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 cannot price discriminate.What is the monopolist's profit from both students and adults?

Question

Quizplus · Accepted Answer

To find the monopolist's profit, first determine the combined demand function: Q = Q^d_S + Q^d_A = (600 - 100P) + (1,200 - 100P) = 1,800 - 200P. The inverse demand function is P = 9 - 0.005Q. The total revenue (TR) is P*Q = (9 - 0.005Q)Q = 9Q - 0.005Q². The marginal revenue (MR) is the derivative of TR: MR = 9 - 0.01Q. Set MR equal to marginal cost (MC = $2) to find Q: 9 - 0.01Q = 2, so Q = 700. Substitute Q = 700 into the inverse demand function to find P: P = 9 - 0.005(700) = 5.5. Total revenue is TR = 5.5*700 = $3,850. Total cost is TC = MC*Q = 2*700 = $1,400. Profit is TR - TC = $3,850 - $1,400 = $2,450.

A Movie Monopolist Sells to Students and Adults