Geography, Technology, and Optimal Trade Policy with Heterogeneous Firms

Transcription

1 Geography, Tehnoogy, and Optima Trade Poiy with Heterogeneous Firms Antonea Noo, Università de Saento Gianmaro I.P. Ottaviano, LSE, University of Boogna, CEP and CEPR atteo Sato, European Commission This version: Deember 25 PRELIINARY AND INCOPLETE DRAFT DO NOT CITE WITHOUT AUTHORS PERISSION Abstrat How shoud mutiatera trade poiy be designed in a word in whih ountries differ in terms of tehnoogy and geography, and firms with market power differ in terms of produtivity? To answer this question we deveop a normative anaysis of the mode by eitz and Ottaviano 28 in the ase of an arbitrary number of asymmetri ountries. We first take the viewpoint of a goba panner maximizing goba wefare onstrained ony by tehnoogy and endowments. We haraterize the orresponding first best aoation in terms of ross-ountry speiaization, trade patterns, firm produtivity distribution and produt variety. We show how the first best aoation departs from the free market equiibrium aong a four dimensions, pinning down the poiy toos needed for its deentraization. As these toos are hardy enshrined in any rea mutiatera trade agreement, we then study aternative senarios, in whih the set of avaiabe poiy toos is inreasingy restrited. Keywords: internationa trade, trade poiy, monopoisti ompetition, heterogeneity, seetion, wefare. J.E.L. Cassifiation: D4, D6, F, L, L. Noo: University of Saento, Department of anagement, Eonomis, athematis and Statistis, Eotekne, via onteroni, 73, Lee, ITALY, antonea.noo@unisaento.it. Ottaviano: London Shoo of Eonomis, Department for Eonomis, Houghton Street, WC2A 2AE, UK, g.i.ottaviano@se.a.uk. Sato: European Commission, Rue de a Loi 2, B- 49, BELGIU, matteo.sato@e.europa.eu. We are gratefu to partiipants at the seminar of the Center of théorie éonomique, modéisation et appiations THEA of the Université Cergy- Pontoise, the XX DEGIT Conferene Graduate Institute Geneva, Université de Genève, 3-4 September 25 and the ETSG Conferene 25 Université Paris Panthéon-Sorbonne, - 2 September 25, for usefu omments and suggestions. The views expressed here are those of the authors and do not represent in any manner the EU Commission.

2 Introdution How shoud mutiatera trade poiy be designed in a word in whih ountries differ in terms of tehnoogy and geography, and firms with market power differ in terms of produtivity? Shoud poiy toos differ in kind or impementation between more and ess deveoped ountries? Shoud smaer ess produtive firms be proteted against arger more produtive foreign rivas? Shoud nationa produt diversity be defended against ompetition from heaper imported produts? What is the optima degree of produt diversity on a goba sae? To answer these and other reated questions we propose a normative anaysis of the monopoisti ompetition mode by eitz and Ottaviano 28. This mode exhibits severa features usefu for our purposes. As even with heterogenous firms it is anaytiay sovabe with a sorts of asymmetries in ountry size, tehnoogy and aessibiity, the mode aows for transparent omparative statis. As it features variabe markups, it aows for firm heterogeneity to beome a key soure of misaoation. As inome effets are neutraized due to quasi-inear preferenes, onstant margina utiity of inome aows for a onsistent goba wefare anaysis based on a straightforward definition of goba wefare for an eonomy with heterogeneous ountries as the sum of a individuas indiret utiities. Whie the absene of inome effets gives our resuts a partia equiibrium favor, this approah shares the fous on soia surpus with mainstream poiy anaysis. eitz and Ottaviano 28 mode an eonomy in whih ountries differ in terms of market size, barriers to internationa trade and state of tehnoogy. Countries are ative in two setors with abor as the ony prodution fator. A traditiona perfety ompetitive setor suppies a freey traded homogeneous good. A modern monopoistiay ompetitive setor suppies varieties of a horizontay differentiated good. In eah ountry the produtivity of entrants in the modern setor is dispersed around a ountry-speifi mean ditated by the nationa state of tehnoogy, whih thus defines the ountry s omparative advantage in the modern setor with respet to the other ountries. oreover, in the modern setor ountries fae different physia transport osts for their internationa and domesti trade as ditated by geography. In equiibrium tehnoogy and geography endogenousy determine a ountry s intersetora speiaization as we as its patterns of inter- and intra-industry trade. They aso determine the produtivity distribution of a ountry s modern produers as we as the number and the pries of varieties the ountry s onsumers have aess to and the dimension of the differentiated good setor in eah ountry. eitz and Ottaviano 28 do not provide any normative anaysis of their mode. The aim of this paper is to show that fiing this gap yieds new insights on optima mutiatera trade poiy. In partiuar, we first take the viewpoint of a goba panner maximizing goba wefare onstrained ony by tehnoogy and endowments. We haraterize the orresponding first best aoation in terms of ross-ountry speiaization and firm produtivity distribution, trade patterns, size of the differentiated good setor and produt variety. We show how the first best aoation departs from the free market equiibrium aong a these dimensions, pinning down the poiy toos needed for its deentraization. These inude ountry-speifi ump-sum instruments for both firms and onsumers as See the disussion in Noo, Ottaviano and Sato 24. 2

