- 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 
U-A 
We can then represent the density of income g (y) by means of 
randomisation as follows: 
—uy 
r ur 
g (y) * //(w-y) e dw - C 
~~q0 i 
''V 
g (y) - o j'r 
where is the Laplace transform of j (w) 
td" A- y A o 
Cr' <1 
1 
The above mixture is a Laplace transform of /(w), shifted to the 
right by y. 
The Laplace transform requires that f (w) is defined as equal to 
sero for w 4 o . If the density function / is shifted to the 
right, the densties 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%)•