A movie theater faces the following hourly inverse demand curves:
Seniors: P_s = 12 - 0.5Q
Adults: P_a = 19 - Q
The marginal cost is constant at $1. If the movie theater uses segmenting, the ticket price charged to seniors is $____.

Question

Quizplus · Accepted Answer

To find the optimal price for seniors, set marginal revenue equal to marginal cost. The marginal revenue for seniors is derived from the inverse demand curve: MR_s = 12 - Q. Setting MR_s = MC gives 12 - Q = 1, solving for Q gives Q = 11. Substituting Q = 11 back into the demand curve P_s = 12 - 0.5Q gives P_s = 12 - 0.5(11) = 6.50.

A Movie Theater Faces the Following Hourly Inverse Demand Curves