ABSTRACT
Title of Dissertation Proposal: ESSAYS ON DIGITAL CONTENT
PROVISION AND CONSUMPTION
Chutian Wang
Doctor of Philosophy, 2022
Dissertation Directed by: Associate Professor, Yogesh V. Joshi
Department of Marketing
Associate Professor, Bo ?Bobby? Zhou
Department of Marketing
Consumption of digital content has become an inseparable part of consumers?
lives today. As providers of digital content, media platforms continuously seek
to pursue pricing and product design strategies that increase their profits. This
dissertation studies media platforms? digital content provision and consumers? con-
sumption decisions. In the first essay, we focus on the pricing of digital content and
analyze the impact of consumers? endogenous content consumption on platforms?
paywall strategies. Paywalls increase subscription revenues for platforms, but they
also impact content consumption and thus advertising revenues. We build an ana-
lytical model that endogenizes consumers? content consumption decisions. We find
that under moderate ad rates, a metered paywall under which a limited amount
of content is provided for free is optimal when consumers display sufficient hetero-
geneity in their costs of consuming content. We also study how the amount of free
content and the subscription price vary with changes in the advertising rate and
consumer preference. In the second essay, we analyze the accuracy of news reported
by the news media. When consumers are seeking the truth and accurate reporting
is costly, determining the optimal level of accuracy in reporting is a strategic de-
cision for a profit-maximizing media firm. We build an analytical model to study
this media firm decision. When consumers and the media firm are both initially
uncertain about the true state of the world, we show that the media firm always
chooses full accuracy if investigation and reporting are of low cost. However, if
achieving accuracy is sufficiently costly, the media firm provides news only when
consumers? priors regarding the truth are not too extreme, so that they see enough
value in news consumption. Interestingly, consumers? truth-seeking and the firm?s
profit maximization can lead to reporting inaccuracy and exaggeration of the more
likely state a priori. We also discuss the implications of polarization in consumers?
prior beliefs and the media firm?s different objectives on the accuracy of news.
ESSAYS ON DIGITAL CONTENT PROVISION AND
CONSUMPTION
by
Chutian Wang
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
2022
Advisory Committee:
Associate Professor Yogesh V. Joshi, Chair
Associate Professor Bo ?Bobby? Zhou, Co-Chair
Professor David Godes
Professor P.K. Kannan
Professor Daniel Vincent, Dean?s Representative
? Copyright by
Chutian Wang
2022
Table of Contents
Table of Contents ii
List of Tables v
List of Figures vi
1 Introduction 1
2 Endogenous Consumption and Metered Paywalls 5
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Related Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.1 The Media Platform . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.2 Consumers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.3 Timing of the Game . . . . . . . . . . . . . . . . . . . . . . . 23
2.4 Model Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4.1 Consumers? Decisions . . . . . . . . . . . . . . . . . . . . . . . 24
2.4.2 The Media Platform?s Decisions . . . . . . . . . . . . . . . . . 25
2.4.3 Equilibrium Strategy . . . . . . . . . . . . . . . . . . . . . . . 28
2.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.5.1 Free Content Provision . . . . . . . . . . . . . . . . . . . . . . 34
2.5.2 Information Flow . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.5.3 Subscription Price . . . . . . . . . . . . . . . . . . . . . . . . 45
2.6 Extension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.6.1 Negative Price and Price-Per-Unit Strategy . . . . . . . . . . 46
2.6.2 Correlation Between Valuation and Consumption Cost . . . . 51
2.7 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3 The Accuracy of News 65
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.2 Related Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.3.1 Media Firm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.3.2 News Consumers . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.3.3 Timing of the Game . . . . . . . . . . . . . . . . . . . . . . . 83
3.3.4 Model Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 84
ii
3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.5 Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.5.1 Impact of Polarization on News Accuracy . . . . . . . . . . . 96
3.5.2 Media Firm As An Objective-Welfare Maximizer . . . . . . . 103
3.5.3 Media Firm with Dual Objectives . . . . . . . . . . . . . . . . 112
3.6 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4 Conclusion 126
A Proof of Lemmas and Propositions in Chapter 2 128
A.1 Proof of Lemmas and Propositions . . . . . . . . . . . . . . . . . . . 128
A.1.1 Proof of Lemma 1 . . . . . . . . . . . . . . . . . . . . . . . . . 128
A.1.2 Proof of Lemma 2 . . . . . . . . . . . . . . . . . . . . . . . . . 129
A.1.2.1 If the Firm Obtains Subscriptions From Both H and
L Segments . . . . . . . . . . . . . . . . . . . . . . . 129
A.1.2.2 If the Firm Obtains Subscriptions Only From the H
segment . . . . . . . . . . . . . . . . . . . . . . . . . 130
A.1.2.3 If the Firm Only Earns Advertising Revenue . . . . . 131
A.1.3 Proof of Lemma 3 . . . . . . . . . . . . . . . . . . . . . . . . . 132
A.1.4 Proof of Proposition 1 . . . . . . . . . . . . . . . . . . . . . . 133
A.1.5 Proof of Proposition 2 . . . . . . . . . . . . . . . . . . . . . . 134
A.1.6 Proof of Lemma 4 . . . . . . . . . . . . . . . . . . . . . . . . . 134
A.1.7 Proof of Proposition 3 . . . . . . . . . . . . . . . . . . . . . . 135
A.1.8 Proof of Proposition 4 . . . . . . . . . . . . . . . . . . . . . . 135
A.1.9 Proof of Lemma 5 . . . . . . . . . . . . . . . . . . . . . . . . . 136
A.2 Other Results and Proof . . . . . . . . . . . . . . . . . . . . . . . . . 138
A.2.1 Free Content Provision . . . . . . . . . . . . . . . . . . . . . . 138
A.2.2 Information Flow . . . . . . . . . . . . . . . . . . . . . . . . . 138
A.2.3 Subscription Price . . . . . . . . . . . . . . . . . . . . . . . . 142
A.2.4 Correlation between c and v . . . . . . . . . . . . . . . . . . . 143
A.2.4.1 Positive Correlation between c and v . . . . . . . . . 143
A.2.4.2 Negative Correlation between c and v . . . . . . . . 144
A.2.5 Heterogeneity in v . . . . . . . . . . . . . . . . . . . . . . . . 145
B Proof of Lemmas and Propositions in Chapter 3 151
B.1 Proof of Lemmas and Propositions . . . . . . . . . . . . . . . . . . . 151
B.1.1 Proof of Lemma 1 . . . . . . . . . . . . . . . . . . . . . . . . . 151
B.1.2 Proof of Proposition 1 . . . . . . . . . . . . . . . . . . . . . . 153
B.1.3 Proof of Proposition 2 . . . . . . . . . . . . . . . . . . . . . . 154
B.1.4 Proof of Proposition 3 . . . . . . . . . . . . . . . . . . . . . . 155
B.1.5 Proof of Corollary 1 . . . . . . . . . . . . . . . . . . . . . . . 155
B.1.6 Proof of Lemma 2 . . . . . . . . . . . . . . . . . . . . . . . . . 155
B.1.7 Proof of Proposition 4 . . . . . . . . . . . . . . . . . . . . . . 156
B.1.8 Proof of Lemma 3 . . . . . . . . . . . . . . . . . . . . . . . . . 157
B.1.9 Proof of Proposition 5 . . . . . . . . . . . . . . . . . . . . . . 158
iii
B.1.10 Proof of Lemma 4 . . . . . . . . . . . . . . . . . . . . . . . . . 159
B.1.11 Proof of Proposition 6 . . . . . . . . . . . . . . . . . . . . . . 160
B.1.12 Proof of Proposition 7 . . . . . . . . . . . . . . . . . . . . . . 161
B.2 Other Results and Proof . . . . . . . . . . . . . . . . . . . . . . . . . 161
B.2.1 Asymmetric Value for States . . . . . . . . . . . . . . . . . . . 161
B.2.2 Ex Post Polarization and the Impact of News . . . . . . . . . 163
iv
List of Tables
2.1 Equilibrium Strategy When 0 < ? < 1 . . . . . . . . . . . . . . . . . 61
3.1 Equilibrium Strategy When 0 < ? < 1 . . . . . . . . . . . . . . . . . . 121
B.1 Equilibrium Strategy When c = kv among Light Readers (? = 1) . . 149
2
B.2 Equilibrium Strategy Under Heterogeneous v and Homogeneous c
(vL < c < vH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
B.1 Conditions for News Provision and Equilibrium Accuracy . . . . . . . 166
v
List of Figures
2.1 Consumers? Subscription and Reading Decisions . . . . . . . . . . . . 62
2.2 Equilibrium Strategy (0 < ? < 1) . . . . . . . . . . . . . . . . . . . . 62
2.3 Impact of the Ad Rate (A) on the Firm?s Decisions When c(A) < c <
max c(A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
A?(A,V )
2.4 Impact of the Upper-bound of Valuation (V ) on the Firm?s Decisions 63
2.5 Impact of the Light Reader Segment Size (?) When c < c < c?? . . . 63
2.6 Equilibrium Strategies (V = 1, ? = 0.5) . . . . . . . . . . . . . . . . 64
2.7 Equilibrium Strategies When c and v Are Correlated Among Light
Readers (V = 1, ? = 0.5) . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.1 Consumer?s Expected Utility Under A Given Belief (v = 1) . . . . . . 122
3.2 Reporting Accuracy and Reported Content in Equilirbium (v = 1,
c = 2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
3.3 Equilibrium Outcomes (v = 1, c = 2) . . . . . . . . . . . . . . . . . . 123
3.4 Examples for f(?; ?) . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
3.5 The Firm?s Equilibrium Strategy (v = 1) . . . . . . . . . . . . . . . . 123
3.6 Alternative (Gross) Objective Functions of the Firm (v = 1, ? = 0.9,
p = 0.2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
3.7 An Objective-Welfare-Maximizing Media Firm?s Equilibrium Strat-
egy (v = 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
3.8 A Dual-Objective Media Firm?s Equilibrium Strategy (v = 1) . . . . . 125
B.1 Impact of the Upper-bound of Valuation (V ) When c > max{c, c?V } . 150
B.2 Equilibrium Strategy Under Heterogeneous v and Homogeneous c
(? = 0.5,c/vH = 0.5) . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
B.1 Reporting Accuracy and Reported Content in Equilirbium (vL = 1,
vR = 1.5, c = 2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
B.2 Expected Ex Post Polarization (v = 1) . . . . . . . . . . . . . . . . . 167
vi
Chapter 1: Introduction
From 2011 to 2018, the time spent by consumers with digital media has risen
significantly, from 3.5 hours per day to 6.5 hours per day (Watson 2019). As
providers in this market, the success of media platforms critically depends on their
understanding of consumers? utility from content consumption. In this disserta-
tion, we investigate media platforms? digital content provision and pricing as well
as consumers? consumption decisions.
The first essay (Chapter 2) investigates platforms? pricing strategy when con-
sumers endogenously decide the amount of content to consume. Media platforms
earn revenues from subscription and advertising. A change in market conditions
can change platforms? main source of revenues as well as their pricing strategies. In
the U.S. newspaper market, market studies have shown that a decline in advertis-
ing revenue can lead newspapers to seek consumer payments and embrace paywalls
(Arrese 2016; Kumar et al. 2013; Media Insight Project 2017). Previous stud-
ies provide several theories on platform?s choice of paywalls, including consumers?
need for learning about content quality (Halbheer et al. 2014; Li et al. 2019),
intertemporal fluctuation in demand (Lambrecht and Misra 2017), and platforms?
management of ad space supply (Halbheer et al. 2014). In the first essay (Chapter
1
2), we build an analytical model to study a platform?s optimal paywall design when
consumers endogenously decide their consumption. We find that when ad rates are
moderate, a metered paywall is optimal when consumers display sufficient hetero-
geneity in their costs of consuming content. We derive three key insights. First,
when ad rates increase, one typically expects platforms to offer more free content
and thus generate higher ad revenues. Instead, we find that sometimes offering less
free content and lowering the price can attract new subscribers, which generates
even higher revenues. Further, the optimal amount of free content may decrease or
increase in consumers? valuation for content, depending on ad rates. As consumers?
valuation increases, their willingness-to-pay for subscription and their desire for con-
tent consumption increases. The former effect dominates under low ad rates and
incentivizes the platform to provide less free content, but the opposite is true under
high ad rates. Thirdly, we also find that total content consumption can increase
with the proportion of light users, because the platform may strategically raise its
meter limit to increase ad revenues from non-subscribers.
