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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.

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Bibliographic Info

Article provided by Elsevier in its journal Economic Modelling.

Volume (Year): 28 (2011)
Issue (Month): 1-2 (January)
Pages: 299-307

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Handle: RePEc:eee:ecmode:v:28:y:2011:i:1-2:p:299-307

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Web page: http://www.elsevier.com/locate/inca/30411

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Keywords: Monopoly Bounded rationality Subjective demand Dynamical system Stability;

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  1. Jin, Jim Y., 2001. "Monopolistic competition and bounded rationality," Journal of Economic Behavior & Organization, Elsevier, vol. 45(2), pages 175-184, June.
  2. 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.
  3. Gian-Italo Bischi & Ahmad K. Naimzada & Lucia Sbragia, 2004. "Oligopoly Games with Local Monopolistic Approximation," Working Papers 81, University of Milano-Bicocca, Department of Economics, revised Nov 2004.
  4. Silvestre, Joaquim, 1977. "A model of general equilibrium with monopolistic behavior," Journal of Economic Theory, Elsevier, vol. 16(2), pages 425-442, December.
  5. 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.
  6. 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.
  7. Bonanno, Giacomo, 1990. " General Equilibrium Theory with Imperfect Competition," Journal of Economic Surveys, Wiley Blackwell, vol. 4(4), pages 297-328.
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