Denoting wealth tor w, let uo write for the density of the 
wealth distribution 
(Vt - M'* - V 
or 
p’O) 
p*(w) 
Oo^HlVt 
0 
w » In V 
for W> 0 
for vf< 0 
the 
fOI 
7 done 
rondos! 
distribution of tho roto of return is given in the ' 
t^cC ——— -d —— " ••■ 
of o density function f XX t y) <21 (whoro r *l»y, 
incone) wo obtain the 
K» aa foliar, /v^ 
diatx*ibt#lan . 
X 
O* 
t av*/) o’ 
• -OG 
(2) 
above which the distribution co^foroa 
The njninua wealth 
to the Yoroto law) is 'token babe m a unit* so that we can 
integrate froa 0 tooo • -ubp incon© density in thus the 
loploco tr'onoforo of the conditional danoity of incooo, 
■Z) \P<X 
^ * i ( r 
A 
Y - y is the rate of rdtum on the wealth* 
If this rote of return lo independent of the wealth then 
the above relation (2) bocoxaoo © convolution* 
For convoaionoo wo shall use inotead of t(Y\U) the 
density function f* (u - X) which 
r -U@ obtain* then * as o special cooc of (2) s 
Vj OP^lZZy 
£ (dt,o ^ *V 
/f 
w 
£ K : 
/W ! 
i