Alice has a ticket for a film festival. Every week, one movie will be screened.

Question

Alice has a ticket for a film festival. Every week, one movie will be screened. There are four movies in the festival and she can choose to watch only one.

The utility that she gets from watching each movie is:

Week 1: bad movie, u1(Movie) = 3

Week 2: good movie, u2(Movie) = 5

Week 3: great movie, u3(Movie) = 8

Week 4: excellent movie, u4(Movie) = 13

Assume Alice is a hyperbolic discounter with x = 1/2 and y = 1.

a) If Alice is naive, what movie will she choose to watch when she gets the ticket? which movie will she end up watching?

b) If Alice is sophisticated, which movie will she watch? If instead of 1 ticket, Alice had gotten 3 tickets:

c) What movie will naive Alice miss?

d) What movie will sophisticate Alice miss?

e) There is an economist who believes that x = 1. He assumes that Alice is an exponential discounter with a certain y.

What is the biggest y that an agent with exponential discounting could have such that he would choose the same 3 movies as naive Alice?

Explanation / Answer

If Alice is naïve, she will watch an excellent movie. , payoff = 13^1/8 = 1.38 If she is sophisticated she would watch the bad movie and receive a payoff = 3. Naïve Alice will miss the bad movie, payoff = 5^1/2+8^1/4+13^1/8 = 5.27 Sophisticated Alice will miss the excellent movie, payoff = 3+5^1/2+8^1/4 = 6.9

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