Problems 1. You have just bought a brand new laptop from Best Buy and are considering whether or not to buy an extended warranty that would cover accidental damage done to it. a) If you used the maximin selection criterion, would you be more or less likely to buy the warranty? b) If you used the maximax selection criterion, would you be more or less likely to buy the warranty? c) Is there any prediction you can make about the actions of a regret minimizer? 2. You are a poor college student who wants to watch the newest Marvel movie, but you don't have Disney+. You are weighing whether to get a subscription for Disney+ or illegally torrent the movie. (a) A Disney+ membership is $7.99/month, but Disney could sue you for up to $750,000 per illegal download. If p is the probability of being caught, what does p need to be so that the expected cost of illegally downloading the movie is equal to the price of Disney+? (b) Assume p is even lower than your answer in part a). Why can Disney still charge $7.99 for a subscription? AKA, what phenomenon that we studied in class would explain people's willing ness to pay a premium to avoid the extraordinarily rare occurrence of being caught for illegal downloading? (c) What would explain a student's willingness to illegally download a movie despite the high risks associated with it? List two distinct reasons. 3. A gamble is resolved by tossing an unbiased coin as many times as is necessary to obtain heads. If it takes only one toss, the payoff is $2. If it takes two tosses, you receive $4. If it takes three tosses, you receive $8. And so on. (Him: This is the St. Petersburg Parades: gamble. a) What is the expected value of this gamble? b) Assume you have a utility function u($) = ln($). What is the expected utility of the gamble? c) What is the certainty equivalent of the gamble? 4. Graphically show the utility functions of agents with a) Riskaverse preferences b) Riskneutral preferences c) Risk-loving preference