STOCHASTIC

EFFECTS OF TAXATION ON RISK-TAKING 273
-Wo(MW(0))-A(W(P)))}¥^-p-+{R(W{9'))
TJ'(e—r\
-WoA(W(n))E- v '
1-t
where 0* is defined as above. If there is constant or increasing relative
risk aversion and constant or decreasing absolute risk aversion,
the first term above is unambiguously positive, and by equation (9)
the second term is identically zero. Thus, a is increased. But from
(10)', if there is decreasing absolute risk aversion, a is increased by
a smaller percentage than the percentage decrease in 1 — t.
If there is decreasing relative and absolute risk aversion, investment
in the risky asset may be unchanged or decreased as the
result of the imposition of an income tax. To see this more clearly,
consider the following utility function, and assume that the probability
of e0
•so absolute risk aversion is
V" d In V — a
>0
V'~ dW W- -W„
and is i decreasing, i since
d- V -
V
dW
•
(W-WoV
i
while relative risk aversion is
-U"W
V
and is decreasing,
U"W
-aW „
>0
W-Wo
V
dW
«JTo
2