Compensating variation and consumer surplus Consider again the quasi-linear utility function given in Problem 1, but now assume that the consumer's income is M = 18 and that hefshe faces initial prices p19 = 1 and p3 = 1. (a) Determine the consumer's initial utility-maximizing bundle (x*, y') and the level of utility hefshe realizes by consuming this bundle. (b) Assume that the price of good x increases to p} : 2.25 Show that the consumer can no longer afford the bundle hefshe was initially consuming in part (a), and as such, is worse off as a result of the price change (19., determine the consumer's new utility level). (c) Calculate the consumer's welfare change associated with the price increase in terms of the compensating variation (C V) measure [Hints: (i) indifference curves for quasi-linear preferences are vertical translations (\"parallels\") of each other; (ii) it may help to sketch a budget constraintfindifference diagram demonstrating this property]. (d) (6) Use simple geometry to approximate the change (or loss) in consumer surplus attributable to the price increase (5.3., you are not required to use integration here) [again, it may help to sketch a graph]. Compare you answers in parts (c) and ((1). Given that E V and CS should be equal under quasi-linear preferences, do you think the approximation made in part ((1) is a \"good" one? Explain