Full text: Konvolut Wealth and Income Distribution 1

A ??G N D l X 
contexts as well. Thus the distribution of wealth 
results from a convolution of the accumulation of 
previous generations with the accumulation of the 
living generation /15/* Denote the accumulation of 
previous generationshy Wj and the total accumulation 
by W , both measured on the log scale. The accumulation 
of the living is V-W ( » r where r is the rate of 
accumulation and T the "spent life" of the living wealth 
owners, reckoned from the time of their inheritance. If 
we may regard ^ (V-W, ), the distribution of the spe^fc 
life time (telescoped by r) as independent of the inher 
ited wealth tf) we can write for the density of the total 
wealth distribution q(¥): 
where (j) (<A/) is the Laplace transform of 
/ (X) the duaay WtfMto replaced by ± 
and where W> W, > 0. 
The wealth will conform to the Pareto law with coefficient 
00, and we do not need to assume scything about the 
distribution of the spent-life time, except that it is in 
dependent of inherited wealth.

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