Suppose that there is a single theater in a college town. The residents of the town are either students or teachers. Suppose that the demand by the teachers (collectively) is Q1 = 12 p1 and that by the students is Q2 = 6 2p2. Assume that the marginal cost of a viewer is zero.

(a) Suppose that the students have ID's. If the theater can charge different prices to teachers and students, will it? What prices will it choose for each? What quantities will each group purchase? What are theater revenues for each group? What is total revenue?

(b) Now suppose that the teachers can obtain fake student ID's (for free). What is the new quantity consumed by the teachers? What is the revenue from teachers? What is total revenue?

(c) Because of the fake ID problem, the theater decides to stop offering student prices. What is the theater's optimal price to charge? What quantities will each group purchase at that price? What are theater revenues for each group? What is total revenue? How does this compare to your answer to part (a)?

(d) In response to the growing problem of fake student ID's, a company develops a Fake ID Identifier (FIDI). How much would the theater be willing to pay for the FIDI?

(e) Suppose that the theater purchases a FIDI for the price pF IDI . What are the prices the theater charges each group? What are revenues from each group and total revenues? Explain the relationship between your answer and pF IDI .

(f) What is the competitive price? What is the quantity that would be consumed at that price?