Non-homothetic preferences, parallel imports and the extensive margin of international trade

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1 Non-homothetic preferences, prllel imports nd the extensive mrgin of interntionl trde Reto Foellmi, Christin Hepenstrick, Josef Zweimüller My 19, 2011 Abstrct We study interntionl trde in model where consumers hve non-homothetic preferences nd where household income restricts the extensive mrgin of consumption. In equilibrium, monopolistic producers set high low) prices in rich poor) countries but thret of prllel trde restricts the scope of price discrimintion between countries. The thret of prllel trde llows differences in per cpit incomes to hve strong impct on the extensive mrgin of trde, wheres differences in popultion sizes hve weker effect. We lso show tht the welfre gins from trde liberliztion re bised towrds rich countries. We extend our model to more thn two countries; to unequl incomes within countries; nd to more generl specifictions of non-homothetic preferences. Our bsic results re robust to these extensions. JEL clssifiction: F10, F12, F19 Keywords: Heterogenous mrkups, non-homothetic preferences, prllel imports, extensive mrgin of trde University of St. Gllen, Deprtment of Economics - SIAW, Bodnstrsse 8, CH-9000 St.Gllen, Tel: , Fx: , emil: reto.foellmi@unisg.ch. University of Zurich, Institute for Empiricl Reserch in Economics, Muehlebchstrsse 86, CH Zürich, Tel: , Fx: , e-mil: hepenstr@iew.uzh.ch University of Zurich nd CEPR, Institute for Empiricl Reserch in Economics, Muehlebchstrsse 86, CH Zürich, Tel: , Fx: , e-mil: zweim@iew.uzh.ch. Josef Zweimüller is lso ssocited with CESifo nd IZA. 1

2 1 Introduction Theories of interntionl trde typiclly ssume tht consumers hve homothetic preferences, showing why product differentition, incresing returns, nd firm heterogeneity re crucil in explining the extensive nd intensive mrgins of interntionl trde e.g. Krugmn, 1980, Melitz, 2003, Helpmn, Melitz, Rubinstein, 2007, Chney, 2008). While both csul observtion nd econometric nlyses of consumer budgets suggest tht homothetic preferences cnnot be defended on empiricl grounds, their nice ggregtion properties nd high trctbility mke them n idel tool for studying settings in which technology rther thn demnd fctors re the min driving force of ggregte outcomes. The ssumption of homothetic preferences, however, is clerly inpproprite for studying how the composition of ggregte income ffects consumption nd trde ptterns. Consider two countries, Austri nd Nigeri. In 2008, their PPP-djusted ntionl income ws roughly of the sme order of mgnitude 311 bill US $ nd 281 bill US $, respectively). While Austri is smll nd rich, with popultion of 8.4 mill nd per cpit income of 37,680 US $, Nigeri is lrge nd poor, with popultion of 152 mill nd per cpit income of 1,940 US $. Should we expect the two countries to disply similr economy-wide demnds for given set of consumer goods? Homothetic preferences predict tht the representtive Nigerin consumer purchses the sme menu of goods s the representtive Austrin consumer, but in quntities tht re 95 percent lower. If this were so, trde ptterns re unffected by the composition of ggregte income nd exclusively shped by supply conditions such s comprtive dvntges, differences in fctor endowments, trde costs, nd other technologicl symmetries. In this pper, we explore the implictions of non-homothetic preferences in the context of the "new" trde theory frmework. While the supply side of our model is identicl to the bsic Krugmn 1980) frmework, we devite from this frmework by introducing non-homothetic preferences in very stylized wy: we ssume tht consumer goods re indivisible nd either consumed in unit quntity or not consumed t ll. 1 Prim fcie, this ssumption my seem overly simplistic. However it is "nturl" devition from the stndrd CES-frmework in the following sense. In our frmework, consumption choices re bout the number of goods the extensive mrgin of consumption while choice long the intensive mrgin is ruled out by ssumption. This is orthogonl to the stndrd CES frmework where consumption choices only ffect the intensive mrgin of consumption nd choice long the long the extensive mrgin is ruled out by infinite reservtion prices hence even the poorest household 1 Preferences of this type were used, inter li, by Murphy, Shleifer nd Vishny 1989) to study how demnd composition ffects technology choices in the development process, by Mtsuym 2000) to study the role of non-homotheticities in Ricrdin trde, nd by Foellmi nd Zweimüller 2006) to study the reltionship between inequlity nd growth. 2

3 will consume ll goods in positive, lbeit tiny, mounts). Adopting this stylized wy of introducing non-homotheticities provides simple nd trctble frmework tht leds to equilibrium outcomes quite different from the stndrd model. To keep things simple nd trnsprent we confine the bsic nlysis to the most simple cse of two countries. First, we show tht, when per cpit endowments of the two countries re very similr, the world economy ends up in full trde equilibrium. In such n equilibrium, ll goods re interntionlly trded nd consumed in both countries. In contrst, when per cpit endowments of the two countries re suffi ciently unequl, prtil trde equilibrium emerges. The reson is tht only households in the rich country consume ll goods produced worldwide wheres households in the poor country cn fford only subset of ll goods. In prtil trde equilibrium, the frction interntionlly trded goods increses in the similrity of per cpit endowments. This result is reminiscent of the "Linder hypothesis", ccording to which more similr countries trde more intensively with ech other. Second, the prtil trde regime provides us with simple generl equilibrium frmework of prllel trde. The prtil trde equilibrium is supported by the price setting behviors of monopolistic firms. With indivisible goods, the highest price firm cn chrge is the representtive consumer s willingness to py which is finite. But this my crete rbitrge opportunities. Consider US firm selling its good both in the US nd in Chin. When price differences re suffi ciently lrge, rbitrge trders will purchse the good cheply on the Chinese mrket, ship it bck nd underbid locl producers on the US mrket. Anticipting this, US firms either set price such tht the incentive for prllel trde vnishes; or US firms do not supply their product on the world mrket, but therefore cn chrge the high price in the US. The generl equilibrium perspective of our model mkes the ltter frction of firms endogenous. This effect is typiclly not considered in prtil equilibrium settings of prllel trde but hs potentilly importnt impct on trde ptterns. Third, we mke precise the reltive importnce of popultion sizes nd per cpit endowments for trde ptterns. The country with lrge popultion is more productive becuse smller frction of resources is wsted due to iceberg) trde costs. When per cpit endowment differences re smll, higher popultion cn compenste lower per cpit endowment so tht world economy tht is initilly trpped in prtil trde equilibrium my switch to full trde equilibrium s result of popultion growth. However, when per cpit endowment differences re high, lrger popultion cn never fully compenste for smll per cpit endowment. In tht cse, the world economy remins trpped in prtil trde even when the popultion grows very lrge. Hence the impct of popultion size differs crucilly from the impct of per cpit endowments. A higher degree of similrity in per cpit endowments lets the world economy lwys escpe the prtil trde regime, whtever the differences in popu- 3