The second essay (Chapter 3) studies news media platforms? product design
strategy. More specifically, we study news media platforms? strategic choice of re-
porting accuracy. News consumers are seeking information and updating their be-
liefs about the true state of the world which is random in nature. While the news
does not always accurately reflect the truth, it can still improve consumers? under-
standing of the truth. The accuracy of news influences both consumers? willingness
to pay and the production cost for the media platform. Previous theoretical re-
search suggests that the existence of news inaccuracy when consumers obtain utility
2
from conforming ideas (Mullainathan and Shleifer 2005; Gal-Or et al. 2012; Xiang
and Sarvary 2007; Zhu and Dukes 2015); or when media platforms get a higher
evaluation by confirming consumers? prior (Gentzkow and Shapiro 2006). In the
second essay (Chapter 3), we suggest that reporting inaccuracy can result from a
platform?s unbalanced resource allocation. We analyze the provision of news when
information provision is costly and consumers are truth-seeking. We model a media
platform?s news provision strategy as well as consumers? news consumption deci-
sions when they have common priors. We find that consumers value news more
under high prior uncertainty. If investigation and reporting are of low costs, the
media firm always offers news with full accuracy. If a higher level of accuracy is
sufficiently costly, news provision will be profitable only when consumers? prior is
not too extreme so that they see enough value in news. Importantly, although con-
sumers only seek for truth, the cost of news provision can still lead to unbalanced
investigative resource allocation. In particular, the media firm would allocate more
resources on accurately reporting the more likely state to increase its probability
of presenting the truth. In equilibrium, such allocation of resources will exaggerate
the likelihood of the state which is more likely a priori. We extend the model to
study the impact of polarization in consumers? prior beliefs on news accuracy. We
find that polarization makes reporting less accurate when the cost of news provision
is moderate, but has no impact when the cost is low or high. The reason is that
although polarization decreases the firm?s incentive to provide accurate reporting,
the significance of its impact varies across cost levels. Interestingly, polarization
can make news more accurate when the media firm considers improving consumers?
3
probability of being correct about the truth in addition to earning profits. Polariza-
tion means consumers initially show less interest in learning from news, which then
incentivizes the firm to attract them with more accurate reporting.
Finally, in Chapter 4, we summarize our findings and highlight our contribu-
tions to literature. We also identify several future directions for this research.
4
Chapter 2: Endogenous Consumption and Metered Paywalls1
2.1 Introduction
Ever since content started going digital, platforms have implemented pricing
mechanisms to generate revenues from such content. In the news industry, The Wall
Street Journal (WSJ) has been one of the early platforms to develop along with its
digital presence a digital pricing strategy. In 1996, WSJ developed an online version
of its print newspaper, The Wall Street Journal Interactive Edition, and charged
readers for access to this digital content.2 At the time, other newspapers wondered
whether this was a good idea, and questioned the willingness of consumers to pay
for access to digital content. The dominant model at the time was to build a digital
news platform but generate subscription revenues primarily from the print versions
of their products. Over time, as consumer reading habits have evolved, demand
for printed newspapers has shrunk, and consumption has shifted dominantly to
digital products (Pew Research Center 2011). To adapt to this shifting landscape,
in 2011 The New York Times (NYT) launched a paywall on its website (Kumar
et al. 2013). With the paywall in place, a non-subscriber could still access any
1This research is conducted with Bo Zhou and Yogesh V. Joshi.
2https://www.wsj.com/articles/SB849581696318836500
5
article on the newspaper?s website, but was limited in the total number of articles
accessible per month.
The product design and pricing tactics of the WSJ and NYT and their sub-
sequent market successes were closely observed by other media firms. By May
2018, 77% of newspapers in the U.S. had launched digital paywalls (Lewis 2018).
Similarly, 63% of newspapers in Europe have implemented paywalls.3 Besides news-
papers, magazines (e.g., The New Yorker, The Atlantic, Wired) and digital news
media (e.g., Medium, ESPN ) have also implemented paywalls.4
Today, while media platforms have adopted paywalls widely, they differ in
their specific product designs. These paywall strategies can be categorized into four
types, depending on the amount of content given away for free: [i] No paywalls,
where all content is provided for free; [ii] Hard paywalls, where there is no free
content; [iii] Freemium paywalls, where access to a pre-determined part of the total
content is provided for free, and consumers have to pay to access the premium or
?exclusive? part of the content (Kumar et al. 2013; Lambrecht and Misra 2017); and
[iv] Metered paywalls, where the platform sets a quota on the content that consumers
can select to access for free (e.g., 20 free articles per month), and consumers have to
pay for accessing the rest of the content (Chiou and Tucker 2013). In other words,
the distinction between freemium and metered paywalls is that in the latter, the
specific content provided for free is not pre-determined by the platform. In May
3https://reutersinstitute.politics.ox.ac.uk/our-research/pay-models-online-news-us-and-
europe-2019-update
4The Atlantic: https://tinyurl.com/y3u8eqwv. The New Yorker and Wired :
https://tinyurl.com/y2xgmhnw. Medium: https://tinyurl.com/yyaasdpp. ESPN : Lambrecht and
Misra (2017).
6
2018, 20% of newspapers in the U.S. had no paywalls, 5% used freemium paywalls,
72% used metered paywalls, 0.4% used hard paywalls, and 2.5% used other strategies
(Lewis 2018). Given the prominence of the use of metered paywalls, in this research,
we focus on the optimality of metered paywalls as an effective product design and
pricing strategy for digital content platforms.
Consumer behavior in the markets for digital content reveals significant het-
erogeneity in terms of consumers? valuation for content and the amount of content
consumed. The Media Insight Project (2014) reports that 55% of Americans enjoy
keeping up with news a lot, 33% only enjoy it some, and 12% don?t enjoy it much or
at all. This survey also finds that 21% of consumers go in-depth on both breaking
and non-breaking news, 49% go in-depth on only one of these two categories, and
30% on neither. A study from MinnPost, an online newspaper in Minneapolis with
no paywall, shows that 29% of its visitors accounted for 68% of the website visits,
while the top 1% accounted for 17%.5 In a recent survey, 15 metro area publish-
ers reported that 91% of their website visitors view no more than five articles in a
thirty-day period, with 68% viewing only one article (Mele et al. 2019). Similarly,
a manager in Tronc, Inc. revealed that only 3-5% of the Los Angeles Times ? unique
visitors hit the five-article limit.6 7
The aforementioned heterogeneity can be attributed to several important char-
acteristics of consumers? digital content consumption. First, consumers have hetero-
5https://www.minnpost.com/inside-minnpost/2009/10/appreciating-and-counting-loyal-
readers.
6Tronc, Inc., now Tribune Publishing Company, was the owner of the Los Angeles Times be-
tween 2007 and 2018.
7https://www.thestreet.com/opinion/l-a-times-tops-100-000-in-digital-subscriptions-14315543.
7
geneous valuation for content, and those with higher valuation are likely to consume
more. Second, consumers are heterogeneous in terms of the amount of time they
allocate for content consumption since their time is spread across different activi-
ties.8 Third, the breadth of consumers? content interests also influences the amount
of content consumed. Consumers with broader news interests tend to consume more
news than others. Finally, consumers? marginal utility from content consumption
is often diminishing, which also impacts the amount of content consumed. Previ-
ous studies have shown that decreasing enjoyment impacts content consumption in
various contexts, such as news (Huang 2009), music (Ratner et al. 1999), televi-
sion shows (Nelson et al. 2009), and mobile apps (Han et al. 2016). For instance,
Nelson et al. (2009) find that consumers exhibit different rates of satiation with con-
tent, and their pleasure from consumption declines as they consume more. When
the marginal utility from content consumption drops below a threshold, consumers
switch to other activities that provide higher marginal utility (Herrnstein and Prelec
1991).
Motivated by the above field observations and research findings, in this paper
we model consumer heterogeneity along two dimensions: [i] consumers? valuation for
content, and [ii] consumers? marginal cost of consumption. For the consumption of
news, consumers? valuation for content can vary for a variety of reasons such as their
perceived relevance of news, income levels, etc. Consumers with higher valuation
for content are more likely to become news subscribers. A high marginal cost for
news consumption could originate from lack of leisure time, narrow interest in news
8https://www.bls.gov/news.release/pdf/atus.pdf
8
topics, or a high satiation rate with news. Consumers with higher costs of news con-
sumption are likely to consume less news. Note that previous research on paywalls
has typically assumed that consumption is exogenous and all consumers consumed
all available content (Halbheer et al. 2014; Lambrecht and Misra 2017). We re-
lax this simplifying assumption and endogenize consumers? consumption decisions
based on their individual valuation and marginal cost of consumption. This allows
our model to capture consumers? heterogeneity in both the valuation for content
and the amount of desired content.
These heterogeneities have important implications for the two distinct revenue
sources, advertising and subscription, for digital content platforms. On the adver-
tising side, heterogeneity in the amount of content consumption implies variation
in the number of ad impressions and hence monetization per consumer. On the
subscription side, heterogeneity in both the valuation for content and the amount
of desired content along with the platform?s paywall strategy will determine the
amount of subscription revenue. By capturing consumers? heterogeneity and en-
dogenizing their consumption decisions, our research sheds new light on platforms?
optimal design of paywalls. Additionally, our research shows that consumers? en-
dogenous consumption coupled with the platform?s paywall design has significant
implications for the information transmitted in the market for news (i.e., the total
amount of news consumption).
Given that a media platform has to balance revenues from both advertising and
subscription, we investigate the following research questions in this paper: How does
heterogeneity in consumers? valuation and their costs of consumption (hereinafter,
9
consumption cost) influence a digital platform?s paywall strategy? What fraction
of content should be provided for free? How does the endogenous consumption of
digital content vary with changes in the marketplace? And finally, what are the
implications of these decisions on the total amount of content consumed?
To answer these questions, we build and analyze a theoretical model of a
digital media marketplace. The firm operates as a typical two-sided platform in
this marketplace, earning revenues from consumer payments for subscriptions on
one side and advertiser payments for ad impressions on the other side. The firm
makes two decisions: the subscription price that it should charge, and the fraction
of content that it should provide for free. Consumers observe the firm?s decisions
and choose whether to subscribe and how much content to consume. Consumers are
heterogeneous in their valuation for content as well as their marginal consumption
cost. Modeling consumption costs explicitly enables us to endogenize a consumer?s
content consumption decisions in this model.
Our analysis shows that consumer heterogeneity in consumption costs along-
side valuation can explain the existence of metered paywalls. Specifically, a metered
paywall is optimal when ad rates are moderate and two consumer segments have a
sufficiently large difference in terms of their segment level consumption costs. Un-
der such conditions, free content can be more effective than a price reduction in
increasing profits earned from low-valuation consumers.
