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1. Consider a utility function u(x1, x2) = x1 + (x2)^a where a > 0. (a)...

1. Consider a utility function u(x1, x2) = x1 + (x2)^a where a > 0. (a) Show that if a < 1, then preferences are convex. (b) Show that if a = 1, then preferences have perfect substitutes form. (c) Show that if a > 1, then preferences are concave. (d) For each case, explain how you would solve for the optimal bundle.

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