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SAMPLINGINFORMATIONGOODS:
HOWMUCHSHOULDBEFREE?
FlorianStahl,DanielHalbheer,OdedKoenigsberg,andDonaldR.Lehmann
February2010
Abstract
Thispaperexaminesoptimalsamplingandpricingofinformationgoodsforfirmsthatgenerate
revenuesfrombothsalesandadvertising. Wedevelopamodelwherethedemandforpaidinfor-
mationgoodsisinfluencedbythesampleportionthatthefirmoffersforfree.Takingintoaccount
the consumers’initialvaluationandexperiencedqualityofthefreeversion, wecharacterizethe
firm’soptimalsamplingandpricingdecisions. Wefindthattheeffectofadvertisingrevenueson
optimalsampleportionandpricedependsonexpectedandexperiencedquality. Moreover,afirm
shouldneverofferafreesamplewhentheexpectedqualityexceedstheexperiencedquality. Our
modelassumptionsandresultsaregenerallyconsistentwithanempiricalanalysisoffirmdataon
themarketfornews. Wecomparethemodels’implicationswithmanagerialdecisionsandshow
thatmanagershaveatendencytooffertoosmallsampleswhenconsumersusethemextensivelyin
updatingtheirexpectationsaboutproductquality.
Keywords
:
InformationGoods,Sampling,Pricing,Advertising,QualityExpectations,QualityEx-
perience,QualityUpdating
WewouldliketothanktoAsimAnsari,JacobGoldenberg,AviGoldfarb,OdedNetzerandseminarparticipantsatHEC
Paris,TilburgUniversityandtheUniversityofZurichforhelpfulcommentsandsuggestions.
FlorianStahl(correspondingauthor)andDanielHalbheer: UniversityofZurich,InstituteforStrategyandBusiness
Economics,Plattenstrasse14,CH-8032Zurich,Switzerland;email:stahl@isu.uzh.chandhalbheer@isu.uzh.ch,respectively;
OdedKoenigsbergandDonaldR.Lehmann,ColumbiaBusinessSchool,517UrisHall,3022Broadway,NewYork,NY10027,
USA;email:ok2018@columbia.eduanddrl2@columbia.edu,respectively.
1
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1 Introduction
OneofthemajorimpactsoftheInternethasbeenthevastincreaseintheamountofinformationavail-
ableforfree. Theprovisionoffreeinformation,ormorespecificallyhowmuchinformationtogive
awayforfreeasaviablebusinessmodel,hasledtoadebateamongobserversaswellasmanagers.
Forexample,overthepastfewyearspublicationssuchastheWallStreet
J
ournalhavegonefromhav-
ingprimarilypaidversionstoprovidingasubstantialamountforfreeandrecentlybacktomoreof
a“payforinformation”model. Afirmproducinginformationgoodshastwoprinciplesourcesof
revenues:advertisingandsales. Insomecases,thefirmgeneratesrevenuessolelyfromsellinginfor-
mationgoods,whileinothercasesfirmsoffertheircontentforfreeandreceiveadvertisingrevenues.
Quiteoften,however,afreecontentsampleandapaid(complete)versionisoffered. Forinstance,
theWallStreet
J
ournaloffersnewsarticlesforfreecombinedwithadvertisingonitswebsitewsj.com.
Backgroundinformation,dossiersandarchivedarticles,bycontrast,areinmostcasessoldforafee.
Thepurposeofthispaperistoexploreofexactlyhowmuchcontentshouldbeofferedforfreeandat
whatpricethepaidversionshouldbesold.
Existingliteratureaddressespropertiesofinformationgoodsthatmakepricingdecisioncomplex.
Partofthecomplexityresultsfromthefactthattheyareexperiencegoods(Nelson1970;Darbyand
Karni1973)andconsumerslearnabout thequalitybyusingthegoodsthemselves(Shapiro1983).
Thecharacteristicsofexperiencegoodsalsoleadtotheinformationparadox(Akerlof1970): While
consumershavetoexperienceaninformationgoodinordertovalueit,aftertheyhaveexperienced
it,theyhavelessornoincentivetopurchasetheproduct. Takingthisspecificcharacteristicofinfor-
mationgoodsintoaccount,theliteraturehassuggestedmanyformsofdifferentialpricing. Quality
discriminationorversioning,offeringaproductlinewithverticallydifferentiatedqualitylevels,has
beenanalyzedanddiscussedbyseveralauthors(Varian2000a;BhargavaandChoudhary2001,2008)
andisrecognizedasacriticalbusinessstrategyforinformationgoods(ShapiroandVarian1998;Wei
etal.2007). Amongothers,Varian(2000a)analyzesthestrategyofverticaldifferentiationandshows
howasuppliercanmaximizeprofitsbyofferingalow-andahigh-qualityversionofthesamegoodat
differentprices.
