Cournot Duopoly when the Competitors Operate Multiple Production Plants

Fabio Tramontana, Laura Gardini () and T?nu Puu ()
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T?nu Puu: CERUM, Ume? University, SE-90187 Ume?, Sweden

No 809, Working Papers from University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini

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 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.

Keywords: Cournot duopoly; isoelastic demand function; cost functions with built-in capacity limits; bifurcation structure. (search for similar items in EconPapers)
JEL-codes: C15 C62 D24 D43 (search for similar items in EconPapers)
Pages: 26 pages
Date: 2008, Revised 2008
New Economics Papers: this item is included in nep-bec, nep-com, nep-ind and nep-mic
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Citations: View citations in EconPapers (1)

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http://www.econ.uniurb.it/RePEc/urb/wpaper/WP_08_09.pdf First version, 2008 (application/pdf)

Related works:
Journal Article: Cournot duopoly when the competitors operate multiple production plants (2009)
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