Eur. Phys. J. B (2018) 91: 265
https://doi.org/10.1140/epjb/e2018-90138-1

Regular Article

Kinetic models for optimal control of wealth inequalities

¹ Department of Mathematics, University of Sussex, Pevensey II, Brighton, BN1 9QH, UK
² Dipartimento di Matematica e Informatica, Via Machiavelli 35, 44121 Ferrara, Italy
³ Dipartimento di Matematica and IMATI, CNR, Via Ferrata 1, 27100 Pavia, Italy

^a e-mail: bd80@sussex.ac.uk

Received: 7 March 2018
Received in final form: 29 June 2018
Published online: 24 October 2018

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 for taxation-redistribution policies and the present approach are also discussed.