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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

11

/)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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17

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