4 ltion size of the two countries. In this sense per cpit endowments re more significnt determinnt of the trde regime thn popultion sizes. A fourth min result of our model concerns the welfre effects of trde. Compring trde to utrky it turns out tht in full trde equilibrium the poor country gins reltively more from trde; in prtil trde equilibrium, however the rich country gins more. Moreover, trde liberliztion reduction in iceberg trde costs) increses welfre of consumers in both countries when the world economy is in full trde equilibrium. However, in prtil trde equilibrium, trde liberliztion is beneficil for the rich country but ctully hurts the poor country. The reson is tht trde liberliztions deteriorte the poor country s terms of trde, becuse interntionl price discrimintion becomes more limited. Exporters of the poor country need to lower the prices they chrge in the rich country to inhibit prllel trde, wheres exporters of the rich country hve no need to djust their export prices. However, they must djust the prices they chrge in their home mrket. This mkes selling on the rich mrket t unrestricted high prices more ttrctive - thus, in the new prtil trde equilibrium more firms of the rich country will concentrte their sles exclusively only on the home mrket nd less products will be vilble on the world mrket. Consumers in the rich country benefit from the decresing prices of the interntionlly trded goods, wheres consumers in the poor country re confronted with lower rnge of import goods t unchnged prices. Our bsic model is simple enough to be extended in vrious directions. First of ll, we show tht our model extends to more generl clss of preferences where consumers hve choice not only long the extensive mrgin but lso long the intensive mrgin. We demonstrte tht, with more generl specifictions of preferences, prtil trde equilibrium emerges provided tht i) the derived individul demnd functions feture finite reservtion prices so tht some consumers optimlly choose not to buy certin goods when prices re too high) nd ii) demnd elsticities decrese nd mrk-ups increse) long the demnd function. This mkes n equilibrium possible where firms re indifferent between selling t high prices nd smll quntities in rich economies or low prices nd lrge quntities on the world mrket so tht prtil equilibrium supported by thret of prllel trde) emerges. Second, we look t world with more thn two countries. It turns out tht in multicountry world our result tht trde liberliztion decreses rther thn increses trde needs to be qulified. With mny rich nd mny poor countries, trde liberliztion stimultes trde nd welfre due to more trde within the rich North nd within the poor South. However, it decreses overll trde nd increses the welfre-gp) between the Northern nd the Southern region. While the North gins for sure, lso the South my gin when within-south trde increses more strongly thn North-South trde flls. Third, we llow for heterogenous trde costs. When trde costs differ for the vrious 4

5 products but re not too lrge to inhibit trde t ll), trde liberliztion implies tht goods with high low) trde costs will be trded more less). The reson is tht high-trde-cost producers cn suffi ciently price discriminte hence they hve n incentive to sell their product lso in the poor country. For low-trde-cost producer trde liberliztion implies fiercer price competition on world mrkets. Therefore more low-trde cost producers will decide to sell their product exclusively on the rich home mrket nd not to sell brod. In such sitution, it depends on the reltive importnce of high-cost nd low-cost producers whether trde liberliztion stimultes or dmpens interntionl trde. In fourth extension we look t the impct of policy-restrictions on prllel trde. Our bsic model ssumes "interntionl exhustion" in which cse prllel imports re not leglly forbidden. The holder of product s property right ptent, trdemrk, copyright) cn no longer exercise his property right once this product is sold either on the home mrket or on the world mrket - his property rights re exhusted. In contrst, mny countries hve implemented "ntionl/regionl exhustion" in which cse the property right runs out when the product is sold on the home mrket, but does not run out when the product is sold brod. It turns out tht restrictions to prllel trde help consumers in the poor country but hurt consumers in the rich country. The reson is generl equilibrium effect. Stronger prllel trde restrictions encourge producers of the rich country to sell their product brod while being ble to chrge high prices t home. This tends to improve the terms of trde for the poor country. Finlly, we explore the consequences of income inequlity. In such context the level of trde costs nd the extent of within-country inequlity determine the equilibrium outcome. For low trde costs there re producers chrging high prices selling to the rich t home nd brod nd other producers chrging low prices selling to ll households. Interestingly, in such sitution with low trde costs, where inequlity rises within countries nd not between countries, lower trde costs ctully benefit the poor. Severl previous ppers hve incorported non-homothetic preferences into the new trde theory frmework. The clssicl contributions re Mrkusen 1986) nd Bergstrnd 1990) who stick to CES-preferences for differentited products but introduce non-homotheticities through homogenous product with minimum consumption requirement. 2 Severl recent 2 Importnt empiricl contributions include Hunter nd Mrkusen 1988), Hunter 1991), Frncois nd Kpln 1996), Dlgin, Mitr, nd Trindde 2008), nd Fieler 2010). Mitr nd Trindde 2005) use nonhomothetic preferences over the industry ggregtes to study how income inequlity ffects trde ptterns. Chung 2005) used qusihomothetic preferences to ddress Trefler s 1995) missing trde puzzle. Flkinger 1990) uses nonhomothetic preferences in dynmic innovtor-imittor model. Flm nd Helpmn 1987) consider qulittive product differentition in North-South model. This model hs been extended by Choi, Hummels, nd Xing 2006), who focus on the role of income distribution in determining the trde ptterns. Krishn nd Yvs 2005) 5

