STOCHASTIC

52 NEAVE
and
the last equality following by conditions analogous to those of Eq. (3.5).
Therefore,
„' _ C "( c ') _ ~ V «( C ) _ _ ~''n(g) " _ JL = ^
0
Av"K(c)
s(v"„(c) + z"H(s))
j SZ%S) z"„{s) - - Cl'n(c) cv"u(c) ^ {
JZ*(s) CV"n(c)
— ,. . ,, . > 0 [by conditions analogous to those of
Z - W V " {C) Eq.(3.5)]
-=> -rz*(s) + rv*(c) ^ 0.
LEMMA 10. If the functions rv* and rt* are nondecreasing, then rv* is
nondecreasing whenever the wealth elasticity of either consumption or risky
investment is nondecreasing.
Proof. The result is an interpretation of Eq. (3.11):
rv*(A) = Vcrv*(c) = rj^*(s). Q.E.D.
2. OPTIMAL CAPITAL ACCUMULATION AND PORTFOLIO SELECTION 513