Including consumption costs in our model allows us to generate four novel
insights regarding the media firm?s paywall strategies and the corresponding market
outcomes. First, as the ad rate increases, we find that the firm may reduce its pro-
10
vision of free content. This goes against conventional wisdom and previous research
which suggest that with a strong ad market, more free content should be provided
to consumers (Halbheer et al. 2014; Lambrecht and Misra 2017). When the dif-
ference in consumption costs between consumer segments is moderate, it becomes
important for the firm to balance the number of ad impressions generated within
each segment. As the ad rate increases, offering less free content and lowering the
subscription price can generate more ad impressions than simply giving away more
free content. The reason is that these two decisions increase subscriptions among
two groups of consumers: those whose valuation for content is moderate, but usage
is heavy (i.e., users with low consumption costs) and those whose valuation for con-
tent is high but usage is light (i.e., users with high consumption costs).9 If the firm
implements a metered paywall, the former group prefers to consume a lot of content
but their intermediate willingness-to-pay (WTP) prevents them from subscribing;
whereas the latter group is satisfied with the amount of free content so they do not
subscribe either. If the firm launches a hard paywall and charges a lower price, both
these consumer groups would pay for unlimited access and contribute more to ad
impressions, and as a result increase the firm?s profits.
Second, we find that under a metered paywall, the impact of consumer valu-
ation on the amount of content provided for free critically depends on the ad rate.
As consumer valuation increases, less content should be offered for free under low ad
rates, while the opposite is true under high ad rates. This pattern occurs because
a higher valuation translates to a higher WTP for paywalled content as well as a
9Throughout the paper, the terms ?user?, ?consumer? and ?reader? are used interchangeably.
11
preference to consume more content. The former benefits the firm more when ad
rates are low, incentivizing the firm to lock more content behind its paywall. By
contrast, the latter matters more when ad rates are high, leading the firm to offer
more free content and obtain ad impressions from non-subscribers.
Third, we find that the total amount of content consumed in the market may
increase in the proportion of light users who have high consumption costs. In general,
when consumers? consumption costs are higher, they consume less content. Thus one
might expect that with more light users, the total amount of consumption should
decrease (i.e., a decrease in the amount of information flow). This logic indeed
would hold true if one did not account for the firm?s strategic response to changes
in segment sizes. When the light user segment is small, the majority of users (heavy
users) prefer a lot of content, but the firm only provides a small amount of free
content in order to charge a high price from the heavy users who subscribe. In
this case, many non-subscribers hit the paywall. As there are many paywall-hitting
users, even a little extra free content can lead to a large increase in ad impressions,
which gives the firm an incentive to raise the meter limit. Hence, the amount of free
content is highly sensitive to a change in segment sizes. Consequently, when the
proportion of light users increases, the firm may find it optimal to offer a lot more
free content, and with many paywall-hitting users consuming this content, leading
to an increase in the amount of information flow.
Finally, we also identify an interesting relationship between consumers? con-
sumption cost and the firm?s subscription price. Intuitively, one would expect that
when consumers? consumption cost increases, their WTP for content decreases,
12
which should incentivize the firm to cut its price. Indeed, this is the case when
there is a small difference between the consumption costs of light and heavy users.
Under such conditions, the firm implements a hard paywall that targets both light
and heavy users. If the consumption costs of light users increases, as expected, the
firm finds it optimal to reduce the price to maintain subscriptions. However, this
is no longer the case if the difference in consumption costs between heavy and light
users is sufficiently large. Here, the firm implements a hard paywall that targets
only heavy users, and ignores light users. Thus, price becomes invariant in the con-
sumption cost of light users. In addition, when the firm operates a metered paywall,
the price would even increase in the consumption cost of light users. A higher con-
sumption cost implies less consumption by light users, so their demand for content
declines. In response, it is optimal for the firm to provide less free content and raise
its price.
Our results offer several managerial implications for media platform managers.
First, offering more free content is not always the optimal choice when the ad rate
increases. When the difference in consumption costs across consumer segments is
moderate, it can be optimal for the platform to reduce the amount of free content
under a higher ad rate. Second, the platform?s best response to an increase in
consumer valuation depends on the ad market. When the ad market is weak, it
should offer less content for free in order to convert more consumers to subscribers.
When the ad market is strong, it should offer more content for free to take advantage
of consumers? appetite for content.
Our paper also contributes to the understanding of paywalls theoretically.
13
Our paper is the first analysis of paywalls that incorporates endogenous content
consumption. Consumers endogenously decide the quantity of content to consume
and obtain utility only from the actual consumption, so their utility may not in-
crease in the total quantity provided by the platform. This is different from the
traditional product line design, where consumers can only choose among the qual-
ity levels provided to them. By endogenizing consumers? decisions on the amount
of content to consume, our model not only captures richer consumer behaviors in
digital content consumption but also allows for a more accurate measure of each
consumer?s contribution to ad revenue. We find that a rise in consumers? valuation
for content can lead to more free content being provided, which does not happen
under exogenous consumption. Besides, we explicitly study heterogeneity in con-
sumers? consumption costs, which helps us provide a novel explanation for media
platforms? paywall strategies and generate new insights into the optimal paywall
design. When consumers have heterogeneous valuation as well as heterogeneous
consumption costs, a metered paywall can be the most profitable strategy even in
the absence of uncertainty and quality learning, which have been the focus of prior
studies (e.g., Halbheer et al. 2014; Li et al. 2019). We also find that an increase in
ad rates can result in a reduction in the amount of free content, which is different
from the findings in previous research (Halbheer et al. 2014; Lambrecht and Misra
2017).
The rest of the paper is organized as follows. Section 2.2 reviews the relevant
literature. Section 2.3 introduces the model and Section 2.4 presents the analysis.
Section 2.5 presents the main results. Section 2.6 extends the analysis in our main
14
model. Finally, Section 2.7 concludes and discusses future research opportunities.
2.2 Related Literature
Our work contributes to research on revenue models for media platforms.
There are three distinct models: [i] ?free?: content is free and revenue is com-
pletely generated via ads; [ii] ?paid?: content needs to be paid for, regardless of
the existence of ads; and [iii] ?free-plus-paid?: there is a free version as well as a
paid version, and ads may be present in both versions.10 In the rest of this section,
we review the previous research on each of these revenue models, and discuss our
contributions relative to past work.
The ?free? model where a firm charges no fee from its audience and earns
revenues via advertising sees widespread use within the media industry. Radio and
television programs often operate on the free model (Steiner 1954; Spence and Owen
1977). Gabszewicz et al. (2001) has found that media firms would set a zero price
and provide content for free under a strong demand for advertising. When view-
ers have a distaste for ads, media firms may choose lower levels of ads to compete
for them (Anderson and Coate 2005; Gal-Or and Dukes 2003). Additionally, com-
petition among pure ad-supported media may also lead to lower program quality
levels (Liu et al. 2004). Our analysis shows that a media platform chooses the free
model when advertisers? WTP for a consumer?s impression exceeds each consumer?s
WTP for content. Otherwise, it would launch a paywall and charge a price for the
10?Freemium? models are a subset of ?free-plus-paid? models. We discuss the distinction between
these models subsequently.
15
subscription.
The ?paid? model is another popular model among media firms. Under this
model, consumers have to pay a price to access the content. A media can choose a
paid-without-ads model (e.g., HBO, Netflix) or a paid-with-ads model (e.g., printed
newspapers and magazines, digital newspapers with hard paywalls). When con-
sumers incur disutility from ads, pure ad-supported media firms can reduce ad
levels and adopt a paid-with-ads model to earn higher profits (Anderson and Coate
2005). If consumers? ad disutility is sufficiently high, media firms may even operate
on a paid-without-ads model (Amaldoss et al. 2020; T?ag 2009). Paid-without-ads
models are analyzed by previous papers with the focus on media bias (Mullainathan
and Shleifer 2005; Xiang and Sarvary 2007; Yildirim et al. 2013) and preview pro-
vision (Xiang and Soberman 2011). In those cases, the media can be viewed as a
one-sided firm rather than a two-sided platform (Anderson and Jullien 2015). More
theoretical papers have studied paid-with-ads models, with the focus on the im-
pact of customer loyalty (Chen and Xie 2007), content substitutability (Godes et
al. 2009; Kind et al. 2009), advertiser heterogeneity (Gal-Or et al. 2012; Lin 2020;
Prasad et al. 2003), and ad externality (Amaldoss et al. 2020; Chatterjee and Zhou
2020; Godes et al. 2009; Kind et al. 2009; Lin 2020). In this stream of research,
several papers study media firms? product line design, where products with different
levels of ads are offered (Appel et al. 2020; Casadesus-Masanell and Zhu 2010; Lin
2020; Prasad et al. 2003; T?ag 2009). In a recent paper, Lin (2020) finds that when
consumers display heterogeneous ad disutility and advertisers possess heterogeneous
ability to convert ad viewers, a media platform can use versioning to screen con-
16
sumers and advertisers on both sides of the market. By contrast, our paper focuses
on a platform?s provision of free content. The platform may choose a paid-with-ads
model (using a hard paywall), but under certain conditions, it is more profitable
with a free-plus-paid model (using a metered paywall). In this product line, the free
and the paid versions do not differ in the intensity of ads, but only in the amount
of content. Our analysis reveals the conditions under which a metered paywall is
favored by the platform.
Our paper also adds to the research on paid models by incorporating con-
sumers? heterogeneous costs of consumption. The cost of consumption has been
considered in this stream of research. Chellappa and Mehra (2018) analyze the im-
pact of homogeneous consumers? usage cost on the versioning of information goods,
where the firm runs a paid-without-ads model. Three papers have incorporated
homogeneous consumption costs in the analysis of paid-with-ads models. Godes et
al. (2009) and Kind et al. (2009) model homogeneous consumption costs when
they study media firms? competition and content substitutability. Guo et al. (2019)
study the implication of consumer ad disutility on mobile apps? reward advertising
strategy in the presence of homogeneous consumption costs. Different from their
papers, our paper focuses on a two-sided media platform?s paywall strategy. We
explicitly model both the level of consumption cost and the heterogeneity of con-
sumption costs across consumer segments. By including heterogeneous consumption
costs in the analysis, we find that an increase in some consumers? consumption costs
can lead to a higher subscription price. This is opposite to the finding under homo-
geneous consumption costs, where the price decreases in the consumption cost. We
17
further discuss this finding in Section 2.5.3.
Besides the free model and the paid model, a media platform may choose
a free-plus-paid model, where it offers a product line with both the free and the
paid versions of its product. Classic papers in product line design examine physical
products with positive marginal costs, which are rarely provided for free (Maskin and
Riley 1984; Moorthy 1984; Mussa and Rosen 1978). By contrast, digital products
can have zero marginal cost, so they can be offered for free (Lambrecht et al. 2014).
Under a free-plus-paid model, the free version and the paid version may
differ in their quality, functionality, and quantity. For example, under a typical
?freemium? model, the firm provides a paid version of a product and a free version
with lower quality or less functionality (Li et al. 2019). Previous research has shown
that firms may choose freemium models in the absence of advertising. This is be-
cause a freemium model can help consumers learn quality (Li et al. 2019; Niculescu
and Wu 2014), generate word-of-mouth (Niculescu and Wu 2014; Kamada and O?ry
2020), or attract free users who bring benefits to paid users through network effects
(Shi et al. 2019). In addition to these benefits, two recent papers have analyzed
freemium models in the presence of advertising. Lambrecht and Misra (2017) show
that platforms will have more flexibility when dealing with intertemporal fluctua-
tions in the demand for content if they launch freemium paywalls rather than hard
paywalls or no paywalls. Appel et al. (2020) suggest that the firm provides two
versions, an ad-supported free version and an ad-free paid version, of its product
when consumers have disutility for ads and uncertainty about product fit.11 In our
11Appel et al. (2020) also consider the impact of satiation on the firm?s strategy. In their
18
paper, we analyze metered paywalls in absence of the above-mentioned benefits of
free products. To design a metered paywall, a platform needs to consider consumers?
endogenous choice of the amount of content to consume. We elaborate on this in
the following discussion.
Under a metered paywall, the free and paid versions have the same quality
and functionality, and they only differ in the quantity provided (Chiou and Tucker
2013). Consumers can endogenously choose a fraction of the available content to
consume based on their valuation and costs of consumption. Once consumers have
reached their personal optimal level of consumption, additional content, though
available, does not increase their utility. In other words, a larger quantity of content
may not directly translate into higher consumers? WTP. If the firm chooses a hard
paywall, its subscription price needs to be sufficiently low to attract consumers who
are interested in a relatively low amount of content. In contrast to a hard paywall,
a metered paywall allows the firm to obtain impressions from those consumers while
maintaining a relatively high subscription price. Our paper shows that consumers?
endogenous choice of consumption quantity plays an important role in a platform?s
paywall design.