6 ppers bndon the CES-ssumption nd insted introduce vrible elsticity of substitution VES-) preferences. One pproch, followed by Mrkusen 2010) nd Simonovsk 2010) ggregtes differentited consumer goods with Stone-Gery subutility with negtive required consumption levels). This formultion implies tht firms chrge higher prices in richer mrkets, n outcome in line with empiricl evidence see e.g. Hsieh nd Klenow 2007, Simonovsk 2010, nd Mnov nd Zhng 2009). Suré 2009) lso uses Stone-Gery subutility nd studies how heterogeneous trde costs ffect trde ptterns mong symmetric countries. Behrens nd Murt 2009) explore the pro-competitive effects of free trde when consumers hve CARApreferences. They find tht trde reduces mrk-ups nd tht low-income countries gin more from trde thn high income countries. These ppers focus on symmetric equilibri, i.e. equilibri where ll goods re consumed by ll households worldwide. 3 Their pproches differ from tht of our pper, which focuses on the symmetric) prtil trde equilibrium where some goods re consumed by ll households worldwide, wheres other goods re only ffordble to households in the rich country. As mentioned bove, our pper contributes to the literture by presenting generl equilibrium model of prllel trde. A lrge prtil-equilibrium literture hs explored the determinnts nd consequences of prllel trde see Mskus 2000, nd Gnslndt nd Mskus 2007, for surveys). The empiricl relevnce nd importnce of prllel trde is undisputed. The question whether prllel imports should be permitted or not or inhibited by pproprite policies) triggers hot politicl debtes in mny countries. While empiricl evidence on the quntittive importnce of prllel trde is hrd to get, existing estimtes suggest tht prllel imports re quntittively importnt. A lrge body of empiricl evidence hs looked t the phrmceuticls mrket, where the pros nd cons of prllel trde re most obvious see Gnslndt nd Mskus, 2004, for n interesting study of prllel trde on prices of phrmceuticls in the EU). However, prllel trde is quntittively importnt in mny other industries. For instnce, KPMG 2003) estimtes tht grey mrket sles of IT products could exceed USD 40 billion nnully nd tht price dvntges drive grey mrket ctivity. According to the estimtes of the Ntionl Economics Reserch Assocition NERA), prllel imports ccount for between 5% nd 20% of trde within the EU for goods such s consumer electronics, cosmetics nd perfumes, musicl recordings, nd soft drinks NERA 1999). In other words, prllel trde is n importnt phenomenon nd relevnt in mny mrkets. It is therefore interesting used consumption indivisibilities in combintion with lbor mrket imperfection to explin possible losses from trde in trnsition economies. 3 Other ppers tht give up the stndrd CES frmework hve studied the role of income inequlity on trde ptterns. Fjgelbum, Grossmn, nd Helpmn 2009) use nested logit demnd system in which income distribution ffects qulity choice nd ptterns of trde. Desdoigts nd Jrmillo 2009) dopt Lncster s idel vriety pproch to study the impct of inequlity on trde ptterns. 6

7 to study the determinnts nd consequences of prllel trde nd/or the thret of it) in generl equilibrium frmework. 4 The reminder of this pper is orgnized s follows. In the next section, we present the bsic ssumptions nd discuss the consumer behvior with non-homothetic preferences. Section 3 first discusses the closed economy cse nd then pplies our bsic frmework to study ptterns of trde mong eqully lrge but uneqully rich countries. Section 4 discusses the role of popultion size versus per cpit incomes. Section 5 shows the vlidness of our results for more generl specifictions of preferences. Section 6 extends the model to other relevnt settings such s multi-country world, restrictions to prllel trde, income inequlity within countries. Section 7 concludes. 2 The Model The economy is populted by P identicl households. Ech household is endowed with L units of lbor, the only production fctor. Lbor is perfectly mobile within countries nd immobile cross countries. The lbor mrket is competitive nd the wge is W. Hence household income is y = W L. Production requires fixed lbor input F to set up new firm nd vrible lbor input 1/ to produce one unit of output, the sme for ll firms. 5 Producing good j in quntity xj) thus requires totl lbor input of F +x j) /. Product mrkets re imperfectly integrted in the sense tht trde costs ccrue when goods re trded interntionlly. Iceberg trde costs imply tht τ 1 units hve to be shipped to the other country in order for 1 unit to rrive t the destintion. Households spend their income on continuum of differentited goods, indexed by j. We ssume tht good j yields positive utility only for the first unit nd zero utility for ny dditionl units. Hence consumption is binry choice: either you buy or you don t buy. Denote n indictor xj) tht tkes vlue 1 if good j is purchsed nd vlue 0 if not. Then utility tkes the simple form U = 0 xj)dj, where xj) {0, 1}. 1) Notice tht utility is dditively seprble nd tht the vrious goods enter symmetriclly. Hence the household s utility is given by the number of consumed goods. Now consider household with income y which cn choose mong mesure of) N goods 4 Note tht due to the sttic setting, we do not need to introduce ptents. The design of ptents is crucil for the outcomes in dynmic setting. Grossmn nd Li 2004, 2006) discuss these models. 5 An extensive literture hs documented the importnce of productivity differences between firms. While relxing the ssumption of homogeneous firms is strightforwrd, we stick to it in order to keep the supply side of the model s simple s possible, llowing us to focus on the new effects due to the demnd side. 7

