The manager of a local movie theater believes that demand for a film depends on when the movie is shown. Early moviegoers who go to films before 5 pm are more sensitive to price than are evening moviegoers. With some market research, the manager discovers that the demand curves for daytime (D) and evening (E) moviegoers are QD = 100 − 10PD and QE = 140 − 10PE, respectively. The marginal cost of showing a movie is constant and equal to $3 per customer no matter when the movie is shown. This includes the costs of ticketing and cleaning.
a. Write down the aggregate demand function and graph the aggregate demand curve.
b. What is the profit maximizing pricing policy if the manager charges the same price for daytime and evening attendance? What is attendance in each showing and what is aggregate profit per day?
c. Now suppose that the manager adopts a third-degree price discrimination scheme, setting a different day and evening price. What are the profit maximizing prices? What is attendance at each session? Confirm that aggregate attendance is as in (b). What is aggregate profit per day?