INTERNATIONAL TRADE
IN GENERAL
OLIGOPOLISTIC EQUILIBRIUM
J. Peter Neary
University of Oxford and CEPR
2011
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
2
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
3
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
4
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
5
Plan
1.
2.
3.
4.
Introduction
Three technical building blocks of “GOLE”:
Demand: “Continuum-quadratic preferences”
Specialisation patterns in an international oligopoly
Linking factor and goods markets
5.
6.
Applications:
General Oligopolistic Equilibrium: Autarky
Free Trade with Symmetry and Full Diversification:
i.
ii.
iii.
7.
Gains from trade
Trade and income distribution
Volume of trade
Changes in International Competitiveness
6
Plan
1.
2.
3.
4.
Introduction
Three technical building blocks of “GOLE”:
Demand: “Continuum-quadratic preferences”
Specialisation patterns in an international oligopoly
Linking factor and goods markets
5.
6.
Applications:
General Oligopolistic Equilibrium: Autarky
Free Trade with Symmetry and Full Diversification:
i.
ii.
iii.
7.
Gains from trade
Trade and income distribution
Volume of trade
Changes in International Competitiveness
7
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
U [{ x ( z )}] 

1
u [ x ( z )] dz
0
 p ( z )  1 u '[ x ( z )]
Also desirable to have aggregation over agents (countries)
– Frisch + Gorman Polar Form
[Pollak RES 1971]
U [{ x ( z )}] 

1

 ( z )[ x ( z )   ( z )] dz
0
i.e., a “translated” CES; special cases: LES, CES, quadratic
8
Continuum-Quadratic Preferences
1
U [{ x ( z )}]  0 [ ax ( z )  12 bx ( z ) ] dz
2
Max U subject to:

1
p( z) x ( z)dz  I
0
 x ( z )  b1 [ a   p ( z )],
 { p ( z )}, I  
a 0 p ( z ) dz  bI
1
1
2
0 p ( z ) dz
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 t1 → Euler equation
• Ignore , which is independent of t
9
2. Continuum-Quadratic Preferences (cont.)
Compare Dixit-Stiglitz preferences:

1

U [{ x ( z )}]  0 x ( z ) dz
 x ( z )   p ( z ) /  

,

1 /
,
  1 /( 1   )
 { p ( z )}, I    / P I

1 
,

P  0 p ( z )
1
1 
dz

1 /( 1  )
• Combined with a Cobb-Douglas aggregator function this
allows a full GE analysis
• Quasi-linear variant introduced by Spence
10
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  a a ,
*
I 
u~ 
a
1
b
[ a   p ( z )]
   
1
*
p
b
2
p
OR
~
2
p
U   2
11
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:
p  a ' b ' x
a'  a /  ,
b'  b /  ,
x  y  ny  n * y *
• Firms in each country have identical costs: c, c*
Home sales with no foreign firms:
y 
a  c
b  ( n  1)
0

c  a
Home sales with foreign firms:
y 
a   ( n *  1) c  n * c *
b  ( n  n *  1)

0

c
a  n * c *
n * 1
( n *  1 )( a   c )  n * ( a   c *)
12
c
H firms unprofitable
when n*=0
 ( c ; n  0)  0
a'
*
a'
c*
13
 ( c , c ; n  0)  0
*
c
a'
*
H firms unprofitable
when n*>0
a'
n 1
*
a'
c*
14
c
a'
H firms profitable
a'
n * 1
a'
c*
15
Symmetrically:
c
a'
F firms profitable
a'
n * 1
a'
n1
a'
c*
16
c
O: No home or
foreign production
F: Foreign
production only
a'
a'
n 1
*
HF: Home
and foreign
production
a'
n 1
H: Home
production only
a'
Equilibrium Production Patterns for
Arbitrary Home and Foreign Costs
c*
17
c
O: No home or
foreign production
F: Foreign
production only
a'
H: Home
production only
a'
Compare Perfect Competition:
Cone of Diversification Vanishes
c*
18
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:
z  [ 0 , ~z *] : No foreign firms profitable
z  [ ~z *, ~z ] : Both home and foreign firms profitable
z  [ ~z ,1 ] :
No home
firms
profitable
• Incomplete specialisation: less efficient firms can survive
19
(z),
*(z)
*+1
(z)
*(z)
Foreign production

