Problem 1: Third-Degree Price Discrimination. Assume that the Wisconsin Badgers have two types of fans: non-students (N ) and students (S). Inverse demand from students is given by P_N = 216 − 2Q_N and inverse demand from students is given by P_S = 176 − 3Q_S The marginal cost of production is MC = 20 for both fan types. 1. Suppose that Badgers sets two separate ticket prices (one for the non-students and one for students). a) How many non-student game tickets are sold? What is the non-student ticket price? b) How many student tickets are sold? What is the student ticket price? c) What are the Badgers profits? d) What is total consumer surplus for all fans? 2. Suppose the NCAA changes its rules so that the Badgers must set a single price for all fans. a) Find the market (inverse) demand curve. b) What single price and quantity will the Badgers choose? c) What are Badgers profits? d) What is total consumer surplus for all fans? Did non-student surplus increase more than students surplus decreased? Briefly explain.

Third-degree price discrimination often comes up in the context of discountsfor certain groups to some form of entertainment (e.g., a play, movie or a sporting event).Consider an event for which there are two audiences (e.g., students and non-students)and assume that the seller’s additional expenses (i.e., marginal cost) associated withhaving an additional seat occupied are essentially zero but the capacity of the venue islimited to K.(a) To make everything a bit more concrete, let the students’ and non-students’ inversedemands beP1 (x1) = 40 − x1 and P2 (x2) = 100 − x2.Solve for the single monopoly outcome (that is, no discrimination) without a capacityconstraint (i.e., K is a very large number).(b) Suppose now that the monopolist engages in third-degree price discrimination. Findthe optimal quantity sold to both groups of consumers, the price and the monopolist’sprofit. How does this compare to the answer you found in part (a) ?In the next two questions assume K = 50.(c) Suppose the monopolist does not engage in price discrimination. Find the profitmaximizing quantities, the price and the monopolist’s profit.(d) Suppose now that the monopolist engages in third-degree price discrimination. Findthe optimal quantity sold to both groups of consumers, the price and the monopolist’sprofit. How does this compare to the answer you found in part (c) ?2

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?

This exercise is about pricing strategies and price discrimination. Choose all the correct answers.Question 1Answera.Selling bread for $4, butter for $4 and bread and butter combined for $7 is an example of second degree price discrimination.b.A monopolist applying third degree price discrimination can improve consumer welfare compared to the scenario in which they set one market-level price.c.First degree price discrimination is efficient, but rarely possible in real world.d.A monopolist knows valuations of consumers, and sets prices individually for each of the consumer at the level of their valuation. This is an example of first-order price discrimination.

Question 10Not answeredMarked out of 2.50Flag questionTipsMCQConsumerWillingness to PayAnya$24Basil$20Celeste$15Dralon$12Esther$7The table above lists the highest prices five consumers are willing to pay for a theatre ticket. If the price of one ticket rises from $10 to $19, __________.Question 10Answera.only three tickets will be soldb.no one will buy a ticketc.consumer surplus decreases from $31 to $6d.consumer surplus increases from $44 to $71

(Third-degree price discrimination) There is a monopolist and two groups of consumers, students andgeneral consumers. The total demand of students is 𝐷1(𝑝) = 10−𝑝, while the total demand of general (non-student)consumers is 𝐷2(𝑝) = 40 − 2𝑝. The monopolist’s (short-run) variable cost function is 𝑐(𝑞) = 2𝑞. Throughout thisquestion, the monopolist uses linear pricing.(a) [5 marks] Discuss reasons why the demands of the two groups may be different. For the purpose of thisquestion, assume that every consumer has unit demand. (Limited to 100 words.)(b) [15 marks] Let us assume that the monopolist sets the same price for both groups of consumers. The problemthen becomes a monopolist’s problem facing the market demand 𝐷1 + 𝐷2. Find the monopolist’s optimalprice, consumer surplus and producer surplus.(c) [20 marks] Now assume that the monopolist sets a price for students and a potentially different price for non-students. Find the optimal pricing, consumer surplus and producer surplus.(d) [5 marks] Explain why the monopolist needs to check student ID if he decides to use the pricing in (c).Solution