Pareto tails in socio-economic phenomena: a kinetic description

Various phenomena related to socio-economic aspects of our daily life exhibit equilibrium densities characterized by a power law decay. Maybe the most known example of this property is concerned with wealth distribution in a western society. In this case the polynomial decay at infinity is referred to as Pareto tails phenomenon (Pareto, Cours d’économie politique, 1964). In this paper, the authors discuss a possible source of this behavior by resorting to the powerful approach of statistical mechanics, which enlightens the analogies with the classical kinetic theory of rarefied gases. Among other examples, the distribution of populations in towns and cities is illustrated and discussed.