We can then represent the density of income g (y) by means of 
randomisation as follows: 
g (y) = 
f t*) * 
where is 
(w-y)e 
0 
the 
dw = 
> 
transform of 
(w) 
The above mixture is a Laplace transform of (w), shifted to the 
right by y. 
The Laplace transform requires that (w) is defined as equal to 
zero for w o . If the density function is shifted to the 
right, the densties for w v will therefore be zero. We have 
thus to assume that w y (in other words, that there are no cases 
of wealth smaller than income, which means the rate of return must 
be less than 100%). 
Equation (2) shows 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 ^wealth ownersffor Holland, Sweden) 
show that income is a linear function of wealth, the regression 
coefficient being smaller than unity. We can easilv take account 
of that by defining a conditional rate of return density or rather 
its mirror function as (kw-v), where k is the regression coefficient 
of y on w. Assuming that the variance and the higher moments of