Question

Mary owns the only ballet school in Santa Barbara. There is demand from college students and long term residents. The inverse demand for private lessons from the students is p(q) = 50−q, and the demand from the residents is p(q) = 170−3q. Assume that Mary charges 20 dollars per class, but only teaches people who have become members of her school. There is a set membership fee, but she has discounts for students.

(Continued from previous question) Assume a new law forbids student discounts. She introduces a package deal for 30 classes (intended for students) that one can buy without becoming a member. She prices this to extract the entire surplus from college students. But she still offers classes at 20 dollars for members. What is the highest price she can charge for the membership so that the residents still buy the membership instead of the package?

(a) 2400 (b) 1350 (c) 3750

(d) 1050 answer

Answer 1