Question

1. Consider a team that can segment its customers into two distinct markets whose demands are given by

                                    P₁ = 25 – .0001Q   P₂ = 50 – .0002Q

The relevant marginal revenue expressions are MR₁=25–.0002Q, and MR₂=50–.0004Q, respectively. Finally, let the marginal cost be MC=5. Assuming that the team can perfectly identify members of each market and prevent them from trading with one another, find    the optimal quantities, Q₁* and Q₂*, and prices, P₁* and P₂*. Given your results, what must be true of the demand elasticities in the two markets (you don’t need to actually calculate them)?   

2. A team has 105 potential fans who may choose to attend one or more of the team’s five home games. 100 of the fans will pay up to $25 to attend a single game, but will pay nothing to attend any additional games. 5 fans, however, have the following demand schedule:

Value of 1^st game: $25

Value of 2^nd game: 20

                        Value of 3^rd game: 15

                        Value of 4^th game: 10

                        Value of 5^th game: 5

Assume the team has a zero marginal cost per fan of supplying games.

(a)What will the team’s total home attendance be if it sets a single game price of $25? What will its total revenue be?   

(b)What is the maximum amount that a multi-game fan will pay for a season ticket?

(c)Suppose the team sets the price of individual game tickets at $25, but offers season tickets at the price you computed in (b). What is the team’s total home attendance, and what is its total revenue? How do your answers compare to part (a)?  

Answer 1

Question 1

Market 1

P₁ = 25 – .0001Q

MR1 = 25 - 0.0002Q

MC = 5

Optimal solution is ascertained at the level where MR equals MC

Equating MR and MC

25 - 0.0002Q = 5

-0.0002Q = -20

Q = 20/0.0002Q = 100,000

P = 25 - 0.0001Q = 25 - (0.0001*100,000) = 25 - 10 = 15

Thus, in Market 1,

Q1 = 100,000 units

P1 = $15 per unit

Market 2

P₂ = 50 – .0002Q

MR2 = 50 - 0.0004Q

MC = 5

Optimal solution is ascertained at the level where MR equals MC

Equating MR and MC

50 - 0.0004Q = 5

-0.0004Q = -45

Q = 45/0.0004 = 112,500

P = 50 - 0.0002Q = 50 - (0.0002* 112,500) = 50 - 22.5 = 27.5

Thus, in Market 2,

Q2 = 112,500 units

P2 = $27.5 per unit

Seller is able to sell more units in Market 2 and that also at higher price compared to Market 1.

Thus, it can be stated that demand is more elastic in Market 1 compared to Market 2.