International Trade: Theory And Evidence

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INTERNATIONAL TRADE: THEORY AND EVIDENCEJames R. MarkusenKeith E. MaskusDepartment of EconomicsUniversity of Colorado, BoulderOctober, 2011Preliminary and Incomplete. This packet constitutes a preliminary submission for evaluationand feed back. It is partial and incomplete, both with respect to the number of chapters and thecontents of many of the chapters included.Copyright 2011, James R. Markusen and Keith E. Maskus. No part of this work may be reproducedwithout written permission of the authors.

INTERNATIONAL TRADE: THEORY AND EVIDENCE(Alternative title suggestions most welcome!)James R. MarkusenKeith E. MaskusUpdated October 15, 2011ACKNOWLEDGMENTPREFACENOTATIONPart OneTECHNICAL CONCEPTS AND THE GAINS FROM TRADE1.GLOBALIZATION AND INTERNATIONAL TRADE1.11.21.31.41.51.6IntroductionSources of globalizationChannels of globalizationEffects of globalizationCan Globalization be RODUCTION, SUPPLY AND PRODUCTION POSSIBILITIES2.12.22.32.42.52.62.7Properties of production functionsEquilibrium for a single producerThe production set and the production possibilities frontierCompetitive equilibriumCost functionsA note on increasing returns to scale and imperfect competitionSummaryReferencesEndnotesFigures1

23.PREFERENCES, DEMAND, AND WELFARE3.13.23.33.43.5Optimization for a single consumerA note on homogeneous functionsAggregating over households to a “community” utility functionInterpreting community indifference curves: aggregate demand versus .GENERAL EQUILIBRIUM IN OPEN AND CLOSED ECONOMIES4.14.24.34.44.54.64.7General equilibrium in the closed (autarky) economyGeneral equilibrium in the open (trading) economyThe excess demand functionThe shape of the excess demand curve, welfare interpretationInternational general equilibriumAn introduction to computing solutions to numerical general-equilibrium modelsSummaryReferencesEndnotesFigures5.THE GAINS FROM TRADE5.15.25.35.45.55.65.75.8Gains from tradeThe gains-from-trade theoremLimitations of the gains-from-trade theoremThe distribution of gains between countriesThe distribution of gains within countries I: heterogeneous preferencesThe distribution of gains within countries II: heterogeneous endowmentsThe static gains from trade: an example from historySummaryReferencesEndnotesFigures

3Part Two:CAUSES AND CONSEQUENCES OF TRADE6.THE CAUSES OF INTERNATIONAL TRADE6.16.2The no-trade modelMethodologyFigures7.DIFFERENCES IN TECHNOLOGY: THE RICARDIAN MODEL7.17.27.37.47.57.67.7Absolute and comparative advantageThe production frontierExcess demand and international equilibriumThe role of absolute advantage in wage determinationThe distribution of gains from trade between countriesEconometric on the Ricardian RENCES IN FACTOR ENDOWMENTS I: THE HECKSCHER-OHLIN MODEL8.18.28.38.48.58.68.78.8The Heckscher-Ohlin model: an intuitive approachThe Heckscher-Ohlin theorem: a more formal approachThe factor-price-equalization theoremThe Rybczynski theoremThe Stolper-Samuelson theoremA caveat: factor-intensity reversalEmpirical evidence on factor endowments and tradeSummaryReferencesEndnotesTablesFigures

49.DIFFERENCES IN FACTOR ENDOWMENTS II: THE JONES SPECIFIC-FACTORSMODEL9.19.29.39.4The Jones specific-factors modelAnalogs to the four theorems of the Heckscher-Ohlin modelEmpirical evidence on preferences for protection or free ORTIONS AND EXTERNALITIES AS DETERMINANTS OF TRADE10.110.210.310.410.510.610.7Departures from our stylized worldDistinguishing among consumer, producer, and world pricesTaxes and subsidies as determinants of trade: a small open economyTaxes and subsidies as determinants of trade: two identical economiesProduction externalitiesTrade and the gains from trade in the presence of production externalitesSummaryReferencesFigures11.IMPERFECT COMPETITION AND INCREASING RETURNS I: OLIGOPOLY11.111.211.311.411.5General discussion of increasing returns, non-comparative-advantage gains fromtradePro-competitive gains: the basicsSpecial case I: quasi-linear preferencesSpecial case II: Cobb-Douglas preferencesSummaryReferencesEndnotesFigures

