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New properties of the Cournot duopoly with isoelastic demand and constant unit costs

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Author Info

  • Fabio Tramontana

    ()
    (Department of Economics, University of Ancona, Italy)

  • Laura Gardini

    ()
    (Department of Economics and Quantitative Methods, University of Urbino, Italy)

  • Tönu Puu

    ()
    (CERUM, Umeå University, SE-90187 Umeå, Sweden)

Abstract

The object of the work is to perform the global analysis of the Cournot duopoly model with isoelastic demand function and unit costs, presented in Puu (1991). The bifurcation of the unique Cournot fixed point is established, which is a resonant case of the Neimark-Shacker bifurcation. New properties associated with the introduction of horizontal branches are evidenced. These properties di¤er significantly when the constant value is zero or positive and small. The good behavior of the case with positive constant is proved, leading always to positive trajectories. Also when the Cournot fixed point is unstable, stable cycles of any period may exist.

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File URL: http://www.econ.uniurb.it/RePEc/urb/wpaper/WP_10_06.pdf
File Function: First version, 2010
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Bibliographic Info

Paper provided by University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini in its series Working Papers with number 1006.

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Length: 19 pages
Date of creation: 2010
Date of revision: 2010
Handle: RePEc:urb:wpaper:10_06

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Web page: http://www.econ.uniurb.it/
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Keywords: Cournot duopoly; isoelastic demand function; multistability; border-collision bifurcations.;

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