Finite market size as a source of extreme wealth inequality and market instability

We study the finite-size effects in some scaling systems, and show that the finite number of agents N leads to a cut-off in the upper value of the Pareto law for the relative individual wealth. The exponent α of the Pareto law obtained in stochastic multiplicative market models is crucially affected by the fact that N is always finite in real systems. We show that any finite value of N leads to properties which can differ crucially from the naive theoretical results obtained by assuming an infinite N. In particular, finite N may cause in the absence of an appropriate social policy extreme wealth inequality α < 1 and market instability.