17
Larger wealth presupposes larger income ( if it had to be saved
out of it)^ therefore the mean income has to be higher for
larger wealth. Prom this point of view it is not surprising
that the increase of income with wealth is less than proportionate
because wealth in an integral of income taken over time,
if saving can be assumed to be a constant proportion of income.
The interpretation is only weakened to the extent to which it
could be argued that the creation of new wealth from earned
income will affect mostly the lower wealth classes ( only
earned income is really relevant in this context where income
is supposed to play an active role vis-a-vis wealth ).
The other regression - wealth on income - should
on the face of it represent the effect of the propensity to
save, the creation of new wealth from earned income
( continuing primary accumulation ). The curvilinear shape
might be compatible with this interpretation, since for the
lower, incomes the saving will play no role and wealth will
only start emerging when income has reached a certain level,
and then it will rise steeply ( because it is an integral,
see above ). Here again, an alternative interpretation is
possible: If income is large, it- probably has been derived
from large wealth, therefore to larger income will
on the average correspond larger wealth ( rate of return relation
.4 *
Thus the two relations or theories or laws
behind the joint distribution of wealth and income seem
to be both relevant for each of the two regression lines,
although possibly not to the same extent ( each of the
regression lines may be be more strongly influenced by
one relation than by the other ).
The preceding arguments implied that, to.' some exent,
each regression line is an inverse to the other regression line.
In order to make this clear let me choose an example from
another field', where there is only one "law" or at least we
can pretend there is only one. Take the size distribution of
manufacturing plants according to output and cost. The law
consists in the effects of scale on cost in relation to output.
The regression of cost ( or employment) on output will show
a coefficient less than one, decreasing cost to scale.
We expect the other regression to be the inverse of the first