r
A ??G N D l X
>»-ff^-A)--(footiK)'bo)
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.