Whilepricingstrategiesarewellunderstood,theliteratureoninformationgoodsonsamplingis
sparse. AnotableexceptionisBoom(2009),whoshowsviaaqualitysignallingmodelthatthefirm
shouldofferafreesampleifthenumberofinformedconsumersissmall.Althoughtheliteraturehas
suggestedseveralformsof“sampling”suchaspreviewsandbrowsing(Varian2000b),thequestionof
2
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Table1:Thekeydimensionsofinformationgoods.
SingleUse
MultipleUse
One Time /
SingleEdition
Event Programming,
MysteryMovies
Reference Books,
Music
Renewed
Newspapers, TV
DramaSeries
“How To o Do It”
Magazines
howmuchinformationtoofferasafreesamplehasbeenignored.
Incontrast,samplingisextensivelydiscussedinthemarketingliteratureonconsumeranddurable
goods. Freesamplesareconsideredoneofthemost t effectivewaystointroduceconsumerstotry
anewproduct(LawrenceandKamins1988; MarksandKamins1988; Jainetal.1995)andreduce
theiruncertaintyaboutitsquality(McGuinessetal.1992). Researchhasexaminedwhichsamplesize
(Heimanetal.2001;BawaandShoemaker2004)andtrialrates(Meyer1982;McGuinessetal.1992)
optimizedemandforaproduct.Jainetal.(1995)showthatahighsamplinglevelisonlyappropriate
ifadurableproducthasahighcoefficientofimitationorthefirmhasahighdiscountrateoralarge
grossmargin. Ontheotherhand,heavysamplingmakeslittlesenseifadurableproducthasahigh
coefficientofinnovation.Heimanetal.(2001)showthatalthoughsamplingeffortshoulddeclineover
aproduct’slifecycle,itmaycontinueformatureproducts. Forbothconsumeranddurablegoods,
productsamplingisexpensiveduetovariablecosts. Thecostcharacteristicsofinformationgoods
(especiallydigitalinformationgoods),highfixedcostsandlowvariablecosts,arequitedifferent.
Thispapercontributestothesetwostrandsofliteratureandaddressestworelatedmarketingques-
tions: First,whatportionofainformationgoodshouldbeofferedasafreesample? ? Second,how
muchshouldafirmchargeforthepaid(complete)version? Tosetthestage,weclassifyinformation
goodsalongtwokeydimensions. Thesegoodscanbeeither“perishable”or“durable”,depending
onwhethertheirvaluedeclinesonceitisconsumedorwhethertheirvalueholdsupovertime. In-
formationgoodscanalsobe“onetime”events(e.g.,aparticularbookormovie)orrenewed(e.g.,
newspapers,magazines,orTVseries).ThesefourcombinationsareillustratedinTable1.Thefocusof
thispaperisonsingleuse,singleeditioninformationgoods.
Wemodelthefirm’schoiceofthepriceandsampleportionofaninformationgood.Aninteresting
featureofthemodelisthatthefirmgeneratesrevenuesfromtwosources: thepricechargedforthe
paidversionandadvertisingrevenuesgainedfromthefreeversion.Westartbymodelingconsumers’
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utilityandderivethedemandforthepaidproductandforthefreesample.Consumerseithersample
aportionoftheproductforfreeorbuythepaidversion. Consumerswhosamplethefreeversion
updatetheirqualityexpectation. Iftheupdatedexpectationarehighenough,theymightpurchase
theproductwhereasabsentthesampletheywouldnothavebought. Wecharacterizeoptimalprice
andsampleportion,andalsoexaminetwoextensionsofthemodelwhichallowforamoregeneral
updatingruleandforthefirmtoreceiveadvertisingrevenuesfromthepaidversionaswell.
