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

Posted by D. Daniel Sokol

Fabio Tramontana (Department of Economics, University of Ancona, Italy), Laura Gardini (Department of Economics and Quantitative Methods, University of Urbino, Italy), and Tönu Puu (CERUM, Umeå University) describe New properties of the Cournot duopoly with isoelastic demand and constant unit costs.

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.