INTERNATIONAL TRADE IN GENERAL OLIGOPOLISTIC EQUILIBRIUM

1. INTERNATIONAL TRADE IN GENERALOLIGOPOLISTIC EQUILIBRIUM J. Peter Neary University of Oxford and CEPR 2011

2. 0. Preview Introduction to this approach: • JEEA 2003 Applications to: • Cross-border mergers: REStud 2007 • Cournot vs. Bertrand (with Joe Tharakan): JIE 2011 • Multi-product firms (with Carsten Eckel): REStud 2010 This file: Core model + applications to trade

3. 1. Introduction Goal: Integrate imperfect competition & intl. trade • Combine insights of trade theory and I.O. • Bring real firms into trade theory Has all this not been done? “new” trade theory revolution? Yes, but … really two revolutions: • Oligopoly in partial equilibrium • IIT (cross-hauling), “strategic” trade policy • Monopolistic competition in general equilibrium • IIT (love of variety), MNC’s, “new” economic geography • Extensions to heterogeneous firms [Melitz, Em 2003] & endogenous organizational form [Antras, QJE 2003; Helpman, JEL 2006] Unfinished part of the revolution: • Oligopoly in general equilibrium

4. Why “General Equilibrium”? - Interaction between goods and factor markets Why oligopoly not competition (perfect or monopolistic)? More realistic assumptions? • infinitely elastic supply of atomistic firms • no barriers to entry or exit • no strategic behaviour New light on central questions in trade theory: • Trade patterns; Gains from trade; Trade policy and income distribution Adding oligopoly to GE also allows new issues to be addressed: • Trade and wages debate: non-price interaction • Trade and competition; competitive advantage [Porter] • Effects of trade on market structure

5. Problems with Oligopoly in General Equilibrium • Large firms have monopsony power • Large firms can influence GNP • Reaction functions badly behaved; equilibrium may not exist [Roberts-Sonnenschein, Em 1977] • Is profit maximization well defined? [Gabszewicz/Vial, JET 1972] Previous attempts to embed oligopoly in GE: • "Perceived" versus "actual" demand curves [Negishi RES 1961] • Imperfect competition in goods & labour markets [Hart QJE 1982] Key idea in GOLE approach: Firms should be large in their own market, but small in the economy Resolution: Model a continuum of oligopolistic sectors: [Samuelson, REStats 1964; DFS, AER 1977] • Firms take factor prices, GNP, and prices in other sectors as given • But: they have market power in their own sector • Labour market economy-wide and perfectly competitive

6. Plan 1. Introduction Three technical building blocks of “GOLE”: • Demand: “Continuum-quadratic preferences” • Specialisation patterns in an international oligopoly • Linking factor and goods markets Applications: • General Oligopolistic Equilibrium: Autarky • Free Trade with Symmetry and Full Diversification: • Gains from trade • Trade and income distribution • Volume of trade • Changes in International Competitiveness

7. Plan 1. Introduction Three technical building blocks of “GOLE”: • Demand: “Continuum-quadratic preferences” • Specialisation patterns in an international oligopoly • Linking factor and goods markets Applications: • General Oligopolistic Equilibrium: Autarky • Free Trade with Symmetry and Full Diversification: • Gains from trade • Trade and income distribution • Volume of trade • Changes in International Competitiveness

8. 2. Demand: Continuum-Quadratic Preferences • How to operationalise “large in the small, small in the large”? • “Frisch demands”  + Additive separability • [Browning-Deaton-Irish Em 1985] • Frisch: demands depend on all prices and marginal utility of income only • Frisch + Additivity: Demands depend on own price and MUI only • MUI a "sufficient statistic" for the rest of the economy Also desirable to have aggregation over agents (countries) • Frisch + Gorman Polar Form [Pollak RES 1971] i.e., a “translated” CES; special cases: LES, CES, quadratic

9. Continuum-Quadratic Preferences Max U subject to: • Add x0 → U becomes quasi-linear → l =1 • Widely used in I.O. • Also (with differentiated products) by Melitz-Ottaviano (REStud 2008) • Stochastic consumption; financial economics: • Combine adjacent periods, t, and t1 → Euler equation • Ignore l, which is independent of t

10. 2. Continuum-Quadratic Preferences (cont.) Compare Dixit-Stiglitz preferences: • Combined with a Cobb-Douglas aggregator function this allows a full GE analysis • Quasi-linear variant introduced by Spence

11. CQ versus DS Preferences • In both: l is a “sufficient statistic” for the rest of the economy in each sector. • Perceived demand functions: linear vs. iso-elastic (iso-elastic much harder in oligopoly) • Satiation is possible with CQ: good and bad • DS homothetic; CQ quasi-homothetic

12. 3. Specialisation Patterns in Cournot Competition Simple Cournot trade model: partial equilibrium [Brander (JIE 1980), but here with integrated rather than segmented markets.] • Given numbers of firms at home & abroad: n, n* • Perceived inverse demand curve: • Firms in each country have identical costs: c, c* • Home sales with no foreign firms: Home sales with foreign firms:

13. c H firms unprofitable when n*=0 a' c* a'

14. c H firms unprofitable when n*>0 a' c* a'

15. c a ' H firms profitable c* a '

16. c Symmetrically: a ' F firms profitable c* a '

17. O: No home or foreign production c F: Foreign production only Equilibrium Production Patterns for Arbitrary Home and Foreign Costs a' H: Home production only HF: Home and foreign production c* a'

18. O: No home or foreign production c F: Foreign production only Compare Perfect Competition: Cone of Diversification Vanishes a' H: Home production only c* a'

