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

PN =2162QN and inverse demand from students is given by

PS =1763QS 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.

 

Problem 2: Menu Pricing. Assume that there are two types of fans of Boston Bruins games: Unenthusiastic (U) and Enthusiastic (E).

Each Unenthusiastic fan has a representative demand curve given by PU =1806QU

Each Enthusiastic fan has a representative demand curve given by PE =30010QE

. The marginal cost of ticket production is constant at MC = 90 for all consumers.

Suppose the Bruins can perfectly distinguish between the two types of fans and set

different 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?

Suppose instead that the Bruins can't distinguish between the two types of fans. Instead of setting a single constant price per game, the Bruins engage in menu pricing.

a) How many tickets do the Bruins sell to each Unenthusiastic fan? What is the price of this package?

b) What is Enthusiastic fan surplus when they buy the Unenthusiastic fan package?

c) How many tickets do the Bruins sell to each Enthusiastic fan? What is the price

of this package?

d) What is the consumer surplus of each type of fan?

e) What are the profits for the Bruins from each type of fan?

f) Compute the average ticket price for each type of fan.