Preferences, entry, and market structure

• Date: 01 November 2016
• Published date: 01 November 2016
• Author: Paolo Bertoletti,Federico Etro
• DOI: http://doi.org/10.1111/1756-2171.12155

RAND Journal of Economics

Vol.47, No. 4, Winter 2016

pp. 792–821

Preferences, entry, and market structure

Paolo Bertoletti∗

and

Federico Etro∗∗

We provide a unified approach to imperfect (monopolistic, Bertrand, and Cournot) competition

when preferences are symmetric over a finite but endogenous number of goods. Markups depend

on the Morishima elasticity of substitution and on the number of varieties. The comparative

statics of free-entry equilibria is examined, establishing the conditions formarkup neutrality with

respect to income, market size, and productivity. We compare endogenous and optimal market

structures for severalnon-CES examples. With a generalized linear direct utility, the markupcan

be constant and optimal under monopolistic competition, and nonmonotonic in the number of

firms under Bertrand or Cournot competition.

1. Introduction

To understand how demand and supply fundamentals affect the structure of a market,

namely, how many firms are active in it, how much they produce, and at which markup they

sell, is a basic concern of economic theory. This important issue arises in the partial equilibrium

analysis of industrial organization, as well as in general equilibrium applications, for instance,

in international trade and macroeconomics.1However, most of the modern theory of imperfect

competition in markets with product differentiation is based on a few, specific microfoundations

of the demand side. Models of monopolistic competition are usually based on CES preferences

∗University of Pavia; paolo.bertoletti@unipv.it.

∗∗University of Venice Ca’ Foscari; federico.etro@unive.it.

We are very grateful to Giuseppe Savar´

e for fundamental clarifications on the properties of symmetric functions, but of

course, the usual disclaimer applies. We also thank Giacomo Corneo, Paolo Epifani, Massimo Filippini, Atsushi Kajii,

Giorgio Rampa, Lorenza Rossi, Ina Simonovska, Kresimir Zigic, two anonymous referees, and especially the Editor,

Mark Armstrong, for useful comments. Seminar participants at the International Workshop on Global Competition

and Innovation (Awaji, Japan, March 1, 2014), Free University of Berlin, Kyoto University, Yonsei University (Seoul),

Padova University, Pavia University, University of Italian Swiss (Lugano), Delhi School of Economics, and the 2015

SAET conference at the University of Cambridge (UK) provided insightful comments. Further results can be found in

the Working Paper version with the title, “A General Theor y of Endogenous Market Structures” (DEM W.P. no. 81,

University of Pavia, Dept. of Economics and Management, June 2014).

1There is a wide empirical literature pointing out that markups are affected by the number of consumers, their

income, and productivity shocks. For recent examples, see Campbell and Hopenhayn (2005) on competition effects

in industrial organization, Simonovska (2015) on pricing to market in trade, and Nekarda and Ramey (2013) on the

cyclicality of markups in macroeconomics.

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BERTOLETTI AND ETRO / 793

or on separable direct utilities as in Dixit and Stiglitz (D-S, 1977) or on quasilinear preferences

as in Spence (1976), and more recently Melitz and Ottaviano (2008), and Anderson, Erkal,

and Piccinin (2012).2As is well known, strategic interactions `

alaCournot or Ber trand add a

competitive element to the equilibrium of monopolistic competition, but also their analysis has

been usually limited to a few microfounded examples. Other cases analyzed in the literature

include those of homothetic preferences (Benassy,1996; Feenstra, 2003 and 2014; D’Aspremont,

Dos Santos Ferreira, and Gerard-Varet, 2007) and of separable indirect utilities (Bertoletti and

Etro, 2014). Beyond these cases, little is known about how preferences shape competition and

the incentives to enter a market.

In this work, we provide a first step to characterize, under a general microfoundation,

the basic elements of an endogenous market structure: the number of active firms and the

quantity/price strategies adopted by them. We endogenize consumer behavior, entry choices, and

market strategies, but wetake as a given the technological conditions and the mode of competition,

which we assume to be either monopolistic competition `

a la Chamberlin, Bertrand competition in

prices, or Cournot competition in quantities. Although this is typical of trade and macroeconomic

applications, we leave for future research the extension to additional interesting aspects of firm

behavior,such as the endogenous determination of technology through Research and Development

(R&D) activity (Sutton, 1991) and of the mode of competition (see D’Aspremont, Dos Santos

Ferreira, and Gerard-Varet, 2007).

Our purpose is to analyze the three main forms of competition when consumers are endowed

with general (nonseparable) preferences that are symmetric3over a largenumber of differentiated

goods, of which only some are endogenouslyprovided. Westar t proposing a generalized definition

of monopolistic competition that applies to all cases with a large but finite number of goods.

Exploiting the properties of symmetric preferences, we show that the relevant demand elasticity

is provided by the so-called Morishima elasticity of substitution (as defined in Blackorby and

Russell, 1981),4and can be computed directly from the utility function. We also show how the

markups relevant in Bertrand and Cournot symmetric equilibria depend on the same elasticity and

on the number of varieties actually provided. These results confirm that the difference between

the true demand elasticity and that perceived by firms under our definition of monopolistic

competition is indeed negligible when the number of goods is large enough.5On this basis,

we characterize the implications of free entry and the comparative statics of the associated

endogenous market structure. To illustrate how to derive imperfect competition equilibria, we

reconsider a variety of preferences used in the literature on monopolistic competition, such as

additive preferences or examples of homothetic preferences.6In addition, we provide the first

characterization of the equilibria under the so-called generalized linear direct utility proposed by

Diewert (1971), and under quadratic utilities that are neither homothetic nor additive.7Following

Feenstra (2003), we account for changes in the functional form representing preferences due to

changes in the number of available goods.

2The case of additively separable preferences has been recently reconsidered by Zhelobodko et al. (2012) and

Bertoletti and Epifani (2014). Many results are also known for quasilinear preferences with an outside good (Vives,

1999), but this assumption has the cost of eliminating any mechanism through which income directly affectsdemand.

3In the economics of product differentiation, the assumption of symmetric preferences is the hallmark of the

“Chamberlinian paradigm,” as first formalized by D-S (1977).

4Notice that in the general case of preferences defined over more than two goods, there are different ways of

defining the elasticity of substitution (see Blackorby and Russell, 1989).

5This is known in models based on additive preferences: see, for instance, Yang and Heijdra (1993) and Bertoletti

and Epifani (2014). We showthat it holds in all models with symmetric preferences.

6In particular, we consider translog preferences and the so-called generalized Leontief preferences: these belong

to the so-called “quadratic mean of order r” (QMOR) expenditure functions recently reexamined byFeenstra (2014).

7Although we are not aware of an earlier use of the quadratic indirect utility considered here, the quadratic direct

utility is derived bythe quasilinear preferences of Melitz and Ottaviano (2008), eliminating the outside good and has been

used elsewhere under monopolistic competition.

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