The Role of Price Normalization in Imperfectly Competitive Economies

This note presents an analytical method to examine when, why, and how rules of price nor- malization have an impact on noncompetitive equilibria in Arrow-Debreu economies. For simple prototype economies it is shown that under smooth strict convexity of preferences and technologies regular monopolistic equilibria depend generically on the parameters of the nor- malization map. Conversely, for an example with consumer preferences from a parametrized class of quasi-concave/quasi-convex utility functions monopolistic equilibria are shown to be invariant under normalization for all parameters under convex technologies as well as under fixed costs or increasing returns. The generic dependence of allocations on rules of price normalization implies alterations of characteristics of outcomes in a much wider class of applications than models of monopolis- tic competition only. Several examples of so-called Cournot-Walras oligopolies are discussed occurring in typical models with monopolistic competition, international trade, welfare eco- nomics, public economics, and macroeconomics revealing the generic impact of price normal- ization on noncompetitive outcomes in Arrow-Debreu economies.