STOCHASTIC

SOME EFFECTS OF TAXES ON RISK-TAKING 303
Taking the deterministic equivalents gives
maxiiiXi(l-t)+n2x2(l-t)~K, ...(3.15)
subject to
x1+x1^M, ...(3.16)
xlnL(l-t)+x2ii2(.l-t)-F- l (a)(l-t)(,a 2 1x 2 i + 2xix2co\12 + alxl) i -K^B,xi,x1^0.
...(3.17)
Since a is assumed to be £ 0-5 (in order to make the constraint meaningful), we can
interpret the third term of (3.17) as a reserve that will not, on the average, be used.
We now apply the Kuhn-Tucker conditions to the problem to yield
,1,(1 -0-«. + «»(!-»L- . 2 ff*' + * 2 cov " )f °~2' 1 = 0 and x,>0, ...(3.18)
L (0 - - (3 - 20)
fa(l-r)-Hl +u2(l-tL2- 2 fri»» + *' ^ 1 g o and *2 - 0. ..(3.21)
L (n2 and ol>o2, we would get a movement toward the risky asset
3. EFFECTS OF TAXES ON RISK TAKING 327