Full text: Konvolut Wealth and Income Distribution 2

can write for the density of the rate of return f (Y - kW) 
and for its symmetric function f* (kW - Y). In this way we 
manage to express the argument of the function f* (which 
actually represents the reciprocal profit rate, /4-^41-mon— A 
s^BjBuhejSLQ; number) in terms of W and Y again, and yet keep 
it independent of W, provided the regression is homo- 
scedastic. k is a constant which equals to regression co 
efficient of Y on (see fig. 1) 
rate of 
If theAreturn decreases with wealth, we have to take 
k<1, if it increases with wealth, we take k. >1. In fig. 1 
the first case is assumed. 
Proceeding as before, the symmetric function f* (kW - Y) 
will now be randomised by means of the wealth function, 
which means taking the Laplace transform of the former: 
q (Y) = c oty I f * (kW - Y) e" Wo6 dW « 
« | dp (£) e "^^ Y dY for kW > Y > 0 (4) 
q (Y) - o 
for kW<Y> 0 
This is now the second result: If there is a log-linear 
dependence of income on wealth which is homoscedastic, with 

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