8 tht re supplied t prices {pj)}. 6 The problem is to choose {xj)} to mximize the objective function 1) subject to the budget constrint N 0 mrginl utility of income, the first order condition cn be written s xj) = 1 if 1 λp j) xj) = 0 if 1 < λp j) pj)xj)dj = y. Denoting λ s household s Rewriting this condition s 1/λ p j) yields the simple rule tht the household will purchse good j if the household s willingness to py 1/λ does not fll short of the price pj). 7 The resulting demnd curve, depicted in Figure 1, is step function which coincides with the verticl xis for pj) > 1/λ nd equls unity for prices pj) 1/λ. Figure 1 By symmetry, the household s willingness to py is the sme for ll goods nd equl to the inverse of λ, which itself is determined by the household s income nd product prices. Intuitively, the demnd curve shifts up when the income of the consumer increses λ flls) nd shifts down when the price level of ll other goods increses λ rises). It is interesting to note the difference between consumption choices under these simple 0-1 preferences nd under the stndrd CES-cse. With 0-1 preferences the household chooses how mny goods to buy but there is no choice bout the quntity in which good is consumed. 8 Under CES preferences, household hs choice bout the positive) quntities of the supplied goods, but essentilly hs no choice bout how mny different goods to buy due to reservtion price of infinity it is optiml to purchse ech product in positive mounts, whtever its price). In other words, the stylized cse of 0-1 preferences is interesting becuse this ssumption shifts the focus of consumer choice to the extensive mrgin, thus deviting from the CES cse with its focus on the intensive mrgin. It is importnt to note, however, tht our centrl results do not depend on the simple 0-1 ssumption. In Section 5 we show tht our results generlize to more generl preferences, llowing for djustments on both the extensive nd the intensive mrgin. 6 Notice tht the integrl in 1) runs from zero to infinity. While preferences re defined over n infinitely lrge mesure of potentil goods, the number of goods ctully supplied is limited by firm entry, i.e. only subset of potentilly producible goods cn be purchsed t finite price. 7 Strictly speking, the condition 1 λpj) is necessry but not suffi cient for cj) = 1 nd the condition 1 < λpj) is suffi cient but not necessry for cj) = 0. The reson is tht purchsing ll goods for which 1 = λpj) my not be fesible given the consumer s budget. For when N different goods re supplied t the sme price p but y < pn the consumer picks t rndom which prticulr good will be purchsed or not purchsed. This cse, however, never emerges in the generl equilibrium. 8 The discussion here rules out the cse where incomes could be lrger thn pn, mening tht the consumer is subject to rtioning i.e. he would wnt to purchse more goods thn re ctully vilble t the vilble prices). While this could be problem in principle, it will never occur in the equilibrium of the model. 8

9 3 Autrky equilibrium nd the emergence of trde Consider n economy living in utrky under monopolistic competition. After incurring the set-up costs, the vrious producers hve nturl monopoly for their products. Since ll monopolists hve the sme cost nd demnd curves nd since there is representtive consumer, we cn omit indices. The monopolistic firm fces demnd curve s depicted in Figure 1. This firm will chrge price equl to the representtive consumer s willingness to py p = 1/λ nd sell output of quntity 1 to ech of the P households. Without loss of generlity, we choose lbor s the numérire nd set W = 1. Two conditions chrcterize the utrky equilibrium. The first is the zero-profit condition, ensuring tht operting profits cover the entry costs but do not exceed them to deter further entry. Entry costs re F W = F nd operting profits re [p W/] P = [p 1/] P. The zero-profit condition cn be written s p = F + P) /P. 9 This implies mrk-up µ - the rtio of price to mrginl cost given by µ = F + P. P which is determined by technology prmeters nd F nd the mrket size prmeter P. The second equilibrium condition is resource constrint ensuring tht there is full employment PL = F N + PN/. From this eqution, equilibrium product diversity in the decentrlized equilibrium cn be clculted 10 N = P F + P L. Mrket size nd technology influence mrk-ups in our frmework. We will show below tht the mrk-up chnnel is crucil chnnel by which non-homothetic preferences ffect ptterns of trde nd the interntionl division of lbor. Now ssume there re two countries, rich nd poor, nd consumers in both countries hve the sme preferences given by 1). Assume further tht firms in the two countries produce different products. Under which condition will the two countries trde? 9 Notice tht we hve rgued tht p = 1/λ nd p = F + P ) /P ; it therefore seems tht p is overdetermined, unless we hve λ = P/ F + P ). To see tht this is in fct the cse, notice tht incresing income by one unit pproximtes n increse in L becuse income is y = W L nd we normlized W = 1). Hence we cn write λ = du/dl = U/ N) N/ L). Since we hve U = N, U/ N = 1, nd we hve N/ L = P/ F + P ) from equilibrium product diversity, this confirms the clim. 10 Notice the difference between the 0-1 outcome nd the stndrd CES-cse. With CES, the mrk-up is determined by the elsticity of substitution between differentited goods; it is independent of technology nd mrket size. In fct, the vribility of the mrk-up with 0-1 preferences will drive mny of our results below. Moreover, with CES, equilibrium product diversity is independent of productivity nd proportionl to set-up costs F nd inversely proportionl to mrket size P. We notice tht with 0-1 preferences product diversity in the decentrlized equilibrium is equl to the socilly optiml product diversity. 9

