5. Modified version of problem 6.14 from Nechyba text. Suppose Mr. T consumes gasoline (Good )) and "all other goods" (Good Y). Assume that his preferences over these two goods are summarized by the utility function U(x, y) = 200x'+ y. Finally, assume that Mr. T's annual income is $50,000, Px = $2.50 and By = $1. a. Find Mr. T's utility-maximizing bundle of X and Y by first computing his MRS(x, y) function and then setting up a system of two equations and two unknowns that the utility-maximizing bundle (x* , y* ) must satisfy. Call it bundle A. b. Nowassume that the government imposes a gasoline tax of $2.50 per gallon, effectively raising the price of a gallon of gasoline to $5 per gallon. Using the same method as in part (@), find Mr. T's new utility-maximizing bundle. Call it bundle B. C. How much gasoline tax ($T) does Mr. T pay per year? Briefly explain your answer. d. Suppose that the government does not need the tax revenue. They were only trying to reduce gasoline consumption for environmental reasons. Therefore, they cheerfully give Mr. T back the gasoline tax revenue he pays in part (@) ($T) as a lump-sum cash transfer, which he is free to spend on more gasoline or all other goods or both The cash transfer effectively raises his annual income to $50,000 + $T. But he still must pay $5 per gallon of gasoline. Using the same method as in parts (@) and (b), find Mr. T's newest utility maximizing bundle. Call it bundle C. e. Does the tax and rebate program succeed in reducing Mr. T's gasoline consumption from part (a)? Does the tax and no rebate program in (b) do a better job of reducing his gasoline consumption? f. Use U(x y) =200x '+ y to determine if Mr. T isjust as well off under the tax and rebate program as he is with no tax and no rebate. Show that his utility is lowest with the tax and no rebate. g. Imagine what these three outcomes would look like in a graph, with gasoline on the horizontal axis. There would be three budget lines, three indifference curves and three tangency points (A, B and C). There is nothing to do in this part except "imagine"