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Cournot duopoly when the competitors operate multiple production plants

Authors
Journal
Journal of Economic Dynamics and Control
0165-1889
Publisher
Elsevier
Publication Date
Volume
33
Issue
1
Identifiers
DOI: 10.1016/j.jedc.2008.06.001
Keywords
  • Duopoly
  • Capacity Limits
  • Border-Collision Bifurcations
  • Discontinuous Reaction Functions

Abstract

Abstract This article considers a Cournot duopoly under an isoelastic demand function and cost functions with built-in capacity limits. The special feature is that each firm is assumed to operate multiple plants, which can be run alone or in combination. Each firm has two plants with different capacity limits, so each has three cost options, the third being to run both plants, dividing the load according to the principle of equal marginal costs. As a consequence, the marginal cost functions come in three disjoint pieces, so the reaction functions, derived on basis of global profit maximization, may also consist of disjoint pieces. This is reflected in a particular bifurcation structure, due to border-collision bifurcations and to particular basin boundaries, related to the discontinuities. It is shown that stable cycles may coexist, and the non-existence of unstable cycles constitutes a new property. We also compare the coexistent short periodic solutions in terms of the resulting real profits.

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