10 Assumption 1 Trde condition) τ F/P + 1. The bove ssumption sttes suffi cient condition for the emergence of interntionl trde. To see this, consider n entrepreneur shipping τ 2 units of his or her product to the other country so tht, due to iceberg trde costs, τ units rrive there. The firm cn exchnge the remining τ units for τ units of symmetric) foreign vriety ship it bck nd sell it on the home mrket t price p. Thus utrky cnnot be n equilibrium if the costs of producing τ 2 units flls short of the locl) utrky prize, i.e. τ 2 / < F + P) /P. Solving for τ yields the trde condition. Note tht the trde condition is independent of the other country s prmeters such s popultion size, lbor endowment, or technology prmeters. The bove trde condition is suffi cient but not necessry condition for the emergence of interntionl trde. We will ssume throughout the pper tht Assumption 1 holds Trde between eqully lrge but uneqully rich countries Let us now ssume tht Assumption 1 holds nd consider world economy with two countries with unequl welth. We denote vribles of the rich country with superscript R nd vribles of the poor country with superscript P. To highlight the importnce of differences in per cpit incomes s source of interntionl trde, we strt by ssuming tht the two countries differ only in per cpit endowments, but hve eqully lrge popultions, hence L R > L P nd P R = P P = P. We lso ssume tht the two countries hve identicl production nd trnsport technologies. 4.1 A full trde equilibrium When the two countries re not very unequl, possible equilibrium is one in which ll producers sell on the world mrket, so tht ll goods re trded interntionlly. In such full trde equilibrium, the price for differentited product in country i = R, P equls the respective households ggregte willingness to py see Figure 1), hence we hve p R = 1/λ R nd p P = 1/λ P. Since country R is welthier thn country P, we hve λ R < λ P nd p R > p P. By symmetry, the prices of imported nd home-produced goods re identicl within ech country. Solving for the full trde equilibrium is strightforwrd. Consider the resource constrint in the rich country. When N R firms enter, N R F lbor units re employed to set up these firms nd N R P 1 + τ) / lbor units re employed in the production to serve the world mrket. Since ech of the P households inelsticlly supplies L R units of lbor, the resource constrint is PL R = N R F + N R P 1 + τ) /. This is nlogous for the poor country P. Solving for N i 11 The cse when Assumption 1 does not hold high trde costs), is vilble upon request by the uthors. 10

11 lets us determine the number of ctive firms in the two countries N i = P F τ) P Li, i = R, P. 2) Now consider the zero-profit conditions in the two countries. An interntionlly ctive firm in the rich country genertes totl revenues equl to Pp R +p P ) nd hs totl costs W R [F τ)p/]. An interntionlly ctive firm in the poor country genertes the sme totl revenues nd hs to incur the sme lbor requirement F τ)p/. Hence, wges per effi ciency unit hve to equlize, W R = W P, for the zero profit conditions to hold in both countries. We use lbor s the numérire in the following, W R = W P = 1. The budget restrictions re therefore p i N R + N P ) = L i. Combining the zero profit condition with the budget restrictions nd the number of firms lets us express the price chrged in country i s L i p i F τ) P = L R + L P, i = R, P. 3) P The prices of ll differentited products re the sme within country, irrespective of whether they re produced t home or brod. Consequently, imported goods generte lower mrk-up thn loclly produced goods s exporters hve to ber the trde costs fully. 12 The mrk-ups price over mrginl cost) producers chrge on their home mrket µ i D = pi nd the mrk-ups set in the export mrket µ i X = pi /τ re given by L i µ i F τ) P D = L R + L P, nd µ i X = 1 F τ) P P τ L R + L P, i = R, P. P In sum, the full trde equilibrium hs simple structure: the rtios of rich reltive to poor country vrieties, prices, nd mrk-ups re identicl to the rtio in reltive lbor endowments nd nominl incomes), i.e. N P /N R = p P /p R = µ P D /µr D = µp X /µr X = W P L P / W R L R) = L P /L R < 1. The differences in per cpit endowments nd incomes trnslte one-to-one into differences in prices, hence interntionl trde estblishes n equilibrium such tht rel incomes nd welfre levels equlize between the two countries. Under utrky, on the other hnd, the poor country is clerly worse off thn the rich country. As result, interntionl trde benefits the poor country more thn it does the rich country. L i 4.2 Prtil trde nd the thret of prllel imports Full trde cnnot be n equilibrium outcome when per cpit lbor endowments nd hence incomes between the two countries re very unequl, i.e. when L P /L R becomes smll. The 12 In this respect, 0-1 preferences differ strongly from CES preferences, s higher costs cnnot be pssed through to prices. With CES preferences, trnsporttion costs re more thn pssed through to prices s exporters chrge fixed mrk-up on mrginl costs including trnsporttion). Notice limited cost pss-through is consistent with empiricl evidence. A number of empiricl studies document tht mrginl cost shocks re not fully pssed through to prices t the firm level nd tht prices re substntilly less voltile thn costs. See Rvn et l. 2007) nd the references quotes there. 11

12 reson is tht if countries re suffi ciently unequl, thret of prllel trde emerges. To see the point most clerly, consider US firm tht sells its good both in the US nd in Chin. The firm chrges price in Chin tht equls Chinese household s willingness to py p P = 1/λ P nd price in the US tht equls the US households willingness to py p R = 1/λ R. Becuse the difference between 1/λ P nd 1/λ R is lrge, rbitrge opportunities emerge. Arbitrge trders purchse the good cheply on the Chinese mrket, ship it bck to the US, nd underbid locl producers on the US mrket. This thret of prllel trde lso concerns Chinese firms which both produce for the locl mrket nd export to the US. When these firm chrge prices in the US tht exploit US households high willingness to py, rbitrge trders hve n incentive to purchse the product in Chin cheply nd prllel export it to the US. Clerly, firms nticipte this thret of prllel trde nd djust their interntionl pricing ccordingly. These firms thus tke dvntge of the lrge world mrket but re constrined in their pricing due to the thret of prllel trde. There is n lterntive, potentilly profitble, strtegy: rich-country firm could bstin from trding its product interntionlly nd focus exclusively on its rich home mrket. This producer type hs smller mrket but cn exploit the rich country households high willingness to py becuse it is not subject to the thret of prllel imports. In equilibrium, both types of firms exist simultneously nd the reltive populrity of the two strtegies djusts such tht both yield the sme profits. We will see below tht ll firms in the poor country re strictly better off selling their product on the world mrket rther thn limiting their sles to exports to the rich country nd not selling on the locl mrket.) This implies tht only subset of ll vilble products is ctully trded, which is why we cll this equilibrium "prtil trde" equilibrium. Denote the price in the rich country of good tht is trded interntionlly by p R T ; the price in the rich country of good tht is not trded by p R N ; nd s bove) the price of good in the poor country by p P. When setting their prices, suppliers of goods trded interntionlly nticipte the thret of prllel trde nd set price tht just prevents ny incentive for rbitrge. This implies tht the prices chrged in the rich country for goods trded interntionlly my not exceed the corresponding prices for these goods in the poor country plus trde costs, i.e. p R T τ/λp, profit mximiztion implies tht this condition holds with equlity. Hence we must hve p R N = 1/λR, nd p P = 1/λ P. The zero profit condition for trded good is p R T + pp )P = [F + P1 + τ)/] W R for n interntionlly ctive rich-country producer nd p R T + pp )P = [F + P1 + τ)/] W P poor-country producer. Both types of firms generte the sme totl revenues nd hve to incur the sme lbor input. As result, the zero-profit condition requires the compenstion per effi ciency unit of lbor to be the sme in the two countries, W R = W P = 1. The prices of for 12

