12
,
income is unity (thus Y = 0), and the reciprocal rate of
return is therefore given by ¥.
jilt should be noted that
ur
a doublesided Laplace transform/sould not help us, because
it could never converge at the empirical values of ©c- /.
The density of the rate of return will thus be truncated.
In the case of dependence the truncation will ^ ,
if k <1, because the function f* (W) will be stretchy
\
by a factor 1/k.
I N.
There is, however,a deeper reason for the restriction:
The validity of the Pareto law cannot be assumed for low
values of ¥ (in fact,for negative values, if we put the
unit of wealth at a level which limits the range of
\ N \ A
linearity of the distribution). / 0wing to the irregular
ity of the wealth distributing for low values of wealth
the possibility of very high ra\es of return might disturb
the regularity of the pattern of Income distribution. ¥e
musb, therefore, set p limit to the permitted rate of
return.
reality the return rates which have been truncated in
*r exercise may, however, exist. The point is, then, that
to the extent that they exist - and that will be the more
likely the smaller k is - the income distribution will be
less regular than the wealth distribution. In practice
;his will mean that the range dominated by the Pareto law
dll be narrower for income than for wealth.