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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

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 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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17

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