music for a song

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An Empirical Look at Uniform Song Pricing and itsAlternatives

Music for a Song



Introductiony Th e paper explores th e profit and welfare implications of

various alternatives, including song-specific pricing, variousforms of bundling, two-part tariffs, nonlinear pricing, andth ird-degree price discrimination

y Th e data is collected from survey-based on nearly 500students· valuations of 50 popular songs in early January,2008

y

Found th

at various alternatives; pure bundling and two-parttariffs, both can raise producer and consumer surplus



y Th e normative th eories question about th e wisdom of uniformpricing wh eth er th at th e Alternatives to uniform pricing such assong-specific pricing, various forms of bundling, two-part tariffs,and nonlinear pricing, can determineh ow much amount of additional profit or consumer surplus.

y Uniform Pricing : For example,Apple iTunes Music storesells all songs for 0.99$ each

y Song- Specific or variable pricing : For example,Amazonlaunch es a music downloading service featuring with differentprices for each song

y If th e seller could observe buyers· reservation prices for songs,th ey could increase more revenue



Uniform PricingiTunes Music Store

Selling at$0.99/song



Song- Specific or variable pricing

Selling differentprices for each

song



y Th e welfare economics of imperfect competition dependscrucially on th e extent to wh ich th e social benefit of a product-th e area under th e demand curve- can be captured as revenue forth e seller

y Th e producer surplus under single-price monopoly can fall sh ortof fixed and variable costs even wh en th e joint surplus wouldexceed costs. Hence, th e market can fail to provide goods with benefits in excess of costs

y Wh eth er sellers can capture surplus as revenue depends on th eeffectiveness of price discrimination



The or e tical S e tupy V is - Each consumer i h as a reservation price for each songs.

- i= determine wh eth er th e individual purch ase 1 or 0 units of each song (assume resale impossible).

y

P - Prices for songs/ group of songs for sellers to ch oose tomaximizeh is profit.- eg. Uniform single-price (only one price for each bundle of songs)

Pk=5p : bundle k contains 5 songs, and p is th e single price per product.



The or e tical S e tupy V ik - individuali·s valuation of song bundlek .y V ik -Pk : Consumer maximizeh is ch oice of k, or wh ich

product (or bundle of songs) to consume.



R e lat e d Lit e ratur e

D efinitiony Song Specific Pricing (Component Pricing)[CP]-

different price for each song.y Pure bundling [PB]- occurs wh en a consumer can

only purch ase th e entire bundle or noth ing.y Mixed bundling [MB] - occurs wh en consumers are

offered a ch oice between th e purch asing th e entire bundle or one of th e separate parts of th e bundle.



R e lat e d Lit e ratur ey Two-product example sh owing th at bundling could produce

more revenue pricing th e products separately wh enconsumers· valuations of th e products are negatively

correlated (Stigler).y MB produced more profit th an PB or product specificpricing (Adams and Yellen)

y PB can be more profitable th an product-specific pricing even

wh en consumer·s valuations are positively correlated(Sch emalensee).



R e lat e d Lit e ratur ey MB always beat PB (McAfee, McMillan, and Wh inston).y If valuation of large bundle is more predictable th an of th e

individual products, PB can extract th e entire surplus (Bakos

and Brynjolffson).y Case study observe on purch ases of individual play tickets as

well as bundles: CP raises revenue 1.4 %, bundle sizepricing raises revenut 2.3%, MB raises revenue 4%, uniformpricing raises revenue of 5%.



D atay Sample

y 465 individuals (Undergraduates at Wh arton)y ExplanatoryVariable (ControlVariable)

y 50 popular songs (Th e top 50 songs at iTune 11th Jan 2008)y

Age (Mostly 18-20)y Gendery Racey Self-reported level of interest in music (not interested, somewh at interested,

very interested)y Th e size of th e th eir music library

y D ependentVariabley Th e willingness to pay (Th e maximum amount)



D atay N early all of th e valuations are ´reasonableµ

y N ot concern with th e actual price ($0.99 for all songs atiTunes)

y 98% of valuations fall on [0,10]y 86% of valuations fall on [0,2]



D atay Th e clustering of valuations and th e focal numbers

y N otably, zero, multiples of $0.25, $0.99 ,and $1.99y ´Sawtooth µ spikes in th e relationsh ip between revenue and price



D atay V iew reported valuations as truth plus some error

y Better approximated as a smooth ed distribution (resulting fromreported valuations plus a zero-mean random error uniform between -$0.125 and $0.125)

y Code negative smooth ed valuations as zero



C he ck on t he datay Wh eth er surveys can elicit meaningful valuation information

y In earlier worky Th e willingness to pay tend to elicit much lower valuations (Rob and

Waldfogel, 2006)y Response to th e argument

y Th e profit-maximizing prices implied by buy-based valuations (Rob andWaldfogel, 2006)



C he ck on t he datay Wh eth er th e songs for wh ich respondents frequently report

h igh valuations are also th e songs with h igh er salesy Cannot observe directly over all sales

y ´Billboard HotD igitalµ ch art, along with its peak single ch art position,provide indirect measures of cumulative sales

y Modify th e concept to ´a willingness to buy are also th e songsselling more digital copiesµ



C he ck on t he datay A regression of th e sh are of respondents reporting valuations of at

least $0.99 on th ese two sales proxies yields:

y chart_weeksindicates th e number of weeks of th e songh ad been on th e ch art as of March 8, 2008

y chart_peakindicates th e song·s peak ch art positiony Standard errors are in parenth esesy Th e R-squared is 0.34

y Th e results support th at data are reasonabley High er sales penetration

y For th e songs with longer period in th e ch art.y For th e songs with lower ch art rank.