Metered paywalls have been studied by several recent papers. Empirical evi-
dence has shown that a metered paywall can bring more digital subscription revenues
to the newspaper (Aral and Dhillon 2020; Pattabhiramaiah et al. 2019) but also has
negative consequences: a declined number of unique website visitors, reduced con-
model, they assume that satiation decreases consumers? utility but does not influence the amount
of consumption. By contrast, the consumption cost in our model directly influences the amount
of consumption.
19
sumer engagement, and less word-of-mouth on social media (Aral and Dhillon 2020;
Cook and Attari 2012; Oh et al. 2016; Pattabhiramaiah et al. 2019). Halbheer et
al. (2014) have provided two theoretical explanations for the optimality of metered
paywalls. First, similar to the explanation in Li et al. (2019) and Niculescu and
Wu (2014), a metered paywall can help consumers learn the quality of content, thus
will be the optimal choice of a platform. Second, a platform may use the amount of
free content to adjust its supply of ad space, which may enable it to charge a higher
price from advertisers. In addition to these explanations, we find that consumer het-
erogeneity in consumption costs also explains the optimality of metered paywalls.
We show the optimality of metered paywalls in the absence of the two factors in
Halbheer et al. (2014). Note that previous research suggests that the amount of free
content should increase when the demand for advertising increases (Halbheer et al.
2014; Lambrecht and Misra 2017). By contrast, we find the opposite can happen.
Compared with giving more free content, reducing free content and cutting the price
can lead to more subscriptions as well as consumption under certain conditions. In
the next section, we describe our model setup.
2.3 Model
In our model, a digital media platform provides content and sells ad space.
To facilitate exposition, we denote this media platform as a digital newspaper. We
assume the newspaper to be a monopolist in the content market and a price taker
in the ad market. The price taker assumption can be supported by the fact that a
20
digital newspaper competes with other media forms (e.g., TV, radio, and magazines)
for advertisers and thus has limited market power. The newspaper chooses its
paywall strategy to maximize profits. Consumers maximize their utility from reading
news by deciding on how much to consume and whether to subscribe. In the rest of
this section, we describe the paywall strategies of the media firm, the decisions of
consumers, and the timing of the game.
2.3.1 The Media Platform
The total number of articles in the digital newspaper is normalized to be
one. The cost of content production is assumed to be zero so that we can focus
on the newspaper?s decision on the pricing stage. Taking the content as given, the
newspaper can offer two versions of newspaper to its readers: a free version with
a fraction f ? [0, 1] of the newspaper that can be accessed to with no charge, and
a paid version with full content that requires a subscription fee of p ? [0,?).12
Consistent with the industry practice (e.g., The New York Times), we assume that
each piece of the article includes one piece of display ad, regardless of the version it
is in. In the rest of the paper, we use ?consumers? and ?readers? interchangeably,
as well as ?the firm? and ?the newspaper.?
Three types of paywall strategy are defined by the amount of free content
provided. A hard paywall strategy means offering nothing for free but only a paid
version (f = 0 and p > 0). A metered paywall strategy means providing a free
version with limited content and a paid version with all the content (0 < f < 1 and
12We discuss the implication of negative prices in Section 2.6.1.
21
p > 0). A no-paywall strategy means making all the content available for free and
earning all revenues from advertising (f = 1 and p = 0). The firm?s problem can be
written as the following:
max?(f, p; ?) = p ?D(f, p; ?) + A ? I(f, p; ?) (2.1)
f,p
In Equation (2.1), ? represents parameters of consumer preference, which we
discuss subsequently. D is the demand for subscription. A is advertisers? valuation
for an ad impression, which is also the ad price per ad impression. I is the total
number of ad impressions. Given consumer preference and the ad price, the news-
paper simultaneously decides the amount of free content and the subscription price
to maximize its profits, ?.
2.3.2 Consumers
Consumers obtain utility from content consumption. Their marginal utility
from consuming news decreases in the number of articles they already read. When
the marginal utility declines to zero (the utility from one?s outside option), a con-
sumer would stop reading. Consumers? utility function is given by Equation (2.2),
cn2
u(n; v, c) = vn? (2.2)
2
In Equation (2.2), n ? [0, 1] is the amount of articles read by a consumer. v is a
consumer?s valuation for each piece of article and is heterogeneous across consumers:
v ? U [0, V ], in which V > 0 is the upper-bound of the uniform distribution.13 c
13If we consider consumers? disutility from seeing ads, then we can interpret v as a consumer?s
22
measures the rate at which a consumer?s marginal utility from content decreases.
A larger c implies a higher consumption cost (i.e., reading cost) due to the lack of
time, a narrow interest, or satiation. In reality, some consumers have a high cost and
only read a small fraction of the newspaper, while others can spend hours reading
news and are thus being called ?news junkie.? We capture such heterogeneity by
assuming that there are two groups of consumers: light readers (L type) with a high
cost, cL > 0, and of size ? ? [0, 1], and heavy readers (H type) with a low cost,
cH = 0, and of size (1 ? ?). In the rest of the paper, we omit the subscript and
use c to represent light readers? consumption cost. c can also be interpreted as the
difference between the two segments? consumption costs. We also assume that a
consumer?s valuation for content is independent of her consumption cost.14
Consumers simultaneously make two decisions: how much to read and whether
to subscribe. If they choose the free version, the number of articles is capped by f .
If they pay a price of p, they will have unlimited access to all the content. If the
newspaper offers everything for free, then they only decide on how much to read.
2.3.3 Timing of the Game
The timing of the game is summarized as below.
1.Paywall strategy : given consumer preference (? = (V, c, ?)) and ad market
condition (A), the firm simultaneously decides the fraction of free content and the
subscription price.
utility from a unit of content net of the disutility from a piece of display ad.
14In Section 2.6.2, we analyze an extension where v and c are correlated.
23
2. Subscription and consumption: each consumer simultaneously decides on
the amount of content to consume and whether or not to subscribe.
3. Revenue realization: the firm obtains subscription and advertising revenues.
2.4 Model Analysis
2.4.1 Consumers? Decisions
We derive the equilibrium through backward induction and start with con-
sumers? decisions. Consumers choose the number of articles to read to maximize
their utility. In our model, a heavy reader with cH = 0 would read as much as
she can. If she doesn?t subscribe, she would finish all the free articles and obtain a
utility of u(f ; v, 0). If she pays p to subscribe, she would read the whole newspaper
and obtain a utility of u(1; v, 0) ? p. We denote vH as the valuation of the heavy
reader who is indifferent between the free version and the paid version. As Figure
2.1 shows, anyone whose v ? [0, vH ] will only read the free articles and hit the meter
limit, while those with v ? (vH , V ] will pay to subscribe.15
???????????????
Insert Figure 2.1 about here
???????????????
For a light reader, the optimal amount to read is v , so light readers with
c
higher valuation tend to consume more news. If v is smaller than f , this reader
c
15If the newspaper offers some free articles but charges a price that is too high, it is possible
that vH > V , which implies that the entire heavy reader (H) segment chooses the free version. We
analyze this case in Appendix A.
24
will be fully satisfied with the free version without hitting the paywall. However,
if her valuation v is sufficiently high, she would like to read more than f . In this
situation, she either stays as a free user and uses up her free quota, or pays to
subscribe and reads articles until her marginal utility declines to zero. If v is greater
c
than 1, then she would finish all the articles. The condition for a light reader to
subscribe is u(f ; v, c) ? u(min{v , 1}; v, c)?p. Define vL as the valuation of the lightc
reader who is indifferent between the free version and the paid version. Given the
price and the amount of free content, there can be three groups of light readers with
different behaviors, as Figure 2.1 indicates. Readers with a sufficiently low valuation
(v ? [0, fc)) read v , while those with an intermediate valuation (v ? [fc, vL]) read fc
and hit the paywall. Those with a sufficiently high valuation (v ? (vL, V ]) become
subscribers and read min{v , 1}. The minimum function restricts the amount of
c
reading to be weakly less than one, which is the total amount of content of the
newspaper.
2.4.2 The Media Platform?s Decisions
Based on consumers? decisions described above, we can calculate the newspa-
per?s subscription demand and total ad impressions. For example, when the firm
obtains subscriptions from both heavy and light reader segments (vH , vL ? (0, V )),
the demand is Equation (2.3) and the total ad impressions are Equation (2.4).
V ? vH V ? vL
D(p, f ; ?) = DH +DL = (1? ?) + ? (2.3)
V V
25
I(p, f ; ?) = IH + IL,?where ? (2.4)vH f V 1
IH = (1? ?)(
0
? ? ??
dv+
V ? ? v VH? ??
dv?),
H,hitting H,paid
fc v ?v L f V min{v , 1}
I = ?(? ? dv+ dv+ cL dv)0 c?V ? ? fc ??V ? ? v VL ?? ?
L,not hitting L,hitting L,paid
With the demand and the ad impressions, we can solve for the firm?s optimal
decisions. When the firm obtains subscription only from one segment, the demand
and the ad impression functions will change, which leads to different solutions to the
profit maximization problem.16 We compare the profits the newspaper can possibly
generate across all strategies to find its equilibrium strategy.
To understand the firm?s trade-off behind its free content provision, it is helpful
to highlight two contrasting effects of free content on the firm?s profits: cannibal-
ization effect and consumption-expansion effect. We describe these two effects in
detail using Equation (2.5), where p?(f) is the solution to the first-order condition,
??(p, f)/?p = 0.
( ) ( )
d?(p?(f), f) ? ?D ?D ?p
? ?p? ?I ?I ?p?
= p ? +?? ?+D ???? +A ? +?? ? (2.5)df ?f ?p ?f ?f ?f ?p ?f
decrease in demand price cut increase in impression
??D ?I= p + A (2.6)
?f ?f
In Equation (2.5), the cannibalization effect of free content on profits consists of
two parts: the lost profit due to a decrease in subscription demand and the lost profit
16This case is analyzed in Appendix A.
26
due to a price cut (the first and second terms in Equation (2.5), respectively). First,
when more free content is provided, marginal subscribers would churn and choose
the free version (captured by ?D ). Faced with this weaker demand for subscription,
?f
the firm cuts its price to retain some subscribers (?D ?p
?
), which attenuates the
?p ?f
negative impact of subscriber churning. Second, the price cut results in subscribers
?
paying less for their access to content, so subscription revenues drop (D ?p ). The
?f
remaining part of Equation (2.5) captures the consumption-expansion effect of free
content on profits. More free content allows some non-subscribers to consume more,
but it also makes some subscribers churn and consume less (both included in ?I ).
?f
Besides, more free content also indirectly influences consumption through the price
?I ?p?( ). As we discussed above, the price cut caused by free content provision can
?p ?f
attract some subscriptions. With a subscription, these readers are no longer limited
by the paywall and would consume more content.
We can simplify Equation (2.5) by removing the terms representing the indirect
effects of free content that sum up to zero.17 This is because given any change in the
amount of free content, the firm adjusts its price accordingly such that the revenues
? ?
from the additional subscribers (p? ?D ?p ) and their ad impressions (A?I ?p ) offset
?p ?f ?p ?f
?
the loss due to the price cut (D ?p ). After removing those indirect effect terms
?f
from Equation (2.5), the terms in Equation (2.6) represent the direct effects of
cannibalization (the first term) and consumption-expansion (the second term). In
the discussion of the results, we will refer to t(hese two equati)ons to elaborate on the
? ? ? ? ?
17In Equation (2.5), p? ?D ?p ?p ?I ?p ? ?D ?I ?p ?? ?p?p ?f +D ?f +A?p ?f = p ?p +D +A?p ?f = ?p ?f = 0, because
?? ?
