10
J
can write for the density of the rate of return f (Y - k¥)
and for its symmetric function f* (kW - Y). In this way we
manage to express the argument of the function f* (which
actually represents the reciprocal profit rote, a—dwaea '
s±-onle3«=gg&fe«r^ in terms of W and Y again, and yet keep
it independent of ¥, provided the regression is homo-
scedastic. k is a constant which equals -fce regression co
efficient of Y on (see fig. 1).
rate of
If thc/ireturn decreases with wealth, we have to take
k<1, if it increases with wealth, we take k-^-1. In fig. 1
the first case is assumed.
Proceeding os "before, the symmetric function f* (k¥ - Y)
will now he randomised by means of the wealth function (
which means taking the Laplace transform of the former:
q (X)
-¥<* ,
e d¥
c d V f * (k¥ - Y)
e -(<*/]$ dY for k¥>Y> 0
(4)
q (X)
0
for k¥<Y> 0
This is now the second result: If there is a log-linear
dependence of income on wealth which is homoscedastic, with
formal grounds we 'might ari'
on coefficient, put since for\ecori
clearly the independent vari
comgt-or- weaUrhiias'iTO'-be used.-'-V