Full text: The Personal Distribution of Income

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17. In a further stage we should cease to take the wealth# distribution 
as given and instead treat wealth and income as joint variables 
in a process evolving over ±±as the generations. We should continue 
to regardthe influence of slcrwiy accumulating wealth and other stocks 
on the current income as a dominant feature of the process but, 
trying to includethe preceding history of accumulation, we should 
now also recognise that in the course of time the income acts on the 
wealthy not* only in so far as it arises from wealth as a return and 
is (partly) re-invested, but also insofar as anew wealth is formed 
from earned income in favorable circumstances and after_a lapse of 
time required for accumulation. 
That means that income and wealth are linked by two hands 
of relationsjOne is the rate of return which links the current income 
of property owners to their wealth, the other is the relation 
between (unearned and) earned income of the past to the accumulation 
of new wealth, in otherwords, the propensity to save. J -n so far 
as the past income is in practice fairly strongly correlated with 
present income, the present earned income appears to have an effect 
on the wealth which corresponds to the savings relation. 
The influence of wealth on income via ihe rate of return 
is the subject to be treated first over the next few pages. 
The dependence of income on wealth 
In the following we shall consider income as flowing from 
wealth. This applies stricily to what we call unearned income. 
The reader may think of that in the first place,but h e has to be 
prepared for a more far reaching and wider interpretation later on; 
in fact, in praiice we cahhot easdidy separate unearned and earned 
income, and the difficulty is perhaps greater than one that could be 
overcome by adequate data ( especially in the case of unincorporated 
business ). 
Instead of the matrix of income transitions ased by 
Champernowne we have to imagine an analogous matrix Wealth-income 
whichshows for each amount of swealth the probability of different 
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incomes. 
n 
x he basis of the analysis is thud the conditional distribution 
of income, given the wealth. Economically speaking this is the 
probability of a certain rate of return to wealth or profit rate. 
From this, if we know it, we can derive the distribution of income 
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