Full text: The Personal Distribution of Income

IV. 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 
the generations. Propensity to save and rate of return 
would be the double link between the two random 
variables. 
We shall not further refer to this last stage in the 
following paper, but shall try to fill some of the 
empty space of stage III. 
Property income 
We shall distinguish property income and earned income 
and deal with the case of property income first, because 
it is simpler than the general case. 
Instead of the matrix of income transitions used by 
Champernowne we have to imagine an analogous matrix 
Wealth-Income which shows for each amount of wealth 
the probability of different incomes. 
The basis of the analysis is thus the conditional dis 
tribution of income, given the wealth. Economically 
speaking this is the probability of a certain rate of 
return to wealth or profit rate. Prom this we can derive 
the distribution of income, provided we know the distribu 
tion of wealth. But the distribution of wealth is known: 
It follows the Pareto law (over a fairly wide range) and 
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