CEP Discussion Paper No 1130 February 2012

Transcription

1 ISSN CEP Discussion Paper No 113 February 212 The Impact of Integration on Prouctivity an Welfare Distortions Uner Monopolistic Competition Swati Dhingra an John Morrow

2 Abstract A funamental question in monopolistic competition theory is whether the market allocates resources efficiently. This paper generalizes the Spence-Dixit-Stiglitz framework to heterogeneous firms, aressing when the market provies optimal quantities, variety an prouctivity. Uner constant elasticity eman, each firm prices above its average cost, yet we show market allocations are efficient. When eman elasticities vary, market allocations are not efficient an reflect the istortions of imperfect competition. After etermining the nature of market istortions, we investigate how integration may serve as a remey to imperfect competition. Both market istortions an the impact of integration epen on two eman sie elasticities, an we suggest richer eman structures to pin own these elasticities. We also show that integration eliminates istortions, provie the postintegration market is sufficiently large. JEL Classifications: F1, L1, D6 Keywors: Selection, monopolistic competition, efficiency, prouctivity, social welfare, eman elasticity This paper was prouce as part of the Centre s Globalisation Programme. The Centre for Economic Performance is finance by the Economic an Social Research Council. Acknowlegements We thank Bob Staiger for continue guiance, Katheryn Russ for etaile iscussion an George Alessanria, Costas Arkolakis, Roc Armenter, Any Bernar, Satyajit Chatterjee, Davin Chor, Steve Durlauf, Charles Engel, Thibault Fally, Rob Feenstra, Keith Hea, Wolfgang Keller, Jim Lin, Emanuel Ornelas, Gianmarco Ottaviano, Mathieu Parenti, Nina Pavcnik, Steve Reing, Anres Roriguez-Clare, Thomas Sampson, Daniel Sturm, Jacques Thisse, John Van Reenen an Mian Zhu for insightful comments. This paper has benefite from helpful comments of participants at AEA, DIME-ISGEP, ISI Delhi, LSE, Oxfor, the Philaelphia Fe, Princeton University an Wisconsin- Maison. Preliminary raft circulate as When is Selection on Firm Prouctivity a Gain from Trae? in 26. Swati thanks the IES Princeton for their hospitality uring work on this paper. Swati Dhingra is a Senior Lecturer with the Globalisation Programme, Centre for Economic Performance. She is also a Lecturer in Economics, Lonon School of Economics. John Morrow is a Research Economist with the Globalisation Programme at the Centre for Economic Performance, Lonon School of Economics. Publishe by Centre for Economic Performance Lonon School of Economics an Political Science Houghton Street Lonon WC2A 2AE All rights reserve. No part of this publication may be reprouce, store in a retrieval system or transmitte in any form or by any means without the prior permission in writing of the publisher nor be issue to the public or circulate in any form other than that in which it is publishe. Requests for permission to reprouce any article or part of the Working Paper shoul be sent to the eitor at the above aress. S. Dhingra an J. Morrow, submitte 212

3 1 Introuction Empirical work has rawn attention to the high egree of heterogeneity in firm prouctivity an the impact of market integration on firm survival an markups Bernar et al. 27, Feenstra 26. The introuction of firm heterogeneity in monopolistic competition moels has provie new insights into the reallocation of resources within inustries. A funamental question within this setting is whether the market allocates resources efficiently. Symmetric firm moels explain when market allocations are efficient by examining the trae off between quantity an prouct variety. When firms are heterogeneous in prouctivity, we must also ask which types of firms shoul prouce an which shoul be shut own. This paper examines how firm heterogeneity affects market efficiency. We focus on three key questions. First, oes the market allocate resources efficiently? Secon, what is the nature of istortions, if any? Thir, can economic integration reuce istortions through increase competition? We answer these questions in the stanar setting of a monopolistically competitive inustry with heterogeneous prouctivity raws an free entry e.g. Melitz 23. Empirical work shows that firms are rarely symmetric an markups are unlikely to be constant. 1 To allow rich interrelationships between prouctivity, markups an efficiency, we focus on the general class of variable elasticity eman systems, consiere by Dixit an Stiglitz When eman elasticities vary with quantity an firms vary in prouctivity, markups will vary within a market. Heterogeneous markups give rise to a range of possible market istortions which woul not arise if firms were symmetric or charge constant markups. Differences in prouctivity across firms change optimal allocation ecisions in a funamental way. In symmetric firm moels, marginal cost pricing an average cost pricing serve as heuristics for first-best an secon-best resource allocations. In heterogeneous firm moels, inucing each firm to price at its marginal cost or average cost will not maximize welfare because neither scheme takes into account sunk entry costs an the effect of heterogeneity on resource costs. Thus, ifferent levels of prouction maximize welfare than what marginal or average cost pricing imply. For example, it coul be welfare-improving to skew resources towars firms with lower costs to conserve resources or towars firms with higher costs to preserve variety. The relative position of a firm in the cost istribution matters, an incorporating ifferences in firm costs can alter welfare an policy analysis substantially. As a heterogeneous cost environment presents information problems for policy, one potential tool to improve efficiency is to integrate with international markets. For instance, the istortions of imperfect competition may be mitigate with increase competition from foreign firms, implying that integration provies opportunities to correct market failure. This iea of welfare gains from 1 CES eman provies a useful benchmark by forcing constant markups that ensure market size plays no role in prouctivity changes. However, recent stuies fin market size matters for firm size Campbell an Hopenhayn 25 an prouctivity ispersion Syverson 24. Foster et al. 28 show that profitability rather than prouctivity is more important for firm selection, suggesting a role for richer eman specifications. 2

