichtakes allocation-price pairs χ= (((xh(s))s∈S,θh,(zh i,(xh i(s))s∈S)2 i=1,qh,(Rh 1,R h 2))3 h=1,(p(s))s∈S) into themselves; here the allocation components of φare given by the correspondences ψh 0for commodity and portfolio demand of factor owners, ψh ifor the demand for factors and commodities of entrepreneurs, ψhfor factor prices, ψ[s]for commodity prices in state s,αfor bond repayment rates, and βfor . The components of ψnare either upper hemicontinuous with closed, convex and nonempty values, or they have open graph and convex values. We now apply the fixed point theorem used in Gale and Mas-Colell (1975) to give the existence of an allocation-price pair ˆχn= (((ˆxh(s))s∈S,ˆ θh,(ˆzh i,(ˆxh i(s))s∈S)2 i=1,ˆqh,(ˆ Rh 1,ˆ Rh 2))3 h=1,(ˆp(s))s∈S,ˆn) such that –for each h, the choice of the factor owner in country h,(ˆxh(s))s∈S,θh), belongs to ψh 0(ˆχn), meaning that it satisfies (1), –for each country h, industry iand firm j,(ˆzh ij,(ˆxh ij(s))s∈S)belongs to φh ij(ˆ ξn),so that it satisfies (2.i); it follows now that –since the solutions to (1) and (2.i) satisfy Walras’law, we have that ((ˆqh)3 h=1,(ˆp(s))s∈S)/∈ψ(ˆχn), so that ψ(ˆχn)=∅, which gives that demand does not exceed supply in any factor or commodity market; 17 –similarly we have that α(ˆχn)=∅, so that loans in country h, industry ido not exceed demand for bonds of this type, and –β(ˆn, ˆχ)=∅. It is easily checked that the allocation-price pair with all these properties is an equilibrium, and we have thereby showed that equilibria exist. References Beladi,H. and N.H.Chau (2000), Endogeneous factor market distortion, risk aversion, and international trade under input uncertainty, Canadian Journal of Economics 33, 523 –39. Burenstam Linder, S. (1961), An essay on trade and transformation, Almqvist and Wicksell, Uppsala. Gale,D. and A.Mas-Colell (1975), An equilibrium existence theorem for a general model without ordered preferences, Journal of Mathematical Economics 2, 9 –15. Helpman,E. and A.Razin (1978), A theory of international trade under uncertainty, Academic Press, New York. Helpman,E. andP.R.Krugman (1986), Marketstructure andforeign trade, TheMIT Press, Cambridge, Massachusetts. Hoff,K.(1996),Areexaminationoftheneoclassicaltrademodelunderuncertainty,Journal of International Economics 36, 1 –27. Mas-Colell,A., M.D.Whinston, and J.R.Green (1995), Microeconomic Theory, Oxford University Press, Oxford. Newbery, D.M.G. and J.E.Stiglitz (1984), Pareto inferior trade, Review of Economic Studies 51, 1 –12. Viner, J. (1953), The customs unions issue, New York. Vanek. J.(1965),Generalequilibriumofinternationaldiscrimination: thecaseofcustoms unions, Cambridge, Massachusetts. 18