Uncertainty dynamics in a model of economic inequality

Abstract

In this article, we consider a stylized dynamic model to describe the economics of a population, expressed by a Langevin-type kinetic equation. The dynamics is defined by a combination of terms, one of which represents monetary exchanges between individuals mutually engaged in trade, while the uncertainty in barter (trade exchange) is modeled through additive and multiplicative stochastic terms which necessarily abide dynamical constraints. The model is studied to estimate three meaningful quantities, the inequality Gini index, the social mobility and the total income of the population. In particular, we investigate the time evolving binary correlations between any two of these quantities.