Full text: The Personal Distribution of Income

13 
Although we do not really know anything about these higher 
moments we shall nevertheless try to use the above 
function and proceed in the same way as before by a 
mixture of the conditional distribution: 
q(Y) = 
p 00 
f( fcw + y Q - y) e -aw dw = 
J o 
= c 1/ K 0(0-4, ) expt-a/^ (y-y Q ) } for #w > y-y Q 
q(y) = o for *w < y-y Q . (9) 
The result is now that the Pareto coefficient of the 
wealth distribution is reproduced in the income 
distribution, but with a larger Pareto coefficient (since 
tC < 1 ) . This is exactly what has to be explained (income 
distributions are in fact more "equal" than the wealth 
distributions,empirically,in so far as they show a larger 
Pareto coefficient).The particular shape of the rate of 
return distribution has no influence on the tail of the 
income distribution as long as it fulfills the 
independence conditions mentioned. 
Concerning the restriction *Cw > y-y Q it should be 
remarked that we are free to shift the coordinate system 
to any y Q we choose so as to make the above condition 
valid,with no consequence except that the conclusion about 
the Pareto tail will be confined to incomes in excess of 
y 
o*
	        

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