4 mitigating istortions goes back to at least Melvin et al Builing on this insight, we moel international integration as access to new markets an examine whether it can be a policy tool to correct istortions. 2 Starting with constant elasticity of substitution CES eman, we show that when firms vary in prouctivity, market allocations are efficient but firms earn positive profits. This result seems surprising, base on the logic of marginal or average cost pricing which is esigne to return proucer surplus to consumers. With prouctivity ifferences, the market requires prices above average costs to inuce firms to enter an potentially take a loss. Free entry ensures the wege between prices an average costs exactly finances sunk entry costs. Therefore, the market implements the first-best allocation an laissez faire inustrial policy is optimal. 3 How broaly oes this efficiency result hol? We generalize the eman structure to the variable elasticity of substitution VES form of Dixit an Stiglitz which provies a rich setting for a wie range of market outcomes Spence 1976; Vives 21; Zheloboko et al Within this setting, market efficiency is unique to CES eman. While the market oes maximize real revenue, private benefits to firms are perfectly aligne with social benefits only uner CES eman. The nature of istortions uner VES eman can be etermine by two eman sie elasticities: the inverse eman elasticity an the elasticity of utility. Misalignment of these elasticities etermines the bias in market allocations relative to optimal allocations. This is in sharp contrast to symmetric firm moels where the elasticity of utility is enough to etermine this bias in market allocations across quantity an variety. When firms are heterogeneous, the market allocates resources across ifferent types of firms an the variable elasticity of eman shapes the istribution of quantities prouce. This istinguishes istortions in heterogeneous firm markets in two respects. First, some firms may over-prouce while others uner-prouce within the same market. This shifts the focus from a general level of prouction to the istribution of prouction. Secon, the istribution of variable markups affects firm entry, an aggregate quantity an variety now epen on both the elasticity of utility an the elasticity of eman. This alters how one thinks about the trae-off between aggregate quantity versus variety. Integration with international markets can potentially mitigate istortions across the istribution of firms. To capture the role integration as a policy tool, we first examine the effects of integration with large markets. Such integration will push outcomes towars what we efine as the monopolistically competitive limit, which eliminates istortions. In this limit firm heterogeneity an market power persist, but market size is so large that the quantity sol from a firm to each 2 International integration is equivalent to an expansion in market size e.g., Krugman As our focus is on efficiency, we abstract from trae frictions which introuce cross-country istributional issues. 3 Melitz 23 consiers both variable an fixe costs of exporting. We show that the open Melitz economy is efficient, even in the presence of trae frictions. In the presence of fixe export costs, the firms a policymaker woul close own in the open economy are exactly those that woul not survive in the market. However, a policymaker woul not close own firms in the absence of export costs. Thus, the rise in prouctivity following trae provies welfare gains by optimally internalizing trae frictions. Market allocations are efficient even with asymmetric countries, but the presence of trae frictions introuces istributional concerns which we o not aress. 3

5 worker is negligible. Most importantly, VES eman operates much like CES eman, an market allocations are efficient. This shows that competition can eliminate istortions while retaining the characteristics of markets with heterogeneous firms who possess market power. Markups become constant across firms, so CES eman might approximate richer eman structures in large economies. However, the monopolistically competitive limit may require a market size which is unattainable even in fully integrate worl markets. Integration with small markets has ifferent effects than integration with large markets. In small markets, heterogeneous markups lea to istortions an small increases in market size may increase welfare, but fail to reuce istortions. We illustrate this with the impact of integration on prouctivity istortions in small markets. Uner VES eman, changes in market prouctivity epen on the inverse eman elasticity, while changes in optimal prouctivity epen on the elasticity of utility. A comparison of these elasticities etermines how integration affects the gap between market prouctivity an optimal prouctivity. When these elasticities are aligne, istortions issipate. However, when the elasticities are misaligne, integration can exacerbate istortions. This implies that integration may increase the scope for policies that anticipate how integration will alter prouction in imperfect markets. In this regar, estimation of richer eman structures becomes imperative in unerstaning how integration impacts market istortions. Our last results provie suggestions about how to assess istortions empirically. The paper is organize as follows. Section 2 relates this paper to previous work an Section 3 recaps trae moels with firm heterogeneity. Section 4 presents efficiency results in a close economy. Section 5 introuces international trae an contrasts the efficiency of CES eman with inefficiency of VES eman, also eriving a monopolistically competitive limit which shows how integration can eliminate istortions. Section 6 characterizes the nature of static istortions an further analyzes the impact of integration on istortions. Section 7 gathers together some theoretical implications useful for esigning empirical strategies an Section 8 conclues. 2 Relate Work Our paper is relate to work on welfare gains in inustrial organization an international economics. The trae off between variety an quantity occupies a prominent place in the inustrial organization literature e.g., Mankiw an Whinston We contribute to this literature by stuying the effects of firm heterogeneity an international trae. The analysis is motivate by efficiency properties which have been stuie at length in symmetric firm moels of monopolistic competition. 4 Recently, Bilbiie et al. 26 show the market equilibrium with symmetric firms is socially optimal if an only if preferences are CES. We generalize the result to heterogeneous firms an show that efficiency is unrelate to the prouctivity istribution of firms. To the best of 4 Spence 1976; Dixit an Stiglitz 1977; Venables 1985; Bilbiie et al. 26; Behrens an Murata 29. 4

