From: John Conover <john@email.johncon.com>
Subject: Re: Will the rich get richer f o r e v e r ?
Date: 17 May 1999 21:41:51 -0000
Edward Flaherty writes:
>
> There's no economic theory on what the ideal aggregate income distribution
> should be, so it's tough to state objectively whether a given distribution
> is too wide, not wide enough, or just right. It's largely a matter of
> opinion.
>
Hi Edward. If one buys into the concept of path dependency, (and many
do, and many don't,) in financial things, the accumulation of personal
wealth over a lifetime would be assumed to be a fractal. To get the
frequency distribution to fit, a fractal dimension of about 0.8 seems
about right-to include the accumulated wealth of B. Gates, against the
median and interquartile range, of the aggregate, etc., (ie., assuming
a Levy Flight, where a fractal dimension of 0.8 is almost a Cauchy
distribution-I just found the homogeneous power law that would fit
B. Gates' fortune, at about 70 billion bucks, against the US wealth
frequency distribution at
http://cher.eda.doc.gov/BudgetFY97/index.html, where the "average"
wealth is a couple of hundred thousand bucks per person.)
If one assumes path dependency, (and many do, and many don't,) and a
fractal dimension of 0.5 as a mathematical expediency, (which is of
dubious merit-someone would have to work out the gambler's ruin for a
fractal dimension of 0.8, or so,) then the chances of any specific
"average person" EVER replacing B. Gates is about (2*10^5)/(7*10^10) =
3*10^-6, which is very poor odds, indeed, (and the time required to do
so would be approximately proportional to the square of B. Gates'
fortune, ie., longer than a lifetime.) However, considering the number
of possible paths, (ie., people in the US,) it would be a virtual
certainty that eventually, many would.
If one believes in the lottery of path dependency, of course.
John
BTW, B. Gates is not so rich by the standards of the rich. For
example, in the early 1900's, J. D. Rockefeller's fortune was 2% of
the US GDP-relatively, about twice what Gates' is today. (If personal
wealth as a fraction of GDP means anything.)
--
John Conover, john@email.johncon.com, http://www.johncon.com/