Fabio Tramontana () (Università Politecnica delle Marche & Dipartimento di Economia e Metodi Quantitativi, Università di Urbino) Laura Gardini () (Dipartimento di Economia e Metodi Quantitativi, Università di Urbino (Italy)) Tönu Puu () (CERUM, Umeå University, SE-90187 Umeå, Sweden)
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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 fi rm 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 costs functions come in three disjoint pieces, so the reaction functions, derived on basis of global pro fit 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 pro fits.
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Paper provided by University of Urbino Carlo Bo, Department of Economics in its series Working Papers with number
0809.
Find related papers by JEL classification: C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium D24 - Microeconomics - - Production and Organizations - - - Production; Capital and Total Factor Productivity; Capacity D43 - Microeconomics - - Market Structure and Pricing - - - Oligopoly and Other Forms of Market Imperfection
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