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Intertemporal Mixed Bundling & the Summer Rock Concert Market
A Discussion with the Center for eBusiness at MIT
Rafi A. MohammedCambridge Strategy & Economics
Product Bundling Strategy: Theory & Evidence 2
From Internet Marketing: Building Advantage in a Networked Economy
Product Bundling Strategy: Theory & Evidence 3
Intertemporal Mixed Bundling and the Summer Rock Concert Market
Common BundlingModel Features
Common BundlingModel Features
Mixed bundling, pure bundlingUnderlying principle of mixed bundling is price discriminationBundle price is less than the sum of the individual component pricesBundle is targeted towards consumers that have a lower valuation of the goods. Individual sales targeted towards higher valuation consumers
Mixed bundling, pure bundlingUnderlying principle of mixed bundling is price discriminationBundle price is less than the sum of the individual component pricesBundle is targeted towards consumers that have a lower valuation of the goods. Individual sales targeted towards higher valuation consumers
Theoretical ModelWinter 1999, Rand Journal of Economics
(Joint with P. DeGraba)
Theoretical ModelWinter 1999, Rand Journal of Economics
(Joint with P. DeGraba)
Under certain parameterizations, the bundle price is greater than the sum of the individual component pricesBundle is targeted towards consumers that have a higher valuation of goods and individual components targeted towards lower value consumersBuying frenzies may be a result of profit maximization. A profit maximization may result in excess demandThis strategy creates uncertainty in a market not previously characterized by uncertaintyIntroduces the concept of intertemporal mixed bundling
Under certain parameterizations, the bundle price is greater than the sum of the individual component pricesBundle is targeted towards consumers that have a higher valuation of goods and individual components targeted towards lower value consumersBuying frenzies may be a result of profit maximization. A profit maximization may result in excess demandThis strategy creates uncertainty in a market not previously characterized by uncertaintyIntroduces the concept of intertemporal mixed bundling
Product Bundling Strategy: Theory & Evidence 4
Intertemporal Mixed Bundling and the Summer Rock Concert Market
Empirical WorkEmpirical WorkMonitor Working Paper: July 2002
Presents one of the first “objective” empirical tests of the effects of bundling to the academic literature
Product Bundling Strategy: Theory & Evidence 5
Agenda
Theoretical Work
Empirical Work
Product Bundling Strategy: Theory & Evidence 6
Underlying IntuitionTheoretical and Empirical Models
Concerts
Concert 1. Uncertainty regarding ticket availabilityConcert 2.Popular but no chance of selling out
Fans
Diehard FansNormal Fans
Two Period Ticket Selling Strategy
Period 1. Only bundles containing both `concert tickets are sold. Bundle price > than sum of individual prices
Period 2. Remaining tickets are sold individually
Increased Profits
All diehard fans purchase bundle
Uncertainty is created in a market not previously characterized by uncertainty
More tickets and ancillaries are sold
PRODUCT / PLAYERS
PRODUCT / PLAYERS STRATEGY STRATEGY OUTCOME OUTCOME
Product Bundling Strategy: Theory & Evidence 7
Theory ExampleDemand Assumptions
StonesNormal
100(B) 60(D) 160 60
BruceDiehard
90(C) 200(A) 290 20
BruceNormal
60(D) 100(B) 160 70
Stones Diehard
Consumer Type
Consumer Type
Expected Number of Customers
Expected Number of Customers
Reservation PricesReservation PricesRPstones RPbruce RPbothRPstones RPbruce RPboth
200(A) 90(C) 290 (0.5 * 20) + (0.5 * 60) = 40
Stones Capacity = Bruce Capacity = 100 = K
Product Bundling Strategy: Theory & Evidence 8
Theory ExampleIntertemporal Mixed Bundling (IMB) Framework
\IMB Time Line
Announce Selling Strategy
Consumer Decision
Period 2 Price Set
Sell RemainingTickets Individually
at $100
ConsumerDecision
Period 1 Price Set
Set BundlePrice (Stones &Bruce Ticket) at
202.50 - ε
Stones/Springsteen
Example
We assume that once tickets are purchased, they cannot be resold
Product Bundling Strategy: Theory & Evidence 9
Theory ExampleDiehard Stones & Bruce Fans’ Decision
Diehard Stones Fans: Purchasing the bundle is their Dominant Strategy
Stones Diehard FansWait Until Period 2
Stones Diehard FansWait Until Period 2
12.5% chance of not getting ticketPrior probability: 50%( 60 DH), 50%(20 DH)Posterior probability = (0.5 * 60) / [(0.5 * 60) + (0.5 * 20)] = 0.75If 60 diehards, probability of not getting ticket is [1 – (100/120)] Probability of not getting ticket = 0.75 * [1 –(100/120)] = 12.5%
Expected surplus from waiting until period 2 to purchase individually: 87.5% * [200 (reservation price) - $100 (ticket price) ] = $87.50
