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Effects of fixed and continuously distributed delays in a monopoly model with constant price elasticity

Author

Listed:
  • Luca Guerrini

    (Polytechnic University of Marche)

  • Nicolò Pecora

    (Catholic University)

  • Mauro Sodini

    (University of Pisa)

Abstract

In this paper, we analyze the dynamics of a monopoly model with constant elasticity in which the monopolist faces a form of bounded rationality due to limited accessibility to information. We assume the firm adopts a gradient mechanism to adjust the output level, and we investigate how the introduction of fixed and continuously distributed delays within the resulting continuous-time system may affect the long-run dynamics. We find that the stability of the equilibrium depends on the weighting function adopted to model continuously distributed delays, and the convergence of the realized output toward the steady state is crucially affected by the choice of the delay type which, in turn, reflects the availability and the weight assigned to information. Indeed, depending on the assumptions on modeling delays, the equilibrium point may undergo a Hopf bifurcation after which a limit cycle arises.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:decfin:v:41:y:2018:i:2:d:10.1007_s10203-018-0222-3
    DOI: 10.1007/s10203-018-0222-3
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    References listed on IDEAS

    as
    1. Matsumoto, Akio & Chiarella, Carl & Szidarovszky, Ferenc, 2013. "Dynamic monopoly with bounded continuously distributed delay," Chaos, Solitons & Fractals, Elsevier, vol. 47(C), pages 66-72.
    2. Christophe Gouel, 2012. "Agricultural Price Instability: A Survey Of Competing Explanations And Remedies," Journal of Economic Surveys, Wiley Blackwell, vol. 26(1), pages 129-156, February.
    3. 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.
    4. 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.
    5. Askar, S.S., 2013. "On complex dynamics of monopoly market," Economic Modelling, Elsevier, vol. 31(C), pages 586-589.
    6. Matsumoto, Akio & Szidarovszky, Ferenc, 2012. "Nonlinear delay monopoly with bounded rationality," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 507-519.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    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. Li, Xiaoliang & Yang, Jing & Zhang, Ally Quan, 2025. "Influence of price elasticity of demand on monopoly games under different returns to scale," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 233(C), pages 75-98.
    3. Xiaoliang Li & Jiacheng Fu & Wei Niu, 2023. "Complex dynamics of knowledgeable monopoly models with gradient mechanisms," Papers 2301.01497, arXiv.org.

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    More about this item

    Keywords

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    JEL classification:

    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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