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Suppose Ann has preferences over two goods, X1 and X2. Her preferences can be represented by the following utility function: u(X1, X2) = Xfxg' Let P1 = 3 be the price of X1 and P2 = 2 be the price of X2, in dollars. In addition, suppose Ann has an income of I = 18. (a) ' Calculate Ann's optimal consumption of X1 and X2 and the total utility at this optimal basket. Fully illustrate the optimal basket in a diagram with X1 on the horizontal axis. Show your work. (b) 1 Suppose that a policy is proposed for a tax of one dollar on each unit of good 1. Calculate what Ann's optimal basket would be under this policy assuming that her income and the price of good 2 do not change. Fully illustrate this new optimal basket in your diagram in part (a). Show your work. (c) What is the size (and sign) of the lump sum transfer needed to be given to Ann so that she is indifferent between the tax increase on good 1 from (b), and no tax increase? Show your work