John is a honours student in economics at UCLA who has to finish his dissertation within 100 days, that is, at time t = 1, t = 2, t = 3….or t = 100. It takes one day to finish the dissertation, and on the day John does so, he incurs an instantaneous disutility cost equivalent to $10. John is a hyperbolic discounter with β = 0:85 and δ= 1.A) Suppose UCLA has a system in which it charges John $1 in fees for every day he does not finish his dissertation. When does John finish if he is naive? How much does he pay in penalties?B) Still in the $1/day system, when does John finish if he is sophisticated?C) Now suppose that the university has a deadline system: John incurs a penalty of$10 if he does not finish his dissertation by day 10 (so finishing on day 9 does not trigger the penalty, but finishing on day 10 does). There are no daily penalties.When does John finish in this system if he is naive? How much does he pay in penalties?D)When does John finish in the alternative system if he is sophisticated?E)Does it make a big difference to a naive hyperbolic discounter whether he is in a day-by-day-penalty or deadline system? Explain intuitively.F) Does it make a big difference to a sophisticated hyperbolic discounter whether he is in a day-by-day-penalty or deadline system? Explain intuitively.
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