Full text: Konvolut Wealth and Income Distribution 3

to pm 9 (footnote) 
^r.:o relation (5) nay haw applications in 
■ contexts as well. Thus the distributor 
results front''a convolution of the accumulation of 
previous generations with the accumulation of the 
living Generation /13/* Denote the accumulation of 
previous generations by Wj and the total accumulation 
by W * both manured on the log acolo* She accumulation 
of Mae living is W-W, « r Tt where r is the rate of 
accumulation and 3* the "spent life* of the living wealth 
owners, reckoned from the tine of their inheritance* If 
we mgr regard ^ 0§4f * the distribution of the ope n 
life time -. (telescoped by r) as independent of the: Inher 
ited wealth V, we can write for the density of the total 
. wealth distribution q(*.): 
<}M a d' * 
R f /( —, ) 
J-oo 
.oCl 
d i 
e 
dtf 
where 
Cx) 
/ 
is t! 
W3 
tumnarmm of 
variable- replaced by 
j ^ ■. / 
> 0. 
The'wealth will conform to the Pareto law with coefficien 
cC % and wo do not need to assume anything about the 
distribution of the spent-life time, except that it is in- 
of inherited wealth*
	        

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