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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

  • 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?


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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


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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


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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


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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?


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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


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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


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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


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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


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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


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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


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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


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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*


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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


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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


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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


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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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