Severalkeyinsightsemergefromthemodel. Forexample,whenadvertisingrevenuespercon-
sumerincrease,theeffectonthesampleportiondependsonconsumers’experiencedquality:Ifcon-
sumers’experiencedqualitynoticeablyexceedsexpectedquality,thefirmshouldofferalargersam-
ple.Incontrast,ifconsumers’experiencedqualityisclosetoexpectedquality,thefirmshouldoffera
smallersampleportion. Further,whenconsumershavehigherqualityexpectations,thefirmshould
offeralargersampleportionwhenexpectedqualityandexperiencedqualityaresimilarandasmaller
sampleportionifexperiencedqualityexceedexpectedquality.Importantly,afirmshouldneveroffer
afreesamplewhentheexpectedqualityexceedstheexperiencedquality.Weprovidefurtherevidence
thatsupportssomeofourassumptionsandresults.Usingadatasetofnewswebsites,wefindthata
higherdemandforthefreesamplegoesalongwithahigherdemandforthepaidversion.Importantly,
whenwecomparethemodelwithmanagers’decisions,wefindthatdecisionmakershaveatendency
toprovidetoosmallsampleportionswhenconsumershighlyweightexperiencedquality.
Thepaperproceedsasfollows.Section2introducesthemodelanddetailstheconsumers’quality
updatinguponsampleexperience. Section3derivesconsumers’demandforthefreeandthepaid
version, whichconsistsofinitialandsampling-induceddemand. . Section4studiesfirmbehavior,
characterizestheoptimalsamplingandpricingpolicy,andderivescomparativesstaticsproperties.
Thesectionconcludeswithadiscussionofoptimalstrategies.Section5extendsthemodelbyallowing
formoregeneralupdatingofconsumers’qualityexperienceandincludingadvertisingrevenuesfrom
thepaidversion.Section6providesrelevantempiricalevidencefromnewswebsitesandamanagerial
studyandSection7discussesconclusionsanddirectionsforfutureresearch.
2 Model
Wedevelopananalyticalmodelforasingleprofit-maximizingfirmproducingasingleinformation
good. Toproducethefirstcopyoftheinformationgoodthefirmincursfixedcosts
F ≥ 0
. The
4
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marginal costof creating a copy of the information goodor of providing access to itis negligible and
assumedbeing zero (Varian 2000b). Furthermore,weassume thatthefirmcanmodifyandsamplethe
informationgood atzero cost.
The firm offers simultaneously a full version of an information good at price
p
and a free sample
of the content
α
. The sample may consist, for example, of anabstract (summary) or a portion of the
information good (teaser). We normalize the content of the information good to unity and define
α∈ (0,1)
as the portionof thecontent containedinthe free sample. In its simplest form,
α
would be
thepercent of thetotalinformation. However,inthecaseofa “summary”,a small samplecanprovide
more contentthanits proportionor,inthecase ofa “teaser”,less than thatproportion.
We considera market with a mass of
N
consumers and normalize
N
to unity withoutloss of gen-
erality. Consumers have an initial valuation (capturing quality expectations)
v
for the information
good that varies across consumers. Following Jain andKannan (2001),weassumethat
v
is uniformly
distributed on the interval
[0,¯v]
.
1
If a firm offers only a paid version, consumers will purchase the
information good if their basic valuation exceeds the price (
v> p
). However, whena free sample is
offered,this allows consumerstoevaluateproductqualitybeforethey decidewhethertopurchase the
paid version. Thus consumers have two options, either to purchase the product at price
p
or to take
the freesampleportion
α
.Consumers’ utility
U
I
from thesetwo optionsis givenby
U
I
=
v− p
iftheconsumerbuysthepaid versionat price
p
αv
iftheconsumertakes thefree sample portion
α
.
Thus, a consumer will purchase the paid version if
v− p > αv
and take the free version otherwise.
This condition canbe rewrittenas
v(1 − α) > p
,which means that the value offered beyond the free
sample has to exceed the price for the full version. Importantly, we assume here that consumers are
abletoobserve the size ofsampleofferedforfreebeforethey eventuallylearnaboutsample quality.
Consumers who chose to take the free sample update their initial valuations. We follow Kopalle
andLehmann(2006) andassume the updatingruleis givenas
v
=αq +(1 −α)v
,
(1)
1
In thespiritofMussaandRosen(1978),wecanwrite
v=θ¯v
,where
θ∼U(0,1)
isthewillingnesstopayforqualityand
¯v
isareal-valuedindexdescribingintrinsic productquality.
5
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where
v
is the consumer’s updated valuation given experienced quality
q
,which we assume to be
uniformly distributed on the interval
[0,¯q]
. We assume that
v
and
q
are independent random vari-
ables,i.e.that prior expectationand experiencedquality are uncorrelated.
2
This specification features
twointuitive properties: First,consumers’putsmore weight on experiencedquality
q
and less onini-
tial valuation
v
the larger the sample portion is. Second, consumers’ updated quality expectation
v
explicitly dependson
q
withtheextent ofthe impact determinedbythesample portion
α
.