19. 4. Factor Markets and Threshold Sectors • Continuum of sectors, indexed by zÎ [0,1] • Assume a Ricardian cost structure: c(z) = wa(z); c*(z) = w*a*(z) • Assume home more efficient in low-z sectors Assumption 1: y(z) decreasing, y*(z) increasing, in z [DFS: a(z)/a*(z) increasing in z] [Special case: a¢>0 , a*¢<0 ] • Perfect competition: specialisation threshold: c(z)=c*(z) • Here: 2 threshold sectors: • Incomplete specialisation: less efficient firms can survive

20. a(z), a*(z) a0*+1 a(z) a*(z) Foreign production a0 Home production 0 1 z Home and Foreign Technology Distributions

21. c Foreign production only O Equilibrium Production Patterns for a Given Cost Distribution c(1) Home production only Home and foreign production c(0) c* c*(1) c*(0)

22. c O F Fig. 1: Illustrative Equilibrium Configurations a' SD SOS H DD SS HF c* a'

23. Plan 1. Introduction Three technical building blocks of “GOLE”: • Demand: “Continuum-quadratic preferences” • Specialisation patterns in an international oligopoly • Linking factor and goods markets Applications: • General Oligopolistic Equilibrium: Autarky • Free Trade with Symmetry and Full Diversification: • Gains from trade • Trade and income distribution • Volume of trade • Changes in International Competitiveness

24. 5. General Oligopolistic Equilibrium: Autarky Full employment: Firm output and price: Equilibrium wage: Welfare: • Competition Effect: Welfare increasing in n • BUT: Only if sectors differ: s2>0 [Lerner RES 1933-34]

25. 6. General Oligopolistic Equilibrium: Free Trade Three nominal variables: w, w*,l • Absolute values are indeterminate • Convenient normalisation: l = 1 Full employment: Threshold sectors:

26. 2. Competition Effect 1. Market Size Effect 3. Comparative Advantage Effect 6a. Free Trade with Symmetry and Diversification Symmetry: L=L*, a=a*, n=n*, m1=m1*, s2= s*2 => w=w*, l=l* Full diversification (“DD”): z~ = 1, z*~=0 Wage: Recall: • d : "technological dissimilarity" a.k.a. "comparative advantage" • Tends to lower wage; may dominate market size effect

27. Symmetric Free Trade (cont.) Gains from Trade? Recall: • Zero in a “featureless world”: s2 = d= 0 • [Lerner, RES 1933-34] • Strictly positive if d = 0 but some technological heterogeneity across sectors: s2> 0 (competition effect) • i.e., pro-competitive gains even when no trade, and all sectors identical ex anteandex post • Compare Brander (JIE 1980): Here, gains even when markets are integrated • Increasingly so the greater is comparative advantage d • [All this, despite complete symmetry and incomplete specialisation]

28. Symmetric Free Trade (cont.) Implications for Income Distribution • Recall: • Market size effect tends to raise wage • Competition and comparative advantage effects tend to reduce it • Latter may dominate for large d • Intuition: At initial wage, more workers are laid off in less productive sectors than are absorbed in more productive ones. • But: Aggregate welfare always rises • Implication: profits may increase because of comparative advantage • Contrary to partial equilibrium [Anderson-Donsimoni-Gabszewicz, IER 1989] • Even stronger result: Share of wages in GDP is decreasing in d • May even be lower than in autarky • Intuition: Barriers to entry allow profit-earners to capture all the gains from trade

29. Symmetric Free Trade (cont.) Volume of Trade? • Import volumes m(z) are increasing in n • Import shares m(z)/x(z) are increasing in n on average • So, oligopoly may explain the “missing trade” mystery [Trefler, AER 1995; Davis/Weinstein, AER 2001; Ruffin, JIE 2003]

30. 7. Changes in International Competitiveness Now: Comparative statics at a free-trade equilibrium with some specialisation Full employment at Home: L = LD(w,w*,n) Effects of a rise in w: • Intensive margin: Active home firms contract • Extensive margin: Home firms exit marginal sectors (though for small changes this effect vanishes) Conversely for a rise in w* Similarly for full employment condition abroad: L* = LD*(w*,w,n)

31. w L* L w* Fig. 2: Stability of Equilibrium

32. 7. Changes in International Competitiveness (cont.) Now: Assume home country becomes more competitive: n­ At initial wages: • LD­ and LD* ¯ • z~unchanged • z~*­ i.e., foreign specialises in direction of comparative advantage

33. w L* L w* Fig. 3: Comparative versus Competitive Advantage: Effects of an Increase in n

34. 7. Changes in International Competitiveness (cont.) Allowing for wage changes: • presumption that w/w* rises [sufficient condition: own effects of w and w* on LD and LD* dominate cross effects] • presumption that w rises and w* falls [sufficient condition: own effects of w,w* and n on LD and LD* dominate cross effects] • presumption that z~ falls i.e., home specialises in the direction of comparative advantage [sufficient condition: w rises and w* falls] Conclusion: Competitive advantage reinforces comparative advantage

35. 8. Conclusion Model: General Oligopolistic Equilibrium [“GOLE”] Details: • Continuum-quadratic preferences • Cournot + Ricardo, or Brander + Samuelson Results, in contrast with perfect competition: • Production patterns more diverse, incomplete specialization • Gains from trade even if countries identical ex post & ex ante • Competition effects operate only if sectors heterogeneous • Profits may rise with free trade • Volume of trade is lower (“missing trade”) • Competitive advantage influences resource allocation Extensions and Applications ... Broader implications: • For some questions, oligopoly richer than competition (either perfect or monopolistic)