Analysis of wealth inequality with a random money transfer model

Increasing gap in wealth distribution is among the key issues that have been discussed worldwide in recent years. In this paper, we use the money transfer model to explain the formation of wealth distribution, by imposing two types of debt constraints, and the analytic function of wealth distribution is derived by adopting Boltzmann statistics. With a limit of individual debt, it is shown that the stationary distribution of wealth follows the exponential law, which is verified by many empirical studies. While the limit is imposed on the total amount of bank loan, the stationary distribution becomes an asymmetric Laplace one. Furthermore, an excellent agreement is found between these analytical probability density functions and numerical results by simulation at the steady state.