3 we as prodution and onsumption subsidies and taxes differentiated aross firms both between and within ountries. As the wide array of poiy toos needed to deentraize the first best is hardy enshrined in any rea mutiatera trade agreement, we then study aternative mutiatera n-th best senarios, in whih the set of avaiabe poiy toos is inreasingy restrited. In the seond best, ump-sum instruments are sti avaiabe but subsidies and taxes an not be differentiated aross firms. In the third best, aso ump-sum instruments for firms are rued out. Finay, when aso ump-sum toos for onsumers are removed, the eonomy an not be drawn away from the free market equiibrium. Our anaysis speaks to two main iteratures. First, there is the iterature on optima trade poiy both under perfet ompetition see, e.g., the disussion in Costinot, Donadson, Voge and Werning, 24 and imperfet ompetition see, e.g., Grossman, 992. This iterature does not feature an arbitrary number of ountries and firms, and firm heterogeneity has been introdued ony reenty in modes that anayse the impat of non wastefu import tariffs that is, trade barriers that generate revenues in monopoistiay ompetitive setors. 2 In this ase, tariffs are either set uniateray by a ountry or in a non-ooperative framework in a setup that onsiders the ase of a sma open eonomy or that of two arge open eonomies. This iterature basiay expores the effets produed in a framework with heterogeneous firms by poiy intervention on the terms of trade i.e. a tariff produes an inrease in the domesti wage that reates an argument in favour of poiy intervention and/or on the monopoisti ompetition distortion i.e. a tariff on imports, or a subsidy on domesti saes, inreases the number of varieties that are offered in the market, where variety is ineffi ienty ow and, thus, orrets the entry distortion and, eventuay, aso the mark-up distortion. 3 Using the eitz and Ottaviano 28 mode, Bagwe and Lee 25 anayze trade poiies finding that in the ase of two symmetri ountries there is an inentive for a ountry to introdue a sma import tariff and they aso identify the onditions under whih two symmetri ountries have uniatera inentives to introdue beggar-thy-neighbor export subsidies. Considering the ase of symmetri trade poiies, they find that goba free trade is generay not effi ient. Within the same framework, Demidova 25 finds that the introdution of pro-ompetitive gains from trade due to variabe markups does not hange the reationship between the impat of uniatera trade iberaization on the wefare eve of the home ountry and the presene of an outside good: with a wastefu import tariff, a uniatera redution in trade tariff inreases wefare in the absene of an outside good both in the ase of two arge eonomies and in the ase of a sma home eonomy; with non wastefu import tariff, on the ontrary, in the absene of an outside good uniatera trade iberaization redues wefare at home in both ases. Our perspetive is, however, different from that 2 The resuts with homogeneous firms and monopoisti ompetition an be reaed making use of the words by Febermayr, Jung and Larh 23, p. 3 who write that: "f]irst, Fam and Hepman 987 show that tariffs orret for a mark-up distortion due to monopoy priing. Seond, Venabes 987 argues that a tariff an indue wefare-enhaning additiona entry. Third, as in other trade modes, there is a terms-of-trade rationae for import tariffs; see Gros The sma-ountry anaysis with one setor buit on the eitz 23 mode started by Demidova and Rodriguez-Caire 29 has been extended to onsider two arge ountries by Febermayr, Jung and Larh 23 or to introdue an outside good setor by Haaand and Venabes 25. 3

4 taken in a these works, as we anayze the "goba" wefare properties of the eitz and Ottaviano 28 mode identifying the ineffi ienies of the market outome and showing how the different n-th best aoations an be attained with different set of poiy instruments. Seond, there is the iterature on optima produt variety without firms heterogeneity Spene, 976, and Dixit and Stigitz, 977 and with firm heterogeneity Dhingra and orrow, 22; eitz and Redding, This iterature fouses on the osed eonomy or open eonomies in whih ountries are symmetri. 5 The rest of the paper is organized as foows. Setion 2 presents the market equiibrium in the mode by eitz and Ottaviano 28 for the ase of trading open eonomies and derives the optimum soutions for the first best panner. Setion 3 anayzes the distortions in the market equiibrium both in the ase of symmetri and asymmetri ountries and disusses the effets on these distortions of an inrease in the number of trading ountries due to gobaization, an enargement of the dimension of the home market size due to demographi growth, an improvement in the tehnoogies of prodution stemming from deveopment and a redution in trade barriers due to proesses of eonomi internationa integration. Setion 4 presents the optima soutions for aternative n-th best panners omparing the main resuts they deiver in terms of seetion, average firms suppy, produt variety, number of domesti and exported varieties and overa size of the differentiated good setor in eah ountry. Setion 5 anayzes how these optima soutions an be impemented by means of appropriate sets of poiy instruments, and Setion 6 onudes. 2 The mode In this Setion we present the mode with trading ountries in order to understand how the distortions in the market equiibrium with respet to that set by a first best goba panner are affeted by the number of trading ountries and the trade barriers they fae, by the dimension of the home market size of eah ountry and by the eve of deveopment of the tehnoogy avaiabe within eah ountry. We set the anaysis in a framework that is that of the traditiona iterature on optimum produt diversity with monopoisti ompetition enrihed by firm heterogeneity in produtivity eves in whih the market an potentiay misaoate resoures not ony within the monopoistiay ompetitive setor but aso between this setor and the rest of the eonomy. This aows us aso to use omparative stati anaysis to evauate how inreases in the number of trading ountries gobaization, in the dimension of eah ountry market size, in the state of deveopment of the eve of tehnoogy avaiabe within eah ountry deveopment, and redutions in trade barriers internationa integration affet the intensity of market distortions. 4 In a osed eonomy setup, Noo, Ottaviano and Sato 23 offer a systemati quantitative anaysis of the impat of different degrees of firm heterogeneity on the extent of market ineffi ienies, and Noo, Ottaviano and Sato 24 provide a disussion of deentraization of the first best outome and of a onstrained soution for a panner that an ony rey on ump-sum toos on onsumers and who an not impose ump-sum taxes/subsidies on firms. 5 See Noo, Ottaviano and Sato 23 for an anaysis of the main deveopments in the iterature of optimum produt diversity with monopoisti ompetition. 4

