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8 provided we ’«crow 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 / i3/- Denoting wealth by of the wealth distribution p* - c W“*” 1 dtf Tf , let us write for the density or putting w » ln W p( w) = c e ~ cLc** for w -^ > 0 (4) p(w) => 0 for w <. 0 If Y denotes income and y= ln T the conditional density function of income can be represented in the form f*(y-w), the density of a certain return on wealth. Sven without knowing this f’unction 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 ^of return is independent of the amount of wealth. In terms of random variables, if ^ and 'Xj denote income, wealth and the rate of return, we have If the random variables wealth and the rate of return are independent, their sum can be represented by a convolution of the corresponding density functions, and we 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 symmetric and have the same value ( in fact, the only difference is in the dimension : TTnile 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: