ECON30019 Assignment 4
Due at 11:59 pm on Oct 1, 2024
Question 1. (65 Points)
It is Friday and Maria is planning when to do her homework. She has to do her homework on one of the following days: Friday, Saturday, Sunday, or Monday. These four options provide diferent utility streams as follows.
Friday Saturday Sunday Monday
Do homework on Friday -5 5 10 4
Do homework on Saturday 0 -5 10 10
Do homework on Sunday 0 5 -5 10
Do homework on Monday 0 5 10 -5
1. (5 Points) Suppose Maria is an exponential discounter with δ = 0.9. On Friday, when does she plan to do her homework? When does she actually do her homework?
2. (5 Points) Suppose Maria is an exponential discounter with δ = 0.7. On Friday, when does she plan to do her homework? When does she actually do her homework?
3. (10 Points) Suppose Maria is a naive hyperbolic discounter with δ = 0.9 and β = 0.9. On Friday, when does she plan to do her homework? When does she actually do her homework?
4. (10 Points) Suppose Maria is a naive hyperbolic discounter with δ = 0.9 and β = 0.8. On Friday, when does she plan to do her homework? When does she actually do her homework?
5. (15 Points) Suppose Maria is a sophisticated hyperbolic discounter with δ = 0.9 and β = 0.8. On Friday, when does she plan to do her homework? When does she actually do her homework?
6. (20 Points) Continue to assume that Maria is a sophisticated hyperbolic discounter with δ = 0.9 and β = 0.8. Suppose now that on any of the four days, Maria can pay an instantaneous cost of 1 and use a commitment device that forces her to do the homework on a particular day. For example, if on Saturday she uses the commitment device to force herself to do the homework on Sunday, it would incur a cost of 1 on Saturday. Can Maria be made better of by using the commitment device? Why?
Question 2. (35 Points)
Bob makes his choices according to the Gul-Pesendorfer model. Bob has been told by his doctor that he must lose weight. Consequently, his long-run utility for salad is u(salad) = 12, as compared with along run utility for less diet friendly dishes, such as pasta with u(pasta) = 4 and steak with u(steak) = 3. Bob finds salad less tempting: v(salad) = 2. He is more tempted by pasta, with v(pasta) = 6, and is even more tempted by steak, with v(steak) = 18.
1. (10 Points) Suppose there are two restaurants, one with the menu {salad} and the other with the menu {salad, pasta}. Which restaurant does Bob prefer? Explain the intuition based on your calculation.
2. (10 Points) Suppose there are two restaurants, one with the menu {salad} and the other with the menu {salad, steak}. Which restaurant does Bob prefer? Explain the intuition based on your calculation.
3. (15 Points) How would Bob rank restaurants ofering (1) salad only, (2) pasta only, (3) steak only, (4) salad and pasta, (5) salad and steak, (6) pasta and steak, and (7) salad, pasta and steak? Give a complete preference ordering, taking care to distinguish between strict preference (>) and indiference (~). For example, a preference order over 4 menus A, B , C, and D may be A > B ~ C > D. Show your calculation carefully.