Cournot, Bertrand or Chamberlin: Toward a reconciliation

• Author: Jacques‐François Thisse,Evgeny V. Zhelobodko,Mathieu Parenti,Alexander V. Sidorov
• DOI: http://doi.org/10.1111/ijet.12116
• Published date: 01 March 2017
• Date: 01 March 2017

doi: 10.1111/ijet.12116

Cournot, Bertrand or Chamberlin: Toward a reconciliation

Mathieu Parenti,∗Alexander V. Sidorov,†Jacques-Franc¸ois Thisse‡and Evgeny V. Zhelobodko§

This paper compares the market equilibria in a differentiated industry under Cournot, Bertrand,

and monopolistic competition. This is accomplished in a one-sector economywhere consumers

are endowed with separable preferences. When firms are free to enter the market, monopolisti-

cally competitive firms charge lower prices than oligopolistic firms, while the mass of varieties

provided by the market is smaller under the former than the latter. Ifthe economy is sufficiently

large, Cournot, Bertrand and Chamberlin solutions converge toward the same market outcome,

which may be a competitive or a monopolistically competitive equilibrium, depending on the

nature of preferences.

Key wor ds Cournot competition, Bertrand competition, monopolistic competition, free entry

JEL classification D43, D41, F12, L13

Accepted 9 January 2016

1 Introduction

The theory of imperfect competition is dominated by two approaches that seem to clash with each

other. Whereasindustrial organization stresses the importance of strategic interactions among firms,

the model of imperfect competition used in economic fields such as trade, economic geography and

growth is the CES model of monopolistic competition developed by Dixit and Stiglitz (1977).In

this model, any form of interaction among firms is absent. In addition, in oligopolistic markets,

price (Bertrand) and quantity (Cournot) competition deliver market solutions that typically differ,

making it hard to formulate robust predictions. The purpose of this paper is to contribute to this

debate by providing a comparison of these three types of competition. This is accomplished in an

economy involving one sector and a population of consumers endowed with separable preferences

and a finite number of labor units. Although we recognize that additive preferences are restrictive,

they are widely used in the literature and suffice to shed new light on old questions. Note also that

the budget constraint implies that firms do not behave like monopolists.

According to the folk theorem of competitive markets, perfect competition almost holds when

firms are small relative to the size of the market. In the same spirit, there was a live debate in the

1930s between, on one side, Chamberlin (1933) and, on the other, Robinson (1934) and Kaldor

∗ECARES, Universit´

e Libre de Bruxelles (Belgium) and CEPR. Email: mparenti@ulb.ac.be

†Novosibirsk State University, Sobolev Institute for Mathematics and NRU-Higher School of Economics(Russia).

‡CORE-UCLouvain (Belgium), NRU-Higher School of Economics (Russia)and CEPR.

§Novosibirsk State Universityand NRU-Higher School of Economics (Russia).

We thank an anonymousreferee, Alexander Osharin and Philip Ushchev for comments and suggestions. This study has

been funded by the Russian AcademicExcellence Project 5-100, and Russian Foundation for Basic Research 15-06-05666.

International Journal of Economic Theory 13 (2017) 29–45 © IAET 29

International Journal of Economic Theory

Cournot, Bertrand or Chamberlin Mathieu Parenti et al.

(1935) about the relevance of monopolistic competition as a possible market structure. Robinson

and Kaldor maintained against Chamberlin that perfect competition must emerge when the number

of firms becomes arbitrarily large relative to market size. No clear answer came out of this debate

because these authors lacked the analytical tools to study the convergence issue. Our paper shows

that the answer depends on the nature of preferences.

It was not until 1980 that Novshekwas able to tackle the convergence issue rigorously for Cournot

games in which firms produce a homogeneous good and face U-shaped average costs. Inthe spir it of

methods used in general equilibrium theory, Novshek (1980) chose to make firms small relative to

the market by replicating the demand side. When the number of replications is sufficiently large, the

equilibrium is nearly competitive. As for Bertrand differentiated oligopoly,Novshek and Chowdhury

(2003) showed that the convergence of the Bertrand equilibria toward the perfectly competitive

equilibrium may not take place, even under strong assumptions on technologies.

Our main findings are as follows. Wefirst show that a Cournot differentiated oligopoly generates

a higher markup than a Bertrand differentiated oligopoly when the number of firms is exogenously

given. This is in accordance with the folk wisdom of industrial organization according to which

Cournot competition is softer than Bertrand competition. Second, as the number of competitors

becomes arbitrarily large, both types of competition deliver the same equilibrium outcome. Whether

the limit of Cournot and Bertrand competition is perfectly competitive or monopolistically compet-

itive depends on consumers’ attitude toward product differentiation. Using the concept of relative

love for variety,which measures the intensity of the preference for variety, we show that each firm op-

erating in a large economy retains enough market power toenjoy a positive markup when the relative

love for variety remains bounded away from zero at arbitrarily low consumption levels. In contrast,

when the relative love for variety vanishes at zero, consumers cease tovalue product differentiation.

A growing number of firms thus leads to the perfectly competitive outcome. In sum, the market

structure that emerges as the limit of oligopolistic competition depends on the nature of preferences. Fi-

nally,when fir ms arefree to enter the market, monopolistically competitive firms are more aggressive

than oligopolistic firms in that these firms charge lower prices, while the mass of varieties provided

by the market is smaller under oligopolistic competition than under monopolistic competition. If

the economy is sufficiently large, Cournot, Bertrand and Chamberlin solutions converge toward the

same market outcome, which need not be a competitive equilibrium.

2 The model

2.1 Firms and consumers

There is one sector supplying a horizontally differentiated good, one production factor (labor),

and a mass Lof identical consumers. Each consumer supplies one unit of labor and owns 1/L of

firms’ profits. The labor market is perfectly competitive and labor is chosen as the numeraire. The

differentiated good is made available in the form of a finite number n≥2 of varieties. Each variety

is produced by a single firm and each firm produces a single variety. To operate, every firm needs a

fixed requirement f≥0 and a marginal requirement c>0 of labor. Since wage is normalized to 1,

the cost of producing qiunits of variety i=1,...,nis equal to f+cqi.

Consumers share the same additive preferences given by

U(x)=

n



i=1

u(xi),(1)

30 International Journal of Economic Theory 13 (2017) 29–45 © IAET