Full text: The Personal Distribution of Income

12 
value. Also speculative capital gains from appreciation of 
shares or of real estate will affect the wealth but not 
the income,and it will presumably be more important in the 
higher wealth classes. 
Now the rate of return will be independent of wealth if 
its conditional distribution is the same whatever the size 
of wealth.lt would seem that we might perhaps restore the 
condition of independence simply by turning the system of 
coordinates in the appropriate way,so that we could reduce 
the present case to the former one.If we can make the 
covariance of w and w-y zero then the coefficient of 
regression of y on w should be one,as in the former case: 
Cov (w,w-y) = Var (w) - Cov (w,y) = 0; 
Cov (w,y) = 
Var (w) 
If the regression line of income on wealth is 
y = tw + y Q ( tc < 1 ) 
and if also the variance and higher moments of the 
conditional income distribution are independent of wealth 
then we should use instead of f(w-y) the function 
f( K w + y Q - y ) because this distribution will be 
independent of wealth. 
Although we do not really know anything about these higher 
moments we shall nevertheless try to use the above
	        

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