4. A consumer with the utility function U(x1, x2) = xix; faces prices p1 = 4, p2 = 5 and has an income of $200. For this consumer, holding prices fixed: a. Derive an expression for the Engel Curve for x2. b. Plot this Engel curve. c. Holding p1 and m fixed, plot this consumer's demand curve for x2. 5. A consumer with the utility function U(x1,x2) = 3x11/3 + 23c2 faces prices p1 = 1, p2 = 10. a. Up to what income level would this consumer spend all their income on x1? Explain briefly. b. Plot this consumer's Engel curve for x1. c. Plot this consumer's Engel curve for x2