Kinetic models for optimal control of wealth inequalities

TL;DR

This paper develops optimal control strategies for kinetic wealth distribution models to reduce inequality, demonstrating how control can alter the Pareto index and providing a new theoretical framework for taxation policies.

Contribution

It introduces a novel control approach for kinetic wealth models using finite horizon approximation, linking microscopic agent dynamics to global redistribution policies.

Findings

Control strategies can modify the Pareto index of wealth distribution.

The approach provides an exact quantification of the impact of control on wealth inequality.

Connections to existing Fokker-Planck models are established.

Abstract

We introduce and discuss optimal control strategies for kinetic models for wealth distribution in a simple market economy, acting to minimize the variance of the wealth density among the population. Our analysis is based on a finite time horizon approximation, or model predictive control, of the corresponding control problem for the microscopic agents' dynamic and results in an alternative theoretical approach to the taxation and redistribution policy at a global level. It is shown that in general the control is able to modify the Pareto index of the stationary solution of the corresponding Boltzmann kinetic equation, and that this modification can be exactly quantified. Connections between previous Fokker-Planck based models and taxation-redistribution policies and the present approach are also discussed.