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Dynamic monopoly with bounded continuously distributed delay

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  • Matsumoto, Akio
  • Chiarella, Carl
  • Szidarovszky, Ferenc

Abstract

A continuously distributed time lag is considered in a monopoly where the time window of past data is bounded from below and its length is fixed. The dynamic behavior of the resulting system is described by a special delayed differential equation with infinite spectrum. The location of the stability switch is determined and a simple rule is developed to determine which ones lead to the loss of stability or the regaining of stability. A simple computer example illustrates the theoretical findings. The distribution delay with finite time lag may be considered as an intermediate case between a finite fixed delay and an infinitely distributed delay, as is usually proposed in the existing literature.

Suggested Citation

  • Matsumoto, Akio & Chiarella, Carl & Szidarovszky, Ferenc, 2013. "Dynamic monopoly with bounded continuously distributed delay," Chaos, Solitons & Fractals, Elsevier, vol. 47(C), pages 66-72.
    • Handle: RePEc:eee:chsofr:v:47:y:2013:i:c:p:66-72
    DOI: 10.1016/j.chaos.2012.12.003
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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. Carl Chiarella & Ferenc Szidarovszky, 2002. "The Birth of Limit Cycles in Nonlinear Oligopolies with Continuously Distributed Information Lags," International Series in Operations Research & Management Science, in: Moshe Dror & Pierre L’Ecuyer & Ferenc Szidarovszky (ed.), Modeling Uncertainty, chapter 0, pages 249-268, Springer.
    3. Matsumoto, Akio & Szidarovszky, Ferenc, 2012. "Nonlinear delay monopoly with bounded rationality," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 507-519.
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    Cited by:

    1. Matsumoto, Akio & Szidarovszky, Ferenc, 2014. "Complex dynamics of monopolies with gradient adjustment," Economic Modelling, Elsevier, vol. 42(C), pages 220-229.
    2. Deborah Lacitignola, 2021. "Handling Hysteresis in a Referral Marketing Campaign with Self-Information. Hints from Epidemics," Mathematics, MDPI, vol. 9(6), pages 1-17, March.
    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. 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.

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