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Monopoly with local knowledge of demand function

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  • Naimzada, Ahmad
  • Ricchiuti, Giorgio

Abstract

In this note, we propose a model where a quantity setting monopolist has incomplete knowledge of the demand function. In each period, the firm sets the quantity produced observing only the selling price and the slope of the demand curve at that quantity. Given this information and through a learning process the firm estimates a linear subjective demand curve. We show that the steady states of the dynamic equation are critical points of the objective profit function. Moreover, results depend on convexity/concavity of the demand. When the demand function is convex and the objective profit function has a unique critical point: the steady state is a globally stable maximum; conversely when then steady state is not unique, local maximums are locally stable, while local minimums are locally unstable. On the other hand when the demand function is concave, the unique critical point is a maximum: there can be stability or instability of the critical point and period two cycles around it via a flip bifurcation. Moreover, through simulations we can observe that, with a mixed inverse demand function, there are different dynamic behaviors, from stability to chaos and that we have transition to complex dynamics via a sequence of period-doubling bifurcations. Finally, we show that the same results can be obtained if the monopolist is a price setter.

Suggested Citation

  • Naimzada, Ahmad & Ricchiuti, Giorgio, 2011. "Monopoly with local knowledge of demand function," Economic Modelling, Elsevier, vol. 28(1), pages 299-307.
  • Handle: RePEc:eee:ecmode:v:28:y:2011:i:1:p:299-307
    DOI: 10.1016/j.econmod.2010.08.020
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    References listed on IDEAS

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    1. D. LĂ©onard & K. Nishimura, 1999. "Nonlinear dynamics in the Cournot modelwithout full information," Annals of Operations Research, Springer, vol. 89(0), pages 165-173, January.
    2. Bonanno, Giacomo, 1990. " General Equilibrium Theory with Imperfect Competition," Journal of Economic Surveys, Wiley Blackwell, vol. 4(4), pages 297-328.
    3. Nyarko, Yaw, 1991. "Learning in mis-specified models and the possibility of cycles," Journal of Economic Theory, Elsevier, vol. 55(2), pages 416-427, December.
    4. Armen A. Alchian, 1950. "Uncertainty, Evolution, and Economic Theory," Journal of Political Economy, University of Chicago Press, vol. 58, pages 211-211.
    5. Bischi, Gian Italo & Naimzada, Ahmad K. & Sbragia, Lucia, 2007. "Oligopoly games with Local Monopolistic Approximation," Journal of Economic Behavior & Organization, Elsevier, vol. 62(3), pages 371-388, March.
    6. Jin, Jim Y., 2001. "Monopolistic competition and bounded rationality," Journal of Economic Behavior & Organization, Elsevier, vol. 45(2), pages 175-184, June.
    7. Takashi Negishi, 1961. "Monopolistic Competition and General Equilibrium," Review of Economic Studies, Oxford University Press, vol. 28(3), pages 196-201.
    8. Bonanno, Giacomo & Christopher Zeeman, E., 1985. "Limited knowledge of demand and oligopoly equilibria," Journal of Economic Theory, Elsevier, vol. 35(2), pages 276-283, August.
    9. Bonanno, Giacomo, 1988. "Oligopoly Equilibria When Firms Have Local Knowledge of Demand," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(1), pages 45-55, February.
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    Cited by:

    1. Sarkar, Biswajit & Saren, Sharmila & Wee, Hui-Ming, 2013. "An inventory model with variable demand, component cost and selling price for deteriorating items," Economic Modelling, Elsevier, vol. 30(C), pages 306-310.

    More about this item

    Keywords

    Monopoly; Bounded rationality; Subjective demand; Dynamical system; Stability;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • L12 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Monopoly; Monopolization Strategies

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