On the role of luck for the concentration of capital and Piketty's 'fundamental force of divergence'

We consider an overlapping generations version of a model suggested by Fargione, Lehmann and Polasky that allows us to show, by means of simulations, that randomness of the rate of return on capital, combined with inheritance of capital and consumption being a concave function of wealth may lead to an increasing concentration of capital. We can also show that the average rate of return being higher than the growth rate of aggregate income, r>g, does not necessarily lead to increasing concentration and that there are cases where concentration of capital does increase while the opposite inequality, g>r, holds.