Full text: Konvolut Wealth and Income Distribution 2

•» 3 •» 
Denoting wealth by W, let us write for the density of the 
wealth distribution 
p(W) » cw dlf 
or p*(w) m ce" ^ Wdw for w > 0 f ^ 
p*(w) * 0 for w < 0 
w « In W 
If we know something (though not everything) about the joint 
distribution of income and wealth, we might use this in order 
to derive from the wealth distribution the income distribution. 
Under certain restrictions this is indeed possible. We shall 
use the conditional density function of income, given the wealth, 
and shall mix (randomise) this with the wealth density. The 
conditional density function of income can be represented 
in the form j^y-w), the density of a certain "rate of return" 
on wealth. We assume tentatively that this rate of return, for 
given wealth is stochastically independent of the wealth. 
This assumption is necessary because we are going to represent 
the income density as a convolution of the rate of return and 
the wealth densities: The random variable income is represented 
Aj L. 
as the sum of the rate of return and the wealth </f ' 
s (JZ + 
= // 

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