Abstract
Abstract 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.
Highlights
IntroductionProbability distribution functions with power decay appear in numerous biological, physical, social and economic contexts, which look fundamentally different
One of the main advantages of this procedure is that while maintaining the same equilibrium density, the limit equation is much easier to handle. In other words this asymptotic theory represents a good balance between the microscopic binary collision dynamics, easy to implement from a modeling point of view, and its macroscopic outcome provided by the equilibrium density
In analogy with some classical argument of kinetic theory, originally developed to establish rigorous relationships between collisional Boltzmann-type and Fokker– Planck type equations in the limit of grazing collisions (Villani, 2002), we introduced and discussed various social and economic phenomena which are characterized by equilibria exhibiting power law tails
Summary
Probability distribution functions with power decay appear in numerous biological, physical, social and economic contexts, which look fundamentally different. Kinetic models of wealth distribution are based on binary trades between agents (Pareschi and Toscani, 2013), and, as noticed in Düring et al (2008, 2009); Matthes and Toscani (2008), the structure of the microscopic trade is responsible of the macroscopic behavior These enlightening studies made possible to identify the types of microscopic interactions which lead to stationary distributions with power tails. In addition to the main known example, we will discuss how the basic principles of kinetic modeling can help to clarify the evolution of the size of a population in towns and cities, justifying the formation of Pareto tails in this case
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