Old friends Ann and Bob are done with fruit and ready to eat ice cream. Each of them is issued $100 on Day 1 to spend on ice cream (which will melt if they don't eat it at once!) on Days 1, 2, and 3. The prices of ice cream on the three days are P = $1, P2 = $2, and P3 = $3. On day t = 1, 2, 3, Ann's preference for consuming on the different days is given by Ut In(SKA). B On day t = 1, 2, 3, Bob's preference for consuming on the different days is given by U+ = In(St) + kB). = = [ k=t (1/2) Ek=t+1 In (Sk Now: (a) Suppose that on Day 1, Ann chooses how much ice cream to purchase on Days 1,2, and 3. What will she choose? (b) Now suppose that on Day 1, Ann chooses only how much to purchase on Day 1. Then, on Day 2, she chooses only how much to purchase on Day 2. On Day 3, she is left to buy with whatever remains of her budget. How does Ann's consumption compare with her plan in part (a)? (c) Suppose that on Day 1, Bob chooses how much ice cream to purchase on Days 1,2, and 3. What will he choose? (d) Now suppose that on Day 1, Bob chooses only how much to purchase on Day 1. Critically, he understands that his marginal utility from Days 2 and 3 will change once it is Day 2. Then, on Day 2, he chooses only how much to purchase on Day 2. On Day 3, he is left to buy with whatever remains of his budget. How does Bob's consumption compare with his plan in part (c)? (e) Finally, suppose that Bob decides how much to purchase on each day, but, unlike in part (d), he mistakenly assumes that his utility function will remain In(SB) + (1/2) (In(SB)+In(S3B)) on Days 2 and 3. How does Bob's consumption compare with his plan in part (c) and his behavior in part (d)?