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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