15
The conditional distributions have all Pareto tails although the
fit is bad ( only 4 values can be used ). The Pareto coefficient
is between 3 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 its 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,
9
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 way 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 anarwers the question which
might well be asked: Thy the pattern of income distribution
could not be derived from the conditional distributions
without reference to the wealth distribution.
Allometrie growth of income and wealth
The discussion of the relations of income and »wealzh will
if
now be extended to take accounyof 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
a "law" well known to biologists"' ' : Various parts of an organism
grow at different but constant rates and as a result the proportions
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 allometrie law in combination with
the progress function in order to explain the Pareto distributio n ,
( in one dimension ); see A Formulation of the Pareto Distribution.
IMM, Science ^entre, 1000 Berlin 33( mimeo ). Although the
use I am trying to make of the law is different, I owe A to
Devendra Sahal to have my attention drawn to it. '