STOCHASTIC

EFFECTS OF TAXATION ON RISK-TAKING
W(G2)
Income Tax: Demand for Risky
Asset Unchanged
271
there is decreasing relative risk aversion, just the opposite may
occur.
Before taking up the more general case, we should note the
special case where r=0, i.e., the safe asset is money and has a zero
rate of return. Then the after-tax budget constraint coincides with
the before-tax budget constraint but T'S is shorter than TS and the
values of W(6i) and W(8i) are identical to their before-tax values:
all the tax does is to induce individuals to hold more risky assets.
(See Figure Illb.)
In the more general case, only slightly stronger conditions are
required to guarantee that a proportional tax will increase risktaking.
The condition for utility maximization is simply
EU'{e-r) =0.
It is of the same form as the no-tax condition, since both the risky
and safe asset are taxed proportionately.
We wish to know, how does a change with t:
JJ"Y. .
:(e-r)
nn. i-r i — r
(10) it -EU"(e-r)m-t)W0
After-tax private risk-taking is again measured by
P=W0a(l-t)