**From:** Phil Dunn (*pscumnud@DIRCON.CO.UK*)

**Date:** Thu Jan 01 2004 - 10:27:36 EST

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From 'Ubiquity' by Mark Buchanan (Crown, NY) ISBN 0-609-60810-X: If you tally up how many people in the United States have a net worth of a billion dollars, you will find that about four times as many have net worth of of about half a billion. Four times as many again are worth a quarter of a billion, and so on. If this special pattern held for just one country under one government at one point in time, then you might write it off as a peculiar quirk [sic] of some government policy. But the very same pattern holds in Britain, the United States, Japan, and virtually every country on Earth. ... the French physicists Marc Me'zard and Jean Philippe Bouchard were able to explain this pattern ... Suppose that each person's wealth grows or shrinks by a random fraction each year... suppose also that each person contributes to the wealth of some other people by virtue of working for them, investing money in their business, and so on. ... Me'zard and Bouchard found that in a simple game including only these effects, the power law distribution of wealth comes tumbling out. The paper, Wealth condensation in a simple model of economy, is at http://arxiv.org/abs/cond-mat/0002374 Abstract: 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.

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