Consider the situation faced by the theater manager in problem 25. Suppose the probabilities given in part c hold.
a. What is the most amount of money the theater manager should pay for advance information regarding the review the movie will receive?
b. The theater manager can subscribe to “Advance Screening,” a rating service that purports to predict the review a movie will receive. The rating service either gives the movie a “thumbs up” or
a “thumbs down.” Based on previous predictions made by this service, the manager believes the following conditional probabilities hold.
If “Advance Screenings” wants a fee of $50 for giving its prediction, should the theater manager purchase the information?
c. What is the efficiency of “Advance Screenings” information?
25. The AMC 24-plex cinema is trying to decide how many screens it should have showing the new action-comedy movie Lost Wages in Las Vegas. The theater must sign a contract with the movie’s distributor indicating how many screens it will play the movie on before reviews of the movie are public. The manager has decided, based on the actors involved in the movie, to devote between one and five screens to this movie during its two-week summer run. The profit the manager expects to earn on the movie is based on the consensus review of the movie (one to four stars). The payoff table showing these estimated profits is as follows.
a. If the theater manager wishes to minimize his maximum regret, how many screens should the movie be booked in?
b. If the theater manager is risk averse and wishes to use the maximin criterion, how many screens should the movie be booked in?
c. Suppose the theater manager believes, based on the director’s previous releases, that the probability the movie will be rated one star is .10, two stars .20, three stars .40, and four stars .30. If the manager wishes to use the expected value criterion, how many screens should the movie be booked in?