Full text: The Personal Distribution of Income

Equation (£) shows that the Pareto form of the wealth distribution 
is reproduced in the income distribution/ provided the independence 
condition is fulfilled, and y w. 
We have now to face the fact that the rate of return on wealth 
will in reality not be independent of wealth. The cross-classifi 
cations of wealth and income of wealth owners (for Holland, Sweden) 
show that mean income is a linear function of wealth, the regression 
coefficient being smaller than unity. We can easily take account 
of that by defining a conditional rate of return density or rather 
its mirror function as f{kw-y), where k is the regression coefficient 
of y on w. Assuming that the variance and the higher moments of 
^(kw-y) are independent of w we can proceed as before: 
It may be noted that the condition kw ^ y is more restrictive 
than the former condition w^>y. 
The result is now that the Pareto shape of the wealth distribution 
is reproduced in the income distribution, but with a larger Pareto

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