Stochastic models with multiplicative noise for economic inequality and mobility

Abstract

In this article, we discuss a dynamical stochastic model that represents the time evolution of income distribution of a population, where the dynamics develops from an interplay of multiple economic exchanges in the presence of multiplicative noise. The model remit stretches beyond the conventional framework of a Langevin-type kinetic equation in that our model dynamics is self-consistently constrained by dynamical conservation laws emerging from population and wealth conservation. This model is numerically solved and analysed to evaluate the inequality of income in correlation to other relevant dynamical parameters like the mobility M and the total income μ. Inequality is quantified by the Gini index G. In particular, correlations between any two of the mobility index M and/or the total income μ with the Gini index G are investigated and compared with the analogous quantities resulting from an additive noise model.