Choosing a Digital Content Strategy:
How Much Should be Free?∗
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Daniel Halbheer, Florian Stahl, Oded Koenigsberg, and Donald R. Lehmann†
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Abstract
Advertising supported content sampling is ubiquitous in online markets for digital
information goods. Yet, little is known about the profit impact of sampling when
it serves the dual purpose of disclosing content quality and generating advertising
revenue. This paper proposes an analytical framework to study the optimal content
strategy for online publishers and shows how it is determined by characteristics of
both the content market and the advertising market. The strategy choice is among a
paid content strategy, a sampling strategy, and a free content strategy, which follow
from the publisher’s decisions concerning the size of the sample and the price of
the paid content. We show that a key driver of the strategy choice is how sampling
affects the prior expectations of consumers, who learn about content quality from
the inspection of the free samples. Surprisingly, we find that it can be optimal for
the publisher to generate advertising revenue by offering free samples even when
sampling reduces both prior quality expectations and content demand. In addition,
we show that it can be optimal for the publisher to refrain from revealing quality
through free samples when advertising effectiveness is low and content quality is
high. To illustrate, we relate our framework to the newspaper industry, where the
sampling strategy is known as the “metered model.”
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Keywords: Information Goods, Content Pricing, Sampling, Advertising,
Dorfman-Steiner Condition
∗ We
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thank Asim Ansari, Jean-Pierre Dubé, Anthony Dukes, Jacob Goldenberg, Avi Goldfarb, Raju
Hornis, Ulrich Kaiser, Anja Lambrecht, Philipp Renner, Catherine Tucker and seminar participants at the
11th ZEW ICT Conference (2013), the GEABA 2012 (Graz), the Marketing in Israel Conference 2011
(Tel Aviv), the INFORMS Marketing Science Conference 2011 (Houston), the University of Hamburg,
the HEC Paris, the University of Passau, the University of Tilburg, and the University of Zurich for
helpful comments and suggestions. Daniel Halbheer gratefully acknowledges support from the Swiss
National Science Foundation through grant PA00P1-129097 and thanks the Department of Economics at
the University of Virginia for its hospitality while some of this research was being undertaken.
† Daniel Halbheer (corresponding author): University of St. Gallen, Department of Economics, Varnbüelstrasse 19, CH-9000 St. Gallen, Switzerland ([email protected]). Florian Stahl: University of Mannheim, Department of Business Administration, L 5, 2, D-68131 Mannheim, Germany
([email protected]); Oded Koenigsberg: London Business School, Regent’s Park, London, NW1 4SA, United Kingdom ([email protected]); Donald R. Lehmann: Columbia Business
School, Uris Hall, 3022 Broadway, New York, NY 10027, United States ([email protected]).
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Introduction
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Digital information goods have been available on the Internet for almost twenty years.
During that time, publishers have developed different strategies to distribute content.
Some publishers provide all their information for free, while some charge consumers for
access to their content. Other publishers employ a hybrid business model, giving away
a portion of their content for free and charging for access to the rest of their content.
Offering free content samples allows publishers to both disclose their content quality
and to generate revenues from advertisements shown to online visitors. According to
Alisa Bowen, general manager of The Wall Street Journal Digital Network, “working
with advertisers to offer open houses has proven to be one of the most valuable and
efficient ways to expose our premium content to new readers and potential subscribers”
(GlobeNewswire 2012). The main contribution of this paper is to provide a formal
analysis of how publishers should choose between different digital content strategies.
Information goods such as digital content are experience goods; hence consumers
must have an experience to value them (Shapiro and Varian 1998). Offering free samples
is a way for publishers to disclose their content quality, thereby allowing consumers
to have actual experience with the good before purchase. Digital information goods
are particularly suitable for sampling because the costs of providing free samples are
negligible and publishers can include advertisements in the free samples to generate
advertising revenues. These two features distinguish sampling of information goods
from the typical sampling of perishable or durable goods.
Recently, publishers introduced business models that allow consumers to select samples of their choice within a set sample size. A prominent example of this is the “metered
model” in the newspaper industry, where publishers offer a number of articles for free
and charge for access to the rest. Such “customer selected sampling” differs from the
approach where the publisher chooses not only the sample size but also the sample
content, which allows the firm to strategically manipulate the sample and creates an
environment where customers are likely to discount the sample quality in estimating
actual quality. A recent study by the Newspaper Association of America (2012) shows
that 62% of the publishers employ a metered model, out of which 95% offer up to
twenty free articles monthly. For example, the New York Times currently offers access
to ten articles for free on its website each month. Advertising supported sampling is also
employed by distributors of music such as Spotify or Rhapsody. Allowing consumers to
choose which content to sample means that publishers have no control over the content
consumers actually sample. Taking this into account is important for publishers when
setting the optimal sample size.
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The business model where publishers set a sample size and let consumers choose
which content to sample differs from versioning or “freemium,” where a firm selected
low-end version is offered for free and consumers have to pay for access to the highend version.1 Such versioning of information goods is often observed in the software
industry (see, for instance, Faugère and Tayi 2007; Cheng and Tang 2010). Customer
selected sampling, in contrast, does not involve quality differentiation: Within the set
sample size, the publisher allows the consumers to sample any of its content for free.
This paper develops an analytical framework to study the optimal content strategy
for online publishers of information goods. Content strategy consists of two decisions:
the size of the sample and the price of the paid content. The publisher is assumed to
receive revenues from content sales and from advertisements, which are embedded in
the free content. A key feature of sampling is that it serves the dual purpose of generating revenues from advertising and disclosing content quality. Consumers have prior
expectations about content quality, which they update in a Bayesian fashion through
inspection of the free samples. The information transmitted through the free samples
affects the consumers’ posterior expectations about content quality, which in turn influence expected content sales. Taking the consumers’ quality updating into account,
the publisher faces a tradeoff between an expansion effect (through learning) and a
cannibalization effect (through free offerings) on expected content demand induced by
sampling. When the publisher makes its sampling and pricing decisions, it should take
both the effects on content demand and the impact on advertising revenue into account.
We assume that the publisher can choose among a “sampling strategy,” a pure “paid
content strategy,” or a pure “free content strategy.” Importantly, under a sampling
strategy, consumers are allowed to sample some content for free, while they have to
pay to access the remaining content (which corresponds the the metered model in the
newspaper industry).
We derive several important results. First, we show how the publisher’s advertisingsales revenue ratio and hence its optimal content strategy is determined by characteristics of both the content market and the advertising market. The analysis confirms
the insight that the elasticities of content demand and advertising demand jointly determine the publisher’s optimal ratio of advertising revenue to sales revenue (Dorfman and
Steiner 1954). Importantly, the elasticity of consumers’ updated expectations with respect to the sample size plays a key role in determining the ratio of advertising revenue to
sales revenue. This elasticity is positive if sampling increases consumers’ expectations
about content quality. In this case, managers can expect the advertising-sales revenue
1 Bhargava
and Choudhary (2008) analyze optimal versioning of information goods.
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ratio to be low due to high revenues from content sales (resulting from the expansion
effect). In contrast, if sampling reduces consumers’ expectations about content quality,
managers can expect the advertising-sales revenue to be high due to low revenues from
content sales (resulting from the cannibalization effect).
Second, we describe a Bayesian learning mechanism and derive expected content
demand from model primitives. This allows us to provide insights into how the effects of pricing and sampling on expected content demand are intertwined with the
consumers’ prior beliefs. We find that managers must consider two demand regimes,
depending on whether consumers’ prior expectations are “high” or “low.” In both cases,
expected content demand is decreasing in price and increasing in expected posterior
quality, as expected. Importantly, we show that sampling can have a demand-enhancing
effect through consumers’ learning when prior expectations are sufficiently low (even
though sampling produces a cannibalization effect). We establish the rule of thumb that
sampling increases content demand if the elasticity of consumers’ updated expectations
exceeds the ratio of sampled to paid content.
Third, to study the publishers optimal pricing and sampling decisions, we bring our
model of the content market together with a standard model of the advertising market.
When content quality is common knowledge, we show that a paid content strategy is
optimal for the publisher only if the effectiveness of advertising is sufficiently low. For
intermediate levels of advertising effectiveness, the publisher should employ a sampling
strategy and generate revenues from both sales and advertising. Once advertising is sufficiently effective, the publisher should switch to a free content strategy. Thus, it can be
optimal for the publisher to offer content samples even if sampling solely cannibalizes
content demand.
In the case where consumers are uncertain about actual content quality and learn
about it through inspection of the free samples, the optimal strategy is determined by
the relationship between advertising effectiveness and quality expectations. As in the
benchmark model, two cut-off values of advertising effectiveness determine the publisher’s optimal content strategy: a lower bound that depends on prior quality expectations (separating paid from sampling strategies) and an upper bound that depends on
posterior quality expectations (separating sampling from free content strategies). Interestingly, it can be optimal for the publisher to generate advertising revenue by adopting
a sampling strategy even when sampling reduces both quality expectations and content
demand. In addition, we find that it can be optimal for the publisher to adopt a paid
content strategy and to refrain from revealing high quality through free samples.
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Finally, we explore three extensions of the model to generate additional managerial
insights. First, when the publisher also includes advertisements in the paid content, the
cut-off values depend not only on the relationship between advertising effectiveness and
quality expectations, but also on consumers’ attitudes towards advertisements. Second,
we provide insight on how the publisher’s optimal content strategy is determined when
the willingness to pay for advertisements is related to content quality. Third, we introduce competition in the content market and analyze how asymmetries in prior beliefs
affect the equilibrium content strategies.
