A Boltzmann-Type Approach to the Formation of Wealth Distribution Curves

57 Pages Posted: 9 Oct 2008  

Bertram Düring

University of Sussex - School of Mathematical and Physical Sciences

Daniel Matthes

Vienna University of Technology - Analysis & Scientific Computing

Giuseppe Toscani

University of Pavia

Date Written: October 7, 2008

Abstract

Kinetic market models have been proposed recently to account for the redistribution of wealth in simple market economies. These models allow to develop a qualitative theory, which is based on methods borrowed from the kinetic theory of rarefied gases. The aim of these notes is to present a unifying approach to the study of the evolution of wealth in the large-time regime. The considered models are divided into two classes: the first class is such that the society's mean wealth is conserved, while for models of the second class, the mean wealth grows or decreases exponentially in time. In both cases, it is possible to classify the most important feature of the steady (or self-similar, respectively) wealth distributions, namely the fatness of the Pareto tail. We shall also discuss the tails' dynamical stability in terms of the model parameters. Our results are derived by means of a qualitative analysis of the associated homogeneous Boltzmann equations. The key tools are suitable metrics for probability measures, and a concise description of the evolution of moments. A recent extension to economies, in which different groups of agents interact, is presented in detail. We conclude with numerical experiments that confirm the theoretical predictions.

Keywords: Wealth and income distributions, Pareto distribution, mixtures

JEL Classification: D31

Suggested Citation

Düring, Bertram and Matthes, Daniel and Toscani, Giuseppe, A Boltzmann-Type Approach to the Formation of Wealth Distribution Curves (October 7, 2008). Available at SSRN: https://ssrn.com/abstract=1281404 or http://dx.doi.org/10.2139/ssrn.1281404

Bertram Düring (Contact Author)

University of Sussex - School of Mathematical and Physical Sciences ( email )

Brighton, BN1 9QH
United Kingdom

Daniel Matthes

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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