IDEAS home Printed from https://ideas.repec.org/p/urb/wpaper/08_09.html
   My bibliography  Save this paper

Cournot Duopoly when the Competitors Operate Multiple Production Plants

Author

Listed:
  • Fabio Tramontana

    () (Università Politecnica delle Marche & Dipartimento di Economia e Metodi Quantitativi, Università di Urbino)

  • Laura Gardini

    () (Dipartimento di Economia e Metodi Quantitativi, Università di Urbino (Italy))

  • Tönu Puu

    () (CERUM, Umeå University, SE-90187 Umeå, 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 fi rm is assumed to operate multiple plants, which can be run alone or in combination. Each firm has two plants with different capacity limits, so each 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 costs functions come in three disjoint pieces, so the reaction functions, derived on basis of global pro fit maximization, may also consist of disjoint pieces. This is reflected in a particular bifurcation structure, due to border collision bifurcations, and to particular basin boundaries, related to the discontinuities. It is shown that stable cycles may coexist, and the non-existence of unstable cycles constitutes a new property. We also compare the coexistent short periodic solutions in terms of the resulting real pro fits.

Suggested Citation

  • Fabio Tramontana & Laura Gardini & Tönu Puu, 2008. "Cournot Duopoly when the Competitors Operate Multiple Production Plants," Working Papers 0809, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2008.
  • Handle: RePEc:urb:wpaper:08_09
    as

    Download full text from publisher

    File URL: http://www.econ.uniurb.it/RePEc/urb/wpaper/WP_08_09.pdf
    File Function: First version, 2008
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Bischi, Gian Italo & Kopel, Michael, 2001. "Equilibrium selection in a nonlinear duopoly game with adaptive expectations," Journal of Economic Behavior & Organization, Elsevier, vol. 46(1), pages 73-100, September.
    2. R. D. Theocharis, 1960. "On the Stability of the Cournot Solution on the Oligopoly Problem," Review of Economic Studies, Oxford University Press, vol. 27(2), pages 133-134.
    3. Hommes, Cars H., 1995. "A reconsideration of Hicks' non-linear trade cycle model," Structural Change and Economic Dynamics, Elsevier, vol. 6(4), pages 435-459, December.
    4. Hommes, Cars H. & Nusse, Helena E. & Simonovits, Andras, 1995. "Cycles and chaos in a socialist economy," Journal of Economic Dynamics and Control, Elsevier, vol. 19(1-2), pages 155-179.
    5. Puu, Tonu & Gardini, Laura & Sushko, Irina, 2005. "A Hicksian multiplier-accelerator model with floor determined by capital stock," Journal of Economic Behavior & Organization, Elsevier, vol. 56(3), pages 331-348, March.
    6. Dana, Rose-Anne & Montrucchio, Luigi, 1986. "Dynamic complexity in duopoly games," Journal of Economic Theory, Elsevier, vol. 40(1), pages 40-56, October.
    7. Furth, Dave, 1986. "Stability and instability in oligopoly," Journal of Economic Theory, Elsevier, vol. 40(2), pages 197-228, December.
    8. Nabih Agiza, Hamdy & Italo Bischi, Gian & Kopel, Michael, 1999. "Multistability in a dynamic Cournot game with three oligopolists," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 51(1), pages 63-90.
    9. al-Nowaihi, A. & Levine, P. L., 1985. "The stability of the cournot oligopoly model: A reassessment," Journal of Economic Theory, Elsevier, vol. 35(2), pages 307-321, August.
    10. Gallegati, M. & Gardini, L. & Puu, T. & Sushko, I., 2003. "Hicks’ trade cycle revisited: cycles and bifurcations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 63(6), pages 505-527.
    11. Bonanno, Giacomo, 1988. "Oligopoly Equilibria When Firms Have Local Knowledge of Demand," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(1), pages 45-55, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ahmad Naimzada & Fabio Tramontana, 2011. "Double route to chaos in an heterogeneous triopoly game," Quaderni di Dipartimento 149, University of Pavia, Department of Economics and Quantitative Methods.
    2. Luciano Fanti & Luca Gori, 2013. "Stability Analysis in a Bertrand Duopoly with Different Product Quality and Heterogeneous Expectations," Journal of Industry, Competition and Trade, Springer, vol. 13(4), pages 481-501, December.
    3. Fabio Lamantia & Mario Pezzino, 2017. "Dynamic analysis of discontinuous best response with innovation," The School of Economics Discussion Paper Series 1708, Economics, The University of Manchester.
    4. Ingrid Kubin & Laura Gardini, 2013. "Border collision bifurcations in boom and bust cycles," Journal of Evolutionary Economics, Springer, vol. 23(4), pages 811-829, September.
    5. Fanti, Luciano & Gori, Luca & Sodini, Mauro, 2012. "Nonlinear dynamics in a Cournot duopoly with relative profit delegation," MPRA Paper 37834, University Library of Munich, Germany.
    6. Dawid, Herbert & Heitmann, Dennis, 2014. "Best response dynamics with level-n expectations in two-stage games," Journal of Economic Dynamics and Control, Elsevier, vol. 41(C), pages 130-153.
    7. Fanti, Luciano & Gori, Luca & Sodini, Mauro, 2015. "Nonlinear dynamics in a Cournot duopoly with isoelastic demand," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 108(C), pages 129-143.
    8. Xin, Baogui & Chen, Tong, 2011. "On a master-slave Bertrand game model," Economic Modelling, Elsevier, vol. 28(4), pages 1864-1870, July.
    9. Tramontana, Fabio, 2010. "Heterogeneous duopoly with isoelastic demand function," Economic Modelling, Elsevier, vol. 27(1), pages 350-357, January.
    10. Angelini, Natascia & Dieci, Roberto & Nardini, Franco, 2009. "Bifurcation analysis of a dynamic duopoly model with heterogeneous costs and behavioural rules," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(10), pages 3179-3196.

    More about this item

    Keywords

    Cournot duopoly; isoelastic demand function; cost functions with built-in capacity limits; bifurcation structure.;

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:urb:wpaper:08_09. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Carmela Nicoletti). General contact details of provider: http://edirc.repec.org/data/feurbit.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.