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

Author

Listed:
  • Fabio Tramontana

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

  • Laura Gardini

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

  • T?nu Puu

    () (CERUM, Ume? University, SE-90187 Ume?, 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.

Suggested Citation

  • Fabio Tramontana & Laura Gardini & T?nu Puu, 2010. "New properties of the Cournot duopoly with isoelastic demand and constant unit costs," Working Papers 1006, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2010.
  • Handle: RePEc:urb:wpaper:10_06
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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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    Cited by:

    1. Yi Wang & Hui Wang & Shubing Guo, 2019. "Research on Dynamic Game Model and Application of China’s Imported Soybean Price in the Context of China-US Economic and Trade Friction," Complexity, Hindawi, vol. 2019, pages 1-13, November.

    More about this item

    Keywords

    Cournot duopoly; isoelastic demand function; multistability; border-collision bifurcations.;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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