Suppose Bethany has m = $100 to spend on alcoholic beverages, x1, and nonalcoholic beverages, x2. The price of alcoholic beverages is p1 = 1 per unit and the price of nonalcoholic beverages is p2 = 2 per unit. The government is considering taxing her consumption of alcoholic beverages with a per-unit (sales) tax t 0 (i.e. the price of alcoholic beverages will become 1 + t). Suppose that Bethanys utility function is U (x1, x2) = x1 + x2.

(a) Find Bethanys ordinary demand (x1, x2) before and then after the tax (your answer should be a function of t in the second case). Find the total change in her demand as a function of t.

(b) For any value of t find an expression for the income and substitution effects on the demand for both goods resulting from the price increase (from p1 = 1 to p1 = 1 + t), i.e. find the Slutsky Decomposition for the total change in demand from part (a).

(c) Find an expression for the government tax revenue collected from Bethany as a function of t .

(d) What is the maximum tax revenue the government can collect?