17 
r&i f 
^ f 
Larger wealth presupposes larger income ( if it had to he saved 
out of it)^ therefore the mean income has to he 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 i^ an integral of income taken over time^ 
if saving can he assumed to be a constant proportion of income. 
The interpretation is only weakened to the extent to which it 
could he 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 areation of new wealth from earned income 
( continuing primary accumulation ). The curvilinear shape 
might he 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 ) 
•t 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,too 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