- 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%)•