A movie monopolist sells to students and adults.The demand function for students is Q^d_S = 600 - 100P and the demand function for adults is Q^d_A = 1,200 - 100P.The marginal cost is $2 per ticket.Suppose the movie theater can price discriminate.What price per ticket does the theater charge adults to maximize profits?

Question

Quizplus · Accepted Answer

To maximize profit, the theater should charge different prices to different customers according to their demand elasticity. We know that the demand elasticity for students is higher than the demand elasticity for adults. Therefore, the theater can charge a higher price to adults. To find the profit-maximizing price for adults, we need to use the following equation: MRasd = MC Where MRasd is the marginal revenue for adults, which can be calculated as: MRasd = (1200-200Qasd)/120 (where Qasd is the quantity of tickets sold to adults) Setting MRasd equal to MC (which is $2), we get: (1200-200Qasd)/120 = 2 Solving for Qasd, we get Qasd = 550 Now, we can plug in Qasd into the demand function for adults to get the price: Q^d_A = 1200 - 100P 550 = 1200 - 100P P = $6.50 (rounded up to the nearest dollar) Therefore, the theater should charge adults $7 per ticket to maximize profits.

A Movie Monopolist Sells to Students and Adults