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Delay dynamics in nonlinear monopoly with gradient adjustment

Author

Listed:
  • Akio Matsumoto

    (Chuo University)

  • Ferenc Szidarovszky

    (Corvinus University)

Abstract

Two types of boundedly rational monopolists are considered, when they are unable to determine the profit maximizing output levels. In the first case, the monopolist knows the price function and in the second case it can access only past output and price values. In applying gradient dynamics, the marginal profit is either known or approximated by finite differences based on two past profit data. Stability conditions are derived first with discrete time scales, which are also applied in a special case. Two models of continuous-time dynamics are then introduced. The first is a natural modification of the discrete model, and the other includes an inertia coefficient with the derivative. In each case, a delay differential equation is obtained with two delays. Stability conditions are derived and the stability-switching curves are constructed and illustrated.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:decfin:v:44:y:2021:i:2:d:10.1007_s10203-021-00342-x
    DOI: 10.1007/s10203-021-00342-x
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    References listed on IDEAS

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    1. Askar, S.S., 2013. "On complex dynamics of monopoly market," Economic Modelling, Elsevier, vol. 31(C), pages 586-589.
    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. 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.
    4. 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, 2022. "The chaotic monopolist revisited with bounded rationality and delay dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    2. Xiaoliang Li, 2021. "Analysis of stability and bifurcation for two heterogeneous triopoly games with the isoelastic demand," Papers 2112.05950, arXiv.org.

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