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

2. 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. 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. 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. 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. 6 Plan 1. Introduction Three technical building blocks of “GOLE”: 2.Demand: “Continuum-quadratic preferences” 3.Specialisation patterns in an international oligopoly 4.Linking factor and goods markets Applications: 5.General Oligopolistic Equilibrium: Autarky 6.Free Trade with Symmetry and Full Diversification: i.Gains from trade ii.Trade and income distribution iii.Volume of trade 7.Changes in International Competitiveness

7. 7 Plan 1. Introduction Three technical building blocks of “GOLE”: 2.Demand: “Continuum-quadratic preferences” 3.Specialisation patterns in an international oligopoly 4.Linking factor and goods markets Applications: 5.General Oligopolistic Equilibrium: Autarky 6.Free Trade with Symmetry and Full Diversification: i.Gains from trade ii.Trade and income distribution iii.Volume of trade 7.Changes in International Competitiveness

8. 8 2. Demand: Continuum-Quadratic Preferences 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 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

9. 9 Continuum-Quadratic Preferences Max U subject to: Add x 0 → U becomes quasi-linear →  =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 , which is independent of t

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

11. 11 CQ versus DS Preferences In both:  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. 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. 13 c c* a' H firms unprofitable when n*=0

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

15. 15 c c* a ' H firms profitable

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

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

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

19. 19 4. Factor Markets and Threshold Sectors Continuum of sectors, indexed by z  [0,1] Assume a Ricardian cost structure: c(z) = w  (z)  c*(z) = w*    (z) Assume home more efficient in low-z sectors Assumption 1: y(z) decreasing, y*(z) increasing, in z [DFS:  (z)/  *(z) increasing in z] [Special case: ,    ] Perfect competition: specialisation threshold: c(z)=c*(z) Here: 2 threshold sectors: Incomplete specialisation: less efficient firms can survive

20. 20 Home and Foreign Technology Distributions z  (z)   *(z) 10 Home production Foreign production  *(z) (z)(z)   *+1 

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

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

23. 23 Plan 1. Introduction Three technical building blocks of “GOLE”: 2.Demand: “Continuum-quadratic preferences” 3.Specialisation patterns in an international oligopoly 4.Linking factor and goods markets Applications: 5.General Oligopolistic Equilibrium: Autarky 6.Free Trade with Symmetry and Full Diversification: i.Gains from trade ii.Trade and income distribution iii.Volume of trade 7.Changes in International Competitiveness

24. 24 Full employment: Firm output and price: Welfare: 5. General Oligopolistic Equilibrium: Autarky Equilibrium wage: Competition Effect: Welfare increasing in n BUT: Only if sectors differ:  2 >0 [Lerner RES 1933-34]

25. 25 6. General Oligopolistic Equilibrium: Free Trade Three nominal variables: w, w*,  Absolute values are indeterminate Convenient normalisation:  Full employment: Threshold sectors:

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

27. 27 Symmetric Free Trade (cont.) Gains from Trade? Zero in a “featureless world”:  2 =  = 0 [Lerner, RES 1933-34] Strictly positive if  = 0 but some technological heterogeneity across sectors:  2 > 0 (competition effect) Recall: i.e., pro-competitive gains even when no trade, and all sectors identical ex ante and ex post Compare Brander (JIE 1980): Here, gains even when markets are integrated Increasingly so the greater is comparative advantage  [All this, despite complete symmetry and incomplete specialisation]

28. 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  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  May even be lower than in autarky Intuition: Barriers to entry allow profit-earners to capture all the gains from trade

29. 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. 30 7. Changes in International Competitiveness Now: Comparative statics at a free-trade equilibrium with some specialisation Full employment at Home: L = L D (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* = L D* (w*,w,n)

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

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

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

34. 34 Allowing for wage changes: presumption that w/w* rises [sufficient condition: own effects of w and w* on L D and L D* dominate cross effects] presumption that w rises and w* falls [sufficient condition: own effects of w, w* and n on L D and L D* 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 7. Changes in International Competitiveness (cont.)

35. 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)