Home production
0
*
~
z
~
z
z
1
Home and Foreign Technology Distributions
20
c
c(1)
Foreign
production only
O
z  1
z  ~
z
Home
production only
*
z  ~
z
c(0)
Home
and foreign
production
c*(1)
z  0
c*(0)
Equilibrium Production Patterns for a
Given Cost Distribution
c*
21
c
O
F
a'
SD
SOS
H
DD
a'
n * 1
SS
HF
a'
n 1
a'
c*
Fig. 1: Illustrative Equilibrium Configurations
22
Plan
1.
2.
3.
4.
Introduction
Three technical building blocks of “GOLE”:
Demand: “Continuum-quadratic preferences”
Specialisation patterns in an international oligopoly
Linking factor and goods markets
5.
6.
Applications:
General Oligopolistic Equilibrium: Autarky
Free Trade with Symmetry and Full Diversification:
i.
ii.
iii.
7.
Gains from trade
Trade and income distribution
Volume of trade
Changes in International Competitiveness
23
5. General Oligopolistic Equilibrium: Autarky
Full employment:
1
L    ( z )ny ( z )dz
0
Firm output and price:
a ' c( z )
y( z) 
Equilibrium wage:
a   w ( z )
p(z) 
b(n  1)
a ' nc ( z )
n 1

a  nw  ( z )
n 1
n 1

 1
wa   wa   a 1 
bL 
n

 2
1 
Welfare:
b '(n  1)


1
 ( z )dz
2 
0
~
2
p
U a   (  2 ) a  

a
1
( n  1)

2
 2 ( z )dz
0
( a  2 an  1 w a  n  2 w a )
2
( n  1)
2

1
2
2
2

2
( a  1  bL )
2
2
2

2
  2  1
2
• Competition Effect: Welfare increasing in n
• BUT: Only if sectors differ: 2>0
[Lerner RES 1933-34]
24
6. General Oligopolistic Equilibrium: Free Trade
Three nominal variables: w, w*, 
• Absolute values are indeterminate
• Convenient normalisation:   1
Full employment:
~
z*
L 
~
z
  ( z) x ( z)dz    ( z)ny ( z)dz
0
~
z*
~z
1
*
*
*
*
*
L    ( z ) n y ( z ) dz    ( z ) x ( z ) dz
~z *
~z
Threshold sectors:
y(~
z) 0
*
*
y (~
z )0


* * *
*
a  n w  (~
z )  ( n  1) w  ( ~
z ), ~
z 1
*
* *
*
a  nw  ( ~
z )  ( n  1) w  ( ~
z ),
*
~
z 0
25
6a. Free Trade with Symmetry and Diversification
Symmetry: L=L*, a=a*, n=n*, 1=1*, 2= *2
=> w=w*, =*
Full diversification (“DD”): z~ = 1, z*~=0
Wage:
2. Competition Effect
Recall:
2n  1
1


w f   w   a1 
bL 
2
n

 2  n
n 1

 1
wa   a 1 
bL 
n

 2
1. Market Size Effect
3. Comparative
Advantage Effect
  2     z   *  z  dz
 : "technological dissimilarity" a.k.a. "comparative advantage"
• Tends to lower wage; may dominate market size effect
26
Symmetric Free Trade (cont.)
Gains from Trade?
~
2
2
U f   (  p ) f  

a
( 2 n  1)
2
( 2 n 1)
2
a
2
 4 an  1 w f  2 n ( 2  2   ) w f
2

22
  a  1
 bL
22  
22  

2
2
1
2

Recall:
~
Ua  
a

2
( n  1)
2
2
2

( a  1  bL )
2

2

22  

 2(  n ) 2
2

2
2
• 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)
•
•
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]
27
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
28
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]
29
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)
30
w
L*
L
w*
Fig. 2: Stability of Equilibrium
31
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
32
w
L*
L
w*
Fig. 3: Comparative versus Competitive Advantage:
Effects of an Increase in n
33
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
34
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)
35