12.5% chance of not getting ticketPrior probability: 50%( 60 DH), 50%(20 DH)Posterior probability = (0.5 * 60) / [(0.5 * 60) + (0.5 * 20)] = 0.75If 60 diehards, probability of not getting ticket is [1 – (100/120)] Probability of not getting ticket = 0.75 * [1 –(100/120)] = 12.5%
Expected surplus from waiting until period 2 to purchase individually: 87.5% * [200 (reservation price) - $100 (ticket price) ] = $87.50
Stones Diehard Fans Purchase Bundle
Stones Diehard Fans Purchase BundleSurplus from purchasing bundle: $200 (RPstones) + $90 (RPbruce) - [202.50 - ε] = $87.50 + ε
Purchasing the bundle is their Dominant Strategy
Surplus from purchasing bundle: $200 (RPstones) + $90 (RPbruce) - [202.50 - ε] = $87.50 + ε
Purchasing the bundle is their Dominant Strategy
Product Bundling Strategy: Theory & Evidence 10
Theory ExampleDiehard Stones & Bruce Fans’ Decision
Bruce Diehard FansWait Until Period 2
Bruce Diehard FansWait Until Period 2
Bruce Diehard FansPurchase Bundle
Bruce Diehard FansPurchase Bundle
Diehard Bruce Fans: Purchasing the bundle is their Best Response
Diehard Stones fans bundle purchases (expected value = 40) extract from Bruce concert capacity. Thus, 60 tickets left
. 33% chance of not getting ticket (90 people vying for 60 tickets)
Expected surplus from waiting until period 2 to purchase individually: 66% * [200 (reservation price) - $100 (ticket price) ] = $66.66
Diehard Stones fans bundle purchases (expected value = 40) extract from Bruce concert capacity. Thus, 60 tickets left
. 33% chance of not getting ticket (90 people vying for 60 tickets)
Expected surplus from waiting until period 2 to purchase individually: 66% * [200 (reservation price) - $100 (ticket price) ] = $66.66
Surplus from purchasing bundle: $200 (RPbruce) + $90 (RPstones) - [202.50 - ε] = $87.50 + ε
Purchasing the bundle is their Best Response
Surplus from purchasing bundle: $200 (RPbruce) + $90 (RPstones) - [202.50 - ε] = $87.50 + ε
Purchasing the bundle is their Best Response
Product Bundling Strategy: Theory & Evidence 11
Theory ExampleIMB: A Profitable Strategy
Profits from IMB Dominate Other
Selling Strategies
Single product sales profits: $19,000 Pure bundling profits: $17,400IMB: $20,150 - 60ε
More ProfitableSeller Equilibriums
Rational expectations over time Risk aversion assumptions
Bundle price greater than individual good pricesBundle aimed at higher value consumers, individual sales towards lower value consumersProfit maximizing strategy characterized by excess demandCreates uncertainty in a market not previously
characterized by uncertainty
ExampleSummary
Product Bundling Strategy: Theory & Evidence 12
IMB: Subgame Perfect Nash EquilibriumKey Theorems and Assumptions
Proposition 1 Proposition 1
If the bundle price (Pb) in period 1 = B + C + min (CP1, CP2) - ε and in period 2, good are sold individually at B, all diehards purchase the bundle and normal customers wait until period 2 to purchase individually
In our example: Pb (202.50 - ε) = B (100) + C (90) + 12.50[min (CP1, CP2)] - ε
If the bundle price (Pb) in period 1 = B + C + min (CP1, CP2) - ε and in period 2, good are sold individually at B, all diehards purchase the bundle and normal customers wait until period 2 to purchase individually
In our example: Pb (202.50 - ε) = B (100) + C (90) + 12.50[min (CP1, CP2)] - ε
Proposition 2 (Central Theorem) Proposition 2 (Central Theorem)
If for all diehard consumers, the expected probability of not getting the good in period 2 is greater than the ratio of (B + ε - C)/(A-B), a subgame Nash equilibrium will involve IMB
Proposition Intuition: Want to set a bundle price that is greater than the sum of the second period individual prices in a manner that it is in the best interests for all Diehard customers to purchase the bundle
From Proposition 1: B + C + CP - ε > 2B. This equals B + C + (probability of not getting the good) * (A - B) > 2B. Proposition 2 is derived from rearranging
If for all diehard consumers, the expected probability of not getting the good in period 2 is greater than the ratio of (B + ε - C)/(A-B), a subgame Nash equilibrium will involve IMB
Proposition Intuition: Want to set a bundle price that is greater than the sum of the second period individual prices in a manner that it is in the best interests for all Diehard customers to purchase the bundle
From Proposition 1: B + C + CP - ε > 2B. This equals B + C + (probability of not getting the good) * (A - B) > 2B. Proposition 2 is derived from rearranging
Parameter Restrictions Parameter Restrictions
Maximum profit from individual sales: 2BK (in our example $20,000)
Maximum profit from pure bundling: 2BK (in our example, $20,000)
In a intertemporal mixed bundling strategy, all remaining goods are sold in period 2 at B.
