4. This question gives us some practice using calculus to think about a utility's properties, and to solve the consumer's problem.] Suppose the consumer's utility is given by u(x) = -(x1 - 1)2 - (x2 - 1)2, and their income and prices are given by (m, P1, P2) = (3, 2, 2). 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 MU1(x) and MU2(x). (b) Show that these preferences are not increasing on X(p, m). (c) Show that the conusmer will optimally spend all their money. Hint: The previous question's first part may be useful.] (d) Explain why the consumer's preferences are convex. (e) What is the consumer's optimal bundle from their budget set