1 Competition Among the Big and the Small Ken-Ichi Shimomura and Jacques-François Thisse.
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Transcript of 1 Competition Among the Big and the Small Ken-Ichi Shimomura and Jacques-François Thisse.
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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) have
showed that the Royer-Raffarin Law
that the enforcement of this law has had
a 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 of
the differentiated product
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The ModelThe Model
Two goods
Two production sectors
One 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
M
j
/)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 i
ij ji
iNi
1,;, 01
(iii) MC-firms(iii) MC-firms
ficqipdipi )(,),()()(
c
p )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 M
cP
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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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CQQfc
FNLf
M
1
11
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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 increases
Proposition 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