onsider the utility function I; {31,32} = $132, with accompanying budget constraint p131 +pgrg : I. {a} Solve the consumer's utility maximization problem and derive the consumer's demand functions for good 1 and good 2, i.e., derive I; lip-1,332, I) and 2:; @hthj. {ll} Find the indirect utility function. {all Iow formulate the expenditure minimization problem and soh'e for the compensated demand functions for good 1 and good 2, ie., derive If [p1,pg,L_-'_] and 2:5; [Imp-3,3] for a xed utility level F. {ii} Let I: 1!} and p1 = P2 = l. Iiiow consider the eifects of increasing the price of good 1 to p1 = Ll. Find the compensating variation, equivalent variation, and the change in consumer surplus associated 1with this price increase. Explain why these dir, and why they bear the relationship they do to one another. {5} Suppose you are ajudge hearing an antitrust case, and have concluded that the rms in this case illegally colluded to set the price 191 of their output higher than the \"market\"I price p'l . You now must determine the ne to impose on these rms. Your goal is to charge a ne equal to the harm caused to consumers by the excessively high price. 'Would the concepts of compensating variation, equivalent variation, and change in consumer surplus help you x: this ne'.r If you could calculate each of these, which one would you use'.' "Which of these would you most likely be able to calculate, and how would you go about doing so'