R e sults Using D iff e re nt Pricing Sc heme sy 1.The Single-Price Monopoly Baseline

y From th e figure given th at MC=0, Surplus is equal to th e areaunder th e demand curve; $27,785 or about $60 per person.

y Wh en calculate th e profit-maximizing price² and th e breakdown of th e available surplus³wit h a smooth ed data;

y R evenue = n * V n ; n = number of songs, V n = price



y Th e h igh est local maxima in revenue function occurs at a price of $1.87 with 4,351 songs sold, generating revenue of $8,158 (29.4% of surplus), consumer surplus is $11,607 (41.8% of surplus),D WL is

$8,020 (28.9% of surplus)y For uniform pricing, $0.99 price, generating revenue of $7,364

(26.5% of surplus), consumer surplus $16,317 (58.7% of surplus),D WL is $4,105 ( 14.8% of surplus)



y 2 . Song- Specific ́ Componentµ Pricingy From Smooth ed data, by calculating maximum revenue, for each

song as we calculated maximum revenue overall abovey From th e model, th e range is close to $2y According to th e calculation, song-specific pricing can sell 5,462

songs delivers 30.5 % of surplus as revenue, 44.4% as consumer

surplus, and 25.1% asD WL.



y 3 . Pure Bundling (PB)y D efinition: is anoth er simple alternative to uniform pricing; th e

entire group of songs is offered, as a group, for a single price.y To calculate th e optimal full (50 song) bundle price, we sum th e

song valuation across songs with in each individual to arrive at th atindividual's valuation of th e entire bundle.

y Th en calculate th e revenue-maximizing bundle price under single-price monopoly

y Th e result: th e price is $36.08, 247 individuals buy th e bundle,resulting in 12,350 songs sold.



y As a result, revenue is $8,931 Consumer surplus is $14,358D WL is $4,497



y 5. Nonlinear Bundle Pricingy Two part tariffs are special case of more general nonlinear prices

th at vary with th e number of units purch asedy ´Bundle size Pricingµy Th e nonlinear tariff can be calculated as a sequence of optimal

prices. For th e 1st,2nd, and nth units in th is case n is up to 50

y Problems: 1. Th e optimal prices do not decline monotonically2.Th e number of buyers of successive numbers of unitsdoes not decline monotonicallyEx.Th e number of persons buying th e th ird unit

exceeds th e numbers of th e first unit, so th is simple meth od cannotcalculate th e nonlinear tariff



y 6 . Comparing Mixed Bundling with Alternativesy Consider a family of two parameter pricing sch emes wh ere pA is th e

uniform á la carte price and pB is a bundle pricey Question 1: Wh at unconstrained combination of {pA,pB} maximizes

revenue



y Question 2: Wh at pB maximizes revenue given th at pA isconstrained to its current value of $0.99



y 7 .Third Degree Price Discriminationy Th e th eory suggests th at sch emes th at can divide consumers

according to th eir valuations will be able extract more of th eirvaluations as producer surplus

y Th e exogenous characteristics such as gender, eth nicity,resident alien, and age are categorized in normal th ird degree price

discriminationy For E xtreme Case , it uses th e person-specific pricing;

pricing schemes³price discriminating by type of person inorder to find th e maximum revenue by calculating th e person-specific profit-maximizing price

y We would create person-specific demand curve ordering th eirvaluation fromh igh est to lowest



Par e to Im proving Pricing Sc heme sy It·s clear th at various different sch emes can produce more

revenue th an current uniform pricing, but th e decision to priceuniformly at $0.99 may reflect a conscious strategy to deliverh igh consumer surplus from music

y According to ParetoImproving Pricing Sch emes, one can getmore revenue from alterative song pricing sch emes doesn·tdemonstrate a Superior alternative to uniform pricing at $0.99

y However, Superiority requires accomplish ing th e objective

ach ieved by th e uniform $0.99 pricing, th en delivering additional benefit



y To examine all pricing sch emes th at deliver at least th e level of consumer surplus delivered by current uniform pricing

y Th e auth or examined by using two-part tariffs, th e (T,p) is th ecombinations delivering at least th e level of consumer surplusdelivered by uniform pricing

y As a result, alternative pricing sch emes could raise revenue wh iledelivering current levels of consumer surplus



Para me tric D em andy N

onparametric is not efficient because of the irregularity of t

heresulting revenue function and surfaces. So an alternative th at

allows for smooth er revenue function is to fix th e valuation datato a parametric family wh ich is more efficient

y The differences between t

he optimal prices identified using t

heparametric and nonparametric approach ed are substantial, and

th ese differences raises a question of wh ich approach is morereliable.

y Th

e benefits of th

e parametric approach

are smooth

ness andparsimony



Nonparametric Parametric

-N on-smooth data-Reflect reality

-T

otal welfare increases sligh

tly

-Smooth ed data-D oesn·t reflect reality

-T

otal welfare increases ingreater amount



C onclusiony D ata on individual·s valuations of 50 popular songs allows us to

calculate th e revenue and th e overall division of surplus, usingvarious pricing sch emes.Alternative Schemes pricing R esults

uniform pricing $0.99 D eliver about 30% of surplus as arevenue

Pure Bundling and Two-part tariffs Both producer and consumer surplusincreases , Relatively to profit-maximizing uniformpricing --increase by nearly 10% , relative to current$0.99 uniform pricing ²increase over one-fifth .

Normal third degree price discrimination Revenue increases byonly a few percent

Individual specific pricing (extreme form of th ird degree discrimination

Revenue increaseabout 7 5%



Th erefore: y Based on th ese data, it migh t be possibly inefficient if th e

sellersh avesubstantial fixed cost .

music for a song

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