Of Wealth Power and Law: the Origin of Scaling in Economics

first approach is mainly phenomenological, whereas the second relys on rather sophisticated mechanisms and seems to be applicable to a restricted set of systems. In this letter we present a simple and generic mechanism which generates power law distributions. We argue that any random multiplicative dynamics, in which at each time step the observables are multiplied by a positive random variable, drawn from a fixed distribution, eventually leads to a power law distribution of these observables. We suggest that in many systems random multiplicative dynamics may be at the origin of the observed power laws. In this letter we focus on the power law distribution of wealth in economic systems. A century ago Pareto 11 has discovered that income is distributed according to a power law (with cut-offs) (Fig. 1). It was later found that this is also true for the distribution of wealth 12 (see Figure 2). In a power law distribution the observable