This paper is related to two literature streams. The first stream is on media strategy
in two-sided markets.2 For instance, Kind et al. (2009) analyze how competition, captured by the number of media platforms and content differentiation between platforms,
affects the composition of revenues from advertising and sales. Godes et al. (2009)
investigate a similar question, focusing on competition between platforms in different
media industries. Our paper examines optimal advertising supported content sampling
and content pricing when the firm can generate revenue from both content sales and
advertising. While papers that examine content sampling from different perspectives
include Xiang and Soberman (2011) for preview provision and Chellappa and Shivendu (2005) for piracy-mitigating strategies, neither consider the impact of sampling
on advertising revenues. To the best of our knowledge, optimal content sampling when
sampling impacts revenues from both content sales and online advertising has not been
addressed by the literature.
This paper is also related to the broad literature on consumer learning about product attributes. Firms typically enable consumer learning through disclosing information about their products and services. This information can be disclosed in various
ways, including through informative advertising (see Anderson and Renault 2006, and
Bagwell 2007 for a comprehensive survey), or product descriptions or third-party reviews (Sun 2011; Hotz and Xiao 2013). Another way for firms to disclose information
is through sampling. Heiman et al. (2001) and Bawa and Shoemaker (2004) study
how sampling affects demand and the evolution of market shares for consumer goods,
while Boom (2009) and Wang and Zhang (2009) investigate sampling of information
goods. However, when firms sample information goods, they only offer a portion of
the good for free to avoid the “information paradox” (Akerlof 1970). Consumers’ inferences about a product’s attributes are most naturally modeled in a Bayesian framework.
Bayesian learning processes based on product experience have been widely employed in
2 See
Rysman (2009) for a general review of the two-sided markets literature. Anderson and Gabszewicz (2006) provide a canonical survey of media and advertising.
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General Framework
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the literature, for instance, by Erdem and Keane (1996), Ackerberg (2003), and Erdem
et al. (2008), and we follow this approach here.
We organize the remainder of the paper as follows. Section 2 presents the general
framework and describes how the publisher operates in two markets: content and advertising. Section 3 describes the content market and studies the impact of sampling
on expected content demand. Section 4 describes the advertising market. Section 5
analyzes the publisher’s optimal content strategy. Section 6 offers extensions of our
analysis. Conclusions and directions for future research are provided in Section 7. To
facilitate exposition, we have relegated proofs to the Appendix.
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We first introduce the three main components of our modeling framework: the publisher,
the content market, and the advertising market. Next, we define the strategies available
to the publisher and characterize the optimal advertising-sales revenue ratio and thus
the optimal content strategy. Table 1 towards the end of the section summarizes the
components of the general framework (as well as its main assumptions) and indicates
where the reduced-form expressions are replaced by specific functional forms.
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Publisher. We consider a publisher who offers a digital information good with
content of size N > 0 through an online channel. Content size may be thought of as
the number of chapters of a book or movie, the number of songs on an album, or the
number of articles on a news platform. To mirror the cost properties of information
goods, we assume that the publisher has fixed costs F ≥ 0 and zero unit costs to produce
the content.3 The cost to provide digital access per subscriber is cs ≥ 0 and the costs
of providing free samples are normalized to zero. The qualities of the content parts are
distributed on the quality spectrum [0,V ], where V is the publisher’s private information.
We treat quality V as an outcome of a previous strategic decision and suppose that the
publisher has two decision variables: the sample size n ∈ [0, N] and the price p at which
to sell the good.4 Notice that in the context of the metered model, the sample size n is
the “meter” and p is the price for the content behind the “paywall,” which separates free
content from paid content.
3 Throughout
the analysis, we assume that the fixed costs do not exceed the product market profit.
Hence they do not change the analysis and can therefore be omitted.
4 The choice of (p, n) is not a multidimensional signal for quality as studied, for instance, by Wilson (1985) and Milgrom and Roberts (1986). In this strand of the literature, n is an advertising signal
for quality. However, in our setting, the publisher’s choice of n allows the consumers to gain information
about the actual content quality through their sample experience before making the purchase decision.
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Content Market. We consider a market with a unit measure of consumers that
observe the publisher’s sampling and pricing decisions. Consumers are uncertain about
content quality. We assume that they update their prior expectations in a Bayesian fashion through inspection of the free samples and denote by Ṽ (n) the consumers’ expected
posterior quality given the sample size n. Expected content demand depends on price p,
sample size n, and Ṽ (n). Specifically, we assume that the publisher’s expected content
demand is given by
DE (p, n) ≡ D(p, n, Ṽ (n)).
(1)
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This representation emphasizes that the sample size has both a direct effect on content
demand and an indirect effect that operates through the impact of n on expected posterior
quality Ṽ (n).
Expected content demand satisfies the following basic assumptions. First, we assume that ∂∂ Dp < 0, i.e. content demand depends negatively on price. Second, we impose
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that ∂∂Dn < 0, so that a larger sample size has a direct negative effect on demand for the
remaining content accessible through the paywall. Third, we require that ∂∂ ṼD > 0, i.e.
content demand depends positively on expected posterior quality. The overall effect of
the sample size n on expected content demand is given by
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∂ DE ∂ D ∂ D 0
=
+
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∂n
∂ n ∂ Ṽ
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where term ∂∂ ṼD Ṽ 0 (n) captures the indirect effect of the sample size on expected content
demand. It is not clear a priori how the sample size affects posterior expectations and
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hence ∂∂Dn . If Ṽ 0 (n) < 0, sampling reduces posterior expectations and is thus demandreducing. Even if Ṽ 0 (n) > 0, that is, if sampling increases posterior expectations, offering an additional sample may be demand-reducing if the direct effect dominates the
indirect effect. However, once Ṽ 0 (n) is sufficiently large, the indirect effect is stronger
E
than the direct effect so that ∂∂Dn > 0 and sampling has a demand-enhancing effect. In
line with Bawa and Shoemaker (2004), we refer to the direct effect of sampling on content demand as the “cannibalization effect” and to the indirect effect as the “expansion
effect.”
Advertising Market. We consider a market where the advertisements are delivered
to the publisher through a representative advertiser (e.g., an advertising agency). We
assume that the publisher includes one advertisement in each free content part. The
inverse advertising demand is denoted by a(n) and maps the publisher’s choice of n into
the market price for ads. Thus, a(n) can be thought of as the advertiser’s willingness
7
to pay for placing n advertisements. We make the natural assumption that the price for
advertisements decreases in sample size, that is, a0 (n) < 0.
p,n
π(p, n) = (p − cs )D(p, n, Ṽ (n)) + a(n)n
s.t.
p≥0
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Optimal Strategy. The publisher receives profits from the content market and from
the advertising market. The expected profit from content sales is (p − cs )D(p, n, Ṽ (n)),
while the profit (revenue) from including advertisements in the free articles is a(n)n.
The publisher makes pricing and sampling decisions so as to maximize its (expected)
profit from the two markets:
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0 ≤ n ≤ N.
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As long as the publisher’s profit function π(p, n) is concave, standard optimization
theory posits that there is a unique constraint global maximizer (p∗ , n∗ ) because the
constraint set is convex. Depending on the optimal pricing and sampling decision, the
following definition gives the strategies available to the publisher.
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Definition 1 (Strategies). Given the optimal pricing and sampling decision (p∗ , n∗ ),
the publisher adopts either (i) a “sampling strategy” if p∗ > 0 and n∗ ∈ (0, N), (ii) a
pure “paid content strategy” if p∗ > 0 and n∗ = 0, or (iii) a pure “free content strategy”
if p∗ = 0 and n∗ = N.
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Notice that both the paid content strategy and the free content strategy are nested
within the sampling strategy: The publisher receives no advertising revenue under a
paid content strategy and no sales revenue under a free content strategy. The following
result describes the optimal strategy as the ratio of advertising revenue to sales revenue.
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Proposition 1 (Advertising-Sales Revenue Ratio). Under a sampling strategy, the
publisher’s optimal ratio of advertising revenue to sales revenue is given by
ηn − ηṼ εṼ
an∗
=
,
Dp∗ (1 − η1 )η p
a
(3)
where η p ≡ −(∂ D/∂ p)(p/D) denotes the elasticity of content demand with respect to
price, ηn ≡ −(∂ D/∂ n)(n/D) denotes the elasticity of content demand with respect to
sample size, ηṼ ≡ (∂ D/∂ Ṽ )(Ṽ /D) denotes the elasticity of content demand with respect
to quality, εṼ ≡ Ṽ 0 (n)(n/Ṽ ) denotes the elasticity of posterior quality expectations with
respect to sample size, and ηa ≡ −n0 (a)(a/n) denotes the price elasticity of advertising
demand.
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This result has two important managerial insights: First, it shows that the publisher’s
advertising-sales revenue ratio and hence its optimal content strategy is determined
by characteristics of both the content market and the advertising market. Specifically,
consumer preferences determine the characteristics of the content market, captured by
the elasticities of content demand with respect to price, sample size, and quality. The
price elasticity of advertising demand reflects advertiser preferences. This general result
thus provides guidance for managers seeking to better understand the contributions of
(expected) sales and advertising to total revenue.
Second, Proposition 1 shows how changes in the “market environment,” captured by
the various elasticities, affect the publisher’s composition of revenues. Unsurprisingly, if
the price elasticity η p increases, the advertising-sales revenue ratio is lower. Intuitively,
for a given sample size, the optimal price for the content is lower, which results in a
higher sales revenue. In contrast, higher elasticity of content demand with respect to the
sample size ηn increases the advertising-sales revenue ratio. Furthermore, the higher
the price elasticity of advertising demand ηa , the lower is the advertising-sales revenue
ratio.
