IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v70y2015icp27-37.html
   My bibliography  Save this article

On periodic and chaotic behavior in a two-dimensional monopoly model

Author

Listed:
  • Al-Hdaibat, Bashir
  • Govaerts, Willy
  • Neirynck, Niels

Abstract

We study the monopoly model of T. Puu with cubic price and quadratic marginal cost functions. A numerical continuation method is used to compute branches of solutions of period 5, 10, 13 and 17 and to determine the stability regions of these solutions. General formulas for solutions of period 4 are derived analytically. We show that the solutions of period 4 are never linearly asymptotically stable. A nonlinear stability criterion is combined with basin of attraction analysis and simulation to determine the stability region of the 4-cycles. This corrects the erroneous linear stability analysis in previous studies of the model. The chaotic and periodic behavior of the monopoly model is further analyzed by computing the largest Lyapunov exponents, and this confirms the above mentioned results.

Suggested Citation

  • Al-Hdaibat, Bashir & Govaerts, Willy & Neirynck, Niels, 2015. "On periodic and chaotic behavior in a two-dimensional monopoly model," Chaos, Solitons & Fractals, Elsevier, vol. 70(C), pages 27-37.
    • Handle: RePEc:eee:chsofr:v:70:y:2015:i:c:p:27-37
    DOI: 10.1016/j.chaos.2014.10.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077914001817
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2014.10.010?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. Grandmont, Jean-Michel, 2008. "Nonlinear difference equations, bifurcations and chaos: An introduction," Research in Economics, Elsevier, vol. 62(3), pages 122-177, September.
    2. Askar, S.S., 2013. "On complex dynamics of monopoly market," Economic Modelling, Elsevier, vol. 31(C), pages 586-589.
    3. Ahmed, E. & Elettreby, M.F. & Hegazi, A.S., 2006. "On Puu’s incomplete information formulation for the standard and multi-team Bertrand game," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1180-1184.
    4. Matsumoto, Akio & Szidarovszky, Ferenc, 2014. "Discrete and continuous dynamics in nonlinear monopolies," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 632-642.
    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. Lahmiri, Salim, 2017. "A study on chaos in crude oil markets before and after 2008 international financial crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 389-395.
    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. Lahmiri, Salim, 2017. "On fractality and chaos in Moroccan family business stock returns and volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 29-39.
    4. Xiaoliang Li, 2021. "Analysis of stability and bifurcation for two heterogeneous triopoly games with the isoelastic demand," Papers 2112.05950, arXiv.org.
    5. Xiaoliang Li & Jiacheng Fu & Wei Niu, 2023. "Complex dynamics of knowledgeable monopoly models with gradient mechanisms," Papers 2301.01497, arXiv.org.
    6. Lahmiri, Salim, 2017. "Investigating existence of chaos in short and long term dynamics of Moroccan exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 655-661.
    7. 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).

    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. Matsumoto, Akio & Szidarovszky, Ferenc, 2022. "The chaotic monopolist revisited with bounded rationality and delay dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    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. 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.
    4. 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.
    5. Theodore Palivos & Dimitrios Varvarigos, 2010. "Education and growth: A simple model with complicated dynamics," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(4), pages 367-384, December.
    6. Cees Diks & Cars Hommes & Valentyn Panchenko & Roy Weide, 2008. "E&F Chaos: A User Friendly Software Package for Nonlinear Economic Dynamics," Computational Economics, Springer;Society for Computational Economics, vol. 32(1), pages 221-244, September.
    7. Ciprian Rusescu & Mihai Daniel - Roman, 2021. "Dynamic Behaviour In A Bertrand Model With Bounded Rational Players," Annals - Economy Series, Constantin Brancusi University, Faculty of Economics, vol. 3, pages 45-55, June.
    8. Calvet, Laurent E., 2001. "Incomplete Markets and Volatility," Journal of Economic Theory, Elsevier, vol. 98(2), pages 295-338, June.
    9. Gori, Luca & Guerrini, Luca & Sodini, Mauro, 2015. "A continuous time Cournot duopoly with delays," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 166-177.
    10. Brock, W.A. & Hommes, C.H. & Wagener, F.O.O., 2009. "More hedging instruments may destabilize markets," Journal of Economic Dynamics and Control, Elsevier, vol. 33(11), pages 1912-1928, November.
    11. Pflüger, Michael & Tabuchi, Takatoshi, 2010. "The size of regions with land use for production," Regional Science and Urban Economics, Elsevier, vol. 40(6), pages 481-489, November.
    12. Askar, S.S., 2018. "Tripoly Stackelberg game model: One leader versus two followers," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 301-311.
    13. 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.
    14. Puga, Diego, 1999. "The rise and fall of regional inequalities," European Economic Review, Elsevier, vol. 43(2), pages 303-334, February.
    15. Dos Santos Ferreira, Rodolphe & Lloyd-Braga, Teresa, 2005. "Non-linear endogenous fluctuations with free entry and variable markups," Journal of Economic Dynamics and Control, Elsevier, vol. 29(5), pages 847-871, May.
    16. Antoine Riche & Francesco Magris & Daria Onori, 2020. "Monetary rules in a two-sector endogenous growth model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(4), pages 1049-1100, June.
    17. Akio Matsumoto & Ferenc Szidarovszky & Keiko Nakayama, 2020. "Delay Cournot Duopoly Game with Gradient Adjustment: Berezowski Transition from a Discrete Model to a Continuous Model," Mathematics, MDPI, vol. 9(1), pages 1-19, December.
    18. Modesto, Leonor & Lloyd-Braga, Teresa & Coimbra, Rui, 2002. "Endogenous Growth Fluctuations in Unionised Economy with Productive Externalities," CEPR Discussion Papers 3230, C.E.P.R. Discussion Papers.
    19. 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.
    20. Ajevskis, Viktors, 2019. "Nonlocal Solutions To Dynamic Equilibrium Models: The Approximate Stable Manifolds Approach," Macroeconomic Dynamics, Cambridge University Press, vol. 23(6), pages 2544-2571, September.

    More about this item

    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:eee:chsofr:v:70:y:2015:i:c:p:27-37. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.