Communications in Mathematical Sciences

Volume 6 (2008)

Number 4

International and domestic trading and wealth distribution

Pages: 1043 – 1058



B. During

G. Toscani


We introduce and discuss a kinetic model for wealth distribution in a simple market economy which is built of a number of countries or social groups. Our approach is based on the model with risky investments introduced by Cordier, Pareschi, and Toscani in On a kinetic model for a simple market economy, and borrows ideas from the kinetic theory of mixtures of rarefied gases. Wealth is exchanged by individuals inside these countries (domestic trade) as well as in between different countries (international trade). Under a suitable scaling we derive a system of Fokker-Planck type equations and discuss its extension to a two-dimensional model with distributed trading propensity. Theoretical and numerical results for two groups show that the wealth distribution develops a bimodal (and in general, a polymodal) shape.


Wealth and income distributions, Boltzmann equation, mixture

2010 Mathematics Subject Classification

35B40, 82C40, 91B60

Published 1 January 2008