Question

Problem 1: Price Discrimination. The Baltimore Ravens are choosing ticket prices. They know that there are two types of fans: super and casual. Super fans have an inverse demand Ps = 60 − Qs and casual fans have an inverse demand Pc = 30 − 1 Qc. The marginal 2 The cost of ticket production is MC = 10.

The Ravens still cannot distinguish between super fans and casual fans. Instead of selling single-game tickets, the Ravens want to create two season ticket packages: one aimed at super fans and one aimed at casual fans. (Assume now that the demand curves given in the problem are for a representative consumer of each type.)

a) What are the optimal season ticket packages (menu pricing) set by the Ravens?

b) What is the consumer surplus of casual fans? Of super fans? From which fan type do the Ravens make higher profits?

Answer 1

Case given here is that :

The Ravens still cannot distinguish between super fans and casual fans which means that each type of fan either casual or super both are same and charged the fixed entry fee and variable.

Let do the detail with one fan of each type.

Variable cost here will be equal to marginal cost and fixed entry fee will be equal to consumer surplus.

[a] If each ticket priced at marginal cost then,

equilibrium quantity of super fan :

Price = MC

Ps = 60-Qs

and Ps = 10

so, 60-Qs = 10

Qs = 60-10 = 50

equilibrium quantity of casual fan :

Price = MC

Pc = 30-0.5Qc

and Pc = 10

so, 30-0.5Qc = 10

Qc = [30-10]/0.5 = 40

Qc= 40

[b] Consumer surplus of super fan = 1/2*[60-10] * 50 = 2500/2 = 1250

Consumer surplus of Casual fan = 1/2*[30-10] * 40 = 800/2 = 400

To calculate which give higher benefits we had to calculate total benefits from each type of fans:

Profit from super fan : = 1250+10*50 -10*50 = 1250

Profit from casual fan = 400 +10*40 -10*40 = 400

By comparision it is clear that super fan yields more benefit to the Baltimore Ravens.