Amy, Jack, Bob and Carol are students in this course. Suppose the deadline for their first problem set is approaching it is due in 3 days from today, so they can do the problem set on any of four days, t = 1, 2, 3, 4 (where t = 1 is today).

The instantaneous utility costs of doing the problem set in periods t = 1, 2, 3, and 4 are 9, 20, 30, and 40 utils, respectively, as shown in the table below (note that all these are negative). Assume that the problem set takes only one day to complete, late submissions are not an option, and the world ends if the problem set is not finished at all, i.e. at the beginning of day t = 4, if the problem set is finished by then, the student will begin, finish, and turn it in on day t = 4.

Period t	u(Psett = 0)	u(Psett = 1)
1	0	-9
2	0	-20
3	0	-30
4	0	-40

Each students utility function is as follows:

where u(Psett) is the (negative) instantaneous utility of doing the problem set on day t with Psett = 1 if the student works on the problem set in period t and Psett = 0 if the student does not work on the problem set in period t.

1. (10 points) Amy is an exponential discounter with = 1, = 1, i.e. she does not discount the future at all. When will Amy do the problem set?

2. (10 points) Jack is an exponential discounter with = 1, = 1/2. When will Jack do the problem set? Explain in words why Jack and Amy do the problem set at different times.

3. (10 points) Bob is a fully naive hyperbolic discounter with = 1/4 , = 1, and = 1. That is, Bob is present-biased, but he does not take into account his future present bias when making decisions. When will Bob do the problem set?

4. (10 points) On day 0 (before day 1), if you ask Bob when hell get the problem set done, what will he predict assuming that he is too busy on day 0 so that day 0 itself is not an option?

5. (10 points) Carol is a fully sophisticated hyperbolic discounter with = 1/4 , = 1, and = = 1/4 . That is, Carol is present-biased, but she fully takes into account her future present bias when making decisions. When will Carol do the problem set? Explain in words why Carol and Bob do the problem set at different times.