512.IMPERFECT COMPETITION AND INCREASING RETURNS II: de and the gains from trade through increased product diversityA more formal approach to Dixit-Stiglitz and love of varietyMonopolistic competition in specialized intermediate inputsThe ideal variety approach to product diversitySome useful algebra for Dixit-StiglitzSummaryReferencesFigures13.TRADE COSTS, TRADE VOLUMES AND FIRM phy and trade costsTrade costs and trade volumes in competitive, comparative-advantage modelsTrade costs, prices discrimination, and trade volumes in oligopoly modelsTrade costs, inter and intra-industry trade in monopolistic-competition modelsThe core-periphery modelHeterogeneous firms and firm-level export behaviorThe gravity equationEmpirical REFERENCES, PER-CAPITA INCOME AND PRODUCT QUALITY14.114.214.314.414.514.6Preferences and per-capita income as a determinant of tradeThe Linder hypothesisIntegrating Linder, monopolistic competition and non-homothetic preferencesProduct quality and willingness to payEmpirical evidence on preferences, quality and tradeSummaryReferencesEndnotesTableFigures

6Part ThreeFACTOR TRADE, DIRECT FOREIGN INVESTMENT, OFFSHORING15.TRADE IN FACTORS OF PRODUCTION15.115.215.3Adding factor trade to goods tradeFactor trade and goods trade as substitutesFactor trade and commodity trade as complements15.4Agglomeration: combining monopolistic competition, trade costs, and mobile CT FOREIGN INVESTMENT AND MULTINATIONAL FIRMS16.116.216.316.416.516.616.7Stylized facts, basic conceptsA basic organizing frameworkA simple monopoly model of location choiceMonopolistic competition and the choice of exporting versus horizontal productionThe knowledge-capital modelOutsourcing versus internalization (vertical 17.FRAGMENTATION, OFFSHORING, AND TRADE IN SERVICES17.117.217.317.417.517.6Stylized facts, basic conceptsFragmentation and newly-traded intermediate goodsFragmentation and trade in “tasks”A gains-from-trade theoremTrade and foreign direct investment in servicesSummaryReferencesTablesFigures

7Part FourTRADE POLICY18.TARIFFS AND TRADE SUBSIDIES IN COMPETITIVE TRADE MODELS18.118.218.318.418.518.618.718.818.9Tariffs, welfare and factor prices in a small economyTwo key equivalencesExport subsidiesGains from trade with many goods, trade taxes and subsidiesMonopoly power and the “optimal” tariffTariffs and the theory of the second bestEffective protectionTariffs versus transport and transaction costs, foreign ownershipSummaryReferencesEndnotesFigures19.QUOTAS AND RELATED BARRIERS19.119.219.319.419.5Quantity and equivalent tariffs in a small economyDistribution and dissipation of quota rentsAn algebraic example(Non) equivalence of tariffs and quotas, other related policiesSummaryReferencesFigures20.STRATEGIC TRADE POLICY20.120.220.320.420.520.6Trade policy with increasing returns and imperfect competitionExport rivalry I: Cournot competitionExport rivalry II: Bertrand competitionCournot with and without entry, adding domestic consumptionOther issues and further readingSummaryReferencesEndnotesFigures

821.MULTILATERAL TRADE AGREEMENTS: THE WORLD ductionThe Logic of Trade AgreementsThe World Trade OrganizationThe Theory of Contingent ProtectionGlobal Trade Policy and Market ExternalitiesEmpirical EvidenceEvidence from econometric and CGE IAL TRADE AGREEMENTS22.122.222.322.422.5IntroductionWelfare Basics: Trade Creation and Trade DiversionA General Welfare TheoremEndogenous FTA FormationEconometric evidenceReferencesTablesFigures

