Full text: The Personal Distribution of Income

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

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