13 trded goods cn be clculted strightforwrdly from these zero profit conditions s p R T = τ F τ) P 1 + τ P nd p P = τ F τ) P. P The zero profit condition for rich-country producer tht sells his product exclusively on the home mrket is p R NP = F +P/, from which we clculte the equilibrium price of non-trded vriety p R N = F + P P. In prtil trde equilibrium, domestic nd interntionlly ctive firms co-exist in equilibrium. To see why this is n equilibrium, consider the lterntive sitution in which ll goods produced in the rich country re trded interntionlly. If ll products were sold t price tht prevented prllel trde, ll goods would be priced below the rich-country households willingness to py. However, this corresponds to sitution where the representtive rich-country household is not ble to spend ll income. This, in turn, implies tht country-r households hve n infinitely lrge willingness to py for dditionl products, which induces some country-r firms to switch strtegy nd sell only on their home mrkets. In contrst to the rich country, do ll producers in the poor country sell their product both t home nd brod? In principle one might think tht country-p producers lso hve n incentive to sell their product exclusively in the rich country exploiting the country-r households high willingness to py nd not to sell their product on the home mrket to prevent prllel exports). While such strtegy genertes the sme totl sles, it genertes high overll costs s the country-p exporter lso hs to ber trde costs. Hence selling exclusively on the R mrket is not profitble option for P producer. We re now redy to solve for the prtil trde equilibrium. The resource constrint in the poor country is still given by PL P = N P F τ)p/) from which we clculte N P = P F τ)p LP. 4) The resource constrint in country R is different from before becuse now we hve to distinguish products tht re exclusively sold domesticlly nd those tht re trded interntionlly. Denoting the trded nd non-trded goods produced in the rich country by N R T nd N R N, respectively, the resource constrint of country R is PL R = NT R F τ)p/) + N N R F + P/). Together with the trde blnce condition N R T pp P = N P p R T P nd the terms of trde pr T /pp = τ we cn clculte N R T = P F τ) P τlp, nd NN R = P L R τl P ). 5) F + P 13

14 4.3 Per cpit incomes nd ptterns of trde It is strightforwrd to see the condition under which the thret of prllel trde becomes binding constrint on price setting in the rich country, llowing prtil trde equilibrium to emerge. In full trde equilibrium, reltive prices re p P /p R = L P /L R nd the thret of prllel trde is not binding s long s the price rtio stisfies p R /p P τ. It follows tht the prllel trde constrint kicks in when τ = LR L P. 6) In other words, full trde equilibrium emerges when per cpit incomes re suffi ciently similr, L R /L P τ, nd prtil trde equilibrium emerges when the gp in per cpit incomes is high, τ < L R /L P. Figure 2 drws condition 6) in the L P /L R, τ) spce. Figure 2 is drwn for vlues of τ tht stisfy the trde condition of Assumption 1. In region F full trde), chrcterized by high vlues of L P /L R nd intermedite vlues of τ, there is full trde. In tht region, consumers in the two countries hve very similr incomes nd hence the differences in their willingness to py re minor) so tht the prllel trde constrint on prices in the rich mrket does not become binding nd rbitrge opportunities do not emerge. In region P prtil trde), chrcterized by low trde costs nd high differences in verge incomes, prtil trde equilibrium emerges. When reltive endowments L P /L R re low, the difference in willingness to py between rich- nd poor-country households is lrge, mking the prllel-trde constrint binding. 13 Figure 2 Let us highlight how the volume nd structure of interntionl trde depend on reltive per cpit incomes L P /L R. We define "trde intensity" φ s twice the vlue of trded goods, 2 [ p R T N P + p P NT R ], over the vlue of totl production worldwide, p R T + p P ) N P + NT R ) + p R N N N R. Using equtions 4) nd 5) we my clculte the trde intensity in prtil trde equilibrium. Alterntively, if L P /L R 1/τ the world economy is in full trde equilibrium where the trde intensity follows from 2) nd 3) 4τ 1+τ φ = L P L P +L R if L P /L R < 1/τ 4 LP L R L P +L R ) 2 if L P /L R 1/τ 7) Eqution 7) revels tht higher L P /L R, i.e. higher similrity between the two countries, is ssocited with higher trde intensity φ. In Figure 3 we drw φ verticl xis) ginst reltive lbor endowments L P /L R horizontl xis) holding worldwide resources P L R + L P ) 13 Notice tht there is interntionl trde even when income differences become extremely lrge nd L P /L R becomes very smll. The rnge of trded goods pproches zero, however, when L P /L R goes to zero. 14

