Relaxing quality differentiation through capacity limitation: A note

• Author: Xavier Y. Wauthy,Nicolas Boccard
• Published date: 01 June 2017
• Date: 01 June 2017
• DOI: http://doi.org/10.1111/ijet.12127

doi: 10.1111/ijet.12127

Relaxing quality differentiation through capacity

limitation: A note

Xavier Y. Wauthy∗and Nicolas Boccard†

We consider a duopoly stage game where an incumbent sells a high-quality product while

enjoyingan ample production capacity. Westudy the quality–capacity best response of an entr ant,

before price competition takes place. We partially characterize equilibrium prices and payoffs

in the corresponding Bertrand–Edgeworth pricing games and show that the entrant tends to

rely exclusively on capacity limitation in a subgame perfect equilibrium, thereby showing that

vertical differentiation is not robust to Bertrand–Edgeworth competition.

Key wor ds capacity constraint, quality, differentiation, Bertrand–Edgeworth competition

JEL classification D43, L13, L51

Accepted 15 June2016

1 Introduction

Building on the original intuition of Edgeworth (1925) and the preliminary results of Levitan and

Shubik (1972), the seminal paper of Kreps and Scheinkman (1983) analyzes the role of capacity

constraints under price competition with homogeneous goods. No comparable analysis has been

carried out for the case of differentiated goods. As discussed in Wauthy (2014), very little is known

about the structure of Nash equilibria in Bertrand–Edgeworth differentiated industries. The aim of

this note is to offer a theoretical contribution to this field of research and to show that the presence

of capacity constraints may drastically impinge on firms’ incentives to differentiate their products.

To this end, we consider a market where an incumbent sells a high-quality product and enjoys

an arbitrarily large production capacity. We study the entry strategy of a challenger who may install

a limited production capacity and commit to some degree of product differentiation. After entry has

taken place, firms simultaneously set prices. We show that there exists a subgame perfect equilibrium

of our stage game in which the entrant chooses not to differentiate by quality but relies exclusively

on capacity commitment to optimally relax price competition.

This note, though mainly of a technical nature, nevertheless offers a methodology to identify

the structure of equilibrium prices and payoffs in price subgames with capacity constraints and

∗Universit´

e Saint-Louis Bruxelles, CEREC and CORE. Email : xavier.wauthy@usaintlouis.be

†Econ Dep, FCEE, Universitatde Girona, Girona, Spain.

Financial support from Generalitat de Catalunya (AGAUR, XREPP) and Ministerio de Econom’a y Competitividad

(contract ECO2013-45395-R) are gratefully acknowledged.

This paper is a revised and shortened version of Center for Operations Research and Econometrics (CORE) Discussion

Paper 2009/50. Weare grateful to seminar participants at ECARES, Ecole Polytechnique, UAB,University of Valencia and

EARIE for comments. Wethank Paul Belleamme for comments on a preliminary draft, and a referee of this journal for

constructive comments. Weretain responsibility for any remaining errors.

International Journal of Economic Theory 13 (2017) 233–244 © IAET 233

International Journal of Economic Theory