Wealth exchange under ceiling and flooring constraints: a modified Bennati-Dragulescu-Yakovenko model

TL;DR

This paper extends the classical BDY wealth exchange model by incorporating wealth ceilings and floors, analyzing the resulting dynamics and inequality effects through a mean-field ODE system and numerical simulations.

Contribution

It introduces a modified BDY model with policy-imposed wealth constraints and derives a mean-field ODE system to study long-term behavior and inequality impacts.

Findings

Derived a mean-field system of nonlinear ODEs for the modified model.

Analyzed the large-time behavior of the wealth distribution.

Numerically explored the effects of wealth caps and floors on inequality.

Abstract

We investigate the classical Bennati-Dragulescu-Yakovenko (BDY) dollar exchange model introduced in \cite{dragulescu_statistical_2000} where the effects of wealth ceiling and wealth flooring are explored. In our model, $N$ identical economical agents involved in the BDY game are also subjected to certain policies issued by a (artificial) government, which prevent agents whose wealth exceeds some prescribed threshold value (denoted by $b \in \mathbb N_+$) from receiving money and which prohibit agents whose wealth falls below certain threshold value (denoted by $a \in \mathbb N$) from giving out their money. We derive a mean-field system of coupled nonlinear ordinary differential equations (ODEs) governing the evolution of the distribution of money as the number of agents $N$ tends to infinity and study the large time behavior of the resulting ODE system. The impact of a wealth cap and a wealth floor on economic inequality (measured by the Gini index) will also be explored numerically.