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

87 Pages Posted: 5 Jun 2017 Last revised: 1 Apr 2021

See all articles by Rajeev R. Bhattacharya

Rajeev R. Bhattacharya

Southern Methodist University (SMU) - Finance Department; Washington Finance and Economics

Date Written: April 1, 2021


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

Suggested Citation

Bhattacharya, Rajeev, Strong Non-Monotonicity of Equilibrium Price - Static and Dynamic Models (April 1, 2021). Available at SSRN: or

Rajeev Bhattacharya (Contact Author)

Southern Methodist University (SMU) - Finance Department ( email )

United States

Washington Finance and Economics ( email )

United States


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