Inequality would exist in a society with equal incomes
Says the maths:
To examine how much inequality you would get even in a perfectly equal society, I whipped up a simple Python script to compute wealth distribution in a society where every person works for the exact same salary (this should be enough equality for anybody, yes?) of which he saves the exact same amount. For a 5% annual interest rate, the five wealth quintiles controlled 2, 7, 15, 28, and 47 percent of total wealth, respectively. For 10%, these quintiles controlled 0, 4, 10, 25 and 60 percent of wealth.
It’s incredible but now that I think of it, I can’t recall any inequality studies adjusting for age.