Full text: The Personal Distribution of Income

9 
For the purposes of the following calculation, it is necessary 
to use the mirror function of f (y-w), that is f (w-y), which 
will be as much independent of wealth as the former. 
In terms of random variables we have then 
- y/zA 
We can then represent the density of income g (y) by means of 
randomisation as follows: 
/s/ /> 
jVt, or > y 3" 0 
!<n., <ur < -p 
g (y) = //(w-y) e dw = C [*) € ^ 
g (y) = o 
where ^«)is the Laplace transform of J (w) 
(V 
The above mixture is a Laplace transform of 
right by y. 
shifted to the 
The Laplace transform requires that r (w) is defined as equal to 
zero for w <C o . If the density function fis shifted to the 
i 
right, the dens'ties for w y will therefore be zero. We have 
thus to assume that w ^ y (in other words, that there are no cases 
of wealth smaller than income, which means the rate of return must 
be less than 100%).
	        

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