Study of a model for the distribution of wealth

TL;DR

This paper analyzes a nonlinear map model for wealth distribution in a closed economy, revealing how wealth inequality can grow over time through explicit evolution equations for distribution moments.

Contribution

It extends previous models by deriving explicit iteration formulas for higher moments, showing how wealth disparity tends to increase.

Findings

Higher moments grow indefinitely, indicating increasing wealth inequality.

Explicit evolution laws for wealth distribution moments are derived.

The model predicts spreading of wealth over time.

Abstract

An equation for the evolution of the distribution of wealth in a population of economic agents making binary transactions with a constant total amount of "money" has recently been proposed by one of us (RLR). This equation takes the form of an iterated nonlinear map of the distribution of wealth. The equilibrium distribution is known and takes a rather simple form. If this distribution is such that, at some time, the higher momenta of the distribution exist, one can find exactly their law of evolution. A seemingly simple extension of the laws of exchange yields also explicit iteration formulae for the higher momenta, but with a major difference with the original iteration because high order momenta grow indefinitely. This provides a quantitative model where the spreading of wealth, namely the difference between the rich and the poor, tends to increase with time.