Abstract
In dynamic models in economics, often “rational expectations” are assumed. These are meant to show that the agents can correctly foresee the result of their own and the other agents′ actions. In this paper, it is shown that this cannot happen in a simple oligopoly model with a linear demand function and constant marginal costs. “Naive expectations,” that is, where each agent assumes the other agents to retain their previous period action, are shown to result in a 2‐period cycle. However, adapting to the observed periodicity always doubles the actual resulting periodicity. In general, it is impossible for the agents to learn any periodicity except the trivial case of a fixed point. This makes the whole idea of “rational expectations” untenable in Cournot oligopoly models.
Highlights
In a note in 1959, Theocharis [5] reconsidered the Cournot [2] oligopoly problem, given a linear demand function and constant marginal costs for the competitors
As discussed in [1], the whole argument was antedated 20 years earlier by Palander in [3, 4], but as this seems to be totally unknown to the economics profession, we continue referring to the “Theocharis problem.”
A linear demand function and constant marginal costs lead to linear reaction functions, which in terms of substance, become nonsense once they result in negative output and profits that are positive due to negative costs dominating over negative revenues
Summary
In a note in 1959, Theocharis [5] reconsidered the Cournot [2] oligopoly problem, given a linear demand function and constant marginal costs for the competitors. He showed that with three competitors, the Cournot equilibrium becomes neutrally stable, and with four, it becomes unstable. As discussed in [1], the whole argument was antedated 20 years earlier by Palander in [3, 4], but as this seems to be totally unknown to the economics profession, we continue referring to the “Theocharis problem.” Both Palander and Theocharis only considered loss of local stability of the Cournot equilibrium point. In [1], the global dynamics of the model was studied. The model necessarily becomes nonlinear, which is needed for the study of the global dynamics.
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