5. This question demonstrates how blindly using calculus can lead us astray.] Suppose the consumer's utility is given by u(x) = x; + (1 + x2), and their income and prices are given by (m, P1, P2) = (12, 2, 3) . In what follows, you may take it for granted that the consumer has some optimal solution to the consumer's problem. (a) Given x E X, write a formula for the marginal utilities MUi(x) and MU2(x). (b) Show that they will optimally spend all their money. (c) A unique bundle x exists such that the consumer spends all their money (p . x = m) and their per-price marginal utility is the same for the two goods ( MU1(2) _ MU2(2) ). What is it? P1 P2 (d) What is the consumer's optimal bundle from her budget set? 2