6 our knowlege, this is the first paper to show market outcomes in Melitz are first best. 5 To highlight the potential scope of market imperfections, we generalize the well known CES eman structure to VES eman. In contemporaneous work, Zheloboko et al. 211 evelop complementary results for market outcomes uner VES eman an emonstrate its richness an tractability uner various assumptions such as multiple sectors an vertical ifferentiation. Unlike Zheloboko et al., our focus is on market efficiency. We also stuy the limiting behavior of a VES economy. A large literature examines whether monopolistic competition arises as a limit to oligopolistic pricing an when monopolistic competition converges to perfect competition in symmetric firm moels Vives 21, Chapter 6. This literature consiers the limiting behavior as the number of firms tens to infinity. Instea, we examine a monopolistically competitive moel with a continuum of firms so there are infinitely many firms even in an economy with finite market size. After establishing the equivalence of increase international trae an increase market size, we stuy the limiting behavior in terms of the moel primitive of market size becoming large. The finings of our paper are relate to an emerging literature on welfare gains in new trae moels. Generalizing Krugman 198 to heterogeneous firms, Melitz shows that opening to trae raises welfare through reallocation of resources towars high prouctivity firms. Consiering 48 countries exporting to the US in 198-2, Feenstra an Kee 28 estimate that rise in export variety accounts for an average 3.3 per cent rise in prouctivity an GDP for the exporting country. In recent influential work, Arkolakis et al. forthcoming show that the mapping between trae ata an welfare is the same across several ol an new trae moels with ifferent prouction structures. This equivalence hols for moels which permit welfare to be summarize by import shares an trae elasticities that can be erive from gravity equations. Once the Spence-Dixit- Stiglitz eman framework is consiere, we fin welfare inferences from import shares require aitional information about eman an become more structural in nature. Unlike Arkolakis et al., we focus on market efficiency an show that the potential gains from integration are larger because of the opportunity to reuce istortions. Our results speak irectly to the mixe finings about trae liberalization an prouctivity in the empirical literature. Following trae liberalization, some countries show a reallocation towars high prouctivity firms while others show a reallocation towars low prouctivity firms. 6 Tybout 5 We consier this to be the proof of a folk theorem. The iea of efficiency in Melitz has been in the air. Within the heterogeneous firm literature, Balwin an Robert-Nicou 28 an Feenstra an Kee 28 iscuss certain efficiency properties of the Melitz economy. In their working paper, Atkeson an Burstein 21 consier a first orer approximation an numerical exercises to show that prouctivity increases are offset by reuctions in variety. We provie an analytical treatment to show the market equilibrium implements the unconstraine social optimum. Helpman et al. 211 consier the constraine social optimum in the presence of a homogeneous goo. Their approach iffers because the homogeneous goo fixes the marginal utility of income. 6 Interpreting firm size as prouctivity, Tybout 23 notes that it was the high prouctivity firms that lost market share in Chile an Colombia while it was the low prouctivity firms that suffere a ecline in Morocco. While prouctivity estimation is fraught with ifficulties in measuring technical efficiency, we focus on the relationship between prouctivity an welfare as in the heterogeneous firm literature. 5

7 23 proposes that these mixe finings coul mean that the selection effects emphasize by Melitz are not robust, or that firm size is a poor proxy for prouctivity. We aress the first issue by examining the robustness of selection effects to general eman specifications. Differences in inverse eman elasticities inuce ifferent patterns of firm selection, reconciling the mixe evience for prouctivity changes across heterogeneous firms. The secon issue of prouctivity measurement has been aresse in several stuies. Instea of measurement, we focus on how VES eman can better explain observe patterns. As both observe markups an physical prouctivity vary with market size uner general eman specifications, our finings reiterate the importance of isentangling changes in markups an prouctivity to unerstan the sources of welfare gains from trae. We characterize when observe prouctivity gains reflect a narrowing of the istortionary gap between market an optimal prouctivity. Therefore, our work is in line with Tybout 23 an Katayama et al. 29 who point to the limitations of the empirical literature in mapping observe prouctivity gains to welfare an optimal policies. 3 Trae Moels with Heterogeneous Firms Trae moels with heterogeneous firms iffer from earlier trae moels with prouct ifferentiation in two significant ways. First, costs of prouction are unknown to firms before sunk costs of entry are incurre. Secon, firms are asymmetric in their costs of prouction, leaing to firm selection base on prouctivity. In this section we briefly recap the implications of asymmetric costs for consumers, firms an equilibrium outcomes. 3.1 Consumers A mass L of ientical consumers in an economy are each enowe with one unit of labor an face a wage rate w normalize to one. Preferences are ientical across all consumers in home an foreign countries. Let M e enote the mass of entering varieties an qc enote quantity consume of variety c by each consumer. A consumer has preferences over ifferentiate goos UM e,q which take the general VES form: UM e,q M e uqcg. VES 1 Here u enotes utility from an iniviual variety an uqg enotes utility from a unit bunle of ifferentiate varieties. In a Melitz economy, preferences take the special CES form with uq = q ρ. 7 More generally, we assume preferences satisfy usual regularity conitions which guarantee well efine consumer an firm problems. 7 The specific CES form in Melitz is UM e,q M 1/ρ e qc ρ G 1/ρ but the normalization of the exponent 1/ρ in Equation 1 will not play a role in allocation ecisions. 6

