set III Instructions: i) When in doubt, round numeric responses to two decimal places ii) It is okay to discuss the course material with your peers, but please solve all the questions independently and write all your responses in your own words. On the coversheet, please write and sign the following honor pledge: "I pledge on my honor that I have not given or received any unauthorized assistance on this problem set." iii) Please submit your assignment by the deadline. Late assignments would not be accepted. Problems: 1) a) Suppose you have beta-delta preferences with = .5, = 1 and log utility (ln). You start with a cake on day 1, and you have to eat it over days 1,2,3. Find your plan on Day 1: How much of the cake do you plan to eat each day (day 1 , 2 ,3)? When you get to day 2, you reoptimize. How much of the cake do you decide to eat on Day 2? Do you follow-through with your plans? How much do you end up eating on day 3? b) Solve problem (a) for when you have exponential discounting ( = 1) and have =