Question

# Consider a utility function u(x1, x2) = x1 + x a 2 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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