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Nonlinear delay monopoly with bounded rationality

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  • Matsumoto, Akio
  • Szidarovszky, Ferenc

Abstract

The purpose of this paper is to study the dynamics of a monopolistic firm in a continuous-time framework. The firm is assumed to be boundedly rational and to experience time delays in obtaining and implementing information on output. The dynamic adjustment process is based on the gradient of the expected profit. The paper is divided into three parts: we examine delay effects on dynamics caused by one-time delay and two-time delays in the first two parts. Global dynamics and analytical results on local dynamics are numerically confirmed in the third part. Four main results are demonstrated. First, the stability switch from stability to instability occurs only once in the case of a single delay. Second, the alternation of stability and instability can continue if two time delays are involved. Third, the occurence of Hopf bifurcation is analytically shown if stability is lost. Finally, in a bifurcation process, there are a period-doubling cascade to chaos and a period-halving cascade to the equilibrium point in the case of two time delays if the difference between the two delays is large.

Suggested Citation

  • Matsumoto, Akio & Szidarovszky, Ferenc, 2012. "Nonlinear delay monopoly with bounded rationality," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 507-519.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:4:p:507-519
    DOI: 10.1016/j.chaos.2012.01.005
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    References listed on IDEAS

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    1. Invernizzi, Sergio & Medio, Alfredo, 1991. "On lags and chaos in economic dynamic models," Journal of Mathematical Economics, Elsevier, vol. 20(6), pages 521-550.
    2. Matsumoto, Akio, 2009. "Note on Goodwin's 1951 nonlinear accelerator model with an investment delay," Journal of Economic Dynamics and Control, Elsevier, vol. 33(4), pages 832-842, April.
    3. Matsumoto, Akio & Szidarovszky, Ferenc, 2011. "Delay differential neoclassical growth model," Journal of Economic Behavior & Organization, Elsevier, vol. 78(3), pages 272-289, May.
    4. Howroyd, T. D. & Russell, A. M., 1984. "Cournot oligopoly models with time delays," Journal of Mathematical Economics, Elsevier, vol. 13(2), pages 97-103, October.
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    Citations

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    Cited by:

    1. Serena Brianzoni & Giovanni Campisi & Luca Guerrini, 2018. "A continuous-time heterogeneous duopoly model with delays," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 259-275, November.
    2. 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.
    3. Chen, Jianxin & Zhang, Tonghua & Zhou, Yongwu, 2020. "Dynamics of a risk-averse newsvendor model with continuous-time delay in supply chain financing," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 169(C), pages 133-148.
    4. Matsumoto, Akio & Szidarovszky, Ferenc, 2014. "Complex dynamics of monopolies with gradient adjustment," Economic Modelling, Elsevier, vol. 42(C), pages 220-229.
    5. Gori, Luca & Guerrini, Luca & Sodini, Mauro, 2015. "A continuous time Cournot duopoly with delays," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 166-177.
    6. 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.
    7. Mikhail Anufriev & Davide Radi & Fabio Tramontana, 2018. "Some reflections on past and future of nonlinear dynamics in economics and finance," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 91-118, November.
    8. Matsumoto, Akio & Szidarovszky, Ferenc, 2015. "Dynamic monopoly with multiple continuously distributed time delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 108(C), pages 99-118.
    9. Caravaggio, Andrea & Sodini, Mauro, 2020. "Monopoly with differentiated final goods and heterogeneous markets," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    10. Xiaoliang Li & Jiacheng Fu & Wei Niu, 2023. "Complex dynamics of knowledgeable monopoly models with gradient mechanisms," Papers 2301.01497, arXiv.org.
    11. Matsumoto, Akio & Chiarella, Carl & Szidarovszky, Ferenc, 2013. "Dynamic monopoly with bounded continuously distributed delay," Chaos, Solitons & Fractals, Elsevier, vol. 47(C), pages 66-72.
    12. 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.
    13. 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).

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