On the Computation of the Hausdorff Dimension of the Walrasian Economy: Addendum

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

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. A subsequent paper (no 16723) modified that assumption, dealt with the self-similarity of the Walrasian economy, and computed the Hausdorff dimensions of the attractor as if it were a space-filling curve. This paper is an extension of the first two. It shows that the path of the equilibrium price vector within the attractor is rather as close as one can get to a Brownian motion that tends to fill up the whole hyperspace available to it. The end analysis is that the economy obeys a homogeneous power law in the form of fβ. Power Spectra and Hausdorff dimensions are then computed for both the attractor and economic time series.

• Item Type: MPRA Paper
• Language: English
• Keywords: Fractal Attractor, Contractive Mappings, Self-similarity, Hausdorff Dimensions of the Walrasian Economy and time series, Brownian Motion, Power Spectra, Hausdorff Dimensions in Higher Dimensions. KEYWORDS: Fractal Attractor, Contractive Mappings, Self-similarity, Hausdorff Dimensions of the Walrasian Economy and time series, Brownian Motion, Power Spectra, Hausdorff Dimensions in Higher Dimensions.
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; C - Mathematical and Quantitative Methods > C0 - General; C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods

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* Formerly Professor of Economics.