5 Foowing eitz and Ottaviano 28, we onsider the ase in whih eah ountry, indexed by =,...,, is popuated by L onsumers, eah endowed with one unit of abor. Preferenes of onsumers in are defined over a ontinuum of differentiated varieties avaiabe in that are indexed by i Ω, and a homogeneous good indexed by. A onsumers in indexed ε share the same utiity funtion given by U = q ε + α q ε i di i Ω 2 γ q ε i 2 di 2 i Ω 2 η q ε i di i Ω with positive demand parameters α, η and γ, the atter measuring an inverse measure of the ove for variety as it represents the degree of produt differentiation, and the others measuring the preferene for the differentiated varieties with respet to the homogeneous good. ore preisey, α represents the intensity of preferenes for the differentiated good reative to the homogeneous good and η represents the degree of nonseparabiity aross the differentiated varieties. The initia individua endowment q of the homogeneous good is assumed to be arge enough for its onsumption to be strity positive in eah ountry at the market equiibrium and optima soutions. Labor is the ony fator of prodution. It is empoyed for the prodution of the homogeneous good under onstant returns to sae with unit abor requirement equa to one. It is aso empoyed for the prodution of the differentiated varieties. The tehnoogy requires a preiminary R&D effort of f > units of abor in ountry to design a new variety and its prodution proess, whih is aso haraterized by onstant returns to sae. The R&D effort annot be reovered resuting in a sunk setup entry ost. The R&D effort eads to the design of a new variety with ertainty whereas the unit abor requirement of the orresponding prodution proess is unertain, being randomy drawn from a ontinuous distribution with umuative density G = k,, ] 2 This orresponds to the empiriay reevant ase in whih margina produtivity / is Pareto distributed with shape parameter k over the support /, for ountry. Hene, as k rises, density is skewed towards the upper bound of the support of G. Notie that the sae parameter determines the eve of rihness, defined as the measure of different unit abor requirements that an be drawn within a ountry. Larger eads to a rise in heterogeneity aong the rihness dimension and to a redution in the omparative advantage of ountry as it beomes possibe to draw aso arger unit abor requirements than the origina ones. The shape parameter k is an inverse measure of evenness, that is of the simiarity between the probabiities of different draws of to happen. When k =, the unit abor requirement distribution is uniform on, ] with maximum evenness. 6 As k dereases, the unit abor requirement distribution beomes ess onentrated at higher unit abor requirements ose to and evenness inreases eading to a rise in heterogeneity aong this dimension making 6 When k tends to infinity, the distribution beomes degenerate at deivering a unit abor requirement with probabiity one. with a draws 5

6 ow unit abor requirements more ikey. Aordingy, more rihness arger omes with higher average unit abor requirement ost-inreasing rihness, more evenness smaer k omes with ower average unit abor requirement ost-dereasing evenness. Countries are aowed to potentiay differ not ony in their size L, but aso in terms of their tehnoogy with ountry having a omparative advantage disadvantage with respet to ountry h =,..., in the differentiated good setor if is smaer arger than h, and differenes aowed aso in the f units of abor required for the preiminary R&D effort in ountry. oreover, differentiated varieties are traded at an ieberg trade ost that an differ both aross and within ountries. Speifiay, we assume that τ h units of the good have to be produed and shipped from the prodution ountry to se one unit in the destination ountry h, and ρ h τ h k, ] measures the freeness of trade for exports from to h. As within ountry trade may not be ostess due to domesti trade osts τ, we assume that ρ τ k, ]. The homogenous good is, instead, assumed to be freey traded. Given that we aow for a potentiay asymmetri muti-ountry framework, we wi try to understand how the differenes in terms of the dimension of the domesti market home market effet, of tehnoogy and omparative advantage deveopment and market aess due to trade barriers geography and number of trading ountries gobaization affet the intensity of market distortions. 2. arket equiibrium and first best optimum We present now the free market equiibrium and then the aoation of the resoures determined by a first best goba panner maximizing goba wefare onstrained ony by tehnoogy and endowments. 2.. The market outome In the deentraized equiibrium, within eah ountry, onsumers maximize utiity under their budget onstraints, firms maximize profits given their tehnoogia onstraints, and a markets ear. It is assumed that the abor market as we as the market of the homogeneous good are perfety ompetitive. The homogeneous good is hosen as numeraire and this, together with its prodution tehnoogy and the fat that it is freey traded, impies that the wage of workers equas one in a ountries. The market of differentiated varieties is, instead, monopoistiay ompetitive with a one-to-one reation between firms and varieties and onsumers buy both oay produed and imported varieties. The first order onditions for utiity maximization give individua inverse demand for variety i in as p i = α γq ε i ηq ε 3 whenever q ε i >, with p i denoting the prie of variety i in, and Q ε = q ε i Ω i di representing the individua aggregate demand in of differentiated varieties. Aggregate demand for eah variety i in ountry an be derived from 3 as q i L q ε i = αl ηn + γ L γ p i + ηn L ηn + γ γ p, i Ω 4 6

