(1)Back to the gym Suppose that the market for gym memberships in Greenwich Village consists of two segments: students (A) and professors (B). Each student has demand q = 100 - P. There are 4000 students. Each professor has demand q = 240 - 2P. There are 1000 professors. Total cost for a newly opened gym in the Village is TC(Q) = 5000 + 20Q.

(a)Suppose the gym can set different two-part tariffs for the two different segments. What are the entry fees that the gym could charge Segment A and Segment B?

(b)Now suppose the gym is unable to discriminate between the two segments. If the gym wants to offer a plan that both segments would join, what are the entry fee and price per unit that would maximize profit?