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

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

No 1006, Working Papers from University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini

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.

Keywords: Cournot duopoly; isoelastic demand function; multistability; border-collision bifurcations. (search for similar items in EconPapers)
JEL-codes: C15 C62 D24 D43 (search for similar items in EconPapers)
Pages: 19 pages
Date: 2010, Revised 2010
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http://www.econ.uniurb.it/RePEc/urb/wpaper/WP_10_06.pdf First version, 2010 (application/pdf)

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