Themes for Profit Maximization

1
Themes for Profit Maximization

• Pro sports teams, like most firms, have some
  degree of market power
• market power lt gt ability to control price
• for pricing decisions, use "monopoly" model
• market power is enhanced by entry restrictions of
  leagues
• What was impact of Alex Rodriguez on ticket
  prices for Texas Ranger games?
• Philadelphia Flyers (hockey) always sell out
• Phillies (baseball, same town) seldom do
• Is someone screwing up?

2
Maximizing Profit

• How do we define profit?
• p TR-TC
• TC includes Opportunity Cost
• Why did the Dodgers leave Brooklyn?
• Were highly profitable, but ...
• OMalley perceived greater profit in LA

3
Where are profits maximized?

• Where MR MC
• Demand Marginal Revenue
• TR PQ
• P is average revenue (TR/Q)
• MR ?TR/?Q
• incremental revenue per unit of incremental sales
• Since D slopes down, MR lt P at every Q

4
MR with Linear Demand

• Ex P 100 - .01Q
• MR 100 - .02Q

• P A - bQ
• TR PQ
• AQ - bQ2
• MR ?TR/?Q
• A - 2bQ
• "The MR Rule"
• MR has same intercept as demand twice the slope

100
D
5000
10,000
MR
5
Optimal Ticket Prices

• Optimal, from the seller's point of view
• What literally are teams selling?
• Tickets the right to sit for 2-3 hours
• The cost of selling 1 more ticket is very low 0
• At least up to capacity
• What kind of cost is Jaromir Jagrs salary?
• Hint What does he cost if 1 million attend?
• What does he cost if 1 thousand attend?

6
Profit Max Ticket Prices

• Assume no capacity constraint
• Let MC 0 for simplicity (rather than 25 cents)
• Optimum where MR MC 0
• MR 100 - 0.2Q 0
• Q 100 / .02 5000
• P 100 - .01(5000) 50

• The Profit Max Price is 50

100
P50
D
MR
Q5000
7
A Paradox and a Solution

• Signing Jagr in 2001 imposed a fixed cost on
  Washington Caps
• Fixed Costs do not affect MRMC
• But teams claim ticket prices go up because of
  higher talent costs
• When Caps signed Jagr, ticket prices jumped
• Does this refute the profit max model of ticket
  prices?
• No. Fans' WTP for games increases with more
  talented players
• Demand ( MR) shifted out

8
Another Paradox

• Do Phillies charge too much?
• Do the Flyers charge too little?
• Some basic assumptions
• Both teams exercise market power
• Demand is same for both teams
• MC 0
• Capacity of stadiums is only difference

9
Phillies' Pricing Strategy

• Why does MC look like this?
• --Stadium Capacity 60,000
• Does it pay for the Phillies to sell out?
• They couldn't do it if they gave tickets away for
  free!

MC
20
D
MR
10
How About the Flyers?

• Arena capacity 17,000
• --What does this mean for their MC curve?
• Does it pay for the Flyers to sell out?
• What does this mean for prices?
• Phillies vs. Flyers

P
MC
D
MR
11
More Sophisticated PricingPrice Discrimination

• Consumer Surplus
• Different individual values, but each pays P
• Also applies to 1 buyer
• MV declines w/ Q
• Can seller can charge different P?
• Ideal P MV each unit
• When is this possible?

P
P0
D
Q
12
Forms of Price Discrimination

• Successful Price Discrimination requires
• 1. market power (obvious)
• 2. information
• Must know differences in MV across consumers, Q
• 3. separation
• Must keep high MV consumers from buying at lower
  P
• First degree price discrimination
• know WTP of all consumers for all Q
• Second degree
• know demand curve slopes down
• Third degree
• know different groups behave different demand
  elasticities

13
First Degree Price Discrimination

• Know what everyone is willing to pay
• Can charge everyone a different price
• Seller captures all consumer surplus
• P MV for each unit
• More efficient
• PMC for last unit
• No DWL
• Hard to do in practice

MC
D
MR
Q
QM
Q
14
2nd Degree Price Discrimination
P

• Dont know WTP for everyone
• Do know demand slopes down
• Charge less for additional tickets
• Captures some consumer surplus
• What happens at right?
• Group sales/season tickets

25
20
15
D
Games
1
4
8
15
Third Degree Price Discrimination
/Q

• Can separate groups
• Here, group 2 WTP more than group 1
• If can keep markets separate, profit max P2 gt
  P1
• What if charges a single price?

P2
D2
P1
MC
Q2
Q1
D1
MR1
MR2
16
Personal Seat Licenses

• New innovation in pro sports
• First used in pros by Carolina Panthers
• Long history of similar payments in colleges
• booster contributions for choice seats
• PSL payment for right to buy season tickets
• Similar to golf course membership pay for right
  to play
• A puzzle to economists where is gain from PSLs?
• If pay for PSL, will pay less for ticket

17
Key to PSLs Consumer Surplus
/Q

• Charge competitive price for tickets
• Not monopoly price
• Walker Course Membership
• Fan is WTP for opportunity to buy tix
• With PSL
• Team gets ABC
• Not just B

A
PM
B
D
C
PC
Q
MR