Dominique, CRene (2009): On the Computation of the Hausdorff Dimension of the Walrasian Economy:Further Notes.

PDF
MPRA_paper_16723.pdf Download (73kB)  Preview 
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 (n1) if there are n copies of sizes (1/(n1)), but that assumption does not hold. This note revisits the problem, demonstrates that the Walrasian economy is indeed selfsimilar and recomputes the Hausdorff dimensions of both the attractor and that of a time series of a given market.
Item Type:  MPRA Paper 

Original Title:  On the Computation of the Hausdorff Dimension of the Walrasian Economy:Further Notes 
Language:  English 
Keywords:  Fractal Attractors, Contractive Mappings, Selfsimilarity, 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:  CRene 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, CR. (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, 157179. (6) Hutchinson, J., E. (1981). “Fractals and SelfSimilarity.” Indiana Univ. Math. Jour., 30, 71347. (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, 1523. (9) Peters, E. (1991). “A Chaotic Attractor for the S&P500.” 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, 157172. (12) Schief, A. (1994). “Separation Properties for SelfSimilar Sets.” Proc. Amer. Math. Soc., 122, 11115. (13) Szpilrajn, E. (1937). La dimension et la mesure.” Fundamenta Mathematica, 28, 8189. * Formerly Professor of Economics 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/16723 