Full text: Konvolut Wealth and Income Distribution 2

to p. 9 (footnote) 
' The relation (3) may have applications in different 
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 /13/. Denote the accumulation of 
previous generations by W, and the total accumulation 
by W , both measured on the log scale. The accumulation 
of the living is W-W, » riT, where r is the rate of 
accumulation and 3* the "spent life" of the living wealth 
owners, reckoned from the time of their inheritance. If 
we may regard ^ (W-W,), the distribution of the spent 
life time (telescoped by r) as independent of the inher 
ited wealth W . we can write for the density of the total 
' - r 
wealth distribution q(W): 
q(W) = (l W f (W-W 
The wealth will conform to the Pareto law with coefficient 
c>C, and we do not need to assume anything about the 
distribution of the spent-life time, except that it is in 
dependent of inherited wealth. 
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