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