Dominique, C-Rene
(2009):
*On the Computation of the Hausdorff Dimension of the Walrasian Economy:Further Notes.*

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## 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.

Item Type: | MPRA Paper |
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Original Title: | On the Computation of the Hausdorff Dimension of the Walrasian Economy:Further Notes |

Language: | English |

Keywords: | Fractal Attractors, Contractive Mappings, Self-similarity, Hausdorff Dimension of an Economy,Hausdorff Dimension of Economic Time Series |

Subjects: | C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling A - General Economics and Teaching > A1 - General Economics C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables |

Item ID: | 16723 |

Depositing User: | C-Rene Dominique |

Date Deposited: | 10 Aug 2009 10:42 |

Last Modified: | 04 Oct 2019 23:22 |

References: | REFERENCES (1) Bernard, S. (2001). Universalité et Fractals. Paris: Collection Champs, Flammarion. (2) Besicovich, A., S. (1929). “On Linear Sets of Points of Fractional Dimensions.” Mathematische Annalen, 101. (3) Dominique, C-R. (2009). “Could Markets’ Equilibrium Sets Be Fractal Attractors?”MPRA Paper no13624 University of Munich. (4) Falconer, J. K. (1985). The Geometry of Fractal Sets. New York: Cambridge University Press. (5) Hausdorff, F. (1919). “Dimension und auberes.” Mathematische Annalen, 79, 157-179. (6) Hutchinson, J., E. (1981). “Fractals and Self-Similarity.” Indiana Univ. Math. Jour., 30, 713-47. (7) Mandelbrot, B. (1982). The Fractal Geometry of Nature. San Francisco: W. H. Freeman. (8) Moran, P. A. (1946). “Additive Functions of Intervals and Hausdorff Measure.” Proc. Cambridge Philos. Soc. 42, 15-23. (9) Peters, E. (1991). “A Chaotic Attractor for the S&P-500.” Financial Analyst Jour., March/April. (10)-------- (1989). “Fractal Structure in the Capital Market.” Financial Analyst Jour., July/August. (11) Scarf, H. (1960). “Some Examples of Global Instability of the Competitive Equilibrium.” Inter’l Econ. Review, 1, 157-172. (12) Schief, A. (1994). “Separation Properties for Self-Similar Sets.” Proc. Amer. Math. Soc., 122, 111-15. (13) Szpilrajn, E. (1937). La dimension et la mesure.” Fundamenta Mathematica, 28, 81-89. * Formerly Professor of Economics |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/16723 |