Johnny Depp 2 This exercise refers to Example 9.10. Suppose instead that you can only watch one of the four movies. Will you watch a the mediocre, b the good, c the great, or d the fantastic movie?

(a) Show that an exponential discounter will watch d the fantastic movie.

(b) Show that a naive hyperbolic discounter will watch c the great movie.

(c) Show that a sophisticated hyperbolic discounter will watch a the mediocre movie. The problem is that sophisticated hyperbolic discounters tend to preproperate, that is, doing something now when it would be better to wait. Preproperation in one sense is the very opposite of procrastination, which is a problem that naive hyperbolic discounters have. Paradoxically, then, there are situations in which naifs are better off than sophisticates – situations in which people do better when they do not attempt to anticipate their own behavior. Of course, people like Seneca and Simon, when encouraging you not to think so much about the future (see Section 8.4), already told you so.