  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 $\alpha$ 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
$\alpha < 1$ and market instability.
