13
/
In reality, profits in excess of 1oo % may exist. In
the case where k <1 we can,however, always ensure/
that the conditions are met and (4) remains applicable:
As before, we rotate the diagonal round a point until
/
it is parallel to the regression line (see fig
and along that line the distribution is truncated. If
we choose the point appropriately, we can reduce the
number of incomes truncated. In algebraic terms, we
define => W-W 0 , and we write (4) ±js the following
form:
GO
q 00
cdY
j* (kW' + *W 0 -Y)/e"^ dW ' =
- I <f C|) exp- I (Y^W b )
(5)
kW’ > (TW b )
The resulting income distribution differs only by a
constant factor from (4). Since the transformation (5),
however, is only applicable to wealth not smaller than
W Q , it can be intuitively seen that the income distrib
ution will start only at the level Y =» W Q to confirm to
the Pareto Law. In other words, the Pareto law will
always be projected from wealth on to income, but de-
peB
ding
on the shape of the regression line, the income
distribution will confirm to linearity only from a more