15 constnt. A decrese in L to quntity nd price effect. An incresing rnge of trded goods N P + N R T is ssocited with n decresing rnge of non-trded goods N N R. The world economy reches full trde when L P /L R 1/τ. With full trde, further increse in L P /L R rises trde intensity through the price effect only. With the poor country getting richer, the reltive prices of trded goods increse. In other words s the similrity of the two countries in per cpit endowments nd per cpit incomes) increses, the intensity of trde φ increses s well. We summrize this discussion in Proposition 1 ) When reltive per cpit endowments re suffi ciently similr so tht L P /L R [1/τ, 1], the generl equilibrium fetures full trde. b) When per cpit endowments become suffi ciently dissimilr so tht L P /L R 0, 1/τ), the generl equilibrium is chrcterized by prtil trde where thret of prllel imports/exports constrins the prices chrged for interntionlly trded goods in the rich country. Proof. In text. It is worth noting tht this simple model fetures the fmous Linder hypothesis. Linder 1961) emphsized tht the similrity of two countries, s mesured by similrity in their per cpit incomes, should be n importnt determinnt of trde between them. 4.4 Welfre nd the gins from trde We proceed by studying welfre implictions nd the gins from trde. In prticulr, we re interested in how trde liberliztions reduction of τ) ffect welfre nd the distribution of trde gins between rich nd poor countries. In full trde equilibrium, households in both countries purchse ll goods produced worldwide. Hence the welfre levels re identicl in both countries despite their unequl endowment with productive resources U R,f = U P,f = P L R + L P ) F τ) P. Firms price setting behvior drives this result. R-consumers re willing to py higher prices thn P -consumers becuse their nominl income is higher. In the full trde equilibrium, higher nominl incomes trnslte one to one into higher prices. Rel incomes nd welfre re therefore identicl. To see the mechnism by which welfre is equlized even though the two countries hve unequl welfre levels under utrky, consider firms mrk-ups. By ssumption, ll firms hve identicl production costs hence different prices reflect differences in mrk-ups cross countries. Since in equilibrium profits re zero, the mrkups re fully used to cover fixed costs nd iceberg losses during trnsporttion. Hence, the higher mrk-ups in the rich country imply tht the rich country households ber lrger shre of these costs. 15

16 In prtil trde equilibrium, welfre levels of consumers in the two countries diverge. Country-P households purchse N R T + N P goods nd country-r households purchse N P + N R T + N R N goods. Using 4) nd 5) we cn clculte the welfre levels U P,p P1 + τ)lp = F τ)p nd U R,p P1 + τ)lp L R = F τ)p + P τl P ). F + P Notice tht while welfre in country R decreses in τ lower trde costs or trde liberliztion increses welfre), the opposite is true for country-p welfre. We re now ble to stte the following proposition. Proposition 2 ) Compred with utrky, country P gins more from trde thn country R. b) R-consumers fvor free trde, i.e. τ = 1, wheres P -consumers derive their highest utility { F/P } when there re trde brriers such tht τ = min + 1, L R /L P. Proof. The proposition cn be redily demonstrted using Figure 4. Pnel ) is drwn for the cse when L R /L P F/P + 1 so tht full trde equilibrium emerges with moderte trde costs. Pnel b) is drwn for the cse when L R /L P > F/P + 1 so tht full trde equilibrium is not fesible. Country-R welfre the bold grph) is monotoniclly decresing in τ in both pnels of Figure 4. Hence the R-consumer reches his mximum welfre when trde costs hve reched their lowest possible level, t τ = 1. However, the welfre of country P the dotted grph) increses in τ in both pnels of Figure 4 when trde costs re suffi ciently low, i.e. in sitution where the world economy is in prtil trde equilibrium. A full trde regime emerges in pnel ) when τ [ L R /L P, F/P + 1) L P /L R] where welfre decreses in τ. The economies remin utrkic for even higher τ > F/P + 1) L P /L R where welfre obviously becomes independent of τ. Figure 4 lso shows tht the highest welfre for country- P consumers occurs t τ = L R /L P when L R /L P F/P + 1 nd t τ = F/P + 1 when L R /L P > F/P + 1. Tken together, this yields the result in Proposition 2. Figures 4, 4b Proposition 2 shows the crucil role of trde costs for welfre. Unequl countries hve different preferred trde brriers or different preferred degrees of trde liberliztions). Consumers in the rich country re essentilly free-trders wheres consumers in the poor country only wnt liberliztion up to positive level of trde costs. Wht is the intuition behind this result? When the world economy hs reched prtil trde equilibrium the thret of prllel imports constrins prices in the rich country to p R T = τpp. Further trde liberliztion forces country-p exporters to lower prices in country-r reltive to prices in country P becuse price 16

17 discrimintion is limited by fctor τ. Hence the terms of trde for the poor country deteriorte leding to the welfre loss. 5 Popultion sizes versus per cpit endowments In the previous section, differences in incomes cross countries were due to differences in per cpit endowments nd the two countries hd eqully lrge popultions. Let us now consider the cse when countries differ long both dimensions. This is interesting becuse it llows us to gin insights on how the composition of ggregte income ffects the extensive mrgin of interntionl trde under non-homothetic preferences s stndrd new trde theory lso predicts tht the two countries sizes ffect trde volume). With 0-1 preferences it becomes most trnsprent how the composition of ggregte income ffects the size of the home mrket if one considers given product. As every household consumes exctly one unit of given vriety, lrger endowment of the representtive home-consumer leves the size of the home mrket unchnged. For the sme reson, lrger popultion increses the home mrket one to one. For interntionlly ctive producers, hving reltively lrger home mrket mens tht trde costs re reltively smller prt of totl costs. As firms locted in lrge country ber reltively fewer iceberg losses s frction of their totl costs, lbor in lrge country is more productive thn lbor in smll country. 5.1 Reltive wges nd generl equilibrium To see how different popultion sizes ffect reltive wges, we need to check the zero-profit conditions of interntionlly ctive firms. Totl revenues re given by p P τp R + P P) nd do not differ by firm loction. However, the mount of lbor needed to serve the world mrket does differ. It is given by F + P R + τp P) / for country-r firms nd by F + τp R + P P) / for country-p firms. We cn clculte reltive wges from the zero-profit conditions note tht the formul is the sme under both full nd prtil trde) ω W P W R = F + τpp + P R F + P P + τp R. 8) It follows tht ω 1 if P P /P R 1. Hence the compenstion per effi ciency unit of lbor is higher in the poor country when the poor country is lrger nd vice vers. The discussion bove suggests tht bckwrd country in terms of per cpit endowment cn get hed in terms of per cpit income if it hs lrge popultion. This rises n interesting question. Could it be tht huge popultion rises incomes nd willingness to py in country P so much tht the prllel-trde constrint on price setting becomes binding in country P rther thn in country R? In other words, is it possible tht producers in poor 17

