Wealth condensation in a simple model of economy

We introduce a simple model of economy, where the time evolution is describ ed by an equation capturing both exchange between individuals and random sp eculative trading, in such a way that the fundamental symmetry of the econo my 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 th is distribution appears to be robust for finite range models, as shown usin g both a mapping to the random 'directed polymer' problem, as well as numer ical simulations. In this context, a phase transition between an economy do minated by a few individuals and a situation where the wealth is more evenl y spread out, is found. An interesting outcome is that the distribution of wealth tends to be very broadly distributed when exchanges are limited, eit her in amplitude or topologically. Favouring exchanges (and, less surprisin gly, increasing taxes) seems to be an efficient way lo reduce inequalities. (C) 2000 Published by Elsevier Science B.V. All rights reserved.