7. (a) strictly quasiconvex. convcx
(b) strictly quasiconvex, convex
(c) strictly quasiconcave. concave
•J. The function v = xyx? is sUicily quasiccmeave but not concave.
II, v = x1/3 = y/J. x > 0 is strictly concave if. for any
A 6 ((), I), v/Aa' 4- (I — A)x" > A/r7-!- (1 -k)Jx" which amounts to (a-' - a")3 -» 0.
I. Proposition (a) is false and proposition (b) is due.
3. (a) Denoting A: "The good is normal" and B:
"The demand for ihe good increases when its price falls," you musi prove (i) by showing A =>• B: not B not A: and that A and not B leads to a contradiction Before proving the second statement in a similar manner, compare U to the first statement.
(d) A(-2, 2,5) 4- (I - AK-3,3,8) = (-34- A,3-k. 8- 3A)
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