INTERNATIONAL TRADE: THEORY AND EVIDENCEAUTHORS' PREFACEOur book is intended primarily for a one-semester or one-quarter course in internationaltrade for undergraduate economics majors. It is written specifically for courses and studentswho have completed a half-year course in intermediate microeconomic theory, a year ofuniversity calculus, and hopefully a half-year course in econometrics. The book is not suited to acourse which covers both international trade and finance in one semester or quarter, nor is itsuited to a course for non-majors. The book also serves as a basic text for master’s courses ininternational economics or business and can in fact be used as a basic reference in higher-levelcourses before students plunge into journal articles.Our interest in producing such a book stems from the fact that virtually all alternativetexts are not designed for a semester course in trade for economics majors with an intermediatemicroeconomics prerequisite. Available competing books generally try to serve combined tradeand-finance survey courses, either for non-economics majors or for students without thenecessary microeconomic training. As a result, they present watered-down theory withsometimes uneven analytical approaches. Further, such books do not offer deep coverage ofimportant and informative empirical studies in the professional literature.Thus, our book is aimed at the upper end of the undergraduate and master’s markets,using a more specialized and consistent approach. Using tools of geometry and calculus, we tryto stay true to the great strength of international trade theory, which is its general-equilibriumapproach to all issues. Competing books have adopted a clear trend toward partial-equilibriumrepresentations of inherently general-equilibrium problems. Even worse is the regrettable use ofpartial-equilibrium “triangles” to try to teach welfare analysis in trade. We also discussanalytically the most significant empirical studies that inform and flesh out the essential tradetheory. We think that this combination of consistent theory supplemented by solid and frontierempirical evidence establishes the volume’s unique contribution to international trade texts.Our approach to trade theory and empirical work embodies a philosophy and pedagogythat helps unify the subject and the analysis. We have long maintained that there are manythings that cause trade. Furthermore, these underlying causes or “bases” for trade are notcompeting theories in the usual sense, but rather all of them operate to varying degrees at thesame time in all countries.We believe that the task of theory is to analyze each cause individually and thenunderstand the consequences of changes in the economic or policy environment surroundingeach basis for trade. For example, a tariff can have very different effects if the underlying causeof trade is differences in factor endowments in a perfectly competitive environment, versus onein which the cause of trade is scale economies and imperfect competition and countries arevirtually identical.We argue that one role for positive empirical analysis is to examine the importance ofalternative bases for trade and to examine which models have assumptions that conform better toreal-world data. Armed with both theory and this empirical evidence, applied economists arethen better positioned to assess counter-factual questions about policy and to makerecommendations with some degree of confidence rather than from a stance of mere ideology.It is all too easy for us to say to politicians and journalists that liberalization is always andeverywhere a good thing. But theory tells us that this is clearly not the case, and both theory and1

2empirical testing of the alternative models and assumptions help us give better advice.What distinguishes the book is partly its analytical approach, but more importantly thebreadth, depth and consistency of its coverage. We have tried to maintain a uniform level ofanalysis throughout the book, and the same basic "tool kit" is used repeatedly to avoid the costsof developing and learning new analytical constructions for each new topic. One of our firsttasks was to develop a standard notation that can be used throughout the book and this notationsheet is attached after the outline. Our perception of standard texts is that they tend to treat onetopic on a fairly formal level, such as the Heckscher-Ohlin model, and then resort to chat andanecdote about other topics, such as the industrial-organization approach to trade. We workedhard to develop analyses of quite different topics at approximately the same analytical level anddepth of presentation. At the same time, we try to avoid introducing an analytical constructionthat requires a lot of time to master but is used only once.The first section of the book, chapters 1-5, first overviews major recent trends in globaltrade and investment, then concentrates on developing analytical tools and techniques (chapters2-4). We develop, for example, the “revealed preference” methodology for assessing incomeand welfare changes that is used repeatedly throughout the book for evaluating the efficiency ofproduction, gains from trade, the effects of distortions, and so forth. Chapter 4 ends with a(optional) section about the methodology for actually solving complex general-equilibriummodels, about which we will say more below. Chapter 5 presents a general and thoroughanalysis of gains from trade. Not only do we analyze the aggregate gains for one country (this isdone in all textbooks, though rarely with proper care), but we also discuss the division of totalgains between countries, and the distribution of one country’s gains among groups within thecountry.The second part of the book, chapters 6-14, presents the positive theory of trade. Herewe present our unified methodology not found elsewhere. As noted above, our view is thatmany things can cause trade. So we begin in chapter 6 with what we call the “no trade model”.What would have to be true for countries to choose not to trade and for there to be no gains fromtrade? The resulting list of conditions then becomes the outline for the following chapters inwhich those restrictions are relaxed one at a time. Trade costs have attracted a great deal ofattention in the last decade or two, and in appreciation of this we will discuss how trade costsmodify the results of each theoretical approach (e.g., factor-price equalization in the HeckscherOhlin model). Following the theory in each chapter, we present econometric evidence on thattheory and evidence from a few numerical simulation models where appropriate.The third part, chapters 15-17, continues to focus on the positive theory of trade, turningto trade in factors, foreign direct investment and trade in intermediate goods and services.Classical topics are covered in the chapter 15 on trade in factors of production while chapter 17focuses on recent work on fragmentation: the expansion of trade at the extensive margin withnew intermediate goods and services becoming tradeable. Chapter 16 has a significantlyexpanded and more analytical treatment of multinational firms and direct foreign investment,topics that have achieved the status of a major theoretical and empirical sub-field.The fourth part, chapters 18-23, turns to trade policy, with analyses of alternativeinstruments (tariffs, quotas, subsidies) grounded in the theory and evidence presented in earlierchapters. After considering these policy instruments, the text discusses several critical areas ofglobal policy that are the subjects of extensive ongoing research. These include the formationand impacts of preferential trade areas, the political economy underlying the selection ofdomestic and international trade policies, and the role of multilateralism in trade agreements.

