A stochastic model of wealth distribution

Abstract

We propose a stochastic model of evolution of wealth in a society of economic agents. In the model, an agent can be in two states: inactive and active. Transitions between the states occur at random time intervals. In the active state, the rate at which wealth increases is greater than that in the inactive state. In both the states, wealth diminishes at a rate proportional to the current wealth. The probability density function describing the wealth distribution in the steady state is found to have the form of a beta distribution. Wealth distributions for the poor, middle and the rich classes are obtained separately. In economic literature, beta distribution and its generalisations, namely, the generalised beta distribution functions have been proposed to describe the income distributions of different economic societies. Our stochastic model provides a simple basis for the appearance of beta-type distributions.