### Full text

provided we know the distribution of wealth. But the distribution of wealth is known: It follows the Pareto law - over a fairly wide range - and its pattern has also been explained theoretically / 13/- Denoting wealth by W , let us write for the density of the wealth distribution p* = c W-*” 11 dW or putting w = In W p(w) = c e - c4tt for w > 0 (4) ak^yxi p(w) = 0 for W < 0 If Y denotes income and y= In Y the conditional dens it;/ function of income can be represented : Ln the form f*(y-w), the density of a certain return on wealth. Sven without knowing this function we might manage to derive the distribution of income from that of wealth provided we can make certain assumptions about independence. We shall provisionally assume that the distribution of the rate oof return is independent of the amount of wealth. In terms of random variables, if y J Cu and ^ denote income, wealth and the rate of return, we have If the random variables wealth and the rate of return are independen their sum can be represented by a convolution of the corresponding density functions, and 7/e shall in this way obtain the distribution of income. For the purposes of this calculation we shall replace the density f*(y-w) by the mirror function f(w-y) which is also independent of wealth. The two functions are sjmmetric and have the same value ( in fact, the only difference is in the dimension : While the former refers to a rate of return per year, the reciprocal value refers to the number of years income contained in the wealth ) The calculation of the density of income q(y) proceeds then by mixing the function f(w-y) with the density of wealth: