10
can write for the density of the rate of return f (Y - kW)
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 rate, /4-^41-mon— A
s^BjBuhejSLQ; number) in terms of W and Y again, and yet keep
it independent of W, provided the regression is homo-
scedastic. k is a constant which equals to regression co
efficient of Y on (see fig. 1)
rate of
If theAreturn 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 as before, the symmetric function f* (kW - Y)
will now be randomised by means of the wealth function,
which means taking the Laplace transform of the former:
q (Y) = c oty I f * (kW - Y) e" Wo6 dW «
« | dp (£) e "^^ Y dY for kW > Y > 0 (4)
q (Y) - o
for kW<Y> 0
This is now the second result: If there is a log-linear
dependence of income on wealth which is homoscedastic, with
ion