STOCHASTIC

(7)
(8)
(9)
linear > 0
convex
concave
Then the following hold
concave # 0
linear > 0
linear < 0
(II) 9 is pseudo-convex on T if T is open and p and a are differentiable
on r.
(Ill) 9 is quasi-convex on J\
If any one of the following assumptions hold on r
0')
(2')
(3')
(4')
(5')
(6')
(7')
(8')
(9')
concave 5= 0
convex < 0
concave < 0
convex > 0
linear
linear < 0
linear > 0
concave
convex
then the following hold
convex > 0
concave < 0
concave > 0
convex < 0
linear # 0
concave =fc 0
convex # 0
linear > 0
linear < 0,
(H') 9 is pseudo-concave on /'if T is open and p and a are differentiable
on r.
(Ill') 9 is quasi-concave on r.
The above results follow from our principal result by observing that
the numerical function q>(y, z) = yjz, (y, z)e Rx R is pseudo-convex and
hence also quasi-convex [9] on either of the convex sets {(y, z) \ (y, z) e
RxR, z> 0} or {(y, z)\ (y, z) e RxR, z