Upload
heather-wade
View
214
Download
0
Embed Size (px)
Citation preview
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
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
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
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
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:
5. General Oligopolistic Equilibrium: Autarky
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
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)
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)