Question I: Choice and Demand with WeH-Behmed Utility Functions. {5'0 ptsl Consider the following utility function: nix. , 3) = .rf".ri'3\". (a) Given income level at. prices p] and pg. nd the demand for both goods. it; = .t'|{p].p1, m) and I; = null. P21!!!)- Hint: use method I as seen in class with the condition MRS = {it (12 pts} (b) Let a = %. m = 24 and Fl = p; = 4. Draw the budget at. the optimal points and the indifference curve in a graph. Make sure to label your axes appropriately and indicate the origin. No need for a precise indifference curve. the general shape is sufcient. {Ill pts} (c) Now. let p1 = 8. Le. there is a change in price of good I. but everything else stays the same. Draw the new graph [budget set. optimal points. origin and the indifference curve). {III} pts) td) Now. suppose that a = 41. but that all the other variables are as in (b): p1 = p: = 4 and m = 24. Draw the new graph {budget set. optimal points. origin and the indifference curve). {I'll pts) (e) Why are the values oh; the same in {b} as in (c)? 1Why are they not the same in {b} as in {d}? (8 PIS} Question 2: Choice and Demand with Special Utility Functions. {30 pts} Consider the following utility function: trim, :3) = Zinfxf} +.r3. (a) (h) (C) id) What kind of preferences are these? Find the MR5 and sketch 3 indifference curves {no need to be precise. but make sure to label the utility level). {5 pts} Suppose that m = 24. p1 = I and p3 = 4. Use method I from class to solve for .t; and .15. Sketch your optimal points in a graph with the budget set and an indifference curve going through your optimal point. Hint: this is a special utilityr function so your answer mayr seem strange. Remember that I: must be a function of at least some of the variables p1. p2 and m. .t:I cannot however be a function of J; (the other good). {I'll pts) Consider an increase in income of = 32. Derive the new optimal bundle and draw a graph with the new bundle the budget set and an indifference curve passing through it. {10 pts) is there a difference in quantities between the bundles in {b} and in {c}? Briey explain while referring to the demand functions. {5 pts}