Oligopoly and Trade. Notes for Oxford M.Phil. International Trade. J. Peter Neary. University of Oxford. November 26, 2009

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1 Oligopoly and Trade Notes for Oxford M.Phil. International Trade J. Peter Neary University of Oxford November 26, 2009 J.P. Neary (University of Oxford) Oligopoly and Trade November 26, / 11

2 Oligopoly and Trade Plan of Lectures Motivation Duopoly in Partial Equilibrium Trade Costs: "Reciprocal Dumping" Oligopoly in General Equilibrium Extensions J.P. Neary (University of Oxford) Oligopoly and Trade November 26, / 11

3 Motivation So far: "Imperfect competition" = Monopolistic Competition BUT: Only one form; closest to perfect competition Shares many properties: 1 Atomistic rms, ex ante identical; 2 No strategic behaviour. Empirical implausible: Increasing evidence that large rms account for bulk of trade; and that they are di erent from smaller ones; see: Bernard, Jensen, Redding and Schott (JEP 2007). Industrial organisation has "Two faces": 1 Size distribution of rms under perfect or monopolistic competition 2 Oligopoly: Small-group interaction. Seems worth exploring oligopoly in trade too; for short run at least. J.P. Neary (University of Oxford) Oligopoly and Trade November 26, / 11

4 Duopoly in Partial Equilibrium Brander (JIE 1981): Two countries, fully symmetric, one rm in each, partial equilibrium: Firms Home Foreign Markets Home x y Foreign x y Assume goods are perfect substitutes (not essential). Autarky: each rm is a domestic monopoly. Positive e ects of moving to free trade: Assume markets are segmented, though this is not essential. Assume rms engage in Cournot competition. Each rm faces competition at home, and sells in other s market. So: "cross-hauling" or "intra-industry trade in identical commodities"! Remarkable: no comparative advantage or diversity motive for trade. So: a new and distinct theory of trade. However: not obvious that in itself it is quantitatively important. Some evidence: Bernhofen (JIE 1999), Friberg-Ganslandt (JIE 2006). J.P. Neary (University of Oxford) Oligopoly and Trade November 26, / 11

5 Duopoly in Partial Equilibrium Autarky versus Free Trade: Figure y F H B F' H' x Cournot competition: Home reaction function (best-response function): HH 0. Foreign reaction function: FF 0. Autarky equilibrium: Zero imports (y = 0): F 0. Free-trade equilibrium: B. J.P. Neary (University of Oxford) Oligopoly and Trade November 26, / 11

6 Now, suppose that trade is costly: As long as trade costs are non-prohibitive, cross-hauling occurs. Markets are identical, so home rm charges the same in each; BUT: This means it must absorb some of the transport cost; Hence its pro t margin is lower on export sales: it is "dumping"; Since both rms are doing this, there is "reciprocal dumping". Welfare e ects of changes in transport costs are not simple: Home welfare is the sum of consumer surplus and home rm pro ts; Consumer surplus: Falls with t, since home prices rise. Pro ts in home market rise with t: reduced competition. Pro ts in foreign market fall with t: reduced export opportunities. These moves in opposite directions imply that pro ts fall for moves away from both autarky and free trade. J.P. Neary (University of Oxford) Oligopoly and Trade November 26, / 11

7 Components of Home Welfare: Figure B π * π 0 t t Figure: Components of Home Welfare as a Function of Transport Costs J.P. Neary (University of Oxford) Oligopoly and Trade November 26, / 11

8 The Linear Example Linear demands; constant marginal costs. p = a bx X = x + y p = a by Y = x + y π = (p c)x + (p c t)x Home Firm s FOC s: H : p c bx = 0! a c 2bx by = 0 H : p c t bx = 0! a c t 2bx by = bx a c Equilibrium in home market: = 1 2 by a c t! x = a 2c+c +t 3b y = a 2c 2t+c 3b Symmetrically: x = a 2c 2t+c 3b y = a 2c +c+t 3b Autarky: y = 0! t A = 2 1 (a 2c + c)! x A = a 2b c Pro ts on Home Sales: π = bx 2! d dt π = 2bx dx dt = 2 3 x > 0! d 2 π = 2 dt 2 3 dx dt = 9b 2 > 0 i.e., " in t raises home sales linearly, and raises pro ts on home sales by more the higher they are already (i.e., the higher is t): So, pro ts on home sales are convex in t. J.P. Neary (University of Oxford) Oligopoly and Trade November 26, / 11

9 The Linear Example II Pro ts on Exports: π = b (x ) 2 x = a 2c 2t+c 3b! d dt π = 2bx dx dt = 4 3 x < 0! d 2 π = 4 dt 2 3 dx dt = 9b 8 > 0 i.e., " in t lowers export sales linearly, but lowers pro ts on these sales by less the lower they are already (i.e., the higher is t): pro ts on foreign sales are convex in t. Total Pro ts (in symmetric equilibrium): d (π+π ) 8 < : dt = 2 3 x 4 3 x < 0 when x = x (i.e., t = 0) > 0 when x = 0 (i.e., t = t A ) = 0 when x = 2x (i.e., t = t M = a 2c+c 5 ) J.P. Neary (University of Oxford) Oligopoly and Trade November 26, / 11

10 The Linear Example III: Intuition Intuition: (i) Starting from free trade: Exports are harmed more by an increase in own costs than home sales are helped by an equal rise in rival s costs; Hence total sales and pro ts fall for a small increase in t at free trade. (ii) Starting from autarky: Exports are helped more by a fall in own costs than home sales are harmed by an equal fall in rival s costs; Hence total sales rise for a small reduction in t at autarky, and continue to rise monotonically as t falls. However, this does not translate into a monotonic rise in pro ts: Exports are initially zero, so the rise in sales has a negligible e ect on pro ts in the export market, whereas home sales are initially maximal, so the fall in sales has a rst-order e ect on home-market pro ts; Hence, overall pro ts fall for a small reduction in t at autarky. J.P. Neary (University of Oxford) Oligopoly and Trade November 26, / 11

11 The Story So Far Recap on the Brander model: Strategic interaction an independent explanation for trade; Competition e ects a new source of gains from trade; Highlights the threats and opportunities of trade for rms: i.e., more competition at home, increased markets abroad. Yet: Not really a full theory of trade. [Krugman: "There are two and a half theories of trade"!] Why: Mainly, because not embedded in general equilibrium So: We need to do this: Put Oligopoly into General Equilibrium: "GOLE" J.P. Neary (University of Oxford) Oligopoly and Trade November 26, / 11

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