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Cournot Duopoly with Capacity Limit Plants

Author

Listed:
  • Fabio TRAMONTANA

    () (Universita' Politecnica delle Marche, Dipartimento di Economia)

  • Laura GARDINI

    () (Universit… degli Studi di Urbino, Istituto di Scienze Economiche)

  • Puu TONU

    (CERUM, Umea University, Sweden)

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 firm is assumed to operate multiple plants, which can be run alone or in combination. Each firm has two plants with different capacity limits, so it 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 cost functions come in three disjoint pieces, so the reaction functions, derived on basis of global profit maximization, as well can consist of disjoint pieces. We first analyze the case in which the firms are taken as identical, and then the generic case. It is shown that stable Cournot equilibria may coexist with several other stable cycles. Then we compare the coexistent periodic attractors in terms of the resulting profits. The main property is the non-existence of unstable cycles. This is reflected in a particular bifurcation structure, due to border collision bifurcations, and to particular basin frontiers, related to the discontinuities.

Suggested Citation

  • Fabio TRAMONTANA & Laura GARDINI & Puu TONU, 2008. "Cournot Duopoly with Capacity Limit Plants," Working Papers 314, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
  • Handle: RePEc:anc:wpaper:314
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    File URL: http://docs.dises.univpm.it/web/quaderni/pdf/314.pdf
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    References listed on IDEAS

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    1. Zhusubaliyev, Zhanybai T. & Soukhoterin, Evgeniy & Mosekilde, Erik, 2007. "Quasiperiodicity and torus breakdown in a power electronic dc/dc converter," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 73(6), pages 364-377.
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    Cited by:

    1. Alberto Russo, 2014. "A Stochastic Model of Wealth Accumulation with Class Division," Metroeconomica, Wiley Blackwell, vol. 65(1), pages 1-35, February.
    2. Ruggero Grilli & Gabriele Tedeschi & Mauro Gallegati, 2015. "Markets connectivity and financial contagion," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 10(2), pages 287-304, October.
    3. Alessandro STERLACCHINI, 2012. "Patent Oppositions as Competitive Tools: An Analysis of the Major Players in the European Market of White Goods," Working Papers 374, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    4. Eralba CELA & Tineke FOKKEMA & Elena AMBROSETTI, 2012. "Links Between Transnationalism Integration and Duration of Residence: The Case of eastern European Migrants in Italy," Working Papers 386, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    5. Fabio FIORILLO & Agnese SACCHI, 2010. "I Want to Free-ride. An Opportunistic View on Decentralization Versus Centralization Problem," Working Papers 346, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    6. Elena AMBROSETTI & Eralba CELA & Tineke FOKKEMA, 2011. "The Remittances Behaviour of the Second Generation in Europe: Altruism or Self-Interest?," Working Papers 368, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    7. Ugo FRATESI, 2010. "The National and International Effects;of Regional Policy Choices: Agglomeration Economies, Peripherality and Territorial Characteristics," Working Papers 344, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    8. Luca RICCETTI, 2010. "Minimum Tracking Error Volatility," Working Papers 340, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    9. Lenzu, Simone & Tedeschi, Gabriele, 2012. "Systemic risk on different interbank network topologies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(18), pages 4331-4341.
    10. Luca RICCETTI, 2011. "A Copula-GARCH Model for Macro Asset Allocation of a Portfolio with Commodities: an Out-of-Sample Analysis," Working Papers 355, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.

    More about this item

    Keywords

    Border Collision Bifurcations; Capacity Limits; Cournot; Discontinuous Reaction Functions; Duopoly; Nonlinear Dynamics;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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