?p = 0 when p = p (f). This result can also be obtained by applying the Envelope Theorem to
Equation (2.5).
27
intuition behind the firm?s decisions.
Next, we study the firm?s equilibrium strategy and discuss how these two
effects guide the firm?s provision of free content.
2.4.3 Equilibrium Strategy
As described in Section 2.4.2, we compare the profits across all strategies and
derive the equilibrium strategy. Specifically, we analyze the game in the following
range of parameters: V > 0, c > 0, 0 ? ? ? 1, and A ? 0. In this subsection, we first
discuss the case where only heavy readers exist in the market (? = 0), then analyze
the equilibrium strategy when both segments are in the market (0 < ? < 1), and
finally present the case where only light readers are in the market (? = 1). Lemma
1 below presents the firm?s equilibrium strategy in a market full of heavy readers.
Lemma 1. When ? = 0, the firm maximizes its profits by choosing a hard pay-
wall strategy targeting the H segment (denoted by subscript ?hard, H?) with fh,H = 0
and p = V?Ah,H when A < V ; or choosing a no-paywall strategy with fn = 1 and2
pn = 0 when A ? V .
When all consumers are heavy readers (? = 0), the firm chooses either a
hard paywall strategy or a no-paywall strategy. Under low ad rates, it launches a
hard-H paywall and provides no free content. This hard paywall strategy targets the
heavy reader (H) segment, which means that all subscriptions are obtained from that
segment. Though free content can generate ad revenues from non-subscribers, it can
also lead to subscriber churning as well as a price cut, resulting in a larger loss in
28
subscription revenues. When the ad rate increases, the firm has a stronger incentive
to earn ad impressions, so it cuts the price to attract subscribers to consume its
content. This negative impact of ad rates (or advertisers? valuation for impressions)
on subscription price is well-documented in the research on media markets (Gal-Or
et al. 2012; Godes et al. 2009; Weyl 2010). When the ad rate exceeds the highest
consumers? WTP for content, the subscription price is cut to zero. As monetizing
eyeballs becomes more profitable than charging for content, the firm would give all
content for free and let readers read as much as they like, i.e., choosing a no-paywall
strategy. This is usually the case for news outlets offering popular articles without
any in-depth analysis.
Next, we summarize the equilibrium outcome when both types of consumers
exist in the market.
Lemma 2. When 0 < ? < 1, the firm?s equilibrium strategy is summarized
?
9c?2?3? 16c(1??)(V?A)+9c2?2
in Table 3.1, where p 2V?2A?c?h,HL2 = (, p = V?A + ,4 h,HL 2(1??) ) 16(1??)2
2
f = V ? (1??)(V?A) , and p = V?A 1? V + (1??)(V?A)
2
m m .
18
c 4c?A 2 c 4c?A
???????????????
Insert Table 2.1 about here
???????????????
When the market consists of a mixture of both consumer segments (0 < ? < 1),
a metered paywall strategy is the equilibrium strategy when ad rates are moderate
(A < A < V ) and consumers display sufficient difference in consumption costs
(c >c). Figure 2.2 illustrates the conditions for different equilibrium strategies.
? 2
18The (implicit) expression of c is given in Appendix A. A = (1? ?) V1?? .
29
???????????????
Insert Figure 2.2 about here
???????????????
It is clear that with a sufficiently high ad rate (A ? V ), the media firm will
completely rely on ad revenues and adopt a no-paywall strategy by offering all the
content for free. In the rest of the discussion of Lemma 2, we focus on the firm?s
paywall strategies under low (A ? A) and intermediate (A < A < V ) ad rates.
Under those conditions, the consumption cost plays an important role in the firm?s
decisions. First, it determines how different the two consumer segments are. This
influences the firm?s choice of target subscribers and thus its price. Second, it also
affects the magnitudes of the two effects of free content discussed in Section 2.4.2,
which in turn determines the provision of free content and therefore the type of
paywall.
The firm always chooses a hard paywall when the difference in consumption
costs is small (c ? c). In this case, even the light readers desire a large amount
of content, especially those with a high valuation for content. As both light and
heavy readers want a similar amount of content and have similar WTP, the firm can
earn more profits by attracting subscribers from both segments than from only one
segment (of heavy readers). In this case, providing free content will conflict with the
firm?s effort in incentivizing light readers to subscribe, because these readers obtain
most utility from the consumption of the first several units of content. Most of
them would choose the free version if it is available. Therefore, the firm offers only
a paid version targeting both segments (a hard-HL paywall or a hard-HL2 paywall),
30
which can be interpreted as setting up a ?mass market? hard paywall. In the real
world, this corresponds to the cases where all the consumers of the firm have similar
interests or tastes for content. When ad rates increase, it would decrease the price
to attract more subscribers, similar to the case in Lemma 1.
A metered paywall can be the equilibrium strategy under a sufficiently large
difference in consumption costs (c > c). Under this condition, light readers want
much less content than heavy readers so that their willingness-to-pay for a subscrip-
tion will be substantially lower. As a result, the firm only targets heavy readers as
its potential subscribers, shifting from the mass market appeal to a niche market
focus. When ad rates are low (A ? A), the firm operates a hard paywall targeting
heavy readers (hard-H), offering no free content. Because low ad rates provide little
incentive for the firm to capitalize on non-subscribers? impressions. This changes
when the ad rate falls in an intermediate range (A < A < V ). Higher ad rates make
non-subscribers? impressions more valuable. The firm would like to attract those
readers, but it is not worthwhile to lower the price to convert them to subscribers,
especially the light readers. Instead, the firm can expand its product line using a
metered paywall strategy. It offers a paid version to get subscriptions from its core
consumers (heavy readers with high valuation) and a free version to obtain ad im-
pressions from all other readers. On the consumer side, the price is higher than that
under a hard-HL paywall, because the firm no longer needs to induce light readers
to subscribe. On the advertising side, more ad impressions are generated than those
under a hard-H paywall, because non-subscribers would consume the free content.
To summarize, when consumers display sufficient difference in consumption costs, a
31
metered paywall dominates hard paywalls under moderate ad rates. Note that we
need to compare the ad rate with the highest valuation to determine whether it is
low or moderate. In the example of WSJ, the price of an ad impression is relatively
low compared with consumers? valuation for the content, because consumers rely
on the information in articles to make investment decisions. By contrast, the ratio
between the ad rate and consumers? valuation for content is larger at NYT. As a
result, a hard paywall targeting heavy readers is more favorable to WSJ, while a
metered paywall is better for NYT.
It is worth noting that the difference in consumption costs across segments
can be viewed as a difference in segment-level price elasticities. The subscription
demand in the light reader segment is more elastic than that in the heavy reader
segment. Light readers? higher consumption costs reduce their valuation for each
unit of content and make them endogenously want less content. As a result, obtain-
ing subscriptions from light readers is optimal only when their subscription demand
is not much more elastic than heavy readers (i.e., c is small). By contrast, the firm
would either focus on the segment with a less elastic demand (i.e., heavy readers)
under low ad rates or offers different versions to serve both segments under moderate
ad rates if the difference in segment-level price elasticities becomes sufficiently large
(i.e., c is large).
Finally, we present the equilibrium outcome when the market is full of light
readers.
Lemma 3. When ? = 1, the firm maximizes its profits by choosing a hard
32
paywall strategy with ph,HL2 when 0 ? A < V and 0 < c ? 2(V?A) ; or a hard paywall3
2
strategy with p = 2(V?A) when 0 ? A < V and c > 2(V?A)h,L ; or a no-paywall9c 3
strategy when A ? V .
When all consumers are light readers (? = 1) and have homogeneous consump-
tion costs, the firm should choose a hard paywall under low ad rates and no-paywall
under high ad rates. As analyzed in the discussion of Lemma 2, a free version can
make it harder to drive light readers to subscribe, so the firm would use hard paywall
strategies under low ad rates, serving only readers with a high valuation. The price
decreases with ad rates and becomes zero under sufficiently high ad rates (A ? V ).
2.5 Results
Our analysis reveals several interesting insights into the design of paywalls
and its implications for the market outcomes. In this section, we present the most
important findings and relegate other findings to Appendix A. Specifically, we first
discuss the optimal provision of free content, and then further discuss its implication
for the information flow from the media to its readers. Finally, we elaborate on the
optimal subscription price under different types of paywalls and how it changes in
the consumption cost. Given our primary interest in metered paywalls, we focus on
the case where metered paywalls can be an equilibrium strategy, i.e., both segments
exist in the market (0 < ? < 1).
33
2.5.1 Free Content Provision
By endogenizing consumers? consumption of content, our model offers novel
insights into the firm?s response to a change in market circumstances. For example,
conventional wisdom suggests that the firm provides a larger fraction of content for
free when the ad market is strong because that should attract more eyeballs and
increase ad revenues. Previous theoretical research, assuming consumers? exogenous
consumption of content, also makes similar recommendations (Halbheer et al. 2014;
Lambrecht and Misra 2017). In our model, we consider endogenous consumption
and obtain an unexpected result: When the ad rate increases, the firm can earn
more by reducing the amount of free content. We summarize this result in the
following proposition.
Proposition 1. As the ad rate (A) increases, the firm can increase its profits
by reducing the amount of free content. This happens under moderate ad rates and
moderate differences in the consumption costs between segments (A = A(c) and
c(A) < c < max c(A)).19
A?(A,V )
Proposition 1 shows that a higher ad rate can lead to a lower amount of free
content. More specifically, under a moderate ad rate and a moderate difference
between light and heavy readers? consumption costs, an increase in the ad rate can
induce the firm to shift from a metered paywall to a hard paywall, decreasing its
amount of free content. For example, when c is slightly larger than the threshold
c(A) (e.g., c = 2 in Figure 2.2), as the ad rate increases, the firm first shifts from a
19A(c) is the inverse function of c(A).
34
hard paywall targeting heavy readers (hard-H) to a metered paywall, then to a hard
paywall targeting both segments (hard-HL), next to a metered paywall again, and
finally to no-paywall. The changes in the firm?s decisions as A increases from 0 to
V are shown in Figure 2.3.
???????????????
Insert Figure 2.3 about here
???????????????
Next, we explain the intuition behind these strategy shifts. When the ad rate
is low (A ? A), the firm chooses a hard-H paywall. As the ad rate increases, the firm
cuts the price to attract more subscribers. When the ad rate exceeds the threshold,
A, the consumption-expansion effect (discussed in Section 4.2, after Equation (2.5))
starts to dominate the cannibalization effect so that the firm switches to a metered
paywall. Further increases in ad rates induce the firm to encourage more content
consumption with more free content and lower prices until the metered paywall is
dominated by a hard-HL paywall.
The shift from a metered paywall to a hard-HL paywall under moderate ad
rates is more nuanced. Under a metered paywall, two groups of readers hit the meter
limit. The first group consists of heavy readers with relatively low valuation, who
thirst for more content but would not pay much for it. The second group consists
of light readers with high valuation, who value the content but only consume a
little. These two groups read only the fm free articles and would not pay the
subscription fee. However, if the firm cuts the price as well as the amount of free
content, it can incentivize some of those readers to subscribe. Heavy readers with
35
intermediate valuation find the low price attractive, and light readers with high
valuation no longer have the free option. The removal of the free version is very
important because light readers enjoy the first several units of content more than the
subsequent units. As a result, the appeal of a subscription increases so that these
two groups of readers are willing to become subscribers. Upon subscribing, their ad
impression will be 1 (for heavy readers) or v (for light readers), much higher than f
c m
under a moderate ad rate. As a result, when the firm shifts from a metered paywall
to a hard-HL paywall, the additional impression gained from these new subscribers
outweighs the impression loss from low-valuation readers in both segments.20
Under a hard-HL paywall, the firm further reduces the price as the ad rate
increases, but it will provide free content again when the ad rate is sufficiently
high. There are two reasons why price reduction will be less effective in generating
revenues than free content provision under these circumstances. First, the price has
to be very low to attract new subscribers. Such a low price means leaving a large
amount of surplus to high-WTP consumers, especially those in the heavy reader
(H) segment. Second, the ad impressions generated by the marginal subscriber also
decline because the light readers who haven?t subscribed yet are those who have
20To elaborate on the intuition, we provide a numerical example for this strategy shift and
compared it with the case where only price reduction or free content provision is considered.
