)
- 10 -
r
Equation (JO shown that the Pareto form of the wealth distribution
is reproduced in the income distribution, provided the independence
condition is fulfilled, and y w.
We have now to face the fact that the rate of return on wealth
will in reality not be independent of wealth. The cross-classifi
cations of wealth and Income of wealth owners (for Holland, Sweden)
show that mean income is a linear function of wealth, the regression
coefficient being smaller than unity. We can easily take account
of that by defining e conditional rate of return density or rather
its mirror function as j^kw-y), where k is the regression coefficient
of y on w. Assuming that the variance and the higher moments of
(kw-y) are independent of w we can proceed as before x
^ OC7
g (y) * t (kw-y)e dw -
c iz c f(£ )**}*{
A- Cj- ^ h ~
O
* c
(6
;
It may be noted that the condition kw > y is more restrictive
than the former condition w> y.
The result is now that the Pareto shape of the wealth distribution
is reproduced in the income distribution, but with a larger Pareto