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9 q(y) - f(w-y) dw - 3 e“ for w £ q(7) -• 0 or j * where V'/j v '1 is the Laplace transform of f(w). / " The above mixture is a Laplace transform of f(w) shifted to the right 07 7. The Laplace transform requires that the argument of the function f be non-hegative. He have therefore to assume that w^ ( we shall further below haw this restriction can be relaxed ). Equation (3) shows that the Pareto form of the wealth distribution is reproduced in the income distribution, provided the independence condition is fulfilled and y •‘C w. He have now to face the fact that the rate of' return on wealth will in reality not be independent of wealth, -he cross-classifications of wealth and income of wealth owners for Holland and Sweden show that mean income is a linear function of wealth, the regression coefficient being smaller than unity. For the decline of the ratd of return with increasing wealth zzzüzs various reasons are responsible; relatively The earned income will be/less important the greater the wealth- In particular the income from ( non-corporate) business will be higher in relation to wealth in the lower wealth classes. Further, capital gains are not counted as income, but they affect wealth, and they will be more important for lagge wealth, because the proportion of shares held increases with wealth. The internal accumulationof firms will not find expression in the income, but quite probably in the wealth of the share holders. Also appreciation of real estate may affect the large wealth proportionately more. * Now the rate of return is independent of we a lth if its conditional distribution is the same whatever the size of wealth. It would seem that we might perhaps restore the condition of independence simply by turning the system of coordinates in the appropriate way, so that we would reduce the present to thd former case. If we nan make the covariance of w and w-y zero then the ceefficient of regression of y on w should be one, as in ~he former case;