
<b
1J
Denoting wealth by \t/, let us write for the density of the
wealth distribution
of 1
^ ( u )
ft*)
or
cw
x
cJ'
for Jff 0
for JH < 0
If we know something (though not everything) about the joint
or
distribution of income and wealth, We might use this in order
to derive from the wealth distribution the income distribution.
Under certain restriction^this is indeed possible. We shall
use the conditional r function of income, given the wealth,
and shall mix (randomize) this with the wealth density. The
conditional density function of income can be represented
a/
in
/ * ou
(yw), the density of yt& certain "rate of return"
on wealth. We assume tentatively that this rate of return, for
given wealth is stochasticallv/of the wealth.
This assumntion is necesary because we are going to represent
the income density as a convolution of the rate of return and
d&Wjititt (04
the wealthy The random variable income y is represented j&ti the
sum of the rate of return and the wealth
( Qtzp'
v = R—h W
(R &•y  W)
For the purposes of the following calculation, it is necessary
or
to use the mirror function of f , that is f (wv) , which
will be as much independent of wealth as the former.
In terms of random variables we have then
)• \ \££J\ A#' v ?£'V'
^y~~= W  A (where A ^W—y)