7 where the set Ω is the argest subset of Ω suh that demand in is positive, N is the measure number of varieties in Ω, that is given by the sum of domesti and imported varieties sod in, and p = /N p i Ω i di is their average prie. Variety i beongs to this set when p i ηn + γ γα + ηn p p max 5 where p max α represents the prie at whih demand for a variety in is driven to zero. 7 The aggregate onsumption in ountry h of a variety that is produed in with produtivity / is q h = q ε hl h where qh ε is the individua onsumption of that variety. Note that when two suffi xes are used, the first one denotes the prodution ountry whie the seond one the ountry in whih the good is onsumed. The quantity q h is obtained by max π h = p h τ h ] q h q h subjet to its aggregate inverse demand in h, that is p h = α γ L h q h η L h Qm h where m abes equiibrium variabes and Q m h j= N j j E q jh dg j represents the tota suppy of differentiated varieties avaiabe in the market in ountry h with N j E denoting the number of firms entering in ountry j. The orresponding first order onditions for profit maximization are satisfied by { qh m L h = 2γ τ h m h if m h ph max = τ h τ α η Q m h L h h 6 if > m h Expression 6 defines a utoff rue as ony entrants in ountry that are produtive enough m h se their variety in ountry h. For them, the prie set in h that orresponds to the profit-maximizing quantity qh m is p m h = τ h m h + /2, impying a markup on saes in h equa to µm h = p m h τ h = τ h m h /2 and maximized profits are given by π h = Lh τ h 2 m 4γ h 2 7 Notie that saes in the domesti market an be obtained onsidering h =. In this ase, the domesti utoff m is aso denoted by m D. 7 eitz and Ottaviano 28 show that rewriting the indiret utiity funtion in terms of average prie and prie variane reveas that it dereases with average pries p, but rises with the variane of pries σ 2 p hoding p onstant, as onsumers then re-optimize their purhases by shifting expenditures towards ower pried varieties as we as the numeraire good. Note aso that the demand system exhibits ove of variety : hoding the distribution of pries onstant namey hoding the mean p and variane σ 2 p of pries onstant, utiity rises with produt variety N. 7

8 Expression 6 impies that for a margina firms seing in h we have τ h m h = τ hh m D h = p h max. Hene, the reationship among utoffs for firms seing in h is suh that m h = τ hh τ h m Dh, h =,..., 8 Due to free entry and exit ondition, in equiibrium expeted profit of firms produing in is exaty offset by the sunk entry ost f and, therefore, { m h } L h τ h 2 m 4γ h 2 dg = f 9 Given 2, 7 and 8, the free entry ondition an be rewritten as L h ρ h τ hh m hh = 2γ k + 2 k + k f This expression, together with the anaogous expressions hoding for a other ountries, yieds a system of equations that, making use of Cramer s rue, an be soved for the equiibrium domesti utoffs given by m D = τ 2γ k + k + 2 L f ] h h k Ch P =,..., where P is the determinant of the trade freeness matrix ρ ρ 2 ρ ρ 2 ρ 22 ρ 2 P =... ρ ρ 2 ρ and C h is the ofator of its ρ h eement. 8 In genera, the tota number of varieties onsumed in ountry is given by the sum of domesti and of imported varieties from a trading partners. Speifiay, the number of varieties produed in h and onsumed in is derived from the seetion onditions and is given by N h = N h EG h h 2 The tota number of varieties onsumed in ountry N is N = N h 3 8 Notie that f h h ] k Ch > =,..., has to be satisfied aso to have a positive prodution for domesti onsumers in a ountries for the market soution. 8

9 Given 2, 2 and 8, produt variety N in 3 an be rewritten in the ase of the market equiibrium as foows N m = τ m k k D ρ h N h E 4 oreover, as the average prie in ountry is h p m = 2k + 2 k + τ m D, 5 it an be ombined with the prie threshod in 5 to express the number of varieties sod in in the market equiibrium as N m 2γ k + α τ m D = η τ m 6 D Hene, N m in 6 an be equaized to N m in 4 to get ρ h NE h h k = 2γ k + α τ m D η τ m k+ D This gives a system of inear equations that using Cramer s rue an be soved for the number of entrants in the ountries 2γ k + ] k α τ hh m D h k+ C h NE m τ hh mdh = =,..., 7 η P whih, as the domesti utoffs in and the utoffs for exporting firms derived making use of 8, is affeted by parameters determining the tehnoogy of prodution avaiabe in eah ountry and by omparative advantage, as we as by the market size of eah ountry, the number of trading ountries and the eve of trade osts The first best optimum Let us now onsider the probem faed by a soia panner who an aoate the resoures avaiabe within eah ountry to design a speifi number of new varieties, with the orresponding unit abor requirement unertain, and to the prodution of ony a speifi subset of these potentiay avaiabe varieties together with the homogenous good. The quasi-inearity of impies transferabe utiity. Thus, soia wefare may be expressed as the sum of a onsumers utiities in a ountries. This impies that the first best unonstrained panner hooses the number of varieties and their output eves so as to maximize the tota soia wefare funtion 9 Notie that in the exampe of two trading ountries with no interna trade osts and ommon sunk entry ost f that wi be presented ater on in Setion 5.., the onditions that have to be satisfied to have positive vaues for both NE m and N 2m E, impy that m 2 < m D and m 2 < m D 2, so that ony a subset of reativey more produtive firms export in the market. 9

10 given by the sum of aggregate utiity of a ountries obtained for eah ountry mutipying individua utiity in for the number of onsumers L. This maximization is subjet to the resoure onstraints, the varieties prodution funtions and the stohasti innovation prodution funtion i.e. the mehanism that determines eah variety s unit abor requirement as a random draw from G after f units of abor have been aoated to R&D that hod for a ountries. In other words, the panner maximizes the utiity derived by a onsumers iving in the ountries from the onsumption of the homogeneous good and of the differentiated varieties that are both those domestiay produed and those imported. Speifiay, the utiity of a L workers iving in ountry is given by W L = q ε L + α γ 2 η 2 L L N h E { N h E N h E h h h q ε hl dg h q ε h L ] 2 dg h ] ] q ε hl dg h ]} 2, Thus, the panner maximizes the goba utiity whih is given by { ]} h W = W L = ql ε + α qhl ε dg h 9 + { γ 2 L η 2 L N h E N h E h h N h E q ε h L ] 2 dg h q ε hl dg h ]} + ] 2 with respet to onsumption of the homogeneous goods in eah ountry, the quantities produed for onsumption in a ountries by a firms in the differentiated good setor and the number of entrants in a ountries, subjet to the resoure onstraints, the firm prodution funtions and the stohasti variety prodution funtion expressed in the seetion onditions 2 that hod for a ountries. From the resoure onstraint of ountry, the suppy of the homogenous good in ountry is given by ] Q = q L + L f NE NE τ h qhl ε h dg 2 This impies that the suppy of the homogeneous good in ountry Q is given by the sum of tota oa endowments of the good q L and its oa prodution obtained empoying abour units oay avaiabe L one subtrated those empoyed, respetivey, to undertake the oa R&D investment f NE and to

