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8 provided we know the di tribution of wealth. But the distribution of wealth :s kn wn! It follows the Pareto law - over a fairly wide range - and its pattern has also been explained theoretically / 13/- Denotin- wealth by W , let us write for the density of the wealth distributinn p* * c W** 1 dW or putting w ® In W p(w) - c e •o( W^W for w 0 (4) 0 for w < 0 If Y den tes inco; e and y* In Y the conditional density functi n f incune can be represented in the f ria f*(y- w ) t the density of a certain return on wealth. liven ithout knowing this functi n we might manage to derive the distribution of income from that of wealth provide! we can make certain assuapti ns about independence. e sha 1 provisionally assume that the istribution of the rate of return is independent of the mount of wealth. In terms of random variables, if / CtT and denote inco e, 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 mirr r functi n f(w-y) which is ala' independent of wealth. The two functi ns are symmetric and have the same value ( in fact, t e nly difference is in the dimension ; While the farmer refers t- a rate f return er year the recipr cal value refers to the number f years inc me c ntained in the wealth ). The calculation of the density of income q(y) proceeds then by mixing the functi n f(w-y) with the density of wealth*