Problem 1 Assume that Moe has utility over r1 and r2 given by u(r1, r2) =...

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Problem 1 Assume that Moe has utility over r1 and r2 given by u(r1, r2) = 2TT+ r2. He has income m and the price of good 2 is normalized to one. Throughout this problem, you may assume that pi and m are such that an interior amount of r1 and r2 is chosen. (a) Solve for the optimal r1 and r2 as a function of P1 and m. (b) Solve for Moe's indirect utility (his maximized utility as a function of p1 and m). (c) Suppose that the price of good 1 changes from 1 to 2. How much would you need to increase m by after the price change in order to return Moe to his original utility level? ("Compensating variation".) (d) How much would Moe be willing to pay (i.e., by how much would you have to reduce m) in order to avoid the price increase? ("Equivalent variation"). (e) What is the change in consumer surplus from this price change? Hint: no math should be required for this part. Problem 1 Assume that Moe has utility over r1 and r2 given by u(r1, r2) = 2TT+ r2. He has income m and the price of good 2 is normalized to one. Throughout this problem, you may assume that pi and m are such that an interior amount of r1 and r2 is chosen. (a) Solve for the optimal r1 and r2 as a function of P1 and m. (b) Solve for Moe's indirect utility (his maximized utility as a function of p1 and m). (c) Suppose that the price of good 1 changes from 1 to 2. How much would you need to increase m by after the price change in order to return Moe to his original utility level? ("Compensating variation".) (d) How much would Moe be willing to pay (i.e., by how much would you have to reduce m) in order to avoid the price increase? ("Equivalent variation"). (e) What is the change in consumer surplus from this price change? Hint: no math should be required for this part.