Kinetic Equations Modelling Wealth Redistribution: A Comparison of Approaches

16 Pages Posted: 16 Jul 2008

See all articles by Bertram Düring

Bertram Düring

University of Warwick - Mathematics Institute

Daniel Matthes

Vienna University of Technology - Analysis & Scientific Computing

Giuseppe Toscani

University of Pavia

Date Written: July 9, 2008

Abstract

Kinetic equations modelling the redistribution of wealth in simple market economies is one of the major topics in the field of econophysics. We present a unifying approach to the qualitative study for a large variety of such models, which is based on a moment analysis in the related homogeneous Boltzmann equation, and on the use of suitable metrics for probability measures. In consequence, we are able to classify the most important feature of the steady wealth distribution, namely the fatness of the Pareto tail, and the dynamical stability of the latter in terms of the model parameters. Our results apply e.g. to the market model with risky investments, and to the model with quenched saving propensities. Also, we present results from numerical experiments that confirm the theoretical predictions.

Keywords: Wealth distribution, Boltzmann equation, Pareto tail

JEL Classification: D31

Suggested Citation

Düring, Bertram and Matthes, Daniel and Toscani, Giuseppe, Kinetic Equations Modelling Wealth Redistribution: A Comparison of Approaches (July 9, 2008). Available at SSRN: https://ssrn.com/abstract=1161019 or http://dx.doi.org/10.2139/ssrn.1161019

Bertram Düring

University of Warwick - Mathematics Institute ( email )

Zeeman Building
Coventry, CV4 7AL
United Kingdom

Daniel Matthes (Contact Author)

Vienna University of Technology - Analysis & Scientific Computing ( email )

Wiedner Hauptstraße 8-10
Wien, 1040
Austria

Giuseppe Toscani

University of Pavia ( email )

Corso Strada Nuova, 65
27100 Pavia, 27100
Italy

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