Proposition 1 also highlights the crucial role which the elasticity of posterior quality
expectations with respect to sample size plays. Because the elasticity of content with
respect to quality ηṼ is positive, the impact of sampling on posterior quality determines
the sign of ηṼ εṼ . If εṼ is negative, the ratio of advertising revenue to sales revenue
tends to be high, while it tends to be low if εṼ is positive. Intuitively, if εṼ < 0, sampling reduces expected content demand as Ṽ 0 (n) < 0, and hence the advertising-sales
revenue ratio is high. In contrast, if εṼ > 0, sampling increases expected content demand as consumer revise their expectations about quality upwards, resulting in a lower
advertising-sales revenue ratio.
Interestingly, the optimal advertising-sales revenue ratio is reminiscent of the wellknown Dorfman-Steiner condition, which states that a monopolist’s ratio of advertising
spending to sales revenue is equal to the ratio of the elasticities of demand with respect to
advertising and price (Dorfman and Steiner 1954). Proposition 1 reduces to this result
in the special case when offering additional samples does not affect posterior quality
(εṼ = 0) and if the advertising demand is perfectly elastic (ηa → ∞).
Our general framework is agnostic about how consumers form posterior quality
expectations. To shed light on effects of sampling on posterior quality expectations,
the next section introduces a Bayesian learning mechanism in which consumers update
their prior expectations about content quality through experience with the sample. Im-
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Inverse Advertising Demand
a(n) . . . ads in free content
a p (N − n) . . . ads in paid content
Endogenous ad effectiveness φ̃ (n)
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Indirect Utility
u(p, n)
Conditional Indirect Utility
ui (x; pi , ni )
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Decision Variables
p . . . content price
n . . . sample size
Expected Posterior Quality
Ṽ (n)
Expected Content Demand
DE (p, n) ≡ D(p, n, Ṽ (n))
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a0p (N − n) < 0
a0 (n) < 0
(2
D p < 0 , Dn < 0 , DṼ > 0
DEn > 0 . . . demand-enhancing
sampling
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Dn < 0 . . . demand-reducing
sampling
Ṽ 0 (n) ≷ 0
General Framework
Assumed Properties
Table 1: Components of the General Framework
Advertiser Parameter
φ . . . advertising effectiveness
Advertising
Market
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Prior Parameters
v0 . . . minimum estimate of V
α . . . uncertainty about v0
Posterior Parameters
ṽ0 (n)
α +n
Preference Parameters
θ . . . valuation of quality
ξ . . . ad attraction / ad repulsion
x . . . preferred product characteristic
τ . . . sensitivity to mismatch
Cost Parameters
F . . . fixed production costs
cs . . . unit distribution costs
m
Content Parameters
N . . . content size
V . . . maximum content quality
Content
Market
Publisher
Variables
Section 4
Section 6.1
Section 6.2
Section 6.3
Section 3.1
Lemma 2
Proposition 2
Lemma 2
Section 3.3
Explicit Form
portantly, we show how the publisher should take the consumers’ learning into account
to gauge the effects of offering free samples on content demand.
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Content Market
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Consumer Behavior
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This section analyzes the impact of customer selected sampling on expected content
demand when the qualities of the content parts are uniformly distributed on the quality
spectrum [0,V ]. We begin by laying out assumptions regarding consumer behavior and
describing the Bayesian learning mechanism. Taking consumers’ learning into account,
we derive the publisher’s expected content demand given its pricing and sampling decisions. Finally, we provide conditions under which sampling increases or decreases
expected content demand.
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Consumers know that the qualities of the free samples are uniformly distributed on
the interval [0,V ], but they do not know the upper bound of the publisher’s quality
spectrum V and are hence uncertain about (average) content quality.5 Consumers have
a common prior belief about V that may stem, for instance, from reviews, ratings or
“word of mouth.” The natural conjugate family for a random sample from a uniform
distribution with unknown upper bound is the Pareto distribution (DeGroot 1970). We
capture uncertainty about V by a prior belief that consists of a minimum estimate v0 of
the upper bound V and a level of uncertainty α about this value. Specifically, we assume
that prior beliefs follow a Pareto distribution with density function
 α

 αv0 , for v > v0
f (v|v0 , α) = vα+1

0,
otherwise.
We assume α > 1 to ensure existence of prior expectations.6 Based on the consumers’ prior knowledge about v0 and α, their prior expectation about V is
E[V |v0 , α] =
5 Note
αv0
.
α −1
(4)
that the upper bound V is monotonically related to the mean, which may be an alternative way
for consumers to think about content quality.
6 Our measure of uncertainty corresponds to the scale parameter α of the Pareto distribution. Hence,
when uncertainty is higher, the prior distribution is more spread out.
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Density
2 2
2
1 1
1
0 0
0.25
0.25
0.50.5
0.75
0.75
1 1
1.25
1.25
1.51.5
1.75
1.75
E[V |v0 , α ] V
v
0.25
0.5
0.75
1
V
0 75 and
10
1.25
1.5
1.75
2
v
E[V |v0 , α ]
(A) v0 = 0.75 and α = 10
(B) v0 1 10 and
3
(B) v0 = 1.10 and α = 3
(2
(A) v0
2 2v
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Density
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Figure 1: Prior expectations about V (where V ≡ 1).
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Obviously, prior expectations increase in v0 and decrease in α. Figure 1 illustrates
two prior beliefs along with the corresponding expectations for different parameter values. Prior expectations are lower than actual quality in Panel A and higher than actual
quality in Panel B. Note that prior expectations can be higher than actual quality even if
v0 < V .
Consumers update their prior belief about the upper bound of the quality spectrum
V by taking the observed qualities of the free samples into account. Specifically, consumers use the n sample qualities Vi = vi (i = 1, . . . , n) to form their posterior belief
ṽ(n) about V . Using standard Bayesian analysis, ṽ(n) follows a Pareto distribution
with minimum value parameter ṽ0 (n) = max{v0 , v1 , . . . , vn } and shape parameter α + n
(DeGroot 1970).7 Hence, the posterior expectation of V is given by
E[V |ṽ0 (n), α] =
(α + n)ṽ0 (n)
.
α +n−1
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Consumers infer the expected quality of the information good E[V |v1 , . . . , vn ] from
the average quality of the sampled content parts. Knowing that qualities are uniformly
distributed on the quality spectrum offered, the expected quality of the information good
is given by
E[V |ṽ0 (n), α]
E[V |v1 , . . . , vn ] =
.
(5)
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Consumers believe that higher quality is better than lower quality but differ in the
way they value quality. To capture this heterogeneity, we introduce a preference parameter for quality θ , which is uniformly distributed on the interval [0,1]. We assume that
7 The
proof of this result appears in the Appendix.
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each consumer either purchases the information good at price p or stays with the n free
samples. A consumer’s indirect utility from these two options is given by

θ NE[V |v1 , . . . , vn ] + ξ n − p, from purchasing at price p
u(p, n) =
θ nE[V |v , . . . , v ] + ξ n,
from staying with the free samples.
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The parameter ξ captures the intensity of ad-attraction (ξ > 0) or ad-repulsion (ξ < 0)
in the population (Gabszewicz et al. 2005). Thus, when consumers exhibit ad-loving
behavior, the utility of both options is augmented by ξ n, while the utility of both options
is reduced by ξ n in the case of ad-avoiding behavior.
The value of the information good is equal to the number of content parts multiplied
by their expected quality.8 This implies that a consumer will purchase the information
good if and only if the indirect utility from buying exceeds the indirect utility from
consuming only the free samples, that is, if
l3
θ (N − n)E[V |v1 , . . . , vn ] − p ≥ 0.
(6)
Expected Content Demand
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This condition means that the (quality-weighted) expected value of the content that has
not been sampled must exceed the price. Importantly, purchase does not depend on
consumer behavior towards advertising.
Fo
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Because consumers do not know the upper bound of the quality spectrum V with certainty, content demand is influenced by consumers’ posterior quality expectations. Thus,
when the publisher makes decisions about the sample size and the price, it has to base
them on expected content demand as consumers have not yet evaluated sample qualities
and updated their expectations about content quality.
In order to compute expected content demand, we assume that the publisher knows
the consumers’ prior parameters v0 and α, which can be learned using standard market
research techniques such as surveys. The calculation involves a three-step procedure:
In the first step, the publisher computes the expected posterior quality by averaging
posterior expectations about V as given by (5) across all possible realizations of sample
qualities:
(α + n) E [ṽ0 (n)]
E [E[V |V1 , . . . ,Vn ]] =
.
2 (α + n − 1)
8 This
additivity assumption is justified for independently valued content parts. However, a concave
or convex relationship between the value and the number of content parts might be more appropriate for
interrelated content parts, that is, if the content parts are substitutes or complements.
13
In the second step, the publisher substitutes the expected posterior quality into the purchase condition given by (6) to obtain expected content demand:
p
2 (α + n − 1)
E
D (p, n) = max 0, 1 −
.
(7)
(N − n) (α + n) E [ṽ0 (n)]
01
4)
In the third step, the publisher calculates E [ṽ0 (n)] to obtain the expected content demand
as a function of the underlying model parameters. This calculation leads to the following
result.
(2
Proposition 2 (Expected Content Demand). When the publisher sells the information
good at price p and offers n ∈ {1, . . . , N − 1} samples, then
(8)
l3
1
#2
(a) if v0 < V , expected content demand is given by
(
)
n
p
2
(α
+
n
−
1)
(n
+
1)V
.
DE{v <V } (p, n) = max 0, 1 −
n+1
0
(N − n) (α + n) vn+1
+
nV
0
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(b) if v0 ≥ V , expected content demand is given by
p 2 (α + n − 1)
E
D{v ≥V } (p, n) = max 0, 1 −
.