11 produe the differentiated varieties sod in the oa and in the foreign ountries NE ] τ h q ε h Lh dg. The ondition that the goba suppy of the homogenous good is equa to its goba demand requires that Q = ql ε 2 whih, making use of 2, impies { ]} ql ε = q L + L f NE NE τ h qhl ε h dg 22 Substituting 22 into 9, and making use of q h = q ε h Lh, the panner maximizes W = = W L = 23 { ]} q L + L f NE NE τ h q h dg + +α { N h E { γ 2 L η 2 L h N h E N h E q h dg h h h ]} + q h ] 2 dg h q h dg h ]} + ] 2 with respet to the quantities produed for a markets by a firms and the number of entrants in a ountries, that is with respet to q ij and N i E with i, j =,...,. The first order onditions obtained for the quantity of a variety produed with produtivity / in ountry i and onsumed in j is W q ij = { α τ ij NE i γ L j N Eq i ij η L j N h E h q hj dg h ] N i E } dg i = ore preisey, in addition to the first order onditions written with respet to q ij and NE i, the first best panner shoud aso onsider the first order ondition with respet to the utoffs. However, making use of the Pareto distribution in 2, it an be shown that the first order onditions with respet to the utoffs beomes redundant beause they identify the same utoffs as those derived from the first order ondition with respet to q ij given in expression 24.

12 that making use of the tota quantity onsumed in ountry j, that is Q o j NE h h q hj dg h, an be rewritten as α τ ij γ L j q ij η L j Qo j = Hene, for quantities produed in to be onsumed in h the panner foows the rue { qh o L h = γ τ h o h o h with o h τ α η Q o h L h h > o 24 h where o abes first best optimum variabes. Resuts in 24 revea that, just ike the market, aso the panner foows utoff rues, one for eah ountry, aowing ony for the prodution in ountry for onsumption in ountry h of those varieties whose unit abor requirements are ow enough with o h. It an be readiy verified from 24 that the first best output eves woud ear the market in the deentraized senario ony if eah produer in pried the quantities sod in h at its own margina ost, that is ony if p h = τ h. Indeed, from the inverse demand funtion, we know that p h = α γ q L h h η Q o L h h = τ h o h γ q L h h that, together with p h = τ h, impies q h = L h γ τ h o h. The definitions of the utoffs in 24 impy that the reationships between the optima utoffs for a margina firms seing in h are suh that o h = τ hh τ h o Dh, h =,..., 25 whih are the same as those for the market equiibrium in 8, even though the utoffs are different. Therefore, we an state that Proposition Prinipe of no disrimination There is no disrimination of the first best panner with respet to the market equiibrium in favour of domesti or imported varieties. The utoffs of the unonstrained panner are derived in Appendix A from the first order onditions for the maximization of 23 with respet to the number of entrants in eah ountry i that is from W = and are given by NE i o D = τ Notie that γ k + k + 2 L f ] h h k Ch P =,..., 26 f ] h h k Ch > =,..., has to be satisfied aso to have a positive prodution for domesti onsumers in a ountries for the first best soution. 2

13 In Appendix A we derive aso the optima number of entrants in eah ountry as a funtion of the utoffs, that is γ k + ] k α τ hh o D h k+ C h NE o τ hh odh = =,..., 27 η P Finay, making use of 2, for eah ountry the optima number of domesti varieties is N o D = G o D N o E and the optima number of exported varieties to ountry h is N o X = G o o h h NE. 3 Equiibrium vs. optimum There are different dimensions aong whih the effi ieny of the market outome an be evauated, suh as: the onditiona ost distribution of firms produing and exporting the different varieties as ditated by the utoff m h and the number of varieties avaiabe for onsumption in eah ountry produt variety. In turn, the ost distributions determine the effi ieny of the orresponding distributions of firm sizes, domesti prodution and exports. oreover, it ontributes in determining the effi ieny of the overa dimension of the differentiated goods setor in the market of eah ountry i.e. tota suppy of differentiated varieties, the mass number of firms that undertake the initia R&D effort entering in eah market, and the number of firms that survive produing the differentiated varieties for the domesti and the foreign onsumers. At the origins of the ineffi ienies of the market equiibrium is the fat that onsumers in eah ountry vaue variety and monopoistiay ompetitive firms heterogeneous in their produtivity eves are prie setters. Setting their prie for eah oaity with a markup over their margina ost, firms redue the average quantity that onsumers buy within eah of these oations with respet to the average quantity that they woud have purhased if differentiated varieties had been sod at their margina ost. 2 As shown in the ast part of Appendix A, most of the evauations in terms of effi ieny of the market outome an be obtained for the genera ase of asymmetri ountries. In this Setion, we use the resuts derived in Appendix A to ompare the equiibrium outome with the optima unonstrained soution aong different dimensions suh as: seetion proesses that identify firms that survive produing for domesti and foreign onsumers; individua and overa average size of firms in the differentiated good setor; produt variety avaiabe for onsumption and entry of innovating firms in eah ountry. These resuts are first presented in the ase of symmetri trading ountries faing no interna trade osts and, then, in the ase in whih ountries differ in terms of the size of their domesti market L, tehnoogy that defines their omparative Notie that in the ase of two ountries with no interna trade osts and ommon sunk entry ost f onsidered in Setion 5.., the onditions that have to be satisfied to have positive vaues for both NE o and N 2o E, impy that o 2 < o D and o 2 < o D 2, so that in eah ountry ony a subset of reativey more produtive firms export in the optima soution. 2 The tradeoffs the first best panner faes when firms are monopoistiay ompetitive and heterogeneous are disussed in Noo, Ottaviano and Sato 24 for the osed eonomy. Speifiay, see expression 8 at page 36 in Noo, Ottaviano and Sato 24 and the subsequent omments. 3

