Question 1 [30 marks] The government considers taxing sugary drinks (e.g., soft drinks, sugaradded juices). A representative consumer has preferences over sugary drinks, m, and all other goods (i.e. the composite good) y, represented by the utility function 15(33, y) : xlfyw. The price of good a: is given by Pm : 2 and that of good y is given by py, which is normalized to 1 (meaning good y is a nummire good). The consumer has income m : 216. a) [5 marks] Find this consumer's optimal bundle and utility level, given initial prices and income. b) [5 marks] The government now decides to levy an ad valorem tax on sugar drinks (good 3:) at a rate of T : 0.20. Find the resulting optimal bundle and utility level. 0) [5 marks] Realizing the loss in welfare for the representative consumer, the govern ment decides to rebate the full amount of the tax. Is this amount enough? Why or why not? Support your answer with appropriate calculations and diagrams. d) [15 marks] By how much should the government compensate a representative con sumer to prevent a change in welfare, if not by the amount of the tax rebate in c)? Argue this point by nding, comparing, and contrasting the compensating variation (CV) and equivalent variation (EV) measurements. Support your answer with appropriate diagrams