You are a theater owner fortunate enough to book a summer box office hit into your single theater. You are now planning the length of its run. Your share of the film’s projected box office is R = 10w - .25w2, where R is in thousands of dollars and w is the number of weeks that the movie runs. The average operating cost of your theater is AC = MC = $5 thousand per week.
a. To maximize your profit, how many weeks should the movie run? What is your profit?
b. You realize that your typical movie makes an average operating profit of $1.5 thousand per week. How does this fact affect your decision in part (a), if at all? Explain briefly.
c. In the last 25 years, stand-alone movie theaters have given way to cineplexes with 4 to 10 screens and megaplexes with 10 to 30 screens (yes, 30 screens!) under one roof. During the same period, total annual movie admissions have barely changed. What cost factors can explain this trend? In addition, what demand factors might also be relevant?
d. The film’s producer anticipated an extended theater run (through Labor Day) and accordingly decided to move back the DVD release of the film from Thanksgiving to January. Does the decision to delay make sense? Explain carefully.