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The Limit-Price Dynamics — Uniqueness, Computability and Comparative Dynamics in Competitiive Markets

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  • Gaël Giraud

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

In this paper, a continuous-time price-quantity trading process is defined for exchange economies with differentiable characteristics. The dynamics is based on boundedly rational agents exchanging limit-price orders to a central clearing house, which rations infinitesimal trades according to Mertens (2003) double auction. Existence of continuous trade and price curves holds under weak conditions and in particular even if there is no long-run competitive equilibrium. Every such curve converges towards a Pareto point, and every Paretian allocation is a locally stable rest-point. Generically, given initial conditions, the trade and price curve is piecewise unique, smooth and computable, hence enables to effectively perform comparative dynamics. Finally, in the 2 x 2 case, the vector field induced by the limit-price dynamics is real-analytic.

Suggested Citation

  • Gaël Giraud, 2007. "The Limit-Price Dynamics — Uniqueness, Computability and Comparative Dynamics in Competitiive Markets," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00155709, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00155709
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00155709
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    References listed on IDEAS

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    1. Smale, Stephen, 1976. "Exchange processes with price adjustment," Journal of Mathematical Economics, Elsevier, vol. 3(3), pages 211-226, December.
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    5. Dimitrios P Tsomocos & Gael Giraud & CNRS & Universite Paris-1, 2004. "Global Uniqueness and Money Non-neutrality in a Walrasian Dynamics without Rational Expectations," Economics Series Working Papers 2004-FE-15, University of Oxford, Department of Economics.
    6. Giraud, Gael, 2003. "Strategic market games: an introduction," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 355-375, July.
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    More about this item

    Keywords

    Non-tatonnement; price-quantity dynamics; limit-price mechanism; myopia; computable general equilibrium; non-tâtonnement; dynamique en prix et en quantités; mécanisme de prix-limite; myopie; équilibre général calculable;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D46 - Microeconomics - - Market Structure, Pricing, and Design - - - Value Theory

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