N‐firm Oligopoly With General Iso‐elastic Demand

Abstract

In this note oligopoly with iso‐elastic demand is analysed. Unlike previous studies we consider general iso‐elastic demand rather than the case of unit elasticity. An n‐firm Nash‐Cournot equilibrium for the case of heterogeneous constant marginal costs is derived. The main result is a closed‐form solution that shows the dependency of the equilibrium on the elasticity of demand and the share of industry costs. The result has applications to a wide range of areas in oligopoly theory by allowing comparisons across markets with different elasticities of demand.

Nonlinear dynamics in a Cournot duopoly with isoelastic demand

“…which implicitly define the reaction functions of firm 1 and firm 2 . The use of (2) and (3) allows us to obtain the unique Nash equilibrium of the game as follows:…”

“…However, the static oligopoly literature has sometimes analysed models with isoelastic demands and price elasticity different from one with several purposes. Examples can be found in Chirco et al [11], Collie [12], Colombo et al [13], Neary [20] and more recently Beard [3]. In particular, Chirco et al [11] develop a Cournot model with managerial incentive contracts (relative profits delegation) to study how the optimal delegation scheme is affected by the elasticity of market demand, while Beard [3] studies a Cournot oligopoly with n profit-maximising firms and shows that the Nash equilibrium depends on both the elasticity of demand and share of industry costs.…”