The "law" of wealth concentration

J. Barkley Rosser, Jr. rosserjb at
Thu Aug 17 11:07:16 PDT 2000

[Yes, I'm back, at least for awhile.]

Pareto-Levy distributions do a pretty good job of describing firm-size and city-size distributions also. I would note, however, that they do not all look identical. The slope on the log-log form can vary, that is the exponent of the function. Different slopes imply varying degrees of equality versus inequality. So, the general pattern of inequality may be the same, but its intensity can vary.

Let me give an example using city size distributions. There is an old rule of thumb about city size distributions in countries called the "rank-size rule." Under that rule you can determine the size of a city by dividing the population of the country's largest city by the rank of the city in question. Thus, the second largest city would have half the population of the largest, the third would have one-third, etc. This would hold for the Pareto distribution if its coefficient equals one. But varying the coefficient one can have the second city either larger than half (as in the US or China or India) or less than half (as in Mexico or France or Japan). One can be "flatter" (more equal) or "steeper" (more unequal), while still having the same general shape or form. Barkley Rosser Professor of Economics James Madison University Harrisonburg, VA 22807 USA website: -----Original Message----- From: Michael Perelman <michael at> To: lbo-talk at <lbo-talk at> Date: Wednesday, August 16, 2000 7:57 PM Subject: Re: The "law" of wealth concentration

>Pareto's initial story was that if you had a complete redistribution of
>so that everybody had the same, soon the previously wealthy would end up
>about the same distribution of income. One interesting point: if Pareto's
>equation is correct, then most statistical estimation methods would not
>very well, since it violates the normal distribution. Mendelbrot has made
>of this, arguing that economists should see the world in terms of fractals
>rather than assuming normal distributions.
>Michael Perelman
>Economics Department
>California State University
>Chico, CA 95929
>Tel. 530-898-5321
>E-Mail michael at

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