22
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
of wealth and income. This could be used then to