When V = 1, ? = 0.25, c = 2, the firm chooses a metered paywall at A = 0.38, with fm = 0.12
and pm = 0.27. In this situation, 69% of heavy readers subscribe, while 31% of heavy readers and
25% of light readers hit the paywall. When the ad rate increases to A = 0.40, the firm shifts to
a hard-HL paywall, with f = 0 and p = 0.18. As a result, 89% of heavy readers and 34% of light
readers subscribe. The shift of strategy converts most of the paywall-hitting readers to subscribers.
If we only consider a price reduction (holding f constant), then at A = 0.40, the price will be cut
to p = 0.26. This results in 70% of heavy readers subscribing and no light readers subscribing.
Alternatively, if we only consider free content provision (holding p constant), then at A = 0.40,
the amount of free content will be increased to f = 0.13. The increase in profits is smaller than
that from jointly optimizing p and f .
36
a relatively low valuation for content. Even if they are converted to subscribers,
they would only read a little. Combining these two factors above, the benefit from
a further price reduction becomes smaller under a high ad rate. Compared with a
hard paywall, launching a metered paywall not only captures the surplus from the
high-WTP readers but also obtains the ad impressions from low-WTP readers. It
is very difficult to convert the latter group to subscribers with a hard paywall, but
a metered paywall can obtain those ad impressions without sacrificing too much on
the price.
Finally, an ad rate as high as the highest valuation makes the no-paywall
strategy optimal, where the consumption of news articles is fully subsidized by ad-
vertising. When consumers? valuation for content is lower than advertisers? payment
for their impressions, being purely ad-supported is the most profitable choice for the
media firm.
Besides studying the impact of advertisers? valuation on free content provision,
we also analyze the impact of consumers? valuation on the provision of free content.
Interestingly, depending on the ad rate, an increase in consumers? valuation for
content can either increase or decrease the amount of free content, as summarized
in the proposition below.
Proposition 2. As the upper-bound of consumers? valuation for content (V )
increases, the firm that operates a metered paywall should decrease the amount of
free content under low ad rates (A < (1??)V ), but increase it under high ad rates
1+?
(A > (1??)V ).
1+?
37
First, note that an increase in the upper-bound of consumers? valuation means
on average consumers have a higher valuation for content. Intuitively, when con-
sumers? WTP increases, the firm should always charge a higher price. However, its
decision on the amount of free content is less straightforward, as it depends on the
ad rate. We explain the specifics below.
In Section 2.4.2, we discussed the cannibalization and consumption-expansion
effects of free content on profits. The optimal amount of free content balances these
two driving forces. Now consider the impact of an increase in the upper-bound,
V , on each of these effects. On the one hand, the cannibalization effect becomes
stronger. Because when readers have a higher valuation for content, the firm can
charge a higher price for the paywalled content (p = (1?fm)(V?A)m ). Consequently,2
giving content away for free means a larger loss. On the other hand, one part of the
consumption-expansion effect, the impression gain from light readers, also becomes
larger, since overall they want to read more content with a higher V (recall that
they read min{v , 1}). To compare these impacts of consumers? valuation on the two
c
effects of free content, we use Equation (2.7) to illustrate the firm?s trade-off.
d?m(pm(f), f) ?D ?I
= pm
df ????H +Af ? ????L? (2.7)f
demand decrease increase in impression, L
2
= ?? (1? ??)(?V ? A)? ?A?(V??? fmc)+4V V ?
loss, H gain, L
Equation (2.7) is a special case of Equation (2.6) in a metered paywall equilib-
rium, and it divides the two effects of free content by segments. In Equation (2.7),
38
the first term in the first row captures the impact of free content on subscription
revenues. Specifically, more free content leads to a drop in subscription demand,
which reduces the subscription revenues from heavy readers, who are the target
subscribers under a metered paywall. The second term captures the fact that more
free content gives light readers more content to consume, generating additional ad-
vertising revenues. The second row in Equation (2.7) summarizes these impacts by
segments, where the first term is the loss from heavy readers and the second term
is the gain from light readers.
Whether the firm should offer more or less free content depends on which
force is enlarged more by an increase in the upper-bound of consumers? valuation.
As V increases, based on Equation (2.7), the loss is enlarged by a size that is
proportional to the unit price of paywalled content ( pm V?A? = ). Meanwhile, the1 fm 2
gain is enlarged by a size that is proportional to the ad rate (A). When the ad
rate is low, the firm should reduce its free content when V increases. The reason
is that under low ad rates, the main impact of an increase in consumer valuation
is enlarging the lost subscription revenues resulting from free content provision. To
avoid the loss, the firm should lock more content behind the paywall and charge a
higher price. By contrast, when the ad rate is high, it should offer more free content
when V increases. The reason is that such an increase in valuation enlarges the gain
from light readers? consumption more than it enlarges the loss from heavy readers.
As a result, the firm should offer more free content to earn greater ad impressions,
taking advantage of the strong ad market. Figure 2.4(b) illustrates these results.
In a metered paywall equilibrium, when the ad rate is relatively low compared with
39
the upper-bound of valuation (i.e., in Figure 2.4(b), the ?low A? condition), the
amount of free content decreases in V . When the ad rate is relatively closer to
the upper-bound of valuation (i.e., in Figure 2.4(b), the ?high A? condition), the
amount of free content increases in V .
???????????????
Insert Figure 2.4 about here
???????????????
To highlight the role of endogenous consumption in the finding of Proposi-
tion 2, we now consider what would happen under exogenous consumption. When
consumption is exogenous, consumers? desired amount of content does not change
with V . In this case, the loss from offering free content still increases in V , because
consumers are willing to pay more for paywalled content. However, the gain from
offering free content does not increase in V , because under exogenous consumption,
the amount of consumption is not influenced by V . Consequently, a higher con-
sumer valuation always leads to the dominance of the loss side, thus driving the
firm to reduce its free content. In our model, we consider the impact of valuation
on consumption by endogenizing consumers? decisions. This enables us to uncover
the new insight that when V increases, the firm may provide more free content.
Our framework also allows us to speak to the impact of the light reader segment
size. Recall that light readers (L) consume less compared to heavy readers (H).
When the proportion of light readers increases, one may intuit that the firm would
provide less content for free. After all, consumers overall want to read less content.
However, the opposite may be true, as summarized in Lemma 4 below.
40
Lemma 4. As the light reader segment size (?) increases, more free content
will be provided under a metered paywall.
In the discussion of Proposition 2, we use Equation (2.7) to illustrate the
impacts of free content on profits in a metered paywall equilibrium. The second row
of Equation (2.7) can also help us understand the impact of a larger L segment on
the firm?s choice of its meter limit. On the one hand, a larger L segment implies a
smaller H segment, which decreases the subscription revenue loss from offering more
free content. On the other hand, a larger L segment increases the ad impression
gains from providing more free content. Therefore, more free content should be
provided in equilibrium, and the price should be decreased accordingly. In the next
subsection, we continue our discussion about the light reader segment size, analyzing
its impact on the information flow.
2.5.2 Information Flow
In our model, the total ad impression, I, also measures the total amount of
content consumed by consumers. If we assume that each unit of content presents
one unit of information, we can also interpret I as the size of the ?information flow?
from the media to its readers. Given that one of the most fundamental functions
of a media firm is to transmit information, we next analyze how the information
flow changes when market circumstances change. Indeed, the firm?s optimal paywall
strategy in response to environmental changes can lead to unexpected changes in
the size of the information flow. For example, when the proportion of light readers
41
increases, consumers? overall desire for content declines, so one might expect a drop
in the information flow. However, we find that the information flow can increase, as
shown in the following proposition.
Proposition 3. Under a metered paywall, as the light reader segment size (?)
increases, the size of the information flow increases if both the light reader segment
size and the difference in consumption costs are small (? < ?? and c < c??), and
weakly decreases otherwise.21
Proposition 3 suggests that under a metered paywall, a larger light reader
segment can result in more content being consumed. This counterintuitive result
happens when a metered paywall is the equilibrium strategy, and both the L segment
size and the difference in consumption costs are small. Figure 2.5 below illustrates
the impact of the light reader segment size on the price, the meter limit, and the
information flow under the condition specified in Proposition 3.
???????????????
Insert Figure 2.5 about here
???????????????
Next, we elaborate on the intuition behind Proposition 3. An increase in ? has
both a direct and an indirect effect on the size of the information flow. The direct
effect is the change in information flow when some heavy readers are replaced by
some light readers. This impact on the information flow is always negative because
an average heavy reader reads more than an average light reader does. Specifically,
2
21The (implicit) expression of ?? is given in Appendix A. c?? =
V (V+A)
2(V?A)A .
42
this direct effect consists of a reduction in I due to the decrease in the size of the
heavy reader segment (the first term in Equation (2.8)), and a lift due to the increase
in the size of the light reader segment (the second term in Equation (2.8)).
( ) ( )?Im ?? ??? pm ? ?fm(2V??? fmc)? (1? ?)(V ? A) ? (V ? fmc) ?fm= 1 + + ? +?? V 2V 2V ?? V ???
smaller H segment size (-) larger L segment size (+) paywall-hitting readers get more free content (+)
(2.8)
Besides the direct effect, a change in ? also has an indirect effect on the
information flow, which is always positive. This is because of the firm?s strategic
response: when there are more light readers, more free content will be provided
(Lemma 4). The readers who used to hit the paywall would read more, leading to
an increase in total consumption. The magnitude of this indirect effect depends
on the size of paywall-hitting readers ( (1??)(V?A) + ?(V?fmc)) and how sensitive the
2V V
amount of free content is to a segment size change (?fm ).
??
When the L segment size and the difference in consumption costs are both
small, the positive effect of more free content outweighs the negative effect due to
the decrease in the H segment size ((1 ? ?) decreases). The intuition can be seen
from the following. First, when the L segment size is small, the size of paywall-
hitting readers is large. In this case, most readers are heavy readers who want a
lot of content, but the firm would offer only a little content for free in order to
charge a high price from the heavy readers who subscribe. Consequently, more non-
subscribers would hit the paywall. Second, with a large group of paywall-hitting
readers, even a small increase in the amount of free content can generate a lot of
additional ad impressions, especially when light readers also want to consume a lot
43
of content (which is the case under a small c). This gives the firm a strong incentive
to provide more free content. As a result, the amount of free content is highly
sensitive to a change in the consumer segment size (in Equation (2.8), ?fm is large).
??
Combining the two factors above, the indirect effect dominates so that the size of
the information flow increases in ?.
However, in the case of a large light reader segment size or a large difference in
consumption costs, there are fewer paywall-hitting readers. In addition, the amount
of free content becomes less sensitive to a segment size change. Both factors lead
to a small indirect effect. Furthermore, when light readers account for a large share
of the market, more content is available for free. In this case, the subscription price
is low, so the losses from the first term in Equation (2.8) become larger. The gain
from a larger L segment (the second term in Equation (2.8)) is small in magnitude
compared with the loss. As a result, the firm?s strategic response does not cancel
out the direct effect of an increase in ?, and the information flow decreases.
After analyzing the free content provision of the media firm and its implications
for the information flow, we next examine the firm?s pricing strategy under a change
of market circumstances. Under different types of paywall, the relationships between
the price and consumers? consumption costs are different. In the next subsection,
we highlight those differences and discuss the intuition behind them.
