1. (Church & Ware, page 180, problem 3) A nightclub manager realizes that demand for drinks is more clastic among students, and is trying to determine the optimal pricing schedule. Specifically, he estimates the following average demands: Under 25 : q" = 18 - 5p Over 25 : q = 10 - 2p The two age groups visit the nightclub in equal numbers on average. Assume that drinks cost the nightclub $2 each. (a) If the market cannot be segmented, what is the uniform monopoly price? (b) If the nightclub can charge according to whether or not the customer is a student but is limited to linear pricing, what price (per drink) should be set for each group? (c) If the nightclub can set a separate cover charge and price per drink for each group, what two-part pricing schemes should it choose? (d) Now suppose that it is impossible to distinguish between types. If the nightclub lowered drink prices to $2 and still wanted to attract both types of consumer, what cover charge would it set? (e) Suppose that the nightclub again restricts itself to linear pricing. While it is impossible to explicitly "age discriminate," the manager notices that everyone remaining after midnight is a student, while only a fraction = of those who arrive before midnight are students. How should drink prices be set before and after midnight? What type of price discrimination is this? Compare profits in (d) and (c)