15
The conditional distributions have all Pareto tails although the
fit is bad ( only 4 values can be used ). The Pareto coefficient
is between 5 and 4 in all except the last two wealth classes,
where it is very low, and it is 2.68 for the whole income distribution.
It appears that the income distribution as a whole is -
as far as Ats tail is concerned - decisively influenced by the
last two wealth classes. This is due to the fact that most
of the top income receivers are in the last two wealth classes,
>
where the income distribution is very unequal simply owing
to the wide range of wealth in these two classes, as already
mentioned before. In this v[ay the peculiar result arises that
the total income distribution is much more unequal than
almost all the conditional income distributions.
This in a way also answers the question which
might well be asked; Why the pattern of income distribution
could not be derived from the conditional distributions
without reference to the wealth distribution.
Allometric growth of income and wealth
The discussion of the relations of income and wwealth will
now be extended to take accounj^f influences in both directions.
The starting point will be the regression of income
on wealth which seems to be linear as far as the data go.
This might be regarded as a case of allometry, in analogy to
1)
a "law" well known to biologists : Various parts of an organism
grow at different but constant rates and as a result the proportion^
of their sizes ( on log scale ) remain constant in the growing body.
-1
) Ludwig von -^ertalanffy, general System Theory. Penguin 1968 p.65.
Devendra S a hal has used the allometric lav/ in combination with
the progress function in order to explain the Pareto distributio n
I in one dimension ); see A Formulation of the Pareto Distribution.
IMM, Science ^entre, 1000 Berlin mimeo ). Although the
use I am trying to make of the Ikw is different, I owe x to
L t
Devendra Sahal to have my attention drawn to it. *