Imagine that a student wants to apply to a master programme. The immediate costs (e.g. effort, semester fees) occasioned by following the master for the following three semesters are c1 = 6, c2 = 15, c3 = 12 Additionally, at t = 0 the student has to pay some registration fee c0 = 2.

The value (prestige, salary, etc.) that the student attaches to the diploma that she will obtain after three semesters at the university is v4 = 40. The student will only obtain the diploma if she follows the program until the end (i.e. she has to stay at the university for three semesters). The student can abandon the program at the beginning of each semester. If she abandons, she can stay at home watching TV which gives her a net utility of 0. The intertemporal preferences of the student can be described by the utility function suggested by O'Donoghue and Rabin (1999).

We consider three types of persons: Time-consistent (TC), Naifs (N) and Sophisticates (S). Assume that = 0.5 for the naive and sophisticated persons. TC's have = 1. Assume as well that = 1 for all three types of persons.

a) Please derive the decision strategy of the student, i.e. the decision to apply to the programme in period t = 0 and the decision to continue or abandon the program in periods 1 to 3, if the student is time-consistent, sophisticated and naive.

b) What is the intuition behind the different behaviors of the naive and sophisticated types?

c) Imagine that a politician decides to increase the registration fees of the program from 2 to 4 to reduce the rate of students dropping in the middle of the program. In your opinion, will this intervention be succesful? Who benefits from this intervention? Are there persons who will experience a utility loss because of this intervention?