Interacting agent models for wealth distribution

Abstract

In this paper a two agent wealth distribution model for a closed economic system developed in [2] is presented and extended. We first extend the model by randomly distributing the propensity to save of the agents. We derive a closed form of the stationary relative wealth measure of an agent. We also see that if we take both the propensity to save and the redistribution measure to be uniformly distributed, then the stationary wealth distribution of agent 1 cannot be Beta distributed. Furthermore we conjecture that given a uniform redistribution measure and Beta distributed propensity to save, the resulting wealth distribution cannot be Beta distributed either. The absence of Beta distributions in the wealth distribution shows that there cannot be product stationary measures in these cases. We also extend the model by assuming zero propensity and that the stationary product measure of one agent is conditionally Gamma(α;β)
distributed, where we condition on α be independently distributed as well. We find that the class of distributions for α defined by ψ(α) = α^-k, k an integer always leads to the wealth distribution for agent 1 to be heavy-tailed. We also take steps in showing that there exists a distribution for α that solves for the wealth distribution of agent 1 to be Pareto Lomax distributed.