IDEAS home Printed from https://ideas.repec.org/a/eee/ecmode/v42y2014icp220-229.html
   My bibliography  Save this article

Complex dynamics of monopolies with gradient adjustment

Author

Listed:
  • Matsumoto, Akio
  • Szidarovszky, Ferenc

Abstract

This paper aims to show that delay matters in continuous- and discrete-time framework. It constructs a simple dynamic model of a boundedly rational monopoly. First the existence of the unique equilibrium state is proved under general price and cost function forms. Conditions are derived for its local asymptotical stability with both continuous and discrete time scales. The global dynamic behavior of the systems is then numerically examined, demonstrating that the continuous system is globally asymptotically stable without delay and in the presence of delay if the delay is sufficiently small. Then stability of the continuous system is lost via Hopf bifurcation. In the discrete case without delay, the steady state is locally asymptotically stable if the speed of adjustment is small enough, then stability is lost via period-doubling bifurcation. If the delay is one or two steps, then stability loss occurs via Neimark–Sacker bifurcation.

Suggested Citation

  • Matsumoto, Akio & Szidarovszky, Ferenc, 2014. "Complex dynamics of monopolies with gradient adjustment," Economic Modelling, Elsevier, vol. 42(C), pages 220-229.
  • Handle: RePEc:eee:ecmode:v:42:y:2014:i:c:p:220-229
    DOI: 10.1016/j.econmod.2014.06.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0264999314002491
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.econmod.2014.06.013?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Askar, S.S., 2013. "On complex dynamics of monopoly market," Economic Modelling, Elsevier, vol. 31(C), pages 586-589.
    2. Farebrother, R W, 1973. "Simplified Samuelson Conditions for Cubic and Quartic Equations," The Manchester School of Economic & Social Studies, University of Manchester, vol. 41(4), pages 396-400, December.
    3. Matsumoto, Akio & Chiarella, Carl & Szidarovszky, Ferenc, 2013. "Dynamic monopoly with bounded continuously distributed delay," Chaos, Solitons & Fractals, Elsevier, vol. 47(C), pages 66-72.
    4. Matsumoto, Akio & Szidarovszky, Ferenc, 2012. "Nonlinear delay monopoly with bounded rationality," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 507-519.
    5. Okuguchi, Koji & Irie, Kazuya, 1990. "The Schur and Samuelson Conditions for a Cubic Equation," The Manchester School of Economic & Social Studies, University of Manchester, vol. 58(4), pages 414-418, December.
    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. S. S. Askar & A. Al-khedhairi, 2019. "Cournot Duopoly Games: Models and Investigations," Mathematics, MDPI, vol. 7(11), pages 1-15, November.
    2. Cavalli, Fausto & Naimzada, Ahmad, 2015. "Effect of price elasticity of demand in monopolies with gradient adjustment," Chaos, Solitons & Fractals, Elsevier, vol. 76(C), pages 47-55.
    3. Caravaggio, Andrea & Sodini, Mauro, 2020. "Monopoly with differentiated final goods and heterogeneous markets," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    4. Chaudhry, Muhammad Imran & Miranda, Mario J., 2018. "Complex price dynamics in vertically linked cobweb markets," Economic Modelling, Elsevier, vol. 72(C), pages 363-378.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Akio Matsumoto & Ferenc Szidarovszky, 2021. "Delay dynamics in nonlinear monopoly with gradient adjustment," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 533-557, December.
    2. Luca Guerrini & Nicolò Pecora & Mauro Sodini, 2018. "Effects of fixed and continuously distributed delays in a monopoly model with constant price elasticity," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 239-257, November.
    3. Cavalli, Fausto & Naimzada, Ahmad, 2015. "Effect of price elasticity of demand in monopolies with gradient adjustment," Chaos, Solitons & Fractals, Elsevier, vol. 76(C), pages 47-55.
    4. Caravaggio, Andrea & Sodini, Mauro, 2020. "Monopoly with differentiated final goods and heterogeneous markets," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    5. Li, Xiaoliang & Li, Bo & Liu, Li, 2023. "Stability and dynamic behaviors of a limited monopoly with a gradient adjustment mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    6. Akio Matsumoto & Keiko Nakayama, 2014. "Dynamic monopoly with demand delay," ERSA conference papers ersa14p40, European Regional Science Association.
    7. Xiaoliang Li & Jiacheng Fu & Wei Niu, 2023. "Complex dynamics of knowledgeable monopoly models with gradient mechanisms," Papers 2301.01497, arXiv.org.
    8. Laura Gardini & Noemi Schmitt & Iryna Sushko & Fabio Tramontana & Frank Westerhoff, 2019. "Necessary and sufficient conditions for the roots of a cubic polynomial and bifurcations of codimension-1, -2, -3 for 3D maps," Working Papers 1908, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2019.
    9. S. S. Askar & A. Al-khedhairi, 2019. "Analysis of a Four-Firm Competition Based on a Generalized Bounded Rationality and Different Mechanisms," Complexity, Hindawi, vol. 2019, pages 1-12, May.
    10. Gori, Luca & Guerrini, Luca & Sodini, Mauro, 2015. "A continuous time Cournot duopoly with delays," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 166-177.
    11. Jaylson Jair da Silveira & Gilberto Tadeu Lima, 2017. "Employee Profit-sharing and Labor Extraction in a Classical Model of Distribution and Growth," Review of Political Economy, Taylor & Francis Journals, vol. 29(4), pages 613-635, October.
    12. F. Cavalli & A. Naimzada & M. Pireddu, 2017. "An evolutive financial market model with animal spirits: imitation and endogenous beliefs," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 1007-1040, November.
    13. Amer Tabakovic, 2015. "On the Characterization of Steady-States in Three-Dimensional Discrete Dynamical Systems," DEM Discussion Paper Series 15-16, Department of Economics at the University of Luxembourg.
    14. Elsadany, A.A., 2012. "Competition analysis of a triopoly game with bounded rationality," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1343-1348.
    15. Askar, S.S., 2018. "Tripoly Stackelberg game model: One leader versus two followers," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 301-311.
    16. Gilberto Tadeu Lima & Jaylson Jair da Silveira, 2018. "Macrodynamic Implications of Employee Profit Sharing as Effort Elicitation Device," Working Papers, Department of Economics 2018_02, University of São Paulo (FEA-USP).
    17. Akio Matsumoto & Ferenc Szidarovszky & Maryam Hamidi, 2023. "On a Special Two-Person Dynamic Game," Games, MDPI, vol. 14(6), pages 1-22, October.
    18. S. S. Askar & Mona F. EL-Wakeel & M. A. Alrodaini, 2018. "Exploration of Complex Dynamics for Cournot Oligopoly Game with Differentiated Products," Complexity, Hindawi, vol. 2018, pages 1-13, February.
    19. Georges SARAFOPOULOS & Kosmas PAPADOPOULOS, 2017. "On A Cournot Duopoly Game With Differentiated Goods, Heterogeneous Expectations And A Cost Function Including Emission Costs," Scientific Bulletin - Economic Sciences, University of Pitesti, vol. 16(1), pages 11-22.
    20. Matsumoto, Akio & Chiarella, Carl & Szidarovszky, Ferenc, 2013. "Dynamic monopoly with bounded continuously distributed delay," Chaos, Solitons & Fractals, Elsevier, vol. 47(C), pages 66-72.

    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:eee:ecmode:v:42:y:2014:i:c:p:220-229. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/30411 .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.