Cournot, Bertrand or Chamberlin: Toward a reconciliation

Abstract

This paper compares the market equilibria in a differentiated industry under Cournot, Bertrand, and monopolistic competition. This is accomplished in a one‐sector economy where consumers are endowed with separable preferences. When firms are free to enter the market, monopolistically 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. If the 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.

The Dixit–Stiglitz economy with a ‘small group’ of firms: A simple and robust equilibrium markup formula

“…This conclusion challenges our general assumption of a given, perfectly inelastic, labor supply. As justly emphasized by Parenti et al (2017) in that respect, most widespread assumptions made in oligopoly models are extreme, either that the labour supply is perfectly elastic, or that it is perfectly inelastic 10 . Clearly, it would be worthwhile to see how a less extreme assumption than a perfectly inelastic labour supply would a¤ect our results.…”

“…Proof. The formula given in the proposition stems directly from formula (17) in the proof of Proposition 1, established on the basis of the …rst order conditions for the same producer's program except for the account taken of Ford e¤ects. Here, in case (iii), xi Y = pi Y = p i x i =Y = i , so that the proof is complete.…”

Product design in monopolistic competition

“…Standard models of monopolistic competition in the tradition of Dixit and Stiglitz (1977) have the property that the degree of differentiation in the industry or product class is given and uniform across pairs of varieties, hence cannot be manipulated by market participants. Recent work on demand theory and monopolistic competition has employed additively separable utility specifications (Zhelobodko et al, 2012; Bertoletti & Etro, 2021a; Parenti, Ushchev, et al, 2017, Parenti, Sidorov, et al, 2017; Sidorov et al, 2019; an early example is Sattinger, 1984), which lead to richer demand structures and market descriptions and allow considering potential asymmetries among varieties. We use a similar approach and use an additively separable utility specification which is identical to a CES utility system under symmetry, in order to study an environment in which producers can manipulate a substitution parameter.…”