Imperfect Competition and Fixprice Equilibria under Consumer Aggregation and Net Substitutes

Abstract

The general question posed here and in a companion paper' is: under what conditions do models of imperfect competition generate equilibria which are also fixprice equilibria? Answers to this question are provided for the Cournot-Walras general equilibrium model originated by Gabszewicz and Vial (1972), and the model of a quantity constraining monopolist due to Bohm et al. (1983). Whereas our earlier paper derived results (for other models) from gross substitute-complement assumptions, here we also offer results based on net substitute-complement assumptions, plus appropriate aggregation of consumers. This note thus extends the earlier paper by analyzing different models using different techniques. The net substitute-complement classification used is the inverse net or Hicksian q classification, described in Section II. For the sake of brevity, the discussion of the models in Sections III and IV restricts attention to equilibria, where price and consumption vectors are strictly positive. Notation and definitions are those of the earlier paper; cf. Madden and Silvestre ( 1991, Section II).