8 Definition 1. Regular Preferences u satisfies the following conitions: 1. u is normalize to zero. 2. u is twice continuously ifferentiable, increasing an concave. 3. u q q is strictly ecreasing in quantity. 4. The elasticity of marginal utility µq qu q/u q is less than one. For each goo inexe by c, VES preferences inuce an inverse eman pqc = u qc/δ where δ is a consumer s buget multiplier. As u is strictly increasing an concave, for any fixe price vector the consumer s maximization problem is concave. The necessary conition which etermines the inverse eman is sufficient, an has a solution provie inaa conitions on u. 8 Multiplying both sies of the inverse eman by qc an aggregating over all c, the buget multiplier is δ = M e ca u qc qcg. 3.2 Firms There is a continuum of firms which may enter the market for ifferentiate goos, by paying a sunk entry cost of f e. Each firm prouces a single variety so the mass of entering firms is the mass of entering varieties M e. Upon entry, each firm receives a unit cost c rawn from a istribution G with continuously ifferentiable pf g. 9 After entry, shoul a firm prouce for the omestic market it faces a cost function TCqc cqc + f where f enotes the fixe cost of prouction. Each firm faces an inverse eman of pqc = u qc/δ an acts as a monopolist of variety c. Post entry profit of the firm from omestic sales is πc where πc max qc [pqc c]qcl f. The regularity conitions guarantee the monopolist s FOC is optimal an the quantity choice is given by p + q u q/δ = c. MR=MC MR = MC ensures that the markup rate is pc c/pc = qu q/u q = µqc. Therefore, the elasticity of marginal utility summarizes the inverse eman elasticity as µq qu q/u q = ln pq/ lnq. When the economy opens to trae, firms incur an iceberg transport cost τ 1 an a fixe cost f x in orer to export to other countries. As a result, firms face a cost function TCq x c τcq x c + f x an a eman function pq x c for sales to the export market. Profit from foreign sales is π x c max qx c[pq x c τc]q x cl f x an the optimal q x choice is given by a similar MR = MC conition. 8 Utility functions not satisfying inaa conitions are permissible but may require parametric restrictions to ensure existence. We will assume inaa conitions on utility an revenue, though they are not necessary for all results. 9 Some aitional regularity conitions on G are require for existence of a market equilibrium in Melitz. 7

9 3.3 Market equilibrium Profit maximization implies that firms prouce for the omestic an/or export markets if they can earn non-negative profits from sales in the omestic an/or export markets, respectively. We enote the cutoff cost level of firms that are inifferent between proucing an exiting from the omestic market as c a in autarky an c in the open economy. The cutoff cost level for firms inifferent between exporting an not proucing for the export market is enote by c x. Formally, let ι = a,,x enote autarky an the omestic an export markets of the open home economy respectively. Each c ι is fixe by the Zero Profit Conition ZPC, π ι c ι = for ι = a,,x. ZPC Since firms with cost raws higher than the cutoff level o not prouce, the mass of omestic proucers M ι supplying to market ι is M ι = M e Gc ι. In summary, each firm faces a two stage problem: in the secon stage it maximizes profits from omestic an export sales given a known cost raw, an in the first stage it ecies whether to enter given the expecte profits in the secon stage. We maintain the stanar free entry conition impose in monopolistic competition moels. Specifically, let Πc enote the total expecte profit from sales in all markets for a firm with cost raw c, then ex ante average Π net of sunk entry costs must be zero, ΠcG = f e. FE The next two Sections examine the efficiency properties of this framework for close an open economies. 4 Efficiency in the Close Economy Having escribe an economy consisting of heterogeneous imperfectly competitive firms, we now examine efficiency of market allocations in the close economy. Outsie of cases in which imperfect competition leas to competitive outcomes with zero profits, one woul generally expect the coexistence of positive markups an positive profits to inicate inefficiency through loss of consumer surplus. Nonetheless, this Section shows that CES eman combine with the Melitz prouction framework exhibits positive markups an profits for surviving firms, yet it is allocationally efficient. However, we also show that the usual relationship between imperfect competition an welfare, that private incentives are not aligne with optimal prouction patterns, is true for all VES eman structures except CES. 8

10 4.1 Welfare uner isoelastic eman In a close economy, a policymaker maximizes iniviual welfare U as given in Equation 1. 1 The policymaker is unconstraine an chooses the mass of entrants, quantities an which firms of various prouctivities prouce. At the optimum, zero quantities will be chosen for varieties above a cost threshol c a. Therefore, all optimal allocative ecisions can be summarize by quantity qc, potential variety M e an prouctivity c a. Our approach for arriving at the optimal allocation is to think of optimal quantities q opt c as being etermine implicitly by c a an M e so that per capita welfare can be written as ca U = M e uq opt cg. 2 After solving for each q opt conitional on c a an M e, Equation 2 can be maximize in c a an M e. Proposition 1 shows the market provies the first-best quantity, variety an prouctivity. Proposition 1. Every market equilibrium of a close Melitz economy is socially optimal. Proof. See Appenix. The proof of Proposition 1 iffers from stanar symmetric firm monopolistic competition results because optimal quantity is a nontrivial function of unit cost, variety an cutoff prouctivity. As the proof is involve, we relegate etails to the Appenix an iscuss the rationale for optimality below. In symmetric firm moels, we know that firms charge positive markups which result in lower quantities than those implie by marginal cost pricing. However, the markup is constant so the market price an hence marginal utility is proportional to unit cost, ensuring proportionate reuction in quantity from the level that woul be observe uner marginal cost pricing Baumol an Brafor 197. Moreover, homogeneous firms choose price equal to average cost so the profit exactly finances the fixe cost of prouction. Each firm therefore internalizes the effect of higher variety on consumer surplus, resulting in an efficient market equilibrium Grossman an Helpman 1993, Bilbiie et al. 26. With heterogeneous firms, markups continue to be constant, ensuring that market prices across firms are proportionate to unit costs. But, average cost pricing is too low to compensate firms for an efficient allocation, because it will not cover ex ante entry costs. The market ensures that surviving firms internalize the losses face by exiting firms, losses which are etermine by aggregate economic eman that epens on qc, c a an M e. Post entry, surviving firms charge prices higher than average costs pc [cqc + f /L]/qc which compensates them for the possibility of paying f e to enter an then being too unprouctive to survive. CES eman ensures that c a an M e are at optimal levels that fix pc a, thereby fixing absolute prices to optimal levels. 1 Free entry implies zero expecte profits so the focus is on consumer surplus. 9