44
2.5.3 Subscription Price
Recall that incorporating consumption costs and thus endogenizing consumers?
content consumption is a key element in our framework. In fact, they have a signif-
icant impact on the firm?s subscription price. Next, we analyze how consumption
costs and endogenous consumption influence the firm?s pricing decision. Usually,
the price is set based on the distribution of consumers? WTP. If there is a decrease
in WTP, the firm should lower its price as a response to the weaker demand. Hence,
one might expect the price to drop when some consumers experience an increase in
their consumption costs and want to consume less. This is indeed the case when
consumers have homogeneous consumption costs (Godes et al. 2009). However, the
result is more nuanced in our model, as presented in the following proposition.
Proposition 4. As the consumption cost of light readers (c) increases, the sub-
scription price decreases under a hard-HL or a hard-HL2 paywall, stays unchanged
under a hard-H paywall, and increases under a metered paywall.
Under a hard-HL or a hard-HL2 paywall, the price decreases in the consump-
tion cost of the light reader segment. This happens when light readers? consumption
costs are close to that of heavy readers. As expected, when the firm targets both
segments, it has to lower the price to keep light readers? subscriptions when their
WTP decreases. Different from these two specific types of hard paywall, the price
does not depend on c under a hard-H paywall, which is chosen under high differences
in consumption costs and low ad rates. Under those conditions, the firm would only
target heavy readers with high valuation and set the price based on their WTP.
45
Light readers thus do not influence the firm?s pricing decision. Finally, under a
metered paywall, the price increases in c. This occurs because the firm provides two
versions to target different consumers. Light readers are not the target of the paid
version but the target of the free version. When their consumption cost increases,
they consume less content. Thus the firm would see less benefit in maintaining its
current meter limit. As a result, it would lock more content behind the paywall and
raise the price.
2.6 Extension
In this section, we consider the non-negative-constraint on price and discuss
the implication of relaxing it. We also incorporate another pricing strategy (price-
per-unit) into our analysis and compare its performance with paywall strategies.
2.6.1 Negative Price and Price-Per-Unit Strategy
In our model, the firm charges p ? 0 for access to the full version of its product.
Once a consumer has access, the price does not influence her decision on how much
to consume. She would consume min{v , 1} if she is a light reader, or consume 1 if
c
she is a heavy reader. This is because a subscription grants this consumer access
to all the content, but does not regulate the amount of content to be consumed. In
this case, the firm cannot enforce the consumption of content (and viewing of ads),
so charging p < 0 does not generate more ad impressions than p = 0. Therefore, it
46
is not optimal to choose a negative price for the subscription.22
Now, we consider what happens if the firm grants access to its content in a
different way. Compared with traditional media firms, digital media firms have more
flexibility in selling their content separately. Suppose the firm chooses a price-per-
unit (PPU) strategy and charges r for each unit of content.23 When r < 0, the
firm pays |r| to the consumer for each unit of content consumed (and earns A from
advertisers for the ad impression). In this case, a consumer solves u(n; v, c)? rn to
decide her optimal amount of consumption. For light readers, this utility function
maximizes at n = v?r .
c
Following the same approach in Section 2.4, we can obtain the firm?s optimal
price when it chooses a price-per-unit strategy, as presented by the lemma below.
Lemma 5. When the media firm chooses a price-per-unit strategy, it sets a
positive price (r = max{2V?2A?c? , r?} > 0) under low ad rates (A < A
4 PPU
}), a
?
(A?c)2+6V c/??A?2c
negative price (r = max{ , V?2A?2c(1?1/?)} < 0) under high ad
3 4
rates (A > APPU), and a price of zero (r = 0) under moderate ad rates (APPU ?
A ? A 24PPU).
The firm would charge a positive price per unit under low ad rates, a price of
22Another reason behind the non-negative subscription price is the assumption that consumers
obtain zero utility from their outside option. With this assumption, free content is sufficient to
attract all non-subscribers, thus the firm does not need to pay consumers. If the outside option
provides positive utility, consumers with low valuation will prefer the outside option to the free
content, and the firm would choose p < 0 to attract those consumers under sufficiently high ad
rates.
23A hard paywall can be viewed as a pure subscription tariff (Armstrong 2006a), while a PPU
strategy can be viewed as a pu?re transaction tariff (Rochet and Tirole 2003).
24 (2V?A)?+2c(1??)? ((V+A)?+2c(1??)2)?2c(V+A)?(1??)r? = 3? when ? 6= 0; APPU =
max{ 2V?c? , V (V ?+2c(1??))}, and A = max{ 2V?c? , V ?+2c(1??)2 2(V ?+c(1??)) PPU 2? 2? } when ? =6 0. When ? = 0,
the firm always chooses r ? 0.
47
zero under moderate ad rates, and a negative price under high ad rates. This, again,
reflects the subsidy from the advertising side to the consumer side. A sufficiently
strong ad market incentivizes the firm to pay its consumer for their consumption.
Next, we compare the profit obtained from PPU strategies with those from paywall
strategies and summarize the result in the following proposition.
Proposition 5. Compared with a price-per-unit strategy, a paywall strat-
egy (i.e., either hard or metered) can be more profitable under moderate ad rates
(A?PPU < A < min{V,A 25PPU}).
Figure 2.6 illustrates the firm?s equilibrium strategies using a numerical exam-
ple. Figure 2.6(a) displays the optimal paywall strategies (as described in Lemma
2), while Figure 2.6(b) incorporates PPU strategies into the analysis. It is worth
noting that some of the paywall strategies earn the same profit as a PPU strategy.
First, it is clear that a no-paywall strategy is identical to a PPU with r = 0. Sec-
ond, according to Lemma 2, when both A and c are low (A < V and c ? 2(V?A)),
2+?
a hard-HL2 paywall with p = 2V?2A?c?h,HL2 is chosen. In this case, the optimal4
PPU strategy also charges r = 2V?2A?c? and earns the same profit as a hard-HL2
4
paywall.26
Proposition 5 suggests that paywalls can be more profitable than PPU strate-
gies when ad rates are moderate. First, when the consumption costs of light readers
25The (implicit) expression of A?PPU is given in Appendix A.
26Although r = ph,HL2 in this case, the consumption behaviors of light readers under a hard-HL2
paywall are different from those under a PPU strategy. Under the hard-HL2 paywall, light readers
with v < v?L do not read, while those with v ? v?L read all the content. Under the PPU strategy,
light readers with r ? v < r + c reads v?rc < 1, while those with r + c ? v ? V reads all the
content.
48
and ad rates are both moderate, a hard-HL paywall is the most profitable strategy.
Compared with a PPU strategy, a hard-HL paywall can be viewed as a special case
of a two-part tariff, with a fixed charge of ph,HL and a marginal price of zero (which
equals to the marginal cost). On the one hand, a hard-HL paywall earns less revenue
from consumers than a PPU strategy. Previous research on price discrimination has
shown that a two-part tariff is better than a uniform price in extracting an indi-
vidual consumer?s surplus and encouraging consumption (Lewis 1941; Armstrong
2006b). However, in our setting, the firm cannot set individualized fixed charges
for different consumers because it has no information on each consumer?s valuation
and consumption costs. As a result, its hard-HL paywall can only fully extract
the surplus of the marginal subscribers, while leaving a larger amount of surplus to
other subscribers than a PPU strategy. On the other hand, a hard-HL paywall earns
more ad revenue than a PPU strategy. Under a hard paywall, the zero marginal
price encourages subscribers to consume as much as they can. By contrast, under
a PPU strategy, the firm needs to set the price per unit above the marginal cost to
make a profit, which discourages consumption. Consequently, a hard-HL paywall
generates more ad revenues because more content is consumed. When the ad rate is
sufficiently high, a hard-HL paywall?s advantage on the advertising side outweighs
its disadvantage on the consumer side, which makes it dominate a PPU strategy.
???????????????
Insert Figure 2.6 about here
???????????????
When c is sufficiently high and A is low (i.e., the bright yellow region in 2.6(b)),
49
a PPU strategy becomes more profitable than a paywall strategy. First, a higher c
enlarges a hard-HL paywall?s disadvantage in earning consumer payment, because
it needs to cut price to keep the subscribers from L segment, leaving an even greater
amount of surplus to other subscribers. Second, a hard-HL paywall?s advantage in
ad revenues shrinks when the ad rate becomes lower. Both factors favor a PPU
strategy over a hard-HL paywall. Thirdly, compared with a hard-H paywall, a PPU
strategy is more profitable because of its flexibility in accommodating the demand of
light readers with high valuation. Under high consumption costs, those consumers
are only interested in a small proportion of content, thus not willing to pay a high
subscription fee. A PPU strategy allows them to pay only for the part that they
want, which not only makes those consumers better off but also generates extra
revenues for the firm.
When c is high and A is moderate, a metered paywall is preferred to a PPU
strategy. The intuition behind this result is similar to that behind the shift from a
hard-HL paywall to a metered paywall (as in the discussion following Proposition 1).
When ad rates increase, the firm cuts the price per unit to encourage consumption.
Note that the drop in the price per unit only influences light readers? consumption,
but has no impact on heavy readers? consumption, so the firm is attracting eyeballs
at the cost of its revenue from consumer payment. By contrast, a metered paywall
can attract consumers with low valuation with free content, which has a relative low
impact on the revenue from the consumer side.
Finally, Figure 2.6(b) also shows that when the ad rates become sufficiently
high (A > APPU), the firm may choose to pay consumers for their eyeballs. Under
50
this condition, the price per unit changes non-monotonically with light readers?
consumption costs. As c increases, the firm first decreases its price from r = 0 to
r < 0, then increases it until the price per unit becomes zero again. This is because
when light readers have a strong desire for content (very low c), most of them would
finish all the content even at r = 0. A negative price only incentives a small portion
of consumers to consume more, so the benefit of paying consumers is little. When
light readers experience very high costs of consumption, though a negative price can
drive all of them to consume more, the marginal impact on total consumption is
small, because consumption is less sensitive to price under high c.27 To summarize,
a negative price is most effective when c is at a moderate level.28
2.6.2 Correlation Between Valuation and Consumption Cost
In our main model, a consumer?s consumption cost (c) and valuation for con-
tent (v) are assumed to be independent. In reality, c and v may be correlated, and
the correlation between them depends on the interpretation of c. First, c and v can
be negatively correlated if c is the cost of processing information. A consumer has
lower costs of processing information if she has expertise in related areas (e.g., know-
ing the jargon and context). On the other hand, the expertise in an area increases
the value of consuming content (e.g., thorough understanding of the content), which
makes c and v negatively correlated. Second, c and v may have no clear correlation
if c represents the (inverse of) breadth of interest or the rate of satiation. Previ-
27Specifically, in n = v?rc , the marginal impact of r is ?
1
c , which gets closer to zero as c increases.
28This result slightly changes under very high ad rates (A > V? ), where a negative price is
optimal when c is low (c < (2A?V )?2?2? ).
51
ous research finds that the satiation rates of individuals depend on factors like age
and trait self-control (Nelson et al. 2009). These factors are not clearly correlated
with the value of consuming content. Thirdly, c and v can be positively correlated
if c measures the tightness of time constraint. People with higher levels of educa-
tion/salaries obtain more value from consuming news (because their decisions based
on news involves higher monetary value), but also have tighter constraint on leisure
time (i.e., higher c).
In this subsection, we incorporate the correlation between c and v by analyzing
two cases. In both cases, consumers? valuation (v) distributes uniformly between
0 and V . We assume that light readers? consumption costs are correlated with
their valuation, while maintaining the assumption that heavy readers have zero
consumption cost. In the first case, light readers? consumption costs increase in
their valuation: c = kv, where k > 0 is a constant. A larger k corresponds to a
larger difference between the consumption costs across segments. Since k > 0, c and
v are positively correlated.29 The equilibrium result can be obtained by following
the approach in Section 2.4. However, this extension does not generate closed-form
solution for all values of ?. In the following, we discuss the result of a special case,
? = 1 .30
2
Figure 2.7(a) illustrates the firm?s equilibrium strategy when ? = 1 . A me-
2
tered paywall is optimal when the ad rate is moderate and the difference in the
29The correla?tion coefficient, corr(c, v) = cov(c,v) ? ??c? = ? , increases in ?, where cov(c, v) =v 3?2+4? ?