3Appendices to the book are motivated by a widespread frustration with the limitations ofanalytical techniques for all but extremely simple general-equilibrium models. Many bookspresent analytical theory under the assumption of two goods, two countries, two factors, and zerotrade costs. In the case of industrial-organization models, there are often only one factor, a zeroincome elasticity of demand for the increasing-returns sector, and various partial-equilibriumassumptions. Empirical researchers take these simple approaches and apply their insights tomulti-good, multi-country, multi-factor trade data generated in a world with multiple tariffs,transport costs, non-tariff barriers, and a host of domestic distortions. It is not always clear thatthe simpler theoretical specifications are consistent with such complex data generation.Because of this tension and especially because of the limitations of analytical theory, wehave decided to include some brief appendices outlining the techniques for the numericalsimulation of theoretical models, but do not feel that we should extend this into the calibration ofmodels to actual data for policy-analysis experiments. Markusen has had long experience withteaching these techniques, and feels that he can open up a world of possibilities for students in arelatively sparse number of pages. Professors, if they wish, can make assignment to students touse these simple models to run counter-factual experiments (e.g., trade liberalization) andinterpret the results in light of theory.

NotationWe have worked to make the notation consistent throughout the book and common to allchapters. This is not an easy task and we went through a number of iterations trying to achieveconsistency and avoid conflicts. Often, we had to begin anew when a plan arrived at a possibleconfusion such as the use of same letter to denote a variable and an index, even though this is nottechnically an inconsistency. For example, it is common to use “C” (upper case, lower case,subscript, superscript) to denote “consumption”, “country” and “cost”, something we very muchwant to avoid. While many letters of the Roman and Greek alphabet are not drafted into service,we worked from the principle that notation should be intuitive if possible or at least not counterintuitive and consistent if possible with common practice.In the end and largely in pursuit of generality, we abandon some of the “classic” notationthat many professors grew up on if not actually love. Instead of goods X and Y and factors ofproduction K and L with prices r and w, we have chosen to adopt more general notation thatpermits us to refer to an arbitrary good, factor or price. This is much more convenient whensumming over sectors and inputs as in, for example, a gains-from-trade proof and it permitsimmediate generalization to more than two goods and factors.The approach we adopt is similar to that taken in more “modern classics” such as Dixitand Norman (1980) and Woodland (1980). When we teach from the book, we use our lecturesrather than the book to inject specific examples to add concrete relevance to the general cases ofthe book, such as translating factors V1 and V2 into capital and labor, or skilled and unskilledlabor.We can now list our general approach, and then turn to the specifics. We do not suggestthat students read through this now, but we hope that it offers a convenient location to allow areader to refer back to when he or she forgets the notation later on.(1) In general, quantities are denoted with upper-case letters, and prices and costs aredenoted with lower-case letters. Taxes and subsidies are also denoted with lower-case letters.In the two-good case, lower case letters are also used to refer to ratios in order to economize onnotation, especially in labeling graphs (this is an element of the “classic” notation).(2) Subscripts can be used to denote or index (a) a specific good or factor of production,(b) a specific country. Double subscripts are common, but when it is perfectly clear, onesubscript may be dropped in order to economize on notation.(3) A superscript is used to denote a specific equilibrium value of a variable, such as itsautarky or free-trade value.(4) Italics are used for variables.(5) Greek letters are used to denote parameters, such as technology parameters.