11 The way in which CES preferences cause firms to optimally internalize aggregate economic conitions can be mae clear by efining the elasticity of utility εq qu q/uq an the social markup 1 εq. We term 1 εq the social markup because at the optimal allocation, it enotes the utility from consumption of a variety net of its resource cost. At the optimal allocation, there is a multiplier λ which encapsulates the shaow cost of labor an ensures u qc = λc. Therefore, the social markup is 1 εq =1 u q/uq =uq λcq/uq. Social Markup For any optimal allocation, a quantity that maximizes social benefit from variety c solves max qc L1 εqcuq/λ f = max q In contrast, the incentives that firms face in the market are L 1 εq cq f. εq µq maxlµqcpq f = max qc 1 µq cq f. Since ε an µ epen only on the primitive uq, we can examine which preferences woul make firms choose optimal quantities. Clearly, if µq/1 µq is proportional to 1 εq/εq, firms will choose optimal quantities q when they prouce, but the set of proucers might be smaller or larger than optimal, epening on which firms can make enough profits to clear the fixe cost f. For the market to also select the optimal range of prouctivity, µq/1 µq must not only be proportional to 1 εq/εq, but in fact be the same. Examining CES eman, we see precisely that µq/1 µq = 1 εq/εq for all q. Thus, CES eman incentivizes exactly the right firms to prouce, in aition to proucing optimal quantities. A irect implication of Proposition 1 is that laissez faire inustrial policy is optimal uner CES eman. This efficiency result may seem surprising in the context of Dixit an Stiglitz 1977 who fin that market allocations are secon-best but not first-best uner CES eman for ifferentiate goos. Dixit an Stiglitz consier two sectors a homogeneous goos sector an a ifferentiate goos sector an assume a general utility function to aggregate across these goos. With a general utility function, the elasticity of substitution between the homogeneous an ifferentiate goos is not constant, leaing to inefficient market allocations. In the next subsection, we examine the role of elasticities in greater etail. In keeping with Melitz, we consier a single sector to evelop results for market efficiency in terms of elasticities. 1

12 4.2 Welfare beyon isoelastic eman Efficiency of the market equilibrium in a Melitz economy is tie to CES eman. To highlight the role of CES eman, we consier the general class of variable elasticity of substitution VES eman stuie by Dixit an Stiglitz 1977 as specifie in Equation 1. With regar to efficiency, comparison of FOCs for the market an optimal allocation shows constant markups are necessary for efficiency. Therefore, within the VES class, optimality of market allocations is unique to CES preferences. 11 Proposition 2. Uner VES eman, a necessary conition for the market equilibrium to be socially optimal is that u is CES. 12 Proof. Proof available upon request. Uner general VES eman, market allocations are not efficient an o not maximize iniviual welfare. Proposition 3 shows that the market instea maximizes aggregate real revenue M e u qc qc LG generate in the economy. Proposition 3. economy. Uner VES eman, the market maximizes aggregate real revenue in the close Proof. See Appenix. Proposition 3 shows that market resource allocation is generally not aligne with the social optimum uner VES eman. The market an efficient allocations are solutions to: ca maxm e u qc qcg ca maxm e uqcg { ca } where L M e [cqcl + f ]G + f e { ca } where L M e [cqcl + f ]G + f e Market Social For CES eman, uq = q ρ while u qq = ρq ρ implying revenue maximization is perfectly aligne with welfare maximization. Outsie of CES, quantities prouce by firms are too low or too high an in general equilibrium, this implies the average prouctivity of operating firms is also too low or too high. Market quantity, variety an prouctivity reflect istortions of imperfect 11 VES utility is aitively separable an therefore oes not inclue the quaratic utility of Melitz an Ottaviano 28 an the translog utility of Feenstra 23. However, Zheloboko et al. 211 show VES eman captures the qualitative features of market outcomes obtaine uner these forms of non-aitive utility. 12 For completeness, we note that constant elasticities of eman are necessary but not sufficient for optimality of market allocations. We exten the CES eman of Melitz to CES-Benassy preferences UM e,c a,q νm e c qcρ gcc. In this example, u is CES but varieties an the unit bunle are value ifferently through νm e. Market allocations uner CES-Benassy preferences are the same as with CES preferences of Melitz. However, firms o not fully internalize consumers taste for variety, leaing to suboptimal levels of quantity, variety an prouctivity. Following Benassy 1996, Bilbiie et al. 26 an Alessanria an Choi 27, when νm e = M ρν B+1 e, these preferences isentangle taste for variety ν B from the markup to cost ratio 1 ρ/ρ. Market allocations are optimal only if taste for variety exactly equals the markup to cost ratio ν B = 1 ρ/ρ. 11

