Any process that spreads things (such as wealth) out in a more-or-less uniform way on a logarithmic scale will produce an approximate power law with a slope of -1. Note that progressive taxation in which the wealthy are taxed at a higher rate than the poor does not alter the power law, only making it grow more slowly from an initial distribution in which everyone has the same wealth. If the initial condition is something close to a power law, it will remain so in the presence of any reasonable taxation and redistribution of wealth. There will always be some segment of the population whose wealth consistently increases faster than another segment. Of course individuals can change where they lie on the curve through hard work, good money management, and luck.
Via Sakis Koukouvis