Maximum profit from individual sales: 2BK (in our example $20,000)
Maximum profit from pure bundling: 2BK (in our example, $20,000)
In a intertemporal mixed bundling strategy, all remaining goods are sold in period 2 at B.
Product Bundling Strategy: Theory & Evidence 13
Agenda
Theoretical Work
Empirical Work
Product Bundling Strategy: Theory & Evidence 14
Empirical AnalysisTestable Implications & Data
IMB is used in approximately 30% of U.S. amphitheaters.
When IMB is used, the number of tickets sold will be higher
Increased number of tickets sold that is attributable to IMB
is positively correlated with the popularity of the other bundle concerts
Cases when the bundle price is greater than the sum of the individual ticket prices
Personally collected data
Summer 1991 data. Focused on concert markets in MSAs with population greater than 1 million and concert facilities with capacity greater than 10,000
Data Sources: Pollstar, newspaper reports, proprietary data from management and agents, Radio & Records, and Billboard
The Data The Data Model: Testable Implications Model: Testable Implications
Product Bundling Strategy: Theory & Evidence 15
The Jimmy Buffett Concert Experience
Product Bundling Strategy: Theory & Evidence 16
Empirical WorkKey Variables
Variable Variable Description ATTENDANCE Dependent variable – specific concert’s attendance
LAST ATTENDANCE
Average regional attendance on the performer’s last concert tour. Excludes concerts that were sold using IMB and dependent variable concert city. This variable is divided by 10.
LAST PRICE Average regional price for the performer’s last concert tour adjusted to 1991 dollars.
CORE LAST ATTENDANCE * LAST PRICE. A proxy for a performers core audience.
UNEMPLOYM-ENT
Unemployment rate in the concert city multiplied by 10. Indicator of economic healthiness.
RADIO # of weeks artist has been regularly played on the top local radio station in their primary format from January 1991 to concert date
DEMO Percentage of radio listeners that listen to performer’s radio format in concert city multiplied by 10
RADIO REACH
(RADIO * RADIO) * DEMO
PRICE Normalized pavilion ticket price for a specific rock concert
Product Bundling Strategy: Theory & Evidence 17
Empirical WorkKey Variables
Variable Variable Description POPULATION City population in thousands
NO ALBUM Indicator variable denoting if the artists did not have a new album on the sales chart since January 1991
BUNDLING Indicator variable denoting if IMB was used to sell concert tickets
BUNDLED CONCERTS
(Last area attendance of the other concerts in the bundle)/(pavilion capacity). A gauge of the popularity of the other concerts in the bundle and uncertainty
LOW INDEX Indicator variable designating that BUNDLED CONCERTS variable is in the bottom 50% of the BUNDLED CONCERTS variable range
HIGH INDEX Indicator variable designating that BUNDLED CONCERTS variable is in the upper 50% of the BUNDLED CONCERTS variable range
Product Bundling Strategy: Theory & Evidence 18
Parameter EstimatesConcert Demand Focusing on IMB Indicator Variable
Dependent Variable: ATTENDANCE
Parameter Estimate Standard Errors
INTERCEPT 8104.08 (2272.16) ***
BUNDLING 1308.75 (701.47) **
CORE 2.45 (0.35)***
UNEMPLOYMENT -162.14 (112.53)
RADIO REACH 24.44 (5.32)***
PRICE -131.75 (78.34)*
NO ALBUM 2251.70 (806.25)***
POPULATION 0.76 (0.20) ***--------------------------------------------------------------------------------------------------Observations: 142, R2: 0.4265, , Adj R2: 0 .3968, F: 14.342***1% level. **5% level. *10% level.
