International and domestic trading and wealth distribution. (English) Zbl 1158.91430

Düring, B.; Toscani, G.

Commun. Math. Sci. 6, No. 4, 1043-1058 (2008).

Summary: 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 S. Cordier et al. [J. Stat. Phys. 120, No. 1–2, 253–277 (2005; Zbl 1133.91474)], 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.

MSC:

91B60	Trade models
82C40	Kinetic theory of gases in time-dependent statistical mechanics
35B40	Asymptotic behavior of solutions to PDEs

Keywords:

Wealth and income distributions; Boltzmann equation; mixture

Citations:

Zbl 1133.91474