INTERNATIONAL TRADE IN GENERAL OLIGOPOLISTIC EQUILIBRIUM

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INTERNATIONAL TRADE IN GENERALOLIGOPOLISTIC
EQUILIBRIUM

• J. Peter Neary
• University of Oxford and CEPR
• 2011

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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), MNCs, 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

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• 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

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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
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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

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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

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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

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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
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c
H firms unprofitable when n0
a'
c
a'
14
c
H firms unprofitable when ngt0
a'
c
a'
15
c
a '
H firms profitable
c
a '
16

• Symmetrically

c
a '
F firms profitable
c
a '
17
O No home or foreign production
c
F Foreign production only
a'
H Home production only
HF Home and foreign production
c
a'

• Equilibrium Production Patterns for
• Arbitrary Home and Foreign Costs

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O No home or foreign production
c
F Foreign production only
a'
H Home production only
c
a'

• Compare Perfect Competition
• Cone of Diversification Vanishes

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4. Factor Markets and Threshold Sectors

• Continuum of sectors, indexed by z Î 0,1
• Assume a Ricardian cost structure
• c(z) wa(z) c(z) wa (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 agt0 , alt0
• Perfect competition specialisation threshold
  c(z)c(z)
• Here 2 threshold sectors

• Incomplete specialisation less efficient firms
  can survive

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a(z), a(z)
a01
a(z)
a(z)
Foreign production
a0
Home production
1
0
z
Home and Foreign Technology Distributions
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c
Foreign production only
O
c(1)
Home production only
Home and foreign production
c(0)
c
c(0)
c(1)

• Equilibrium Production Patterns for a Given Cost
  Distribution

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c
O
F
a'
SD
SOS
H
DD
SS
HF
c
a'

• Fig. 1 Illustrative Equilibrium Configurations

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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

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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 s2gt0
  Lerner RES 1933-34

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6. General Oligopolistic Equilibrium Free Trade

• Three nominal variables w, w, l
• Absolute values are indeterminate
• Convenient normalisation l 1
• Full employment

Threshold sectors
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6a. Free Trade with Symmetry and Diversification
Symmetry LL, aa, nn, m1m1, s2 s2
gt ww, ll Full
diversification (DD) z 1, z0 Wage
Recall

• d "technological dissimilarity" a.k.a.
  "comparative advantage"
• Tends to lower wage may dominate market size
  effect

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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 gt 0
  (competition effect)

• 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 d
• All this, despite complete symmetry and
  incomplete specialisation

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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

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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

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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)

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w
L
L
w
Fig. 2 Stability of Equilibrium
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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

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

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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)