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.What is the difference in the monopolist's profit when it is able to price discriminate and when it cannot?

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Quizplus · Accepted Answer

Without price discrimination, the monopolist will produce where MR=MC, which is when 400-P=2, or P=398. The monopolist will sell 400 tickets to both students and adults, making a total revenue of (600-100*398)*400*(1+1)=$240,000.

With price discrimination, the monopolist will charge a higher price to adults than to students. The monopolist will set the price for students where MRs=MC, which is when 300-Ps=2, or Ps=298. The monopolist will sell 300 tickets to students, making a revenue of (600-100*298)*300*(1+1)=$234,000.

The monopolist will set the price for adults where MRa=MC, which is when 600-Pa=2, or Pa=598. The monopolist will sell 400 tickets to adults, making a revenue of (1200-100*598)*400*(1+1)=$476,000.

Thus, the total revenue with price discrimination is $710,000. The monopolist's profit with price discrimination is higher by $710,000-$2*700=$709,300.

A Movie Monopolist Sells to Students and Adults