Afterupdating,consumershave twooptions:eitherpurchasetheproductgivensampleexperience
at price
p
or staywiththefree sample. Consumers’utility
U
S
from thesetwo optionsisgivenby
U
S
=
v
−p
if theconsumerbuys thepaidversionatprice
p
αv
if theconsumerstayswiththefree sample
α
.
Thevariationininitial valuationand quality experienceare exogenoustothefirm. We assumethat
the firm has private information about the distributions of
¯v
and
¯q
. For instance, the firm can learn
about suchinformationemploying standard marketresearchtechniques suchas surveys. Weassume
further that the firm generates revenues from two sources. First, it receives advertising revenues
a
f
per consumer who take (e.g. download) the free sample.
3
Second, it receives revenues from selling
the paid version. We assume that
a
f
is exogenously given and constant. This price-taking behavior
is justified in markets in which theCPM (costperthousand customers)is theoutcome ofcompetitive
interaction.
4
Insuchan environment,the firm makes two decisions: the price
p
tocharge forthepaid
versionand theportion
α
of the goodtoprovide as a free sample.
3 Consumer Demand
The sectionderives the demandforthepaid versionandthedemandforthe free sampleasa function
oftheprice
p
andthesampleportion
α
.Demandforthepaidversionstemsfromtwogroupsofbuyers.
The firstgroup consists ofthoseconsumerswho buytheproductwithout taking the free sample, and
2
Alternatively,onecouldargueeitherthatthosewithhighexpectationstendtoconfirmthis (positivecorrelation)orthat
thosewiththehighestexpectationsarethemost criticaland hencetend tobedisappointed(negativecorrelation). Similarly
thosewithlowexpectations maybeaccurateinthoseexpectationsorpleasantlysurprisedbyactualquality.
3
In Section5,weextendourmodelandconsideralsoadvertisementrevenuesfromthepaidversion
4
Godeset al.(2009) modeladvertisingrevenues asan outcomeoftwo-sided competition. Whileendogenizingtheprice
ofadvertisingyields interestinginsights when studyingoptimalbundling of content and advertisements, weassumethat
theprovideroftheinformationgood hasnomarketpowerontheadvertisingmarket.
6
v
0
Density
p
1−α
¯v
1
¯v
D
I
(p,α)
D
F
(p,α)
(1a) Initial Demand
v
0
Density
p
1−α
¯v
1
¯v
D
I
(p,α)
D
F
(p,α)
(1b) Changein Demand
Figure1: Initial demand and thedemandfor thefree sample.
the second group consists of those who buy the product after firstexperiencing the sample. We refer
tothesecomponentsof demand forthe paid version,respectively, as “initial demand” and“sampling
induceddemand”.
3.1 Initial Demand
Given an initial valuation
v
,a consumer buys the paid version at price
p
if and only if she enjoys a
surplus
v− p
thatexceeds the value obtained by choosing the free sample
αv
. Initial demand is thus
givenby
D
I
(p,α) ≡ Pr
v>
p
1− α
=1 −
p
(1 −α)¯v
.
We assume that initial demand is strictly positive. Put differently, this assumption requires that the
consumers with thehighestvaluations inthemarket buy theproduct without taking thefree sample,
which happens if
¯v > p/(1 − α)
. Note that the firm loses consumers that might initially buy when
either the price or the sampling portion are increased, as these consumers become more inclined to
take thefreesample.
Thedemandforthe freesamples thenbecomes thenumber ofconsumers minus thosewhochoose
tobuy theproductinitially:
D
F
(p,α) = 1 −D
I
(p,α) =
p
(1 −α)¯v
.
Offering a free sampleincreases the demand forthe free versionperse, thereby reducing the demand
forthe paid version. Figure 1 illustrates therespective demands (panel a) andshows thatthedemand
for the free sample is increasing in both sample size
α
and price
p
(panel b). Further note that initial
demand is increasing in
¯v
and therefore that the demand for the free sample is decreasing in
¯v
by
7
construction. It is important to note that the firm’s choice of
p
and
α
separates consumers into two
groups: a group of consumers that initially buy and a group of consumers that take the free sample.
The demand of the latter group determines advertising revenue. To obtained the demand and hence
revenuesforthepaid version,we havetotake into account thoseconsumers who buyafterexperienc-
ingthesample. Thenextsectionaddressesthis andderives sampling-induceddemand.