h, fcountries or regions: home (h) and foreign (f), often used as subscripts on quantityor price variables. Occasionally, subscript r (region) give the general reference, r h, fXigoods or services: i 1,.,n; a specific good is denoted by a number; e.g., X1, X2Xi:Di:Mi:Ei:production quantity of Xiconsumption (demand) quantity of Xiimports or excess demand (Di - Xi) for Xi(N.B., Mj is negative when good j is exported)exports or excess supply (Xi - Di) for Xisometimes also used with a country/region subscript; e.g., Mhi , Mfi imports ofgood i by country/region h or f.X, D, Mwith no commodity subscript, these denote production and consumption vectorsor bundles; e.g., X {X1,., Xn}, D {D1,.,Dn} (typically used to label graphs)sometimes used with a country/region subscript; e.g., Xh, XfVjfactors of production such as capital (K), labor (L), other (S) such as skilled labor,land or natural resources, subscript is a number: j 1,.,m.sometimes used with a specific-good subscript: Vij is the use of factor j in good iVwith no factor subscript, this denotes a vector of all factors of production; e.g., V {V1,., Vm}.sometimes used with a country subscript; e.g., Vh, Vf, to denote a country’sendowment (total supply) vector. These are general fixed (in inelastic supply).in the two-good case, a lower-case v may be used to refer to the ratio of V1 to V2,as in the capital-labor ratio of the classic approach; e.g., v V1/V2, vh Vh1/Vh2 .Uutility or welfare, often used with a country subscript superscript; e.g.,in country/region r., utility

e supercriptdenotes a specific equilibrium, such as e a (autarky), e * (free trade), e t(tariff- restricted) or e s (subsidized trade). Examples:autarky utility in country/region cvector of production in free trade in country/region cgood i’s use of factor j under tariff protectionworld price of Xidomestic price of good Xi in country or region r in equilibrium e; e.g.,is theautarky price of good i in region h.with no commodity subscript, p is a vector of goods prices: p {p1,.,pn}sometimes used with a country subscript and/or a specific equilibrium superscript;e.g.,is the vector of autarky commodity prices in region r.in the two-good case, p will denote the relative price of good 1 in terms of good 2:e.g.,used to denote consumer price of Xi and price of Xi in country r in situationswhere taxes or subsidies make consumer and producer prices unequal. In thetwo-good case, q is the relative price of good 1 in terms of good 2: q q1/q2.price of factor Vi, vector of factor prices.sometimes used with a country and/or equilibrium subscript: e.g.,is theautarky price of factor V1 in country r.in the two-good case, w will denote the relative price of factor 1 in terms of factor2:e.g.,cost of producing good i as a function of factor prices.

F(.)denotes a function of the variables and/or parameters within parenthesis; e.g.,is read X1 is a function of the amounts of V1 and V2 used inX1 production and the parameter ". F may carry a sector (industry) subscript.MRSmarginal rate substitution:in the case of utility, it is the slope of an indifference curve between two goodsin the case of production, it is the slope of an isoquant between two factorsMRTmarginal rate of transformation: the slope of the production possibilities frontierin the two-good case.PPFproduction possibilities frontier (two-good case)mrimarginal revenue of an individual firm in industry itcitotal cost of an individual firm in industry i (just ci in competitive models).mcimarginal cost of an individual firm in industry ifcifixed cost of an individual firm in industry iREFERENCESDixit, Avinash K. and Victor Norman (1980), Theory of International Trade, Cambridge:Cambridge University Press.Woodland, Alan, D. (1982), International Trade and Resource Allocation, Amsterdam: NorthHolland.

PART ONETECHNICAL CONCEPTS AND THE GAINS FROM TRADECopyright 2009, James R. Markusen and Keith E. Maskus. No part of this work may bereproduced without written permission of the authors.

