An analytic treatment of the Gibbs–Pareto behavior in wealth distribution

We develop a general framework, based on Boltzmann transport theory, to analyze the distribution of wealth in societies. Within this framework we derive the distribution function of wealth by using a two-party trading model for the poor people, while for the rich people a new model is proposed, where interaction with wealthy entities (huge reservoir) is relevant. At equilibrium, the interaction with wealthy entities gives a power-law (Pareto-like) behavior in the wealth distribution, while the two-party interaction gives a Boltzmann–Gibbs distribution.