Statistical Physics Models for Economic Systems

Abstract

The goal of this thesis is to construct an extension of the econophysical model by V. M. Yakovenko, that describes the distribution of goods or incomes, by combining it with the utility-based model of J. Mulder. The dynamics of the model of V. M. Yakovenko are aimed at pairwise interactions in single good markets while the dynamics of the model of J. Mulder depicts the interaction in a two goods market based on utility. The model of Yakovenko shows how maximization of entropy leads to Boltzmann distributed income distributions while the model by Mulder shows that the maximization of utility does not. In this thesis we analyse and combine these two models to ?nd a single master equation. Using this equation we examine the transition matrix. This examination illustrates that the model is stable but not Boltzmann distributed. The analysis of the simulations illustrates the stability of the system and the effects of both models on utility and the income distribution.