Strong Non-Monotonicity of Equilibrium Price - Static and Dynamic Models

Abstract

This paper examines the implications for equilibrium price of a shift in demand. Counterfactual predictions are serious negatives of a model which then is clearly inferior to a general and parsimonious model that predicts, within the model, all empirical observations.

First, I consider two static Cournot oligopoly models with linear demand, linear costs, and a finite number of firms, and I prove strong non-monotonicity of any equilibrium price within each model.

Second, in a stochastically indefinite horizon simultaneous moves Cournot oligopoly model with a countable number of firms, with the discount factors and the demand parameters following general stochastic processes, I prove that for a path which follows a stationary function of the demand parameter and which is sustainable in a strategy profile that is efficient among the set of perfect equilibrium strategy profiles, any equilibrium price is strongly non-monotonic within each model.

The fact that equilibrium price is strongly non-monotonic even in a parsimonious simple linear structure makes an even stronger statement that these strong non-monotonicities are not artifacts of the complexity of the problem but an inherent part of oligopoly.

Keywords: Price, Demand, Non-Monotonicity, Cournot, Static, Dynamic, Lebesgue Measure, Stochastic Discount Factors

JEL Classification: L13, D43, C72, C73