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