Problem 2: Menu Pricing. Assume that there are two types of fans of Boston Bruinsgames: Unenthusiastic (U ) and Enthusiastic (E).Each Unenthusiastic fan has a representative demand curve given byPU = 180 − 6QUEach Enthusiastic fan has a representative demand curve given byPE = 300 − 10QE. The marginal cost of ticket production is constant at M C = 90 for all consumers.1. Suppose the Bruins can perfectly distinguish between the two types of fans and setdifferent two-part tariffs for each type.a) What fixed fee and per unit price will they set for Unenthusiastic fans?b) What fixed fee and per unit price will they set for Enthusiastic fans?c) What is the consumer surplus for each type of fan?d) What are the profits for the Bruins from each type of fan?
Question
Problem 2: Menu Pricing. Assume that there are two types of fans of Boston Bruinsgames: Unenthusiastic (U ) and Enthusiastic (E).Each Unenthusiastic fan has a representative demand curve given byPU = 180 − 6QUEach Enthusiastic fan has a representative demand curve given byPE = 300 − 10QE. The marginal cost of ticket production is constant at M C = 90 for all consumers.1. Suppose the Bruins can perfectly distinguish between the two types of fans and setdifferent two-part tariffs for each type.a) What fixed fee and per unit price will they set for Unenthusiastic fans?b) What fixed fee and per unit price will they set for Enthusiastic fans?c) What is the consumer surplus for each type of fan?d) What are the profits for the Bruins from each type of fan?
Solution
a) For Unenthusiastic fans, the Bruins will set the per unit price equal to the marginal cost, so P_U = MC = 90. To find the quantity demanded at this price, we substitute P_U into the demand equation: 90 = 180 - 6Q_U, which gives Q_U = 15. The fixed fee is the consumer surplus, which is the area under the demand curve and above the price line. This is given by (1/2)(180-90)(15) = 675.
b) For Enthusiastic fans, the Bruins will again set the per unit price equal to the marginal cost, so P_E = MC = 90. Substituting P_E into the demand equation gives: 90 = 300 - 10Q_E, which gives Q_E = 21. The fixed fee is the consumer surplus, which is (1/2)(300-90)(21) = 2205.
c) The consumer surplus for each type of fan is zero, because the fixed fee extracts all of the consumer surplus.
d) The profits for the Bruins from each type of fan are the fixed fees plus the profits from selling the tickets. For Unenthusiastic fans, this is 675 + (90-90)*15 = 675. For Enthusiastic fans, this is 2205 + (90-90)*21 = 2205.
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