18 country with lrge popultion fce thret of prllel trde leding to "reversed" prtil trde equilibrium in which only subset of poor-country vrieties re interntionlly trded? The nswer is no. To see this, recll tht the households budget constrints in full trde equilibrium re W i L i = p i N P + N R ), i = R, P from which we cn clculte reltive prices under full trde p P p R = F + PR + τp P F + τp R + P P L P L R. Verifiction tht lim P P p P /p R = τl P /L R < τ is strightforwrd. Even if the popultion in country P becomes extremely lrge, country-p households willingness to py while eventully exceeding tht of country-r households will remin below τp R. Hence rbitrge opportunities nd therefore thret of prllel trde do not exist. equilibrium will never emerge. In sum, "reversed" prtil trde Figure 5 demonstrtes tht per cpit incomes ffect trde volumes for given ggregte size of the economy. The bold line represents the combintions of reltive per cpit endowments nd reltive popultion sizes such tht the world economy just enters the full trde regime FP-boundry). More precisely, long this line the reltive willingness to py p R /p P re exctly equl to trde costs τ. Per cpit incomes re more similr to the right of this curve L P /L R closer to unity) so tht the reltive willingness to py is strictly lower thn τ. Per cpit income differences re too dissimilr to the left of this curve, creting thret of prllel trde so tht prtil equilibrium emerges. 14 The figure shows tht, whtever reltive popultion sizes P P /P R, the world economy cn rech full trde equilibrium provided tht reltive per cpit endowments L P /L R suffi ciently pproch unity. However, we cnnot rgue in the sme wy with increses in reltive popultions. When per cpit incomes re suffi - ciently similr, n increse in popultion in the poorer country my push the world economy out of prtil trde into full trde equilibrium. However, when per cpit endowments re very dissimilr, L P /L R < 1/τ 2, the world economy remins trpped in prtil trde equilibrium even when reltive popultion size P P /P R goes to infinity. In this sense, the model predicts tht per cpit incomes re more importnt thn popultion sizes in shping ptterns of interntionl trde. To consider the distinct impct of per cpit income, we drw dotted iso-size line, i.e. the combintion of reltive per cpit endowments nd reltive popultion sizes for which ggregte endowments of the two economies re identicl, L P P P = L R P R. Recll tht, under CES preferences, such sitution would feture world equilibrium with perfect symmetry). Since the iso-size line is fltter thn the FP boundry, the two curves cross when L P /L R becomes suffi ciently low. Hence two countries with identicl ggregte endowments end up in 14 The FP boundry is defined by ωp P /P R )L P /L R = τ. From eqution 8) we hve ω > 0, which implies negtive reltionship between P P /P R nd L P /L R. 18

19 prtil trde when one country is rich but smll nd the other country is lrge but poor. 15 Figure Welfre implictions When we llow popultions to differ between the two countries, welfre implictions remin qulittively unchnged. In full trde equilibrium, the welfre levels re U i,f = U i,f = PR L R + ωτ)p P L P F + P R + τp P, i = R, P the sme for both countries. Compring full trde with utrky, it my be tht the rich rther thn the poor) country gins more thn the poor country. Welfre levels under utrky re U i, = L i / F/P i + 1/ ), i = R, P, which revels tht country-r households gin more from full trde when L P P P /L R P R ) > F + P P )/F + P R ). This sitution rises when the rich country is very smll so tht ccess to the lrge world mrket genertes lrge gin in effi ciency. In prtil trde equilibrium we hve P U P,p P + τp R) L P = F + τp R + P P, nd P U R,p P + τp R) L P L R = F + τp R + P P + ωτ)τl P ) PR F + P R. It cn be shown tht U P,p / τ > 0 nd U R,p / τ < 0. Hence, llowing for unequl popultion sizes does not chnge the welfre implictions of trde liberliztion. When the world economy is in prtil trde equilibrium, trde liberliztion improves welfre of country-r consumers but hurts consumers in country P. The reson is the sme s bove. In prtil trde equilibrium, trde liberliztion deteriortes terms of trde for the poor country. The higher reltive price of imported goods implies tht the consumption bsket poor country consumers cn fford becomes smller. The preferred level of openness is τ = 1 in the rich country nd τ > 1 in the poor country, where τ stisfies ω τ)l P /L R = τ. Notice tht τ is lso the criticl level of trde costs tht lets the world economy switch from full trde to prtil trde equilibrium. 6 More generl preferences We ssumed 0-1 preferences in the nlysis bove. On the one hnd, this ssumption yields frmework tht is highly trctble nd genertes closed-form solutions. On the other hnd, 15 Note the reltion to the so-clled home bis in economies with incresing returns to scle. In prticulr, Hnson nd Xing 2004) show tht lrger countries host industries with more differentited products nd higher trde costs. There is lso relted result in Fjgelbum et l. 2009). 19