- 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 he as much Independent of wealth as the former. 
In terms of random variables we have then 
^ \A> • - YY - L J J 
We can then represent the density of income g (y) by means of 
randomisation as followst 
where C is the Laplace transform of 
/ 
(w) 
The above mixture is a Laplace transform of 
right by y. 
shifted to the 
The Laplace transform requires that j (w) is defined as equal to 
aero for w o . If the density function f lm shifted to the 
right, the denstles for y will therefore be sero. 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%)•