14 advantage and the f units of abor required for the preiminary R&D effort, and, finay, trade barriers τ h that identify their aessibiity in eah ountry/oaity. 3. The ase of symmetri ountries Let us first onsider the ase of perfety symmetri trading ountries without interna trade osts that is with τ = impying ρ = =,..., to evauate how the intensity of market distortions is affeted by different phenomena suh as: a proess of gobaization that inreases the number of trading ountries /; demographi growth and proesses that inrease the size of eah ountry L aowing to evauate home market effets ; internationa eonomi integration that redues trade barriers inreasing the freeness of trade ρ; improvements in the tehnoogy avaiabe within eah ountry deveopment that redue the highest ost draw or the entry/innovating ost f, or, eventuay, inrease the hanes of having a high produtivity draw reduing the shape parameter k. Rea that whie a smaer redues heterogeneity aong the ostrihness dimension impying ower average unit abor requirement, a smaer k inreases heterogeneity aong the evenness dimension reduing the average unit abor requirement. Notie that a the resuts disussed in the ase of symmetri ountries are onsistent with those of a osed eonomy, whih an be obtained with = and/or ρ =, presented in Noo, Ottaviano and Sato 23, Seetion and firm size In the ase of perfety symmetri ountries, 3 τ h = τ and ρ h = ρ, h =,..., impy P = + ρ] ρ and C h ] = ρ, and therefore the market equiibrium domesti utoffs in an be rewritten as { } 2γ k + k + 2 f m k D = 28 + ρ] L and the first best domesti utoffs in 26 as o D = { } γ k + k + 2 f k + ρ] L 29 Comparing the equiibrium domesti utoff in 28 with the optima one in 29 reveas that m D = 2/ o D, whih impies o D < m D. Aordingy, varieties with o D, m D ] shoud not be suppied in the domesti market. oreover, differenes in the strength of seetion transate aso into the export status. In partiuar, omparing expressions 28 with 29 together with 8 and 25, reveas that the utoffs for exporting firms denoted as X when ountries are symmetri are suh that m X = 2/ o X, whih impies o X < m X. Aordingy, varieties with o X, m X ] shoud not be exported or, equivaenty, ooking this phenomenon from the other side of the oin, shoud not be imported by other ountries. 3 Rea that in a this subsetion, we onsider the ase in whih there are no domesti trade osts. 4

15 The intuition behind the auses at the origin of these ineffi ienies is that, in the market equiibrium, firms are prie setters and a firm with margina ost produing in sets the prie for its variety sod in h with a markup over its margina ost that is equa to µ m h = τ h m h /2. This impies that the pries of differentiated varieties are ineffi ienty high within eah ountry with respet to the prie of the numeraire good and, onsequenty, this biases the onsumption in favor of the homogeneous good softening the seetion proess among the produers of the differentiated varieties. The resuts on optima seetion proesses have aso impiations in terms of optimaity of the firm size distribution of domesti and exporting firms. Adapting to the speifi ase of symmetri ountries the genera resuts derived in the fina part of Appendix A for asymmetri ountries, we find that, with respet to the optimum, the market equiibrium undersuppies varieties produed with margina ost, 2 2 / o D, and oversuppies varieties with margina ost 2 2 / o D, m D ] in the domesti ountries. oreover, in the market equiibrium firms export a quantity that is smaer than optima of varieties produed with margina ost, 2 2 / o X, and arger than optima of those produed with margina ost 2 2 / o X, m X ]. The intuition behind this an be expained by the fat that the markup µ m h is a dereasing funtion of and this impies that more produtive firms do not pass on their entire ost advantage to onsumers as they absorb part of it in the markup. As a resut, the prie ratio of ess to more produtive firms is smaer than their ost ratio and thus the quantities sod by ess produtive firms are too arge from an effi ieny point of view reative to those sod by more produtive firms. oreover, the utoff ranking impies that in the market not ony the average prodution of firms in eah ountry for any of their destination ountry is ineffi ienty ow as q m D < qo D and qm X < qo X, resuting in an ineffi ienty ow average firm size, but aso that the average quantity suppied by a, domesti and foreign, firms within eah ountry is smaer than optima as q m < q o. 4 The intuition behind this is that the ower utoff impied by margina ost priing foowed by the first best panner makes firms on average arger in the optimum than in the market equiibrium. Finay, the impiations of the resuts and omparative statis in Appendix A aow us to state that the perentage gap in the utoffs, in average firm size and in the average quantity suppied within eah ountry and the within setor misaoation that materiaizes as the overprovision of high ost varieties and underprovision of ow ost varieties are not affeted by any of the foowing proesses: gobaization that inreases the number of trading ountries /; demographi growth that inreases the home market size L of eah ountry; internationa integration that redues trade barriers inreasing ρ; deveopment that improves the tehnoogy avaiabe within eah ountry reduing and/or 4 Again, these resuts are obtained adapting the more genera ones for asymmetri ountries in 69, 7 and 7 presented in the ast part of Appendix A. Notie that when ountries are symmetri we avoid in the variabe the suffi x that denotes the ountry i.e. we use q m instead of q m h. 5