13 competition, an therefore, increase competition through opening markets to trae might improve efficiency. This leas us to an examination of the impact of trae on market istortions. 5 Efficiency in an Open Economy Motivate by empirical stuies of firm heterogeneity, Melitz 23 shows that reallocation of resources towars high prouctivity firms provies a new source of gains from trae. In this Section, we examine how international trae affects market an optimal allocations in a Melitz economy. We start by showing that CES eman continues to inuce efficient allocations in an open economy. Uner VES eman, market allocations are suboptimal so we examine when market expansion from trae eventually mitigates the istortions of imperfect competition while preserving firm heterogeneity. 5.1 Welfare uner isoelastic eman Trae provies prouctivity gains by reallocating resources towars low cost firms, an increase prouctivity is gaine at the expense of variety. One might therefore expect artificially selecting low cost firms to prouce woul improve welfare in autarky. In fact, this is not the case. Proposition 1 shows that the autarkic market equilibrium is efficient. This implies that the open economy prouctivity level is unesirable in autarky as it generates too little variety. However, as Proposition 4 below shows, the prouctivity level selecte in an open economy is efficient. Thus trae itself makes a new mix of prouctivity an variety efficient. Proposition 4. Every market equilibrium of ientical open Melitz economies is socially optimal. Proof. See Appenix. Why is the higher prouctivity level of the open economy inefficient in autarky? Proposition 4 implies that market selection of firms is optimal if an increase in size can only be attaine at a cost of exogenous frictions τ, f x. Compare to a frictionless worl, trae frictions reuce the potential welfare gains from trae. The market minimizes the losses from frictions by weeing out high cost firms. Conitional on trae costs, market selection of firms is optimal an provies a net welfare gain from trae. Proposition 4 is striking in that the ifferences in firm costs o not generate inefficiencies espite heterogeneity of profits an the ifferent effects that trae frictions will have on firm behavior. Furthermore, selection of firms performs the function of allocating aitional resources optimally without any informational requirements. Uner CES eman, laissez faire inustrial policy is optimal for the worl economy However, terms of trae externalities may exist an lea to a breakown of laissez faire policies. Demiova an 12

14 Moeling trae between equally size countries makes the role of trae frictions extremely clear cut. When countries iffer in size, trae frictions introuce cross-country istributional issues which obscure the pure efficiency question. Specifically, consier two countries of ifferent sizes with cost istribution Gc = c/cmax k an CES eman. Market allocations are efficient when these countries trae with each other an face no trae frictions. These market allocations maximize social welfare with equal Pareto weights assigne to every iniviual in the two countries. Introucing trae frictions will continue to inuce efficient market allocations, but with unequal Pareto weights. This shows the market is implicitly favoring certain consumers, so that firm selection patterns reflect istributional outcomes in aition to cost competitiveness. The cross-country istribution of welfare gains is important but beyon the focus of this stuy. In what follows, we wish to stuy efficiency rather than istribution so we moel the stylize case of frictionless trae an consier more general eman structures which can explain a greater range of trae effects. 5.2 Welfare beyon isoelastic eman This subsection examines market istortions in an open economy with variable elasticities. We abstract from trae costs to focus on efficiency rather than istributional issues. The market equilibrium between freely traing countries of sizes L 1,...,L n is ientical to the market equilibrium of a single autarkic country of size L = L L n. Thus, opening to trae is equivalent to an increase in market size, echoing Krugman This result is summarize as Proposition 5. Proposition 5. In the absence of trae costs, trae between countries of sizes L 1,...,L n has the same market outcome as a unifie market of size L = L L n. Proof. Available upon request, see also Krugman Proposition 5 allows us to think about increase trae as an increase in market size L of a close economy. An increase in market size has the ientical effect of increase competition which will impact efficiency by altering market istortions. We turn to efficiency properties of the open VES economy, an investigate how far increase competition from trae can go towars improving market outcomes Market Efficiency uner VES Deman Having establishe that opening to trae is equivalent to an increase in the size of a VES economy, we can follow the same reasoning as in the close VES economy to infer that market allocations in an open economy are suboptimal. Marginal revenues o not correspon to marginal utilities so market allocations are not aligne with efficient allocations. This is particularly important when Roriguez-Clare 29 incorporate terms of trae consierations an provie omestic policies to obtain the first-best allocation in an open Melitz economy with Pareto cost raws. Chor 29 also consiers when policy intervention is appropriate in a heterogeneous firm moel with multinationals an a homogeneous goos sector. 13

