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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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    File URL: https://mpra.ub.uni-muenchen.de/16723/1/MPRA_paper_16723.pdf
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    References listed on IDEAS

    as
    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;

    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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