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On the Computation of the Hausdorff Dimension of the Walrasian Economy:Further Notes

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  • Dominique, C-Rene

Abstract

ABSTRACT: In a recent paper, Dominique (2009) argues that for a Walrasian economy with m consumers and n goods, the equilibrium set of prices becomes a fractal attractor due to continuous destructions and creations of excess demands. The paper also posits that the Hausdorff dimension of the attractor is d = ln (n) / ln (n-1) if there are n copies of sizes (1/(n-1)), but that assumption does not hold. This note revisits the problem, demonstrates that the Walrasian economy is indeed self-similar and recomputes the Hausdorff dimensions of both the attractor and that of a time series of a given market.

Suggested Citation

  • Dominique, C-Rene, 2009. "On the Computation of the Hausdorff Dimension of the Walrasian Economy:Further Notes," MPRA Paper 16723, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:16723
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    References listed on IDEAS

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    1. Herbert E. Scarf, 1959. "Some Examples of Global Instability of the Competitive Equilibrium," Cowles Foundation Discussion Papers 79, Cowles Foundation for Research in Economics, Yale University.
    2. Dominique, C-Rene, 2009. "Could Markets' Equilibrium Sets Be Fractal Attractors?," MPRA Paper 13624, University Library of Munich, Germany.
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    More about this item

    Keywords

    Fractal Attractors; Contractive Mappings; Self-similarity; Hausdorff Dimension of an Economy; Hausdorff Dimension of Economic Time Series;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • A1 - General Economics and Teaching - - General Economics
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables

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