Question Rosario has to finish her dissertation within 100 days, that is, at time t = 1, t = 2, t = 3, . . . , ort = 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 (We will measure utility in dollar terms, as in willingness-to-pay, for this problem). Rosario is a hyperbolic discounter with B = 0.85 and S = 1. Thus, on day t = 1, Rosario seeks to maximize her discounted utility: t=lm "1+ NH 2 m t=2 = 111+0851(\"2+U3+U4+...+u%+ugg+ulm) U1 Suppose the university has a system in which it charges Rosario $1 in fees for every day she does not nish her dissertation (so if she finishes on day 2, she pays $1 in fees). The accumulated fees are assessed on day 100, so that is when they enter her instantaneous utility. Lastly, suppose Rosario is naive about her time inconsistency. a) On day 1, what is Rosario's discounted utility of nishing her dissertation immediately? what is her discounted utility of planning to finish on day 2? what is her discounted utility of planning to nish on day 3? Use your answers to show that Rosario will not finish on day 1, and briefly say why. b) Now consider Flosario's decision on day 2. Use the same method above to show that she will not finish her dissertation on day 2. c) When will Rosario actually do the problem set? How much will she pay in fees? d) 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 inpenalties