  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.
