12 
the condition is even more restrictive: The rate of return 
must not be larger than w k ' 1 '.loo p.c. whithin the range of 
wealth sizes in which the empirical data lie. 
The restriction is unavoidable because the Laplace transform 
in defined only for positive values of the argument of f^ w ^. 
For negative values the derq^iity f is by definition zero. 
If the argument is shifted to the right by Y the transform will 
be defined only for d&wities of a rate of return below loo p.c. 
Similarly, for an argument of kW-Y the transform will be defined 
k -"I 
only for rates of return below w .loo p.c. 
In reality, rates of return in excess of the limit given may 
exist. In this case we can, however, always ensure that the 
above condition is fulfilled and the transformation (4) remains 
valid provided we make the unit of welfath, W Q (Wo = 0) sufficient 
ly large. 
Indeed the condition 
y <w 
w 
k-i 
k 
or 
y \w 
(5) 
will be more easily fulfilled if w and y are both measured in 
a large unit, because then their values will be both lower in 
the same proportion, and that will automatically make it easier 
to fulfill the condition (5), if k <1. 
The choice of a large unit, however, will mean that the conclusions 
with regard to the distribution of income which are implied in (4)