16 the entry ost f. Instead, more heterogeneity due to more ost-dereasing evenness, that is a smaer k that impies a higher hane of having high produtivity draws: eads to a arger perentage gap in the utoffs between the market equiibrium and the optimum; makes the overprovision of varieties reativey more ikey than its underprovision in the market equiibrium and dereases the perentage gap in the average prodution of firms in eah ountry for their domesti and foreign markets and in the average quantity suppied by a firms within eah ountry Size of the differentiated setor, produt variety and entry Adapting the genera resuts in 72 and 73 in Appendix A, we find that, aso in the speifi ase of symmetri ountries, o D < m D impies that the market misaoate resoures between setors as the tota suppy of differentiated varieties is smaer than optima in eah ountry that is, N m q m < N o q o. In this ase, the perentage gap in the tota output of differentiated varieties between the market equiibrium and the optimum is N o q o N m q m N o q o = m D o D o D o D α o D where m D o D /o D is ony affeted by k, whih, together with γ, L,, f and, affets aso o D / α o D. Speifiay, as arger vaues of the market size L, of the number of trading ountries and of the freeness of trade ρ, and smaer vaues of γ, f and derease o D / α o D, they impy smaer vaues for the ratio N o q o N m q m /N o q o. oreover, we find that there an exist a threshod vaue of k, k, 5 suh that more ost-dereasing evenness dereases the gap in the tota output of the differentiated varieties between the market equiibrium and the optimum if k > k and, vieversa, it inreases the gap if k < k. The threshod vaue k inreases with L,, ρ and, and dereases with γ and f. However, if L,, ρ and are suffi ienty sma and/or γ and f are suffi ienty arge, more ost-dereasing evenness does aways derease the gap. Consequenty, we an state what foows: Proposition 2 With symmetri ountries, the tota suppy of diff erentiated varieties in the market equiibrium is smaer than optima in a oations. This gap is smaer arger: in arger overa eonomies due to arger smaer home markets, more ess integrated ountries or to a arger smaer number of trading ountries, in more ess deveoped eonomies that benefit from better worse avaiabe tehnoogies, ower arger entry osts and higher smaer hanes of having ow ost firms, and in ountries in whih varieties are oser farther substitutes. ore ost-dereasing evenness dereases the gap if k > k and, vieversa, it inreases the gap if k < k. 5 ore preisey, more ost-dereasing ] evenness inreases the gap if 2 n 2 2k / k + / 2 + n k + k + 2] > n { + ρ] L 2 / γf} ; vieversa, it dereases the gap if the opposite inequaity sign hods. The threshod k orresponds ] to the vaue at whih the funtion 2 n 2 2k / k + / 2 + n k + k + 2, whih is inreasing in k, rosses n { + ρ] L 2 / γf}, and it exists ony if L,, ρ and are suffi ienty arge and/or γ and f are suffi ienty sma. 6

17 Hene, inreases in the overa size of the eonomy due to gobaization, demographi growth and eonomi integration and proesses of deveopment that redue or f, derease the perentage gap in the tota output of the differentiated varieties between the market equiibrium and the optimum. Turning to the mass number of varieties suppied respetivey in the domesti and in the foreign markets, they are, respetivey, given by N m D = 2γ k + α m D η + ρ] m D and NX m 2γ k + = ρ η + ρ] α m D m D 3 whie their optima vaues orrespond to N o D = γ k + α o D η + ρ] o D and NX o γ k + = ρ η + ρ] α o D o D 3 Comparing the number of domesti and exported varieties in 3 and 3, and overa produt variety avaiabe within eah ountry from 6 and 67, we find that m D = 2/ o D impies N D m > N D o, N X m > N X o and N m > N o as ong as α > α 2 k+ o D = 2 k+ { } γ k + k + 2 f k + ρ] L 32 whih is the ase when α as we as L, and ρ are arge and when γ,, f and k are sma. On the ontrary, N m D < N o D, N m X < N o X and N m < N o when α < α. Turning to entry, the equiibrium number of entrants in 7 an be rewritten in the ase of symmetri ountries as NE m = 2γ k + k α m D η + ρ] m D k+ whie that for the first best panner in 27 as N o E = γ k + k α o D η + ρ] o D k+ These an be used to show that m D = 2/ o D impies N m E α > α 2 22/ 2 / o D = 22/ 2 / > N E o as ong as { } γ k + k + 2 f k > α + ρ] L 33 whih is the ase when α as we as L, and ρ are arge and when γ,, f and k are sma. On the ontrary, N m E < N o E when α < α 2. In summary, we an state that Proposition 3 In the ase of symmetri ountries, entry, overa produt variety and the number of domesti and imported varieties are arger smaer in the market equiibrium than in the optimum when market size is arge sma, the number of trading ountries is arge sma, their eve of integration is high ow, varieties are ose far substitutes, the sunk entry ost is sma arge, the differene between the highest and the owest possibe ost draws is sma arge, and the hanes of having ow ost firms are arge sma. 7

