- 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%)•