15 consiering trae as a policy option, as it implies that opening to trae may take the economy further from the social optimum. For example, market expansion from trae may inuce exit of low prouctivity firms from the market when it is optimal to keep more low prouctivity firms with the purpose of preserving variety. So when oes integration mitigate or exacerbate istortions? As acknowlege by Spence, perfectly general propositions are har to come by an the nature of istortions can be highly epenent on parameter magnitues. To make progress, we follow Stiglitz 1986 an first stuy market an optimal outcomes as market size becomes arbitrarily large. This allows us to examine when international trae enables markets to eventually mitigate istortions. Later, we also examine istortions in small markets Market Efficiency in Large Markets Looking at efficiency in large markets explains whether integrating with worl markets enables a small economy to overcome its market istortions. From a theoretical perspective we will term a large market the limit of the economy as the mass of workers L approaches infinity, an in practice we might expect that sufficiently large markets approximate this limiting case. 14 The large economy concept is similar in spirit to the iea of a competitive limit, in that the number of entrants grows unbounely large while the quantity supplie from each firm to each worker becomes small. However, when firms are heterogeneous, simply knowing there are a large number of entrants oes not explain the istribution of prouctivity, prices an quantity. At least three salient outcomes can occur. One outcome is that competitive pressures might wee out all firms but the most prouctive. This occurs for instance when marginal revenue is boune, as when u is quaratic or CARA constant absolute risk aversion. 15 It may also happen that access to large markets allows even the least prouctive firms to amortize fixe costs an prouce. To retain the funamental properties of monopolistic competition with heterogeneous firms, we chart out a thir possibility between these two extremes: some, but not all, firms prouce. To o so, we maintain the previous regularity conitions for a market equilibrium. In orer to ai the analysis, we make three assumptions on eman at small quantities. The first assumption enables a clear istinction between the three salient outcomes in large markets. Assumption Interior Markups. The inverse eman elasticity an elasticity of utility are boune away from an 1 for small quantities. Formally, lim q µq an lim q εq,1. The assumption of interior markups guarantees that as the quantity sol from a firm to a consumer becomes small as happens for all positive unit cost firms, markups remain positive µ > an prices remain boune µ < 1. It also guarantees that the ae utility provie 14 How large markets nee to be to justify this approximation is an open quantitative question. 15 See Behrens an Murata

16 per labor unit at the optimum converges to a non-zero constant e.g., Solow An example of a class of utility functions satisfying interior markups is the expo-power utility where uq = [1 exp αq 1 ρ ]/α for ρ,1. It nests the CES for α =. 17 When markups are interior, there is a sharp taxonomy of what may happen to the istribution of costs, prices an total quantities Lqc prouce by a firm as follows: Proposition 6. Assume markups are interior. Then uner the market allocation: 1. lim c mkt a = iff lim p c mkt a = iff lim Lq c mkt a =. L L L 2. lim c mkt a = iff lim p c mkt a = iff lim Lq c mkt a =. L L L 3. lim c mkt a, iff lim p c mkt a, iff lim Lq c mkt a,. L L L Similarly, uner the optimal allocation: 1. lim c opt a = iff lim u q c opt a /λq L L 2. lim c opt a = iff lim u q L L c opt a 3. lim c opt a, iff lim u q L L Proof. See Appenix. /λq c opt a c opt a c opt a /λq = iff lim Lq L = iff lim c opt a L Lq c opt a c opt a =. =., iff lim L Lq c opt a,. Proposition 6 shows that when markups are interior an the cost cutoff converges, one of three things must happen. 1 Only the lowest cost firms remain lim c mkt a L = an prices go to zero akin to perfect competition, while the lowest cost firms prouce infinite total quantities lim Lq c mkt a =. 2 Post-entry, all firms prouce inepenent of cost lim c mkt a = while L L prices become unboune an the total quantities prouce become negligible lim Lq c mkt a =, L akin to a rentier case where firms prouce little after fixe costs are incurre. 3 The cost cutoff converges to a positive finite level lim c mkt a L,, an a non-egenerate istribution of prices an total quantities persists. Although each of these possibilities might be of interest, we focus on the case when the limiting cost raw istribution exhibits heterogeneity lim c mkt a > but fixe L costs still play a role in etermining which firms prouce lim <. We therefore make c mkt a L the following assumption, which by Proposition 6 will guarantee non-egenerate prices an total quantities: 16 Kuhn an Vives 1999 fin that lim q 1 εq = lim q µq uner relatively mil assumptions. Let ν = V qq/v q where V q = uq/q in our notation. Then their assumption is that there exist positive constants ρ an κ such that lim q [νq ν]/q ρ = κ so νq ν has an asymptotic expansion at q = with a leaing term of the constant elasticity type. Examples of such utility functions inclue uq = q ρ e κq for ρ,1 an κ < 1 ρ/1 + ρρ, uq = q κ 1 q for κ,1 an uq = q1 q κ for κ >. 17 The expo-power utility form was propose by Saha 1993 an recently use by Holt an Laury 22 an Post et al. 28 to moel risk aversion empirically. 15

17 Assumption Interior Convergence. In the large economy, the market an optimum allocations have a non-egenerate cost istribution in which some but not all entrants prouce. Uner interior markups an convergence, the economy converges to a monopolistically competitive limit istinct from a perfectly competitive limit or at the other extreme a rentier limit. As the economy grows, each worker consumes a negligible quantity of each variety. At these low levels of quantity, the inverse eman elasticity oes not vanish an firms can still extract a positive markup µ. This is in sharp contrast to a competitive limit, in which firms are left with no market power an µ rops to zero. Similarly, the social markup 1 ε oes not rop to zero in the monopolistically competitive limit an each variety contributes at a positive rate to utility even at low levels of quantity. In fact, this monopolistically competitive limit has a sharper characterization very close to the conitions which characterize a finite size market uner CES eman incluing efficiency. To obtain this result, we introuce one last regularity conition. Assumption Market Ientification. Quantity ratios istinguish price ratios for small q: If κ κ then lim pκq/pq lim p κq/pq. q q Market ientification guarantees prouction levels across firms can be istinguishe if the firms charge istinct prices as quantities sol become negligible. Combining these three assumptions of interior markups, convergence an ientification ensures the large economy goes to the monopolistically competitive limit, summarize as Proposition 7. Proposition 7. Uner the above assumptions, as market size L approaches infinity the market approaches the monopolistically competitive limit. This limit has the following characteristics: 1. Prices, markups an expecte profits converge to positive constants. 2. Per capita quantities qc go to zero, while aggregate quantities Lqc converge. 3. Relative quantities Lqc/Lqc converge to c/c 1/α with α = lim q µq. 4. The entrant per worker ratio M e /L converges. 5. The market an socially optimal allocations coincie. Proof. See Appenix. Proposition 7 shows that integration with large markets can push economies base on VES eman to the monopolistically competitive limit. In this limit, the inverse eman elasticity an the elasticity of utility become constant, ensuring the market outcome is socially optimal. Firms charge constant markups which exactly cross-subsiize entry of low prouctivity firms to preserve variety. This wipes out the istortions of imperfect competition as the economy becomes large. Intuitively, we can explain Proposition 7 in terms of our previous result that CES preferences 16