0
(N − n) (α + n) v0
(9)
Fo
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m
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Expected content demand has the intuitive properties that we assumed in our general
framework: it decreases in price and increases in expected posterior quality. In addition,
sampling has both a direct demand-reducing effect and an indirect effect that operates
through its impact on posterior expectations. The direct effect kicks in through the
1
factor N−n
and mirrors the cannibalization effect ∂∂Dn < 0. This follows because a larger
sample size reduces the utility of the remaining content consumers have to pay for.
Proposition 2 nests the expected content demand under a paid content strategy (n = 0), in
which case D(p, 0) is a function of prior quality expectations as there is no learning. In
contrast, when the publisher employs a free content strategy (n = N), consumers do not
purchase the information good as they can download it for free and hence D(p, N) ≡ 0.
Which of the two demand functions reported in Proposition 2 emerges depends on
the value of the minimum estimate v0 about V vis-à-vis the actual upper bound of the
quality spectrum V : If v0 ≥ V , sampling necessarily reduces expected content demand.
In contrast, if v0 < V , sampling may have a demand-enhancing effect. We next address
this possibility.
14
3.3
The Role of Quality Expectations
(2
01
4)
For a given level of prior expectations about content quality, sampling either increases or
decreases expected content demand. Whether sampling compensates for cannibalization
through consumers’ learning depends on the gap between expected posterior quality and
actual quality. Expected posterior quality is

(α + n) vn+1
+ nV n+1

0


 2 (α + n − 1) (n + 1)V n , if v0 < V
Ṽ (n) =
(10)

(α + n) v0



,
if v0 ≥ V
2 (α + n − 1)
1
#2
and the quality gap is Ṽ (n) − V2 . Consumers overestimate (underestimate) quality if
the expected posterior quality is higher (lower) than actual quality. This leads to the
following result.
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Lemma 1 (Quality Gap). When v0 < V , consumers overestimate quality after their
sample experience if
1
v0
α − 1 n+1
,
(11)
>
α +n
V
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and underestimate it if the inequality is reversed. If v0 ≥ V , consumers overestimate
quality irrespective of the sample size and their level of uncertainty α > 1.
Fo
rth
co
m
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Prior expectations can be higher than actual quality even if v0 < V (a high level of
uncertainty about v0 is captured by a low α). Condition (11) applies when consumers
overestimate quality based on posterior expectations: This is likely to be the case for
a low α and when the publisher offers a small number of free articles n. On the other
hand, consumers underestimate quality if their uncertainty is low and the sample size is
large.
When v0 < V , the shaded area in Figure 2 illustrates the set of parameters for which
consumers overestimate and underestimate quality, respectively. By construction, where
α > 1, condition (11) holds and consumers overestimate quality. The parameter region
for which consumers overestimate quality shrinks as n gets larger since Ṽ (n) → V2 as
n → ∞, meaning that consumers learn actual quality once the sample size gets “large
enough.”
The definition of Ṽ (n) allows us to rewrite the expected content demand derived in
Lemma 2 more compactly as
p
E
D (p, n) = max 0, 1 −
,
(12)
(N − n)Ṽ (n)
15
α
10
n=1
n=5
n = 10
n = 1000
8
6
n↑
2
0
2
4
6
8
01
4)
4
10 v0
(2
V
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1
#2
Figure2:2:The
Thequality
qualitygap
gapfor
forthe
thecase
casev v0 <VV(where
(whereVV ≡10).
10).The
Theshaded
shadedarea
areaindicates
indicates
Figure
where consumers underestimate quality.
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Vo
which is a specific version of the reduced-form demand function in Equation (1). Hence
the number of free samples n has both a direct effect on expected content demand and
an indirect effect that operates through posterior quality expectations Ṽ (n). The next
result uses this demand function to identify conditions under which sampling has a
E
demand-enhancing effect (that is, ∂∂Dn > 0).
m
in
g
Lemma 2 (Effects of Sampling). Offering free samples has a demand-enhancing effect
n
, that is, if the elasticity of consumers’ posterior quality expectations exceeds
if εṼ > N−n
the ratio of sampled to paid content.
Fo
rth
co
Lemma 2 shows that offering free samples may increase expected content demand
through consumers’ learning, even though it produces a cannibalization effect. Intuitively, the indirect effect dominates the direct cannibalization effect if sampling results
in a sufficiently large upwards revision of consumers’ prior expectations.
4
Advertising Market
This section derives inverse advertising demand of a representative advertiser that places
advertisements in the free samples offered by the publisher. The representative advertiser can be thought of as an advertising agency that delivers independent product
advertisements to the publisher. Following Godes et al. (2009), we let the advertiser’s
16
utility from placing n advertisements be given by
n2
− an,
2N
where φ > 0 is a parameter capturing the marginal benefit of an advertisement and a
denotes the unit price set by the publisher to run an advertisement. This specification
captures decreasing marginal utility from placing advertisements caused by decreasing
consumer recall and retention rates for ads (Burke and Srull 1988).
The advertiser maximizes its utility to determine how many advertisements to run
on the publisher’s platform. The implied inverse advertising demand has the linear form
n
(13)
a(n) = φ − ,
N
where φ is referred to as “advertising effectiveness.” Inverse demand slopes downward,
implying that the publisher’s revenue per ad impression is decreasing in sample size.
Intuitively, a(n) can be thought of as the advertiser’s willingness to pay for placing n
advertisements.
Optimal Content Strategy
Vo
5
l3
1
#2
(2
01
4)
u(n) = φ n −
Fo
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This section analyzes the publisher’s optimal content strategy with customer selected
sampling. We first analyze the benchmark case in which the consumers know V and
hence the publisher’s quality spectrum. In this case, sampling does not affect the
consumers’ expectations about quality and simply serves to generating advertising revenues. Next, we analyze the case where V is not known to consumers. In contrast to the
benchmark case, sampling not only generates advertising revenues but also influences
consumers’ expectations about quality.
We consider three strategies: the paid content strategy, the sampling strategy, and
the free content strategy. In order to study the tradeoffs between the three strategies, we
focus on the case where φ > 1.9 For expositional purposes, we normalize the costs of
providing digital access cs to zero and present analysis ignoring the integer constraint
on the number of free samples.
5.1
Strategy with Known Quality
We first derive content demand under a sampling strategy and subsequently derive the
demands for the two boundary strategies when consumers know content quality. Next,
9 When
φ ≤ 1, the free content strategy is never optimal because the advertising revenues and hence
the publisher’s profit is zero. Thus, the publisher’s choice is only between the paid content strategy and
the sampling strategy. The analysis where φ > 1 encompasses this special case.
17
we characterize the optimal pricing and sampling decisions for each of the three strategies. Finally, we determine the optimal content strategy.
01
4)
Content demand. When consumers know the upper bound V and hence the quality
spectrum, the minimum estimate v0 of the upper bound V is equal to V with certainty
and thus α → ∞. Proposition 2 implies that content demand can be expressed as
)
(
p
(14)
D(p, n) = max 0, 1 −
(N − n) V2
for n ∈ {0, . . . , N − 1}. Recall that D(p, N) ≡ 0 under a free content strategy.
1
#2
(2
Optimal Pricing and Sampling. In the benchmark case with known quality, the
publisher makes its pricing and sampling decisions so as to
!
p
n
max π(p, n) = p 1 −
+ φ−
n
p,n
N
(N − n) V
Vo
p≥0
s.t.
l3
2
0 ≤ n ≤ N,
IJ
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where content demand is given by (14) and inverse advertising demand by (13). From
the first-order conditions, the optimal price for a given sample size is
(N − n)V
.
4
(15)
in
g
p(n) =
rth
co
m
This implies that the more free samples the publisher chooses to offer, the less it will be
able to charge the consumer for the remaining content. The next result summarizes the
optimal pricing and sampling decisions for each of the three strategies.
Fo
Lemma 3 (Pricing and Sampling). Suppose that consumers know the upper bound of
content quality V . Then, (i) under a sampling strategy, p∗ = NV (8(2 − φ ) +V )/64 and
n∗ = N(8φ −V )/16, (ii) under a paid content strategy, p∗ = NV /4 and n∗ = 0, and (iii)
under free content strategy, p∗ = 0 and n∗ = N.
The parameters V and φ have opposite effects on the optimal price and on the optimal sample size under a sampling strategy: As expected, p∗ increases in V while n∗
decreases in quality. In contrast, p∗ decreases in φ , and n∗ increases in advertising
effectiveness. Both the optimal price and the optimal sample size increase in content
size N. The following proposition characterizes the publisher’s optimal strategy.
18
Proposition 3 (Optimal Strategy). If consumers know the quality spectrum, then: (i)
if φ ≤ V8 , the publisher should follow a paid content strategy, (ii) if φ ∈ ( V8 , V8 + 2),
the publisher should employ a sampling strategy, and (iii) if φ ≥ V8 + 2, the publisher’s
optimal strategy is a free content strategy.
l3
1
(φ − V8 )( V8 + φ )
an∗
.
=
V V
Dp∗
(
+
2
−
φ
)
4 8
#2
(2
01
4)
Proposition 3 shows that the choice of the optimal strategy is driven by the relationship between content quality V and advertising effectiveness φ . Thus, for a given
content quality, a paid content strategy is optimal if the effectiveness of advertising is
sufficiently low. For intermediate levels of advertising effectiveness, a sampling strategy
that generates revenues from both sales and advertising on the free samples is optimal. If
advertising is sufficiently effective, the publisher should switch to a free content strategy.
The effects of φ and V on the optimal strategy can also be understood by inspection
of the advertising-sales revenue ratio. The ratio follows from (3) and is
R
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The ratio of advertising revenue to sales revenue tends to zero as φ approaches the lower
bound V8 , implying that the publisher should employ a paid content strategy. A sampling
strategy is optimal only if advertising is not “too effective,” that is, as long as φ ≤ V8 + 2.
