A kinetic model of wealth distribution and migration phenomena

DAMIAN KNOPOFF; TORRES GERMAN

Beijing

Congreso; International Congress of Industrial and Applied Mathematics (ICIAM); 2015

A kinetic model for wealth distribution within a population based on the kinetic theory for active particles is presented, where individuals are characterized by a microscopic variable (the activity) describing their state and are subdivided into  classes \cite{[BKS13]}, including the eventual migration of individuals between populations \cite{[KNOP13]}. In contrast to previous models, it is assumed that interactions among individuals (viewed as trades) are non-conservative and that an external agent (e.g. the State) implements certain distribution policies, since it is clear that wealth can be created and destroyed within a society and consequently the total wealth and the mean wealth per capita evolves in time.The model is stated in terms of a system of differential equations modelling the time evolution of a distribution function that represents the proportion of individuals in each class. Existence and uniqueness of solutions are shown and some selected simulations representing different scenarios and a parameter sensibility analysis are performed.