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

INTERNATIONAL TRADE

IN GENERAL

OLIGOPOLISTIC 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 marketsWhy 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”:

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

Plan

1. Introduction





Applications:






8

2. Demand: Continuum-Quadratic Preferences

1

0[{ ( )}] [ ( )]U x z u x z dz

Also desirable to have aggregation over agents (countries)– Frisch + Gorman Polar Form

[Pollak RES 1971]

1( ) '[ ( )]p z u x z

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

1

0[{ ( )}] ( )[ ( ) ( )]U x z z x z z dz

9

Continuum-Quadratic Preferences

10

221 ])()([)}]([{ dzzbxzaxzxU

Max U subject to:p z x z dz I( ) ( ) 0

1

10

2

101

)(

)()},({,)]([)(

dzzp

bIdzzpaIzpzpazx b

Add x0 → 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 t1 → Euler equation

• Ignore, which is independent of t

10

Compare Dixit-Stiglitz preferences:

2. Continuum-Quadratic Preferences (cont.)

)1/(1,)()}]([{/11

0 dzzxzxU

)1/(1110

1 )(,/)},({,/)()(

dzzpPIPIzpzpzx

• 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: 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

x z x z x z a p zb( ) ( ) ( ) [ ( )]* 1

a a a * *,

pp

p

UORba

Iu 2

2

2

1 ~~

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:

**,/',/''' ynnyyxbbaaxbap

• Firms in each country have identical costs: c, c*

Home sales with no foreign firms:

acnbca

y

0)1(

Home sales with foreign firms:

1***

0)1*(

**)1*(

ncna

cnnb

cncnay

*)(*))(1*( cancan

13

c

c*

a'

a'

H firms unprofitablewhen n*=0

*( ; 0) 0c n

14

c

c*

a'

a'

a

n

'* 1

H firms unprofitablewhen n*>0

* *( , ; 0) 0c c n

15

c

c*a '

a '

a

n

'

*1

H firms profitable

16

Symmetrically:

c

c*a '

a '

a

n

'

*1

a

n

'

1

F firms profitable

17

Equilibrium Production Patterns forArbitrary Home and Foreign Costs

c

c*

HF: Homeand foreignproduction

O: No home orforeign production

a

n

'* 1

a

n

'

1

F: Foreign production only

H: Homeproduction only

a'

a'

18

Compare Perfect Competition:Cone of Diversification Vanishes

c

c*

O: No home orforeign productionF: Foreign

production only

H: Homeproduction only

a'

a'

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:

profitable firmsforeign No:*]~,0[ zz profitable firmsforeign and homeBoth :]~*,~[ zzz

profitable firms homeNo :]1,~[ zz

• Incomplete specialisation: less efficient firms can survive

20Home and Foreign Technology Distributions

z

(z)*(z)

10~z~*z

Home production

Foreign production

*(z) (z)*+1

21

Equilibrium Production Patterns for a Given Cost Distribution

c

c*

O

c*(0)

z z~

z 0

z 1

z z~ *

c*(1)

c(0)

c(1)

Homeand foreignproduction

Foreign production only

Homeproduction only

22Fig. 1: Illustrative Equilibrium Configurations

c

c*

a'

a'a

n

'

1

1*

'

n

a

O

SS

SOS

SD

DD H

F

HF

23

Plan

1. Introduction





Applications:






24

Full employment: 1

0( ) ( )L z ny z dz

Firm output and price:' ( ) ( )

( )'( 1) ( 1)

a c z a w zy z

b n b n

Welfare:


12

1 1 21 20 0

1 1

( ) ( )

a a

nw w a bL

n

z dz z dz

Equilibrium wage:

• Competition Effect: Welfare increasing in n• BUT: Only if sectors differ: 2>0 [Lerner RES 1933-34]

1

)(

1

)(')(

n

znwa

n

zncazp

)2()1(

1)(

~ 22

21

222

2aaa

pa wnwana

nU

212

2

2

21

2

2

2

2 )(

)1(

bLa

n

a

25

6. General Oligopolistic Equilibrium: Free Trade

Three nominal variables: w, w*,• Absolute values are indeterminate

• Convenient normalisation: Full employment:

L z x z dz z ny z dzz

zz

( ) ( ) ( ) ( )~*

~~*

0

1

~

*~

~

**** )()()()(* z

z

z

dzzxzdzzynzL �

Threshold sectors:

1~),~()1()~(0)~( **** zzwnzwnazy

0~),~()1()~(0)~( ******* zzwnznwazy

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:

12

2 1 1

2f

nw w a bL

n n

12

1 1a

nw a bL

n

Recall:

1. Market Size Effect

2. Competition Effect

3. ComparativeAdvantage Effect

*2 z z dz

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

27

Symmetric Free Trade (cont.)Gains from Trade?

22

2

2

2

21

2

2

2

2

22

21

2

)12(122

)(2

2

2

2

2

2

)12(

)2(24)(~

2

nbLa

n

a

wnwanaU ffnfpf

• 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]

2

21

2

2

2

2 )(

)1(

~

bLa

n

aU a

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

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


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

L

L*

Fig. 2: Stability of Equilibrium

w

w*

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

L

L*

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

w

w*

34

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~ fallsi.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

8. ConclusionModel: 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)

Documents

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