## Full text: The Personal Distribution of Income

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Outlook on further developments.
In this paper the idea has been elaborated that the amount
of wealth determines the chances of having certain amounts
of income.But it may be thought that also the inverse
relation - influence of income on wealth - plays a role.
Certainly the increment of wealth per year depends on
income,given the rate of saving out of various incomes. If
we take into account that the present income is usually
strongly correlated with the past incomes of the same
person,or even of his ancestors, then it appears that the
chances of a certain wealth may be determined,indirectly,
by the present income.And we may connect this relation
with the regression line of wealth on income (which in the
Swedish data appears so very distorted on account of the
truncation of the distribution). There are,then, two
theories ,and two regression lines. It would be very
convenient if we could regard each of the regression lines
as a true picture of the corresponding theory. This
correspondence is,however,marred by the greater or lesser
dispersion of values round each of the regression lines.
It can easily be seen that the dispersion round one of the
regression lines will influence the shape of the other
regression line. If the rate of return of a given wealth
is widely dispersed then the persons with a high rate of
return will be classified in the high income classes,those
with the same wealth but with a low rate of return among
the small incomes. This will more or less strongly
counteract the tendency of wealth to increase with income,
it will flatten out the regression line.
It seems to me that the joint distribution of two
variables like income and wealth should be approached from
the standpoint of a more elaborate theory. One could
imagine a stochastic process,in the simplest case a Markov
chain, in two stages: One matrix would show for each
amount of wealth at the beginning of the year the
probabilities of various incomes in that year. Another
matrix would show for each of these incomes the
probability of wealth at the end of the year - which
results from the addition of the saving out of the various
incomes to the initial wealth.In this way both
parameters,the rate of return on wealth and the rate of
saving out of income, would play their role in the
process. A multiplication of these matrices would describe
a continuing process of accumulation,starting from
certain initial conditions of wealth distribution. We may
then, under certain conditions,if we allow also for new
entries, derive a steady state of the joint distribution
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