Power Law Distribution of Wealth in a Money-Based Model 8 0 cn 77 a.) 794 0 cd E C.) 00 00 0 7t. ct 0 >< •-1 Yan-Bo Xie, Bo Hu, Tao Zhou and Bing-Hong Wang" Department of Modern Physics and The Nonlinear Science Center, University of Science and Technology of China, Hegel Anhui, 230026, PR China (Dated: February 2, 2008) A money-based model for the power law distribution (PLD) of wealth in an economically inter- acting population is introduced. The basic feature of our model is concentrating on the capital movements and avoiding the complexity of micro behaviors of individuals. It is proposed as an extension of the Equfluz and Zimmennsum's (EZ) model for crowding and information transmission in financial markets. Still, we must emphasize that in EZ model the PLD without exponential correction is obtained only for a particular parameter, while our pattern will give it within a wide range. The Zipf exponent depends on the parameters in a nontrivial way and is exactly calculated in this paper. PACS numbers: 89.90.+n, 02.50.Le, 64.60.Cn, 87.10.-1-e I. INTRODUCTION Many real life distributions, including wealth alloca- tion in individuals, sizes of human settlements, website popularity, words ranked by frequency in a random cor- pus of tat, observe the Zipf law. Empirical evidence of the Zipf distribution of wealth [I-9] has recently attracted a lot of interest of economists and physicists. 'lb under- stand the micro mechanism of this challenging problem, various models have been proposed. One type of them is based on the so-called multiplicative random process110- 21]. In this approach, individual wealth Ls multiplica- tively updated by a random and independent factor. A very nice power law is given, however, this approach es- sentially does not contain interactions among individu- als. which are responsible for the economic structure and aggregate behavior. Another pattern takes into account the interaction between two individuals