18 inuce efficiency. In large markets, the quantity qc sol to any iniviual consumer goes to zero, so markups µqc converge to the same constant inepenent of c. 18 This convergence to constant markups aligns perfectly with those generate by CES preferences with an exponent equal to 1 lim q µq. Thus, large markets reuce market istortions until they are aligne with socially optimal objectives. It is somewhat remarkable that the large market outcome, which remains imperfectly competitive, is socially optimal. Firms charge positive markups but they exactly recover both average costs an ex ante entry costs. Therefore, market allocations are efficient espite positive markups. Such persistence of imperfection in competition is consistent with the observation of Samuelson 1967 that the limit may be at an irreucible positive egree of imperfection Khan an Sun While the monopolistically competitive limit is optimal espite imperfect competition, it is an open empirical question whether markets are sufficiently large for this to be a reasonable approximation to use in lieu of richer VES eman. When integrate markets are small, variable markups are crucial in unerstaning istortions. We iscuss a small VES economy in the next Section. 6 Distortions an the Impact of Integration The previous section showe how integration with sufficiently large markets can improve welfare an eliminate istortions. However, this outcome is an iealistic statement about the effects of intense competition in an otherwise imperfectly competitive market. When competitive forces are weaker, istortions remain espite integration. Although we have ientifie the source of istortions as a conflict between private markups µ q capture by firms an social markups 1 ε q that woul maximize welfare, we have not etaile the nature of these istortions. In this section we first characterize market istortions in prouctivity, quantity an entry. We then show that small increases in market size that fall short of large market integration may magnify istortions. Although it is reasonable to expect small increases in market size to improve welfare, aitional gains can be capture using policies which mitigate istortions. 6.1 Market Distortions uner VES Deman Here we compare the market an optimal quantity, prouctivity an variety to unerstan the nature of istortions in a VES economy. We show that istortions epen on markups µq an 1 εq. Specifically, the bias in market quantity, prouctivity an variety is etermine by how the markups vary with quantity µ q an 1 εq. We start with a iscussion of the relation 18 The rate at which markups converge of course epens on c an is in any case highly enogenous see Appenix. 19 Stiglitz 1986 notes that the CES moel violates the assumptions of the competitive limit of the monopolistically competitive economy erive by Hart 1985 who assumes markups are completely wipe out in the limit. 17

19 between markups an quantity, an then characterize istortions by these eman characteristics Relation between Markups an Quantity The pattern of markups across firms in a VES economy is etermine by µ an 1 ε. When µ q >, markups are positively correlate with quantity. This is the case stuie by Krugman 1979: firms are able to charge higher markups when they sell higher quantities. Our regularity conitions guarantee low cost firms prouce higher quantities Section 3.1. This means high cost firms have both high q an high markups. When µ q <, small boutique firms charge higher markups. For CES eman, markups are constant µ =. The richer VES eman brings out the istinction between µ > an µ <, which turns out to be important in characterizing istortions. The sign of 1 εq etermines how social markups vary with quantity. When it is positive 1 εq >, social markups are higher at higher levels of quantity. As above, this implies a negative correlation between social markups 1 ε an unit costs c. Conversely, when 1 εq <, the boutique varieties which are consume in small quantities provie relatively higher social markups. Uner CES preferences, the elasticity of utility is 1 εq = 1 ρ implying 1 εq =. We use the relationship between markups an quantity to characterize market istortions in an open VES economy. To fix ieas, Table 1 summarizes µ an 1 ε for commonly use utility functions. Among the forms of uq consiere are expo-power, HARA an generalize CES propose by Dixit an Stiglitz. 2 µ > Table 1: Private an Social Markups for Common Utility Forms 1 ε < 1 ε > Generalize CES α > : CARA, Quaratic q + α ρ HARA α > : 1 ρ [ q/1 ρ + α ρ α ρ] /ρ Expo-power [ α > : 1 exp αq 1 ρ ] /α µ < HARA α < : Generalize CES α < : 1 ρ [ q/1 ρ + α ρ α ρ] /ρ q + α ρ Expo-power α < : [ 1 exp αq 1 ρ ] /α 6.2 Quantity, Prouctivity an Entry Distortions We characterize the bias in market allocations compare to the optimal allocation by eman characteristics. For ease of reference, Table 2 summarizes these biases an iscussion of results 2 The relevant parameter restrictions are ρ,1 for each form, q/1 ρ + α > for HARA an q + α > for Generalize CES. 18