Kinetic model for international trade allowing transfer of individuals

Abstract

We propose a kinetic model to describe trade among different populations, living in different countries. The interaction rules are assumed depending on the trading propensity of each population and also on non-deterministic (random) effects. Moreover, the possible transfers of individuals from one country to another are also taken into account, by means of suitable Boltzmann-type operators. Consistent macroscopic equations for number density and mean wealth of each country are derived from the kinetic equations, and the effects of transfers on their equilibrium values are commented on. Finally, a suitable continuous trading limit is considered, leading to a simpler system of Fokker–Planck-type kinetic equations, with specific contributions accounting for transfers. This article is part of the theme issue ‘Kinetic exchange models of societies and economies’.