(4) (10 pts.) Let S = A = [0, 1]. Define f (x, a) = S...

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(4) (10 pts.) Let S = A = [0, 1]. Define f (x, a) = S x A and y(a) = [0,a] for a y(a), and f*(a) = max{f(x, a) |x = y(a)}. (a) (5 pts.) Check if y*(a) is upper-hemicontinuous, compact-valued, or convex-valued. S x A R and 7: A 25 by f(x, a) = x for A. Let y*(a) be the set of maximizers of f(., a) on (b) (5 pts.) Check if f*(a) is a continuous function. (4) (10 pts.) Let S = A = [0, 1]. Define f (x, a) = S x A and y(a) = [0,a] for a y(a), and f*(a) = max{f(x, a) |x = y(a)}. (a) (5 pts.) Check if y*(a) is upper-hemicontinuous, compact-valued, or convex-valued. S x A R and 7: A 25 by f(x, a) = x for A. Let y*(a) be the set of maximizers of f(., a) on (b) (5 pts.) Check if f*(a) is a continuous function.

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