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Thea owns an arthouse movie theater chain, the San Jacinto Alehouse, with locations in College Station and Killeen. Like most cinemas, the Alehouse has entered into a revenue sharing agreement with major film distributors. The Alehouse receives a fraction F of ticket sale revenue, while the distributors receive the remaining fraction 1F . Each cinema has a fixed cost C. The Alehouse has a monopoly on arthouse films in College Station and Killeen. Thea is considering introducing a student discount in College Station. Under the student discount, students pay Ps while non-students pay Pn. Students have a demand curve of

Qs = 100 8Ps

while non-students have a demand curve of

Qn = 100 4Pn

(a) Write down the profit function for the College Station cinema. What are the first order conditions of Thea's profit maximization problem? (b) What are the profit maximizing prices? Do these prices depend on F and C? (c) Does the student discount increase the cinema's profit? Thea is considering introducing a military discount in Killeen. Under the military discount, members of the military pay Pm while civilians pay Pc. The demand curve for members of the military is

Qm = 100 4Pm

while civilians have a demand curve of

Qc = 100 8Pc

(d) What needs to be true about Pm and Pc for the cinema to implement a military discount? Will the cinema implement the military discount? (e) Write down the profit function for the Killeen cinema. What is the first order condition of Thea's profit maximization problem? (f) What is the profit maximizing price?

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