Product Bundling Strategy: Theory & Evidence 19
Empirical WorkKey Variables
BUNDLED CONCERTS
BUNDLED CONCERTS is a proxy of uncertainty
Example Bundle = Concerts A,B,C & D
BUNDLED CONCERTSA =
(LAB + LAC + LAD)Pavilion Capacity
Intuition: summing the last attendance of all of the other acts in the bundle provides an indicator of the popularity of the other acts in the bundle
Intuition: given the popularity of the bundle, the higher the pavilion capacity, the lower the uncertainty
Product Bundling Strategy: Theory & Evidence 20
Empirical WorkKey Variables & Intuition
HIGH INDEXIndicator variable designating that observation is in
the top 50% of BUNDLED CONCERTS variable. Very attractive concert bundles
LOW INDEXIndicator variable designating that observation is in
the bottom 50% of BUNDLED CONCERTS variable. Less attractive concert bundles
Individual concert demand (i.e., The Who in Boston) is a function of several demand variables including if the show is being sold as part of a highly desirable or less desirable concert bundle
.The Whoboston = F(Xi, HIGH INDEX, LOW INDEX)
EmpiricalIntuition
Product Bundling Strategy: Theory & Evidence 21
Parameter EstimatesConcert Demand Focusing on Low & High Bundle Popularity Variables
Dependent Variable: ATTENDANCE
Parameter Estimate Standard Errors
INTERCEPT 7921.64 (2241.74)***
LOW INDEX 760.10 (751.43)
HIGH INDEX 3185.51 (1302.31)**
CORE 2.39 (0.32)***
UNEMPLOYMENT -162.59 (122.56)
RADIO REACH 25.27 (5.04)***
PRICE -136.61 (76.31)*
NO ALBUM 2414.93 (798.02)***
POPULATION 0.87 (0.18)***--------------------------------------------------------------------------------------------------Observations: 142, R2: 0.4329, Adj R2: 0.4060, F: 12.91***1% level. **5% level. *10% level.
Product Bundling Strategy: Theory & Evidence 22
Price: An Endogenous Variable?Assumptions and 2SLS Analysis
Recursive Systems (Wold 1954)Model refers to a sequence of years, months, or other unitsModel has only one casual relationship for each endogenous variable
Concert MarketTicket prices set 6-8 months in advance. Between time prices set and concert date, two key variables are often realized: (1) New CD sales and (2) Radio airplayOnce ticket prices are set, they are never adjusted
Two Stage Least Squares ModelFirst Stage - Instrument for potentially endogenous variable, price, PIVSecond Stage - Use instrumented variable (PIV) in model2SLS presented on following slide. Coefficient estimates are robust and qualitative results remain the same
Recursive Systems Recursive Systems Two Stage Least Squares Analysis Two Stage Least
Squares Analysis
Product Bundling Strategy: Theory & Evidence 23
Two Stage Least Squares Parameter Estimates Concert Demand Focusing on Bundle Popularity Variables
Dependent Variable: ATTENDANCE
Parameter Estimate Standard Errors
INTERCEPT 6315.67 (9,214.04)
LOW INDEX 721.31 (892.51)
HIGH INDEX 3331.04 (1241.41)***
CORE 2.51 (0.54)***
UNEMPLOYMENT -151.21 (121.26)
RADIO REACH 24.51 (8.21)***
PRICE -132.41 (332.21)
NO ALBUM 2305.85 (885.02)**
POPULATION 0.78 (0.40)*--------------------------------------------------------------------------------------------------Observations: 142, R2: 0.4387, Adj R2: 0.3980, F: 12.71***1% level. **5% level. *10% level.
Product Bundling Strategy: Theory & Evidence 24
Parameter Estimates forIV Analysis of Price
Parameter Estimate Standard Errors
INTERCEPT 19.87 (1.74)***
NO ANCILLARY 1.50 (0.75)**
ARENA -3.66 (1.36)***
COMP -1.17 (0.98)
LOW INDEX -1.71 (0.88)**
HIGH INDEX -0.57 (1.41)
CORE 0.00066 (0.0004)***
UNEMPLOYMENT -0.076 (0.126)
RADIO REACH 0.018 (0.006)***
NO ALBUM -0.45 (0.86)
POPULATION 0.00098 (0.0002)***------------------------------------------------------------------------------------------------------------------Observations: 142, R2: 0.4297, Adj R2: 0.3960, F: 12.62***1% level. **5% level. *10% level.
Dependent Variable: Price
Product Bundling Strategy: Theory & Evidence 25
Hausman Test Parameter Estimates
Parameter Estimate Standard Errors
INTERCEPT 8314.14 (5723.11)
PREDICTED PRICE -22.80 (276.25)
LOW INDEX 709.28 (799.28)
HIGH INDEX 3184.25 (1313.51)**
CORE 2.47 (0.40)***
UNEMPLOYMENT -143.28 (113.95)
RADIO REACH 25.23 (6.54)***
PRICE -135.77 (80.21)*
NO ALBUM 2377.51 (837.25)***
POPULATION 0.87 (0.33)***--------------------------------------------------------------------------------------------------Observations: 142, R2: 0.4297, Adj R2: 0.3960, F: 12.62***1% level. **5% level. *10% level.
Dependent Variable: ATTENDANCE