Rosario has to finish her 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 Rosario does so, she incurs an instantaneous disutility cost equivalent to $10. Rosario is a hyperbolic discounter with = 0.85 and = 1.

(a) Suppose the university has a system in which it charges Rosario $1 in fees for every day she does not finish her dissertation. When does Rosario finish if she is naive? How much does she pay in penalties?

(b) Still in the $1/day system, when does Rosario finish if she is sophisticated?

(c) Now suppose that the university has a deadline system: Rosario incurs a penalty of $10 if she does not finish her 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 Rosario finish in this system if she is naive? How much does she pay in penalties?

(d) When does Rosario finish in the alternative system if she is sophisticated?

(e) Does it make a big difference to a naive hyperbolic discounter whether she is in a day-by-day-penalty or deadline system? Explain intuitively.