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Themes for Profit Maximization Pro sports teams, like most firms, have some degree of market power market power < = > ability to control price for pricing decisions, use "monopoly" model market power is enhanced by entry restrictions of leagues

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themes for profit maximization
Themes for Profit Maximization
  • Pro sports teams, like most firms, have some degree of market power
    • market power < = > 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?
maximizing profit
Maximizing Profit
  • How do we define profit?
    • p= TR-TC
    • TC includes Opportunity Cost
  • Why did the Dodgers leave Brooklyn?
    • Were highly profitable, but ...
    • O’Malley perceived greater profit in LA
where are profits maximized
Where are profits maximized?
  • Where MR = MC
  • Demand & Marginal Revenue
    • TR = P*Q
      • P is average revenue (TR/Q)
    • MR = ΔTR/ΔQ
      • incremental revenue per unit of incremental sales
    • Since D slopes down, MR < P at every Q
mr with linear demand
P = A - bQ

TR = PQ

= AQ - bQ2

MR = ΔTR/ΔQ

= A - 2bQ

"The MR Rule"

MR has same intercept as demand & twice the slope

Ex: P = 100 - .01Q

MR = 100 - .02Q

MR with Linear Demand

$100

D

5000

10,000

MR

optimal ticket prices
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 Jagr’s salary?
    • Hint: What does he cost if 1 million attend?
    • What does he cost if 1 thousand attend?
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

Profit Max Ticket Prices

$100

P*=$50

D

MR

Q*=5000

a paradox and a solution
A Paradox – and a Solution
  • Signing Jagr in 2001 imposed a fixed cost on Washington Caps
  • Fixed Costs do not affect MR=MC
  • 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
another paradox
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
phillies pricing strategy
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

how about the flyers
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

more sophisticated pricing price discrimination
More Sophisticated Pricing:Price 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

forms of price discrimination
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
first degree price discrimination
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
    • P=MC for last unit
    • No DWL
  • Hard to do in practice

$

MC

D

MR

Q

QM

Q*

2nd degree price discrimination
2nd Degree Price Discrimination

P

  • Don’t 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

1

4

8

# Games

third degree price discrimination
Third Degree Price Discrimination

$/Q

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

P2

D2

P1

MC

Q2

Q1

D1

MR1

MR2

personal seat licenses
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
key to psls consumer surplus
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

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