Cournot duopoly when the competitors operate multiple production plants
AbstractThis 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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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Economic Dynamics and Control.
Volume (Year): 33 (2009)
Issue (Month): 1 (January)
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Web page: http://www.elsevier.com/locate/jedc
Duopoly Capacity limits Border-collision bifurcations Discontinuous reaction functions;
Other versions of this item:
- Fabio Tramontana & Laura Gardini & Tönu Puu, 2008. "Cournot Duopoly when the Competitors Operate Multiple Production Plants," Working Papers 0809, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2008.
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
- D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
- D43 - Microeconomics - - Market Structure and Pricing - - - Oligopoly and Other Forms of Market Imperfection
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