Once φ exceeds this level, the publisher should switch to a free content strategy.
Strategy with Unknown Quality
co
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Summary. When content quality is known to consumers, the publisher’s optimal
strategy is determined by the relation between advertising effectiveness and content
quality. The more effective advertising is, the more free samples the publisher should
offer—even if it solely cannibalizes content demand.
Fo
rth
We first determine the optimal content strategy when consumers do not know content
quality and compare our findings to the results from the benchmark case. Next, we
study how the interplay of prior expectations and advertising effectiveness governs the
optimal choice of content strategy.
Optimal Pricing and Sampling. When content quality is not known to consumers,
the publisher makes its pricing and sampling decisions so as to
p
n
E
max π (p, n) = p 1 −
+ φ−
n
p,n
N
(N − n)Ṽ (n)
s.t.
p≥0
0 ≤ n ≤ N,
19
where expected content demand is given by (12) and inverse advertising demand by
(13). The only difference between this expected profit and the profit when content
quality is known to consumers is the dependence on expected quality rather than actual
(average) quality. Based on (15) and recalling that Ṽ (n) is the posterior estimate of
average quality V2 , we thus obtain that
(N − n)Ṽ (n)
.
2
01
4)
p(n) =
Substituting p(n) back into the profit function allows us to rewrite the profit maximization problem as
Ṽ (n) n
+ φ−
n
4
N
(2
n
π E (n) = (N − n)
0 ≤ n ≤ N.
s.t.
(16)
#2
max
Vo
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In contrast to our benchmark case, it is not possible to characterize the publisher’s
optimal pricing and sampling decisions (and hence profits) analytically. Nevertheless,
we have the following result.
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Proposition 4 (Optimal Strategy). Suppose that consumers are uncertain about the
upper bound of content quality V and that the profit function π E (n) is strictly concave.
Then, there are cut-off values φ = 41 (Ṽ (0) − NṼ 0 (0)) and φ = 2 + Ṽ (N)
4 such that a paid
content strategy is optimal for φ ≤ φ , a sampling strategy is optimal for φ ∈ (φ , φ ), and
a free content strategy is optimal for φ ≥ φ .
Fo
rth
co
m
This result is consistent with the insights from the benchmark case when quality
is known: a paid content strategy is optimal only if the advertising effectiveness is
sufficiently low, a sampling strategy is optimal for intermediate levels of the advertising
effectiveness, and the publisher should switch to a free content strategy once advertising
is sufficiently effective. Figure 3 illustrates the optimal strategy for varying advertising
∗ for the sampling strategy,
effectiveness φ and the expected profit for each strategy (πSC
∗ for the paid content strategy, and π ∗ for the free content strategy).
πPC
FC
Hence prior expectations determine the lower of the two cut-off values for a sampling strategy to be optimal whereas posterior expectations for sample size n = N determine the upper cut-off value. In effect, φ is determined by the impact of the “first” free
content part on posterior expectations, while φ is determined by posterior expectations
after inspection of the “last” free content part. The next lemma shows that the model
where quality V is not known to consumers nests the full information benchmark case
(see Proposition 3).
20
(Expected) Profit
∗
πFC
30
25
20
∗
πSC
15
∗
πPC
Sampling
Paid
1.5
2.0
2.5
α v0
8(α −1)
φ
Free
3.0
+1
3.5
φ
4.0
φ
(2
5
01
4)
10
l3
1
#2
Figure 4: Optimal strategy with unknown quality (for v
5,
2,
Figure 3: Optimal strategy with unknown quality (for v0 = 5, α = 2, V = 10, and
N = 10).
and the upper bound φ converges to
R
V
8
V
8
+ 2.
IJ
to
M
Vo
Lemma 4 (Cut-off Values). Suppose that consumers are uncertain about content quality V and that the profit function π E (n) is strictly concave. Then, when consumers have
correct quality expectations, that is, if v0 = V and α → ∞, the lower bound φ converges
Fo
rth
co
m
in
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The Impact of Prior Expectations. Proposition 4 shows that the optimal strategy
depends not only on advertising effectiveness φ and quality V as in the benchmark case,
but also on the specific values of the prior parameters v0 and α (as well as content size
N). Figure 4 illustrates the optimal strategy for given advertising effectiveness and prior
expectations. Panel A depicts the cut-off thresholds between the different strategies in
the (φ , v0 )-space (given α = 2). Similarly, Panel B illustrates the publisher’s optimal
strategy in the (φ , α)-space (given v0 = 5). Here prior expectations are correct and coincide with actual quality when v0 = 5 and α = 2. The following observation summarizes
our insights.
Observation 1 (Prior Expectations). If advertising effectiveness is high and actual
content quality is relatively low, it can be optimal for the publisher to adopt a sampling
strategy to generate advertising revenue even when it reduces prior quality expectations
and content demand. In contrast, if advertising effectiveness is low and actual content
quality is relatively high, it can be optimal to adopt a paid content strategy and not
reveal high quality, even though sampling would increase content demand.
21
v0
α
10
10
2.5
Sampling
Paid
88
2.0
66
Free
Free
Free
44
1.5
Sampling
1.5
1.5
2.0
2.0
Paid
2.5
2.5
3.0
3.0
3.5
3.5
φ
1.5
2.0
2.5
(A) Based on v0 and φ
(B) Based on
3.5
φ
(B) Based on α and φ
and
(2
(A) Based on v0 and
3.0
01
4)
22
#2
Figure 4: Optimal strategy (for V = 10 and N = 10).
co
m
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1
The shaded areas in Figure 4 illustrate these important managerial insights. Notice
that the larger areas correspond to the case where prior expectations are high relative
to actual content quality. In such market environments, the publisher should sacrifice
content demand to boost advertising revenues. The figure also shows that when prior
expectations are sufficiently low relative to actual content quality (that is, if v0 is small
or α is large), the choice is between a sampling strategy and a free content strategy
only. Intuitively, the publisher has an incentive to reveal its higher than expected quality
through free samples, possibly offering its content for free. In contrast, when prior
expectations are sufficiently high, the optimal strategy is either a paid content strategy
or a free content strategy. In such market environment, the publisher has no incentive to
reveal its lower than expected quality when φ is low.
Fo
rth
Summary. When actual content quality is not known to consumers, the optimal
strategy is determined by the relation between advertising effectiveness, prior quality
expectations, and posterior quality expectations. As in the benchmark case, employing
a paid content strategy is optimal only if advertising effectiveness is sufficiently low
compared to prior quality expectations. For intermediate levels of advertising effectiveness, the publisher should use a sampling strategy. The publisher should switch to
a free content strategy once advertising is sufficiently effective compared to posterior
quality expectations. Counter to intuition, it can be optimal for the publisher to generate
advertising revenue by adopting a sampling strategy even when sampling reduces both
prior quality expectations and content demand. In addition, it can be optimal for the
publisher to adopt a paid content strategy and to refrain from revealing high quality
through free samples.
22
6
Extensions
This section relaxes three key assumptions and studies the effects on our findings. First,
we allow the publisher to generate advertising revenues from paid content as well.
Second, we allow advertising effectiveness to depend on content quality. Third, we
introduce competition into the model.
Including Advertisements in the Paid Content
01
4)
6.1
(2
In this section, we extend the model by allowing it to include advertisements in both
the free articles and the paid content. To this end, we assume that the market price for
advertisements included in the paid content is given by
n̂
,
(17)
N
where n̂ ≡ N − n and φ p > 1 denotes the advertising effectiveness for ads in the paid
content. This inverse demand is a natural counterpart to the advertising demand a(n)
given by (13) and indicates that the ad price depends on the number of articles n̂ that
have not been offered as free samples. Differences in the levels of advertising effectiveness φ p and φ capture differences in reach or the degree of targeting in the advertising
markets for paid and free content.
When allowing for advertisements in the paid content, a consumer’s indirect utility
from the two options is

θ NE[V |v1 , . . . , vn ] + ξ N − p, from purchasing at price p
û(p, n) =
θ nE[V |v , . . . , v ] + ξ n,
from staying with the free samples.
in
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l3
1
#2
a p (n̂) = φ p −
m
1
n
Fo
rth
co
Importantly, the utility of the purchase option now depends on the overall number of
advertisements shown to the consumer rather than the number of ads contained in the
free samples only. This augmented specification implies that a consumers will purchase
the information good if and only if
θ (N − n)E[V |v1 , . . . , vn ] ≥ p − ξ (N − n),
(18)
that is, if the expected value of the content that has not been sampled exceeds its full
price p − ξ (N − n). Intuitively, the full price of the content is lower if consumers are
ad-lovers (ξ > 0) and higher if they are ad-avoiders (in which case exposure to the ads
in the paid content results in a nuisance cost ξ (N − n) that has to be added to the price
p). From the purchase condition (18), expected content demand can be derived as
1
p
E
D̂ (p, n) = max 0, 1 −
−ξ
.
(19)
E[V |v1 , . . . , vn ] N − n
23
Compared to the case where consumers are ad-neutral, content demand is higher when
consumers are ad-lovers and lower when consumers are ad-avoiders.
The publisher makes its pricing and sampling decisions so as to
n
E
E
max π (p, n) = (p + R p (n̂))D̂ (p, n) + φ −
n
p,n
N
p≥0
s.t.
01
4)
0 ≤ n ≤ N,
#2
(2
where expected content demand is given by (19) and inverse advertising demand by
(17). Notice that R p (n̂) ≡ a p (n̂)n̂ are the additional revenues from including ads in the
paid content. By definition, R p = 0 under a free content strategy, while R p = (φ p − 1)N
under a paid content strategy. We summarize our insights as follows.
