  We introduce a simple model of economy, where the time evolution is described
by an equation capturing both exchange between individuals and random
speculative trading, in such a way that the fundamental symmetry of the economy
under an arbitrary change of monetary units is insured. We investigate a
mean-field limit of this equation and show that the distribution of wealth is
of the Pareto (power-law) type. The Pareto behaviour of the tails of this
distribution appears to be robust for finite range models, as shown using both
a mapping to the random `directed polymer' problem, as well as numerical
simulations. In this context, a transition between an economy dominated by a
few individuals from a situation where the wealth is more evenly spread out, is
found. An interesting outcome is that the distribution of wealth tends to be
very broadly distributed when exchanges are limited, either in amplitude or
topologically. Favoring exchanges (and, less surprisingly, increasing taxes)
seems to be an efficient way to reduce inequalities.

Condensed Matter