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On controlling chaos in a discrete tâtonnement process

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  • Ahmad K. Naimzada
  • Serena Sordi

Abstract

The simple pure exchange model with two individuals and two goods by Day and Pianigiani (1991), extensively analyzed by Day (1994, Ch. 10) and taken up again by Mukherjy (1999), is discussed and extended with the purpose of showing that chaos in a discrete tâtonnement process of this kind can be controlled if the auctioneer uses a smooth, nonlinear formulation of the price evolution process such that the price adjustment is a sigmoid-shaped function of the excess demand, with given upper and lower limits. This formulation o¤ers some advantages over previous speci?cations. In particular, given the speed of adjustment and the excess demand function, we show that, acting on the lower and/or upper limits that constrain price dynamics, the auctioneer can (i) stabilize the dynamics, (ii) reduce the complexity of the attractor and (iii) increase the economic signi?cance of the adjustment process.

Suggested Citation

  • Ahmad K. Naimzada & Serena Sordi, 2016. "On controlling chaos in a discrete tâtonnement process," Department of Economics University of Siena 729, Department of Economics, University of Siena.
    • Handle: RePEc:usi:wpaper:729
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    File URL: http://repec.deps.unisi.it/quaderni/729.pdf
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    References listed on IDEAS

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    1. Jacques Lesourne & André Orléan & Bernard Walliser, 2006. "Evolutionary Microeconomics," Springer Books, Springer, number 978-3-540-28537-3, June.
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    3. Goeree, Jacob K. & Hommes, Cars & Weddepohl, Claus, 1998. "Stability and complex dynamics in a discrete tatonnement model," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 395-410, January.
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    More about this item

    Keywords

    Price adjustment; tâtonnement; chaos; control;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General

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