3.2 Sampling-Induced Demand
Thissectionderivesthesampling-induceddemandthatstemsfromthoseconsumerswhobuythepaid
version afterexperiencing the quality of the sample portion
α
. The probability that a consumer buys
at price
p
crucially depends on
¯q
. Depending onthe value of
¯q
,two cases may arise. The first case is
whereall consumers may buy. Thesecondcase is wherelow-valuationconsumersneverbuy.
3.2.1 Consumers’ Updating ofQuality Expectations
Importantly, only consumers who take the free sample can learn about product quality and update
their initial valuation. Given sample experience, a consumer buys if and only if his or her surplus
v
−p
frombuyinggivenrevisedexpectations exceedsthevalue
αv
derivedfromstaying withthefree
sample. Usingthe updating rule giveninEq.(1), the probabilityof buyingafter experiencing product
quality canbe expressedas
Pr
αq +(1− α)v ≥
p
1−α
.
We follow Buehler and Halbheer (2009) to compute this probability and note thatthe joint density of
the bivariate uniform distributionof
(v,q)
onthe rectangular type space
T ≡ [0,
p
1− α
]× [0,¯q]
is givenby
f(v,q)=
1
¯v¯q
if
(v,q) ∈ T
0
otherwise,
wherethedefinitionof
T
followsby notingthatonlyconsumerswithvaluation
v< p/(1− α)
take the
free sample. With this in mind, we can express the probability of buying given sample experience in
8
more compact notationas
Pr
αq+ (1− α)v ≥
p
1−α
=
1
¯v¯q
p
1−α
0
¯q
0
1
{
αq+(1−α)v≥
p
1−α
}
dqdv
,
where
1
A
is the indicator function taking value 1 on the set
A
(which is here the set of consumers
that buy givensample experience)and 0 otherwise. We show in the nextsectionthat this probability
crucially depends uponthe experiencedquality
¯q
.
5
3.2.2 Sampling asa Persuasion Device
We assume that sampling persuades some of the consumers withthe highestpost sample experience
and hence valuations to buy. Given sample experience, consumers buy if the following condition
holds.
Condition1. Consumerswiththehighestvaluationsbuytheproductonlyiftheyexperienceasufficientlyhigh
samplequality, that is,if
¯q > p/(1 −α)> 0
.
To intuitively graspthe meaning of this condition, itisuseful define thesetofconsumersthatbuy
the productgivensample experienceas
(v,q) ∈ T | αq+ (1 −α)v ≥
p
1−α
.
The boundary of this set defines the set of indifferent consumers and hence an “indifference curve”,
whichcanbewrittenas
q= f(v) =
p
α(1− α)
(1 −α)v
α
,
implying
f
p
1−α
=
p
1−α
.
This conditionensures thattheconsumerswith the highestvaluation (among those who take the free
sample) buy the productif they experience a sufficiently highsample quality. A graphical illustration
of this condition is given in Figure 2. Also, the figure visualizes that all consumers may buy if
¯q
is
5
Buonocore et al. (2009)providea closed-formsolutionfortheconvolutionintegral. However, thederiveddistribution
function alsodependsonspecificparametervalues.
9
v
0
0
q
¯q
p
1−α
¯v
p
α(1−α)
p
(1−α)
Indifference curve
Typespace
T
(2a)
v
0
0
q
¯q
p
1−α
¯v
p
α(1−α)
p
(1−α)
Consumers who buy
(2b)
Figure 2: Consumers whobuy after sampling.
sufficiently large (dark shadedarea inPanel 2a) and that low-valuationconsumers never buywhen
¯q
is relatively small (Panel 2b).
Case I
:
All ConsumersMay Buy
Even the consumers with the lowest valuations may buy the productgiven sample experience if the
following conditionholds.
Condition 2a. Consumerwiththelowestvaluationinthemarketcanbepersuadedtobuytheproductifthey
experience ahigh enough sample quality,thatis,if
¯q > p/(α(1− α))
.
This condition is best understoodby inspection oftheindifference curve drawn in Figure 2a. The
condition requires that the indifference curve hits the vertical axis below
¯q
, which is equivalent to
assuming
f(0) =
p
α(1 −α)
<¯q
.
Thenext lemmagives thedemandinducedby lettingconsumersevaluateproduct quality.
Lemma 1. Whenallconsumersmaybuy,thefirmfacessampling-induceddemand
D
S
1
(p,α) = D
F
(p,α)−
(1+ α)p
2
2α(1−α)
2
¯v¯q
.
10
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