STOCHASTIC

598 NILS H. HAKANSSON
and s > 0. In this case, setting dT/dc = 0 and solving for c, we get,
or
c' _1 - aky(l - (aJty)"' 1 "'»)'"'(s - c) v_I = 0
(51) c*(x) = (1 - (afcy) 1/(1 ~ r) )(* + y)-
In Model I, (50) is satisfied whenever (44) and (47) hold; as noted earlier, no
solution exists in Model I for those cases in which ky > 1/a. In Model II, (50) is
always satisfied as seen from (45) and (46).
Inserting (51) in (48) we obtain
z*(x) = {aky) inl -%'(x + Y) (i = 2,..., M)
and (24) follows from (6) upon insertion of c*(x) and the z*(x). T(x) now becomes,
upon insertion of c*(x) in (49),
T(x) = -(1 - {txky) l ' il - y) )V + ak(l - (a*?) 1 " 1- ")'" V(a*y)"