Dismal Science

From: Phil Dunn (pscumnud@DIRCON.CO.UK)
Date: Thu Jan 01 2004 - 10:27:36 EST

 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


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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