18 This has interesting impiations for the impat of inreases in the overa dimension of the eonomy driven by different hannes suh as: internationa integration proesses that inreases ρ, gobaization proesses that inrease the number of trading ountries and/or demographi growth or other proesses that inrease the home market size. oreover, it has aso interesting impiations for the impat of eonomi deveopment that redue the highest ost draw or the entry/innovating ost f, or, eventuay, inrease the hanes of having a high produtivity draw reduing the shape parameter k. Indeed, starting from suffi ienty sma eves of the overa size of the eonomy and/or eves of deveopment of the tehnoogies, inreases in one or both of these eves due to inreases in ρ, L and or to dereases in, f and k an swith the ountries from a situation in whih α < α to one in whih α > α, dereasing α. Then, this woud ause the transition from a situation in whih produt variety, the number of domesti and exported varieties are ineffi ienty poor in eah ountry N m < N o, ND m < N D o and N X m < N X o to a situation in whih they beome ineffi ienty rih N m > N o, ND m > N D o and N X m > N X o. As arger overa sizes of the eonomies and tehnoogy improvements redue α 2, they may we ause the transition from a situation in whih the resoures devoted to deveop new varieties are ineffi ienty sma in eah ountry NE m < NE o to a situation in whih they are ineffi ienty arge N E m > N E o. Given that 32 and 33 impy α < α 2, the market provides too itte entry with too itte variety in eah ountry for α < α and too muh entry with too muh variety in eah ountry for α > α 2. For α < α < α 2 it provides, instead, too muh variety and too itte entry. 3.2 The ase of asymmetri ountries Let us now turn to the ase of asymmetri ountries to understand if the effi ieny properties of the market hange with respet to the ase with symmetri ountries Seetion and firm size The anaysis in Appendix A reveas that aso in the genera ase of asymmetri ountries, seetion in the market equiibrium is weaker than optima in eah ountry: varieties with o D, m D ] shoud not be suppied in domesti markets, and varieties with o h, m h ] shoud not be exported by firms produing in to be onsumed in ountry h. In turn, the ost distribution determines the effi ieny of the firm size distribution and we find that resoures are misaoated within the differentiated good setor. Indeed, the resuts for the genera ase onfirm those for symmetri ountries as, with respet to the optimum, the market equiibrium undersuppies in eah ountry h varieties produed in ountry with ow margina ost, that is varieties produed with, 2 2 / o h, and oversuppies varieties with high margina ost, that is varieties produed with 2 2 / o h, m h ]. Finay, aso in the genera ase of asymmetri ountries, the utoff ranking o h < m h ditates the same average output ranking with the average quantities produed in eah ountry for eah destination and the average suppy of 6 For the anaytia derivation of the resuts see the fina part of Appendix A. 8

19 a variety in eah ountry smaer than optima in the market as q m h < qo h and q m h < qo h. Hene, summarizing the resuts disussed above for both the symmetri and asymmetri ountries, we an state what foows: Proposition 4 In the market equiibrium with respet to the optimum: firm seetion in the prodution status for domesti and foreign ountries is weaker than optima; high ow ost firms oversuppy undersuppy their varieties in a ountries they are serving; both the average prodution of firms in eah ountry for any of their destination ountry and the average quantity suppied by a domesti and foreign firms within eah ountry are smaer than optima. oreover, from omparative statis in Appendix A we find that in genera for both the ases of symmetri and asymmetri ountries: Proposition 5 The number of trading ountries, the size of eah eonomy, the tehnoogy avaiabe for the prodution of the modern diff erentiated goods as determined by the upper-bound ost and the ost of innovation, and trade barriers that aff et the aessibiity of other ountries by exporting firms have no impat on the overprovision or on the underprovision of varieties in both domesti and foreign ountries and on the perentage deviation of the market equiibrium from the optimum for domesti and export utoff s, for the average suppy of firms in eah of their destination ountry and for the average quantity suppied by a firms within eah ountry. However, more heterogeneity among firms due to more ess ost-dereasing evenness that redues inreases k, inreases dereases the perentage gaps in the utoff s, makes the overprovision of high ost varieties reativey more ess ikey than its underprovision in the market equiibrium and dereases inreases the perentage gap in average firm size and in the average quantity suppied by a firms within eah ountry Size of the differentiated setor, produt variety and entry The ranking of the domesti utoffs o D < m h D is aso responsibe of the ranking h of the overa size of the differentiated good setor that is smaer than optima in the market in eah ountry as Nh oqo h > N h mqm h. oreover, the ratio N h oqo h Nh mqm h /N h oqo h is affeted by k as we as by the tehnoogy avaiabe in a ountries for the prodution of the modern differentiated goods as determined by the upper-bound osts and the ost of innovation, and by the number of trading ountries and their aessibiity to other oaities as defined by trade barriers, that is by a fators affeting the term f ] h h k Ch / P. Turning to produt variety, Nh o in 67 an be used to evauate the number of produt suppied in the market in 6. In this ase Nh o and N h m an not be ranked unambiguousy. ore preisey, as m D = 2 / o h D we have that h 9

20 N m h > N o h when α > α h τ hh o D = h 2 k+ 2 k+ γ k + k + 2 L h f ] k Ch P whih is the ase when α as we as L h are arge and when γ and the term f ] h h k Ch / P are sma. On the ontrary, Nh m < N h o when α < α h. In the genera ase of asymmetri ountries, the omparison between NE o in 27 and NE m in 7, and, onsequenty the omparison between exported and domesti varieties determined by the first best panner and the market, is ompiated by the presene of the summation in the numerator of the soutions. Speifiay, whie the terms in the summation are smaer in the market and this works in favour of having ess entry in the market NE m < N E o, the numerator of the soution for the market has a 2 in the numerator that, on the ontrary, works in favour of having more entry in the market N m E > N o E. This aptures two ontrasting effets present in the market, that were aready desribed by Spene 976. Indeed, adapting his words to this speifi ase, revenues in the market may fai to over the osts of a soiay desirabe produt beause of setup osts, whie they oud be overed by a soia panner who oud aow for prodution at a oss. This produes a fore that tends to produe in the market ess entry and produt variety than optima. On the other hand, as firms in the market hod bak output setting their prie above their margina ost, they eave more room for entry than woud margina ost priing that woud be foowed by the first best panner deentraizing his/her hoies, produing a business steaing effet that tends to generate more entry and produt variety than optima. Finay, the number of domesti produers and of exporters in the market is eary not optima as N o D = G o D N o E is different from N m D = G m D N m E and N o X = G o o h h NE is different from N m X = G m m h h NE. However, as for the ase of the number of firms entering the market, the omparison between the two ases is not straightforward and requires to speify a the parameters of the mode. 4 The onstrained panners We show in the next Setion that the first best optimum an not be deentraized when differentiated prodution subsidies/taxes are not avaiabe. However, the onstrained seond or third best panner reies on a ommon prodution subsidy eventuay tax if it is negative that in an open eonomy framework impies that profits of a firm produing in h for are π h = p h + s h] q h τ h q h 2