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

Abstract

In a general version of Dixit–Stiglitz two-sector economy, we present three variants of the concept of oligopolistic equilibrium in price-quantity pairs (d’Aspremont and Dos Santos Ferreira, 2016) integrating income feedback effects in three different ways. For the first two variants (Ford effects ignored or restricted to profits), a single and simple equilibrium markup formula is derived involving, for each firm, a conduct parameter indicating its degree of competitive toughness. Different specifications of these conduct parameters lead to different oligopolistic equilibria in prices and/or in quantities. In particular in the standard Dixit–Stiglitz economy, we show, that the first order conditions of a symmetric oligopolistic price equilibrium correspond to a unique degree of competitive toughness in the general markup formula, This degree is decreasing (and the markup increasing) as more feedback effects are taken into account by firms. On the contrary, for the third variant, introducing full Ford effects leads to lower markups and higher competitive toughness in the standard Dixit–Stiglitz economy and under conditions ensuring the equilibrium markup to remain in tne right interval,