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. 
Arnab Das and Sudhakar Yarlagadda