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Observation 2 (Ads Included in Paid Content). When the publisher includes advertisements in the paid content and consumers are neutral about advertisements or
ad-lovers, the range of advertising effectiveness φ for which the sampling strategy is
best expands. In contrast, when consumers are ad-avoiders, the range of φ for which
the sampling strategy is optimal can shrink.
Endogenizing Advertising Effectiveness
Fo
6.2
rth
co
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Figure 5 illustrates the profit effects of including advertisements in the paid content
when consumers are neutral about advertisements. Intuitively, exploiting revenues from
advertisements in the paid content increases the unit margin from selling content, which
translates into a higher profit under a sampling strategy. These profit effects are more
pronounced when advertising effectiveness for ads in paid content φ p increases. Further,
the profit under a sampling strategy is higher when the consumers are ad-lovers (for
given φ p ) and lower when they are ad-avoiders.
Up to now, we considered advertising effectiveness to be exogenous and independent
of content quality. In this section, we relax this assumption and allow the advertiser’s
willingness to pay for advertisements to be positively related to expecteded posterior
quality, in effect having product quality have a halo effect on ad effectiveness. Specifically, we let inverse advertising demand be given by
a(n) = φ̃ (n) −
24
n
N
(20)
(Expected) Profit
∗
πFC
30
25
20
∗
πSC
15
∗
πPC
5
Sampling
Paid
1.5
2.5
Free
3.0
3.5
′
4.0
φ′
φ
(2
φ
2.0
01
4)
10
l3
1
#2
Figure 6: Optimal strategy with (dashed lines) and without advertisements in paid conFigure 5: Optimal strategy with (dashed lines) and without advertisements in paid content (solid lines) for ξ = 0, v0 = 5, α = 2, V = 10, N = 10, and φ p = 1.1.
M
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and capture the effect of expected posterior quality Ṽ (n) on quality-adjusted advertising
effectiveness φ̃ (n) in the following way:
IJ
R
φ̃ (n) ≡ φ
Ṽ (n)
,
Ṽ (0)
Fo
rth
co
m
in
g
where φ is advertising effectiveness (as introduced in Section 4) and Ṽ (0) denotes prior
quality expectations. This specification reflects the idea that free samples become more
attractive as an advertising platform when consumers’ posterior expectations exceed
their prior expectations, which in turn increases the advertiser’s willingness to pay for
the advertisements (and vice versa).
When advertising effectiveness is positively related to posterior content quality,
offering free samples affects the willingness to pay for advertisements in two ways:
Through changes in the quality-adjusted advertising effectiveness φ̃ (n) and through
changes in the number of ads shown to consumers. Therefore, advertising demand
can be increasing in the number of free samples when prior expectations are sufficiently
low relative to consumers’ updated expectations (see Panel A in Figure 6 for a graphical
illustration). Over the range of where a(n) increases, the marginal benefit of higher
advertising effectiveness outweighs the disutility of showing an additional ad to consumers.
25
α
a(n)
10
4
8
Paid
Ṽ (n)
3
3
2
2
1
1
a(n) = φ Ṽ (0) − Nn
6
Sampling
4
2
Free
a(n) = φ − Nn
2
2
4
6
4
6
8
10 10
8
n
1.5
2.0
2.5
3.0
3.5
01
4)
4
φ
(B) Optimal strategy
and
(2
(A) Advertising demand
Advertisingdemand
demandwith
withquality-dependent
quality-dependentadvertising
advertisin effectiveness
(A)
(A)Advertising
(B) Based on
#2
Figure 6: Impact of endogenizing advertising effectiveness (for α = 2, V = 10, N = 10;
in addition, in Panel A v0 = 2 and φ = 2).
1
4 4
s.t.
p≥0
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1 1
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The publisher makes
its pricing and sampling decisions so as to
3 3
p
n
E
max 2 2 π (p, n) = p 1 −
+ φ̃ (n) −
n
p,n
N
(N − n)Ṽ (n)
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0 ≤ n ≤ N,
2 2
4 4
6
8
10
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where expected content demand is given by (12) and inverse advertising demand by
(20). The next observation summarizes our insights.
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Observation 3 (Endogenous Ad Effectiveness). When consumers’ prior expectations
are low and the advertiser’s willingness to pay for advertisements is positively related
to the expected posterior content quality, it can be optimal for the publisher to adopt a
free content strategy even when baseline advertising effectiveness φ is low.
Panel B of Figure 6 illustrates this observation. In the figure, the lines depict the
cut-off thresholds between the different strategies in the (φ , v0 )-space. The solid lines
correspond to the case with quality-adjusted advertising effectiveness and show that a
free content strategy can also be optimal for low φ , whereas a sampling strategy yields
a higher profit when advertising effectiveness is exogenous (indicated by the dashed
lines reproduced from Panel A in Figure 4). This occurs because when prior expectations are low, sampling not only reveals high quality, but also increases the advertiser’s
willingness to pay for ads and thus to boost advertising revenues.
26
6.3
The Impact of Competition
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Thus far, we have examined a publisher operating in a monopoly setting. Here, we allow
for competition between two publishers that offer differentiated information goods. We
add horizontal product differentiation to capture the intensity of competition between
the two publishers.10 In the newspaper industry for instance, horizontal product differentiation may arise due different political opinions among consumers (Gabszewicz et
al. 2005).
The analysis of the competitive case indicates that, as in the monopoly case, advertising effectiveness is a key driver of the publishers’ strategy choice. Specifically,
if consumers’ prior expectations about content qualities are similar and advertising effectiveness is high, it is optimal for both publishers to adopt a free content strategy in
equilibrium. However, two other drivers that affect strategy choice in the competitive
case: the gaps in prior expectations about the quality of the competing products and the
degree of horizontal product differentiation. The following observation summarizes our
insights.
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Observation 4 (Competition). If the gap in prior expectations regarding the product
qualities is large and advertising effectiveness is high, both publishers should adopt a
sampling strategy. As the degree of horizontal product differentiation increases and the
products become less substitutable, the parameter region in which the sampling strategy
is optimal for both publishers shrinks.
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Counter to intuition, our results show that it is not per se optimal to choose a free
content strategy when advertising effectiveness is high. What matters in addition is
the gap in prior expectations between the two publishers: if it is small, then both firms
should adopt a free content strategy. Instead, if the gap in prior expectations is large,
then both firms should adopt a sampling strategy. Intuitively, the publisher that faces
lower prior expectations from consumers has a stronger incentive to reveal its higher
than expected quality—and it is a best-response of the rival publisher to also adopt a
sampling strategy.
The second insight is that the parameter region in which the sampling strategy is
optimal for both publishers shrinks when products are perceived as less substitutable
(e.g., when the readers with left-wing preference consider a right-wing newspaper a
less good alternative). For the publishers, this results in less ability to acquire consumers
who purchase from the competitor. Consequently, the publishers try to generate as much
revenue as possible from the advertising market by employing a free content strategy.
10 All
details of the model and the analysis of the competitive case are in the Appendix.
27
This result mirrors the findings from the monopoly case: as the degree of horizontal
product differentiation increases and publishers tend to become monopolists in their
respective market segment, they should employ a free content strategy once advertising
effectiveness exceeds a certain threshold level.
7
Conclusion
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This paper analyzed digital content strategies when content sampling serves the dual
purpose of disclosing content quality and generating advertising revenue. One of the
key features of the model is that consumers evaluate free samples of their choice within
the limit set by the publisher. Consumers then use the information gathered from the free
samples to update their prior expectations about content quality in a Bayesian fashion.
Taking consumers’ quality updating into account, the publisher can adopt a sampling
strategy, a paid content strategy, or a free content strategy.
We derived several important results. First, we show in our general framework how
the publisher’s advertising-sales revenue ratio and hence its optimal content strategy is
determined by characteristics of both the content market and the advertising market.
We capture the characteristics of the content market by the elasticity of consumers’
updated quality expectations and the elasticities of content demand with respect to price,
sample size, and posterior quality. The corresponding characteristic in the advertising
market is the price elasticity of advertising demand. We show that, all else equal, the
advertising-sales revenue ratio is higher the lower the price elasticity of content demand,
the higher the elasticity of content demand with respect to sample size, and the lower
the price elasticity of advertising demand. In addition, managers can expect the ratio
of advertising revenue to sales revenue to be low when sampling increases consumers’
quality expectations (resulting from the expansion effect) and high when sampling reduces quality expectations (resulting from the cannibalization effect).
Second, when consumers make purchase decisions based on the price of the content
behind the paywall, content demand depends on consumers’ posterior quality expectations, which can be influenced by the publisher through its sampling decision. Expected
content demand has the natural properties that it is decreasing in price and increasing
in expected posterior quality. Further, sampling has a demand-enhancing effect through
consumers’ learning when prior expectations are sufficiently low (even though sampling
produces a cannibalization effect). We uncovered the rule of thumb that sampling increases content demand if the elasticity of consumers’ updated expectations exceeds the
ratio of sampled to paid content.
28
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Third, we characterize the publisher’s optimal content strategy when consumers
are uncertain about actual content quality and learn about it through inspection of free
samples. We identify two cut-off values that determine the publisher’s optimal content
strategy: a lower bound that depends on prior quality expectations (separating paid from
sampling strategies) and an upper bound that depends on posterior quality expectations
(separating sampling from free content strategies). From a managerial perspective, it
can be optimal to reduce both prior quality expectations and content demand in order
to generate advertising revenue. In addition, it can be optimal for managers to adopt a
paid content strategy and to refrain from revealing high quality through free samples.
