A Trade-Investment Model for Distribution of Wealth.pdf

a r X i v : c o n d - m a t / 0 3 0 6 5 7 9 v 2 [ c o n d - m a t .s t a t - m e c h ] 1 5 S e p 2 0 0 3 A Trade-Investment Model for Distribution of Wealth Nicola Scafetta a, Bruce J. West a, b and Sergio Picozzi a aDepartment of Physics and Free Electron Laser Laboratory, Duke University, Durham, NC 27708, USA bMathematics Division, Army Research Office, Research Triangle Park, NC 27709-2211, USA Abstract Econophysics provides a strategy for understanding the potential mechanisms un- derlying the anomalous distribution of wealth found in real societies. We present a computational nonlinear stochastic model for the distribution of wealth that de- pends upon three parameters and two mechanisms: trade and investment. To avoid economic paradoxes, the trade mechanism is assumed to be related to the poorer trader’s wealth and to statistically advantage the poorer of the two traders. The two mechanisms together are shown to generate a distribution that reproduces the full range of the empirical wealth distribution, and not only the inverse power-law tail that Pareto found in western societies at the end of the 19th century. Key words: Anomalous, condensation, interaction, Pareto, wealth PACS: 89.65.Gh, 87.23.Ge, 05.45.Df, 02.60.Cb 1 Introduction The science of complexity leads to an understanding of complex physical phe- nomena through the construction of both equilibrium and dynamical models. These ideas have found application in engineering, biology, sociology and eco- nomics; specifically, in areas where phenomena have both the characteristics of randomness and determinism [1], present nonlinear and non-extensive be- haviors and/or anomalous distributions. To understand the main mechanisms ? Corresponding author. Email address: ns2002@ (Nicola Scafetta). Preprint submitted to Physica D 2 February 2008 that lead to the empirical distribution of wealth in a society is one of such applications. More than a century ago the Italian sociologist and economist, Vilfre