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Competition Among the Big and Competition Among the Big and the Smallthe Small
Ken-Ichi Shimomura and Jacques-François Thisse
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Armchair evidence shows that many industries are characterized by the coexistence of a few large commercial or manufacturing firms,
which are able to affect the market outcome, as well as of a myriad of small family-run
businesses with very few employees, each of which has a negligible impact on the market
To the best of our knowledge, such a mixed market structure has been overlooked in the
literature
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According to SchumpeterAccording to Schumpeter
“In the case of retail trade the competition that matters arises not from additional shops of the same type, but from the department store, the chain store, the mail-order house and the supermarket
which are bound to destroy those pyramids sooner or later”
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Bertrand and Kramarz (2002) haveshowed that the Royer-Raffarin Lawthat the enforcement of this law has
hada negative impact on job creation.
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The purpose of this paper is precisely to provide a unified approach to study
(i) how those two types of firms interact to shape the market outcome and
(ii) whether or not it is socially desirable to have large and/or small firms in
business
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the oligopoly à la Cournot with differentiated products
and
the monopolistic competition model of the Chamberlin-type
Two standard models of industrial organizationTwo standard models of industrial organization
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The mixed market structure model obeys different rules than standard
oligopoly models
A specific model
CES
discrete (atoms) and negligible varieties ofthe differentiated product
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The ModelThe ModelTwo goods
Two production sectorsOne production factor
(labor)
The first good is homogenous and produced under constant returns and perfect competition
The other good is a horizontally differentiated product.
It is supplied both by oligopolistic firms and by monopolistically competitive firms (MC-firms)
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Two sub-sectors governed by different forms of competition
Let N > 1 be the number ofoligopolistic firms and M > 0 the
massof MC-firms
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(i) A representative consumer(i) A representative consumer
XdiiqQN
j
Mj
/)1(
10
)(Maximize
MN
jjj YXdiiqipQP
01
)()(subject to
Price index of the MC-subsector
/)1(
0)1/(
0 )(
M
diipP
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/)1(
0
)1/(
N
jjP
Price index of the differentiated product
Demand functions
,,1 )1/()1/(1iii PDPQ
,),()(1)( )1/()1/(1 ipdipiq
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(ii) Oligopolistic firms(ii) Oligopolistic firms
FCQQQ
QQQQ iij ji
iNi
1,;, 01
(iii) MC-firms(iii) MC-firms
ficqipdipi )(,),()()(
cp )1/(
)1/(1
1
c
q and
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The Market OutcomeThe Market OutcomeA mixed market equilibrium is defined as a
state in which the following conditions simultaneously hold
(i) the representative consumer maximizes her utility subject to the
budget constraint
(ii) both oligopolistic and MC-firms maximize their own profits with respect to
output(iii) the mass of MC-firms is positive and they earn zero profits while oligopolistic firms earn
positive profits
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/1
0 )()(1 QNQ
Firms are “income-takers”
A symmetric mixed market equilibrium in which all oligopolistic firms choose the same output
Q, whereas all MC-firms have the same production policy q
Equilibrium price indices
/)1(
0 McP
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Proposition 1. The price at which oligopolistic firms sell their output decreases when the mass of MC-firms increases
Proposition 2. There exists a unique symmetric market equilibrium. This equilibrium is mixed if and only if …
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CQQfcFNLf
M
1
1111
The Industry StructureThe Industry Structure
Proposition 3. Both the equilibrium mass of MC-firms and quantity index of this sub-sector decrease when the number of oligopolistic firms increases
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Proposition 5. The industry price index decreases when the number of oligopolistic firms increases
The shrinking of the MC-sector generated by the entry of a large firm is sufficiently strong to permit the expansion of the output of each
oligopolistic firm
Proposition 4. The equilibrium output of an oligopolistic firm increases when the number of oligopolistic firms rises
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Is Schumpeter right?Is Schumpeter right?
The MC-subsector disappears when the number of oligopolistic firms is sufficiently larg
e
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)1(11 W
WelfareWelfare
Proposition 6. Consider a symmetric mixed market equilibrium, then, the total net income increases when the number of oligopolistic firms increasesProposition 7. Consider a symmetric mixed market equilibrium, then the social welfare increases when the number of oligopolistic firms increases
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CONCLUSIONSCONCLUSIONS
(i) A mixed market with several large firms and a small number of small firms is more efficient than a market with fewer large firms and a larger number of small firms
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(ii) Considering a traditional economy populated with small businesses, more affluent societies and technological progress have combined to facilitate the entry of a growing number of big firms. This in turn triggers the decline of small businesses in mixed markets endowed with old and small firms as well as modern and big firms. This concurs with the prediction made by many observers, ranging from Karl Marx to Robert Lucas. However, the fall in small firms' fixed costs sparked by the development of the new information technologies has permitted the revival of SMEs.
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THE BOTTOM LINETHE BOTTOM LINE
Small need not be beautiful