We also explore several model extensions that are relevant for managerial decision
making. First, when the publisher also includes advertisements in the paid content, the
analysis shows that the cut-off values between the content strategies depend not only
on the relation between advertising effectiveness and updated quality expectations, but
also on consumers’ attitudes towards advertisements. Second, when the willingness to
pay for advertisements is related to content quality, we show that a free content strategy
can be optimal even when advertising effectiveness is low. Third, we show that under
competition the advertising effectiveness is a key driver of the publishers’ equilibrium
strategy choices. This analysis also sheds light on recent developments in the newspaper
industry and explains why publishers have moved away from pure advertising-financed
business models to metered models (Abramson 2010).
Our general framework offers several avenues for future research. Regarding consumers, we assume they correctly update quality expectations based on their sample
experience. One alternative is to assume a consistent bias in the consumers’ judgments.
In addition, in circumstances where the firm selects the samples, consumers are likely
to adjust (discount) observed quality, assuming that the publisher has provided a nonrepresentative set of samples to choose from in order to persuade them to buy the paid
content. Further, one could assume that consumers do not evaluate the quality of all free
samples because of “sampling costs,” for example due to the opportunity cost of time or
mental costs. One could also enrich the model by allowing for internal competition,
where the publisher offers two websites to serve different categories of consumers,
which relates to the versioning literature.11 Thus, there are several further directions
which research in these areas could take. We view this paper a step in this process and
hope the paper encourages work in these and related directions.
11 For
instance, The Boston Globe operates the ad-supported site boston.com and the subscriber-only
site BostonGlobe.com.
29
Appendix
A.1
Sampling From a Uniform Distribution
01
4)
The Pareto Distribution. A random variable X has a Pareto distribution with parameters w0
and α (w0 > 0 and α > 0) if X has a density
( αwα
0
for x > w0
xα+1
f (x|w0 , α) =
0
otherwise.
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#2
(2
αw0
For α > 1 the expectation of X exists and it is given by E(X) = α−1
. Regarding sampling from
a uniform distribution, we use the following result.
Theorem (DeGroot 1970).12 Suppose that X1 , . . . , Xn is a random sample from a uniform distribution of the interval (0,W ), where the value of W is unknown. Suppose also that the prior
distribution of W is a Pareto distribution with parameters w0 and α such that w0 > 0 and α > 0.
Then the posterior distribution of W when Xi = xi (i = 1, . . . , n) is a Pareto distribution with
parameters w00 and α + n, where w00 = max{w0 , x1 , . . . , xn }.
Vo
Proof. For w > w0 , the prior density function ξ of W has the following form:
1
wα+1
.
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ξ (w) ∝
in
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Furthermore, ξ (w) = 0 for w ≤ w0 . The likelihood function fn (x1 , . . . , xn |w) of Xi = xi (i =
1, . . . , n), when W = w (w > 0) is given by:13
(
1
wn for max{x1 , . . . , xn } < w
fn (x1 , . . . , xn |w) = f (x1 |w) · · · f (xn |w) =
0 otherwise.
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It follows from these relations that the posterior p.d.f. ξ (w|x1 , . . . , xn ) will be positive only for
values w such that w > w0 and w > max{x1 , . . . , xn }. Therefore, ξ (w|·) > 0 only if w > w00 . For
w > w00 , it follows from Bayes’ theorem that
ξ (w|x1 , . . . , xn ) ∝ fn (x1 , . . . , xn |w)ξ (w) =
1
wα+n+1
(the marginal joint probability density function fn (x1 , . . . , xn ) of X1 , . . . , Xn is a normalizing constant).
12 Theorem
1, p. 172.
W = w, the random variables X1 , . . . , Xn are independent and identically distributed and the
common probability density function of each of the random variables is f (xi |w).
13 Given
30
A.2
Proofs
Proof of Proposition 1. By strict concavity of the profit function, the solution to problem (2)
must satisfy the necessary and sufficient first-order conditions
∂ D(p, n; Ṽ (n))
+ λ1 = 0
∂p
D(p, n; Ṽ (n) + (p − cs )
01
4)
∂ D(p, n; Ṽ (n)) ∂ D(p, n; Ṽ (n)) 0
(p − cs )
+
Ṽ (n)
∂n
∂ Ṽ
(A.1)
+ a0 (n)n + a(n) + λ2 − λ3 = 0
(A.2)
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(2
and the constraints λ1 p = 0, λ2 n = 0, and λ3 (n − N) = 0, where the λi ’s are non-negative real
numbers (whose existence is assured by the Kuhn-Tucker theorem). Suppressing the arguments
of content demand, (A.1) can be rewritten as
1
p − cs
λ1
=
1+
.
(A.3)
p
ηp
D
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Vo
Dividing (A.2) through p and substituting from (A.3) produces
1
a0 (n)n a(n) λ2 − λ3
λ1
∂D ∂D 0
Ṽ (n) +
1+
+
+
+
= 0.
ηp
D
∂ n ∂ Ṽ
p
p
p
in
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1
(from the inverse function theorem) and using the definitions of the
Recalling that n0 (a) = a0 (n)
respective elasticities, the preceding equation can be rearranged to obtain
λ1
1
λ2 − λ3
pD 1
1+
ηn − ηṼ Ṽn = 1 −
+
.
(A.4)
an η p
D
ηa
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Under a sampling strategy there is an interior solution and hence the λk ’s are zero. Thus, (A.4)
can be rewritten as
an
ηn − ηṼ εṼ
=
.
Dp (1 − η1 )η p
a
Fo
Proof of Proposition 2. (a) In order to calculate E [ṽ0 (n)] when v0 < V , we first derive the distribution of ṽ0 (n) = max{v0 ,V1 , . . . ,Vn }. Before doing so, we state a preliminary fact: The
distribution function of M = max{V1 , . . . ,Vn } is given by
FM (t) ≡ Pr{max{V1 , . . . ,Vn } ≤ t}
= Pr {{V1 ≤ t} ∩ . . . ∩ {Vn ≤ t}}
n
n
t
.
= ∏ Pr {Vi ≤ t} =
V
i=1
(A.5)
As an immediate implication, the density function of M is given by
fM (t) =
nt n−1
.
Vn
31
(A.6)
Next, we derive the density function of ṽ0 (n). By definition, ṽ0 (n) cannot be smaller than v0 .
Therefore, ṽ0 (n) = v0 if and only if max{V1 , . . . ,Vn } ≤ v0 . The probability of this event follows
from (A.5) and it is given by
n
v0
.
FM (v0 ) =
V
(2
(A.7)
#2
nt n−1
f˜(t) =
, if v0 ≤ t ≤ V
Vn
by (A.6). The distribution of ṽ0 (n) has a mixed structure with
n
v0
Pr {ṽ0 (n) = v0 } =
V
01
4)
For ṽ0 (n) > v0 , let F̃(·) denote the truncated distribution function of ṽ0 (n). After removing
the lower part of the distribution, we have F̃(t) = FM (t) − FM (v0 ) for t ∈ [v0 ,V ]. This implies
f˜(t) = fM (t) for t ∈ [v0 ,V ], and hence
and density
(A.8)
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1
nt n−1
f˜(t) =
, if v0 ≤ t ≤ V .
Vn
The expectation of this mixed distribution is given by
n Z V n
v0
nt
E [ṽ0 (n)] = v0
dt
+
V
v0 V
vn+1 + nV n+1
= 0
.
(n + 1)V n
in
g
Substituting this expression into (7) produces (8). (b) If v0 ≥ V , then ṽ0 (n) is equal to v0 , which
in turn implies that E [ṽ0 (n)] = v0 . Substituting this expression into (7) yields (9).
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Proof of Lemma 1. If v0 < V , the quality gap can be expressed as
Ṽ (n) −
vn+1 (α + n) −V n+1 (α − 1)
V
.
= 0
2
2(α + n − 1)(n + 1)V n
(A.9)
Fo
Clearly, the sign of the quality gap depends only on the sign of numerator (A.9). The latter can
easily be rearranged to obtain (11). If v0 ≥ V , the quality gap can be written as
(α + n) v0 −V +V
V
Ṽ (n) − =
,
2
2(α + n − 1)
which is strictly positive by our assumptions.
Proof of Lemma 2. Differentiating (12) with respect to n yields
(N − n)Ṽ 0 (n) − Ṽ (n) p
∂ DE (p, n)
=
.
2
∂n
(N − n)Ṽ (n)
Clearly, sampling is demand-enhancing if (N − n)Ṽ 0 (n) − Ṽ (n) > 0, which can be rewritten as
Ṽ 0 (n)n
n
> N−n
.
Ṽ (n)
32
Proof of Lemma 3. The optimal decisions on size of the sample and on the price follow from
solving the Kuhn-Tucker conditions in Proposition 1.14 Under a sampling strategy, the λk ’s are
zero and it follows that p∗ = NV (8(2 − φ ) + V )/64 and n∗ = N(8φ − V )/16. Under a paid
content strategy, λ1 = λ3 = 0, leading to p∗ = NV /4 and n∗ = 0. Under a free content strategy,
we have that p∗ = 0 and n∗ = N.
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Proof of Proposition 3. Using Lemma 3, it is straightforward to derive the profits under a free
content strategy (FC) and a paid content strategy (PC). The profits are given by, respectively,
∗ = (φ − 1)N and π ∗ = NV /8. Comparing the two profits shows that π ∗ ≥ π ∗ if and
πFC
PC
FC
PC
only if φ > V8 + 1. The profit under a sampling strategy (SC) follows from Lemma 3 and is
∗ = N V 2 − 16V (φ − 2) + 64φ 2 /256. Employing a sampling strategy is optimal if
given by πSC
∗ > π ∗ and π ∗ > π ∗ . It is immediate that these conditions hold if φ ∈ ( V , V + 2). A paid
πSC
PC
SC
FC
8 8
∗ ≥ π ∗ and π ∗ ≥ π ∗ , that is, if φ ≤ V . A free content strategy
content strategy is optimal if πPC
SC
PC
FC
8
V
∗
∗
∗
∗
is optimal if πFC ≥ πSC and πFC ≥ πPC , that is, if φ ≥ 8 + 2.