Chapter 1GLOBALIZATION AND INTERNATIONAL TRADE1.1IntroductionWe live in a world that is highly interconnected by a bewildering array of complex economictransactions, social and environmental problems, and international political collaborations and conflicts.Examples from global economics are found in the news everyday. A decision by American policymakersto subsidize the production of ethanol, a form of gasoline containing an additive produced from corn, isseen by many as a key reason that grain prices are high around the world. The spectacular emergence ofChina as a major exporter of manufactured goods has affected wages in both rich and poor countries. Aslarge corporations, such as Microsoft, Intel, Toyota, General Electric, and Siemens have expanded theirinvestments in affiliates in many nations around the world, they have built global production networksthat share technological knowledge across locations to produce increasingly complex goods that could besold anywhere. Today, a major cultural product, such as a Hollywood movie or a jazz band’s latestcompact disk, is likely to employ creative personnel from around the world, with various components ofthe product recorded, mixed or edited in different locations.The importance of international connections in trade, investment, and skilled services can beillustrated by considering the apparently simple act of making and bringing to market an item of apparel,say a fashionable woolen men’s suit. The initial task is to design the suit, a highly creative activity thatgenerally takes place in the headquarters of a major fashion label, such as Armani or Hugo Boss. Beyondthat, the firm must locate reliable suppliers of raw wool, which could be farmers in New Zealand,Argentina, Scotland, or elsewhere. The wool needs to be spun into yarn and then woven into finishedfabrics, tasks that are likely to be done in low-wage economies with abundant labor, such as Vietnam orBangladesh, both major centers of fabric manufacture. The fabrics then are shipped to locations wherethey are combined with such other materials as buttons and zippers into high-quality sewn garments.These locations are most likely to be in somewhat higher-productivity economies, such as China,Malaysia or Mexico and the firms involved typically work as independent sub-contractors to manyretailers rather than affiliates of one. The garments are then shipped to brand-name apparel companies,who sell them to high-end department stores and specialty retailers, and to generic trading companies thatmay ultimately sell them in discount or outlet stores.This simple story illustrates a number of key factors in global trade and investment. The brandname firms generally do not engage in actual production. Rather, their role is to design products that willentice consumers to pay for quality and fashion. Indeed, they are rarely involved in managing theinternational supply chain because their focus is on original design. Thus, there are specializedoutsourcing firms that take on this supply management task, becoming an important middle actor in theact of getting suits from raw wool to consumer apparel. One prominent example is Li & Fung Limited, aHong Kong-based sourcing company with offices in dozens of rich and poor countries and globalrevenues in 2008 of more than 14 billion.1 Its business is to work with thousands of sub-contractorsacross the world in many industries to have products assembled according to the originating firms’1See Gereffi and Memedovic (2003) for a primer on global production chains in apparel, whilethe Li & Fung company is described at http://www.lifung.com/eng/business/service chain.php.1

2specifications. As such, it is an excellent example of a multinational enterprise, even if unfamiliar to mostAmericans, Canadians and Europeans. Finally, there are several international trade flows described inthis example, with wool moving from New Zealand to Vietnam, yarn moving from Vietnam to Mexico,and garments being transported from Mexico to the United States and Canada for final purchase.This textbook explains the fundamental determinants and impacts of this extensive internationalorganization of economic activities into trade, investment, outsourcing, and the global use of knowledge.To begin this journey, consider how modern-day globalization came about.1.2Sources of GlobalizationThe concept of globalization has numerous definitions, depending on the subject matter beingexplained. To international economists it has a simple definition, albeit one with powerful implications.Specifically, globalization occurs when the markets of different countries become more integrated andinterconnected through economic transactions that cross national borders. These transactions can be inreal merchandise, various forms of services, financial instruments, investments in local productionfacilities by multinational firms (a process called foreign direct investment, or FDI), temporary andpermanent labor migration, and technological information. They can involve individuals, trade betweenunrelated firms, transactions within international enterprises, and governments. What drives thesetransactions and how they are organized is endlessly fascinating, and the subject of this book.It is useful to distinguish among the sources of globalization, the channels through whichtransactions occur, and the effects such integration seems to have on national economies. Consider firstthe sources: what causes economies to become more integrated over time? Economists generally focus onthree major factors, all of which have been important in spurring more interconnected

13.2 Trade costs and trade volumes in competitive, comparative-advantage models 13.3 Trade costs, prices discrimination, and trade volumes in oligopoly models 13.4 Trade costs, inter and intra-industry trade in monopolistic-competition models 13.5 The core-periphery model 13.6 Heterogeneous firms and firm-level export behavior 13.7 The gravity .

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