A Generalized Asset Exchange Model With Economic Growth and Wealth Distribution

An agent-based yard-sale model of the economy is generalized to incorporate economic growth and its distribution to the agents according to their wealth as determined by a parameter λ. In addition to providing insight into the relation between the nature of economic growth and wealth inequality, we find that the model has a phase transition at λ = 1 between a equilibrium phase with economic mobility and a non-stationary phase for which there is no mobility and wealth is concentrated among a few agents. We show that the critical exponents obtained for a fixed number of agents do not obey the usual scaling laws. However, the critical exponents are consistent with the scaling laws and mean-field theory if the Ginzburg parameter, which controls the accuracy of the mean-field approximation, is held fixed as the transition is approached and is much greater than one. The transition raises questions about whether the methods of equilibrium statistical mechanics can be applied to economic systems. We also discuss possible implications of our results for economic systems and for understanding critical point behavior in systems with long, but finite, range interactions such as metals, biological systems and polymers.