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Proof of Proposition 4. At an interior solution, the optimal sample size n∗ satisfies the first-order
condition
Ṽ 0 (n∗ ) Ṽ (n∗ )
2n∗
(N − n∗ )
−
+φ −
= 0.
4
4
N
For a corner solution involving n∗ = 0, the Kuhn-Tucker conditions imply
R
M
NṼ 0 (0) Ṽ (0)
−
+φ ≤ 0
4
4
⇐⇒
φ ≤ φ.
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At the other extreme, when n∗ = N, the Kuhn-Tucker conditions require that
g
Ṽ (N)
+φ −2 ≥ 0
4
in
−
⇐⇒
φ ≥ φ.
φ=
(2α(α − 1) + N) v0
.
16(α − 1)2
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Proof of Lemma 4. Using the definition of Ṽ (n) in (10), the lower bound can be expressed in
terms of the underlying model parameters as
Setting v0 = V and letting α → ∞ yields that φ → V8 . Likewise, we have that
φ=
(α + N)V
+ 2.
8(α + N − 1)
Letting α → ∞, we obtain φ → V8 + 2.
14 It
is straightforward to show that the objective function is concave for all parameter values.
33
A.3
Analysis of the Competitive Case
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We study competition between two publishers indexed by i = 1, 2 and suppose that they offer
differentiated information goods to a population of consumers through an online platform. We
frame the analysis in terms of the newspaper market and assume that the readers (consumers) can
be politically ranked from left to right on the political spectrum captured by the unit interval [0, 1]
(Gabszewicz et al. 2005). Horizontal differentiation captures different editorial opinions, and
we assume that the publishers are located at the extremes of the political spectrum at x1 = 0 and
x2 = 1, respectively. Vertical differentiation captures the firms’ different content qualities such as
the level of investigative reporting (which are unrelated to the publishers’ political orientation).
We again assume that the perceived quality qi (ni ) of information good i is equal to its number
of content parts Ni multiplied by its expected posterior quality, that is, qi (ni ) = Ni E[Vi |v1i , . . . , vni ].
Consumers make a discrete choice and decide which of the two information goods to purchase.
A consumer’s conditional indirect utility from buying information good i is given by
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ui (x; pi , ni ) = qi (ni ) − τ |x − xi | − pi ,
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where x ∈ [0, 1] is the consumer’s political orientation and the parameter τ > 0 captures the
sensitivity to horizontal mismatch |x − xi |. Intuitively, the mismatch arises because consumers
make a discrete choice and cannot purchase the information good that perfectly matches their
political preferences. Political orientations are drawn independently across consumers from a
uniform distribution over the interval [0, 1].
The publishers compete for consumers by making their pricing and sampling decisions. To
derive expected content demands, we determine the location x̂ of the consumer who is indifferent
between buying from publisher 1 and from publisher 2 for given prices p = (p1 , p2 ) and sample
sizes n = (n1 , n2 ). Clearly, the location of the indifferent consumer x̂(p, n) is a solution to the
indifference condition u1 (x̂(p, n)) = u2 (x̂(p, n)), which ensures that the indirect utilities from
the two information goods are the same. With linear mismatch, the consumer located at x̂(p, n)
segments the market: Consumers located to the left of x̂(p, n) purchase from publisher 1, while
consumers located to the right of x̂(p, n) purchase from publisher 2.15 Ignoring cannibalization,
publisher 1 thus faces x̂(p, n) consumers, while publisher 2 faces 1 − x̂(p, n) consumers. To
i
denote the
capture that sampling not only reveals quality but also cannibalizes sales, we let NiN−n
i
conditional purchase probability given sample size ni . Hence expected content demands can be
expressed as
DE1 (p, n) =
N1 − n1
x̂(p, n) and
N1
DE2 (p, n) =
N2 − n2
(1 − x̂(p, n)),
N2
Consumers thus choose their preferred publisher based on prices and posterior quality expeci
tations and subsequently purchase the content with probability NiN−n
. Similar to the monopoly
i
15 See
Anderson et al. (1992) for an in-depth treatment of Hotelling-type models.
34
Firm 2
Firm 1
PC
π1PP
SC
π1SP
FC
π1FP
SC
π1PS
π2PP
π1SS
π2SP
π1FS
π2FP
FC
π1PF
π2PS
π1SF
π2SS
π1FF
π2FS
π2PF
π2SF
01
4)
PC
π2FF
#2
(2
Figure A.1: Strategy choices and corresponding profits.
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case, the sampling decision ni therefore has a direct effect on expected content demand through
the conditional purchase probability (a cannibalization effect) and an indirect effect on x̂(p, n)
(an expansion effect). Note that publisher i’s expected content demand is zero under a free
content strategy due to the cannibalization effect.
Publisher i makes its pricing and sampling decisions so as to
ni
E
E
ni
max πi (p, n) = pi Di (p, n) + φi −
pi ,ni
Ni
pi ≥ 0
IJ
s.t.
g
0 ≤ ni ≤ Ni ,
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where φi is the advertising effectiveness of publisher i’s advertising. Compared to the monopoly
case, each publisher now has to take into account the rival’s choice of strategy to make its optimal
decision. Thus, there are nine possible outcomes, summarized in Figure A.1. If both firms use
a paid content strategy, the firms’ corresponding (expected) profits are denoted by π1PP and π2PP ,
respectively (and likewise for the other outcomes). For each outcome, the profit levels can be
obtained by solving the publishers’ decision problems. The optimal strategy choices are then
obtained as a Nash equilibrium of the matrix game depicted in Figure A.1.
To analyze the optimal strategy choice, we focus on a market environment where consumers
have different prior beliefs about the content quality of the two publishers. Specifically, we
suppose that the consumers’ minimum estimate v01 differs from v02 , while the publishers are
actually symmetric and in particular offer the same quality spectrum (V 1 = V 2 ). Figure A.2
illustrates the publishers’ optimal strategy choices as a function of the gap in prior expectations
and advertising effectiveness (φi ≡ φ ). The figure holds v02 constant (at v02 = 1) and plots
different values of v01 on the vertical axes. Notice that where v01 < v02 , consumers believe that
publisher 1 offers a lower content quality than publisher 2.
35
v01
1.25
1.
(FC, FC)
0.75
τ↑
0.5
(SC, SC)
01
4)
τ = 0.50
τ = 0.75
τ =1
0.25
φ
2.25
2.5
(2
2.
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Figure A.2: Equilibrium strategies (for v02 = 1, α = 2, Vi = 3, and Ni = 10).
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The key insights from the analysis of the competitive case can be summarized as follows: If
consumers’ prior expectations about content qualities are similar and advertising effectiveness
is high, it is optimal for both publishers to adopt a free content strategy in equilibrium. Instead,
if the gap in prior expectations is large and advertising effectiveness is high, both publishers
should adopt a sampling strategy. Further, the parameter region in which the sampling strategy
is optimal for both publishers shrinks when consumers are more sensitive to horizontal mismatch
and products thus are less substitutable.
To understand these insights, it is important to notice that each point in the (φ , v01 )-space
in Figure A.2 corresponds to a (pure-strategy) Nash equilibrium of the matrix game described
above.16 The solid line depicts the cut-off threshold between the two types of Nash equilibria:
sampling (SC, SC) and free content (FC, FC). Counter to intuition, it is not per se optimal to
choose a free content strategy when advertising effectiveness φ is high. What matters in addition
is the gap in prior expectations among the two publishers: if it is small, then both firms should
adopt a free content strategy. Instead, if the gap in prior expectations is large, then both firms
should adopt a sampling strategy. Intuitively, publisher 1 has a stronger incentive to reveal its
higher than expected quality—and it is a best-response of publisher 2 to also adopt a sampling
strategy (that is, publisher 2 attains a higher profit under a sampling strategy than under a free
content strategy when taking publisher 1’s strategy as given).
Figure A.2 also illustrates that the parameter region in which the sampling strategy is optimal for both publishers shrinks when consumers are more sensitive to horizontal mismatch
τ. Intuitively, a higher τ means that products are less substitutable from the viewpoint of the
consumers (e.g., when readers with left-wing preferences consider a right-wing newspaper a less
16 The
code to numerically compute the Nash equilibria is available from the authors upon request.
36
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4)
good alternative). For the publishers, this results in a lower ability to engage in business stealing
in the content market. Consequently, the firms try to generate as much revenue as possible in the
advertising market by employing a free content strategy. This comparative statics result mirrors
the findings from the monopoly case (cf. Figure 3): When τ increases and publishers become
monopolists on their respective market segment, the firms should employ a free content strategy
once φ exceeds a certain threshold level—irrespective of the gap in prior expectations (observe
that this threshold level lies at around φ = 2 in Figure A.2).
Up to now, the focus has been on strategy choices in the upper-right corner of the matrix
game in Figure A.1. The reason is that these strategy combinations capture the essence of the
debate in the newspaper industry: whether to offer the content for free or to employ a metered
model. Of course, there is also a symmetric industry configuration where both publishers employ
a paid content strategy. Unsurprisingly, this equilibrium arises if advertising effectiveness is low.
In addition, there are asymmetric strategy choices such as (PC, SC), which are optimal when
consumers overestimate the content quality of publisher 1 (and hence the incentive to not reveal
low quality) and underestimate the content quality of publisher 2 (and hence the incentive to
reveal high quality through free samples).
M
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