?kV 2 2
12 , ? = kV
?3? +4?
c 12 is the standard deviation of c, and ?
3V
v = 6 is the standard deviation
of v.
30In Appendix A, we discuss another special case where ? = 1, which means c and v are perfectly
positively correlated for all consumers.
52
consumption costs between segments is sufficiently large. When k ? 1, all readers
want more content than the total amount of available content (i.e., 1 ? 1). Un-
k
der this condition, the cannibalization effect of a free version is greater than its
consumption-expansion effect, so the firm chooses either a hard paywall or no pay-
wall. When k > 1, the amount of free content weakly increases in the ad rate.
Similar to the main model, an increase in the ad rate makes the firm shift from a
hard-HL paywall to a metered paywall when the difference between segment-level
consumption costs is moderate. However, further increases in the ad rate do not
make the firm shift back to a hard paywall. This is because under this metered pay-
wall, the amount of free content provided equals to the amount that light readers
want (f ? = 1 ), so no light reader hits the limit. Meanwhile, heavy readers with
k
low valuation also get a large portion of content for free when k is close to 1. In
this case, shifting back to a hard-HL paywall does not generate much additional
impressions. The strategies under higher differences in segment-level consumption
costs are similar to those in the main model.
???????????????
Insert Figure 2.7 about here
???????????????
In the second case, light readers? consumption costs decrease in their valuation:
c = k(V ?v), where k > 0 is a constant. This implies a negative correlation between
c and v.31 Note that in this case, a hard-H paywall does not exist, because the light
31The correlation coeffic?ient, corr(c, v) = cov(c,v)? ? = ?? ?? , decreases in ?, wherec v 3?2+4??
2 2
cov(c, v) = ??kV , ? = kV ?3? +4?12 c 12 , and ? =
3V
v 6 .
53
reader with the highest valuation (V ) has zero consumption cost, thus her WTP
is the same as her counterpart in the heavy reader segment. As a result, any
hard paywall will obtain subscriptions from both segments. We analyze the model
following the approach in Section 2.4. Figure 2.7(b) provides a numerical example
of the firm?s equilibrium strategies. Similar to the main model, a metered paywall
is chosen under moderate ad rates and sufficiently large differences in segment-level
consumption costs. As k increases, the area for a metered paywall equilibrium
expands. A higher k means that the light readers with low valuation have even
higher consumption costs and become even more reluctant to pay for a subscription.
Under this condition, a metered paywall can keep obtaining impressions from those
consumers, while a hard paywall loses both the subscriptions and impressions from
those consumers, so a metered paywall becomes more likely to be chosen.
2.7 Concluding Remarks
In this paper, we study the paywall strategies of a digital media platform. The
platform decides on the amount of free content and the subscription price to maxi-
mize its profits. It does not have information on each consumer?s characteristics but
does know the distribution of consumers? valuation for content and the distribution
of their consumption costs. Consumers optimize their content consumption deci-
sions and their subscription decisions. Our analysis demonstrates that the firm?s
optimal strategy depends on consumers? valuation for content, the proportions of
light versus heavy readers, the difference between their consumption costs, and the
54
advertising rate.
Our model and findings contribute to the theoretical analysis of paywalls.
First, our paper introduces endogenous consumption into the analysis of paywalls.
We explicitly model consumers? decisions on the quantity of content consumption,
which have important implications for platforms? product line design. Unlike that
of the quality level, platforms have limited control over the quantity levels of con-
sumption. As a result, understanding the amount of content that consumers will
choose to consume is important for optimally designing a paywall. Second, we pro-
vide a novel explanation for metered paywalls in the absence of uncertainty and
quality learning. Specifically, in the presence of heterogeneous valuation as well
as heterogeneous consumption costs, we find that a metered paywall is the optimal
strategy when the ad rate is moderate and the difference in consumption costs across
consumer segments is sufficiently high.
Our research identifies several interesting findings regarding the optimal pro-
vision of free and paid content by a platform. First, we find that the fraction of
free content may decrease under higher ad rates. In fact, there is a non-monotonic
relationship between the ad rate and the firm?s amount of free content. A higher
ad rate typically incentivizes the firm to obtain more impressions by offering more
content for free. However, under a moderate ad rate and a moderate difference
in consumption costs, it is profitable to attract two groups of consumers to sub-
scribe: the heavy users with intermediate valuation and the light users with high
valuation. To convert these two groups of consumers to subscribers, the firm lowers
both the amount of free content and the price. When the ad rate becomes even
55
higher, the firm increases the amount of free content again to obtain impressions
from low-valuation consumers.
Second, when consumers? valuation for content increases, the platform should
offer less content for free under low ad rates, but more content for free under high ad
rates. This is because of two implications of a higher valuation. On the one hand, a
higher valuation means an increase in consumers? WTP for paywalled content. On
the other hand, it implies consumers? desire for more content. When ad rates are
low, the firm relies on consumer payments and locks more content. Under high ad
rates, it encourages more consumption and thus offers more free content.
We also discuss the implications of paywalls on the amount of information flow.
When the proportion of light users increases, although the average consumption
cost increases, the total amount of content consumed may increase. This happens
because of the platform?s strategic response to changes in segment size. When the
light user segment is small, consumers overall have a strong desire for content, but
the platform offers only a little content for free in order to charge a high subscription
price. Hence, many consumers hit the paywall. Under this situation, increasing the
meter limit can significantly increase ad revenue. The incentive for the platform
to raise the limit is even stronger when light users want to consume a lot (i.e.,
they have low consumption costs). As a result, the amount of free content can
be highly sensitive to a change in segment size. With a large number of paywall-
hitting consumers, this highly sensitive free content provision can increase the total
consumption, leading to a larger amount of information flow. This result cautions
us against the conventional wisdom that a higher average level of consumption cost
56
amongst all consumers will result in a reduction in total information flow.
This paper offers several important managerial insights. First, when the ad
rate increases, a media platform should jointly optimize its subscription price and its
free content provision to maximize profits. Under certain conditions, it can benefit
from offering less free content even if ad rates increase. The reason is that when
different consumer segments have moderately different consumption costs, acquiring
subscribers with a price reduction can be more effective in generating additional ad
impressions than attracting low-valuation readers with free content. Second, when
there is an increase in consumers? valuation for content, the media platform should
paywall more content if the ad rate is low, but offer more free content if the ad rate
is high. The key is that the firm?s paywall decision depends on the interplay of both
sides of the market.
Our model focuses on the impact of consumer heterogeneity and endogenous
content consumption on media platforms? paywall strategies. Additional factors
may also influence consumer behaviors and platform strategies. First, consumers
may have disutility from seeing ads alongside the content, which we do not explicitly
model in consumers? utility function. However, if we interpret v as a consumer?s
utility from a unit of content net of the disutility from a piece of display ad, the
results of our model still hold. In other words, consumers? ad disutility is implicitly
captured in our model.
Second, we assume the platform to be a price taker in the ad market. Given
its monopoly power in the content market, it is possible that its decisions, which
determine the supply of ad impressions, can influence the price charged to adver-
57
tisers. This mechanism, proposed by Halbheer et al. (2014), can also explain the
optimality of metered paywalls. In this paper, we assume exogenous advertising
rates and abstract away from the platform?s influence on the ad market in order to
focus on its impact on the content market. However, even if the advertising rates
are influenced by the platform, the analysis should lead to similar conclusions as
long as the ad price elasticity is not too high. In reality, both mechanisms drive
media platforms to consider a metered paywall strategy, and our research enriches
the understanding of the consumer side of two-sided media platforms.
Third, our model focuses on the consumption decisions made in a single period,
so the changes in consumers? valuation for content across time are not incorporated.
Previous research has studied the temporal fluctuation in consumer valuation and
found it has an impact on a firm?s paywall strategy (Lambrecht and Misra 2017).
Although the dimension of time is not explicitly modeled in our paper, the compara-
tive statics analysis can shed some light on the implications of changes in valuation.
We find that a rise in valuation can lead to either more or less free content, depend-
ing on the ad rate. If we incorporate the changes in valuation by modeling multiple
periods, our result should hold as long as the platform optimizes its paywall design
at the beginning of each period. If the platform needs to commit to a paywall de-
sign, we expect it to be more likely to choose a metered paywall than in the case
with no commitment. Without commitment, the optimal strategy may be a hard
paywall for the high-demand season and no paywall for the low-demand season (or
the reverse if consumer valuation changes in the way described by Lambrecht and
Misra (2017)). With commitment, the platform would design its paywall based on
58
the average valuation across time, which makes a metered paywall more preferred.
Fourth, consumers? perception of content value may depend on the amount of
free content. One mechanism for that is consumers? learning of quality (Halbheer
et al. 2014). In our model, consumers? valuation is independent of the firm?s me-
ter limit. Relaxing this assumption can lead to an expansion or shrinkage of the
area for a metered paywall equilibrium. If giving more content for free leads to a
decline in valuation, the consumption of content and the subscription demand will
decrease. Hence, the firm will have less incentive to provide free content. In this
case, the parameter range for a metered paywall to be optimal shrinks. If giving
more free content raises consumer valuation, the opposite should happen. It merits
further exploration whether the amount of free content under a metered paywall
will increase or decrease, because the ad rate will also influence the firm?s decision,
as in Proposition 2.
Additionally, some media platforms have a ?leaky? paywall, which allows con-
sumers to access more articles than the meter limit by deleting cookies or using
?private? browsing.32 Though we didn?t consider this in the model, leaky paywalls
could shape platforms? strategies and profits in the following fashion. Consumers
who take advantage of a leaky paywall are either light readers with a high valuation
or heavy readers. For those consumers, a leaky paywall allows them to read more
and generate more ad impressions. However, a leaky paywall can also lead to a loss
in subscriptions. If the impression gain dominates, the platform is more likely to
choose a metered paywall (compared to a hard paywall) and make it ?leaky.? If
32https://www.cjr.org/business of news/news-paywalls-new-york-times-wall-street-journal.php
59
instead, the subscription loss is more significant, the platform would choose a hard
paywall or make its metered paywall less porous.
Finally, we assume that the platform knows only the distribution of consumers?
preferences but not any individual consumer?s preference. As the technology of
big data and analytics improves, platforms may know more about their consumers,
which could allow for more ?individualized? paywalls. On the one hand, the platform
can capture more consumer surplus with more sophisticated price discrimination.
On the other hand, it should also be cautious about potential backlash from upset
consumers who face tighter meters or higher prices. The latter can make a metered
paywall more favorable than an ?individualized? paywall.
There are quite a few directions for future research. In this paper, we assume
that each consumer has the same valuation for all content. This assumption can be
relaxed to capture each consumer?s heterogeneous tastes for different types of content
(e.g., political news, entertainment news). As for the market structure, the media
firm in our model is a monopolist. It would be interesting to study how competition
between media firms will influence their paywall strategies. For the advertising side
of the platform, because the readers of the free and paid versions of the newspaper
are different, advertisers may have different WTP for the impressions obtained from
different readers. Additionally, a consumer?s cost of content consumption is assumed
to be exogenous in this paper. Previous behavioral research suggests that this cost
can be influenced by interventions (Redden 2008). Incorporating firms? strategic
actions to influence consumers? consumption costs can offer further insights into the
optimal design of paywalls.
60
Readers? Consumption
Parameter Range Paywall Source of Meter Limit Subscription
Behavior
Strategy Sub- (f) Price (p)
scribers
All subscribers read the
A < V and c ? 2(V?A) Hard-HL2 H, L 0 p
2+? whole newspaper h,HL2
Some subscribers only
A < V and Hard-HL H, L read part of the 0 ph,HL
2(V?A) < c ? c newspaper
2+?
A ? A and c > c Hard-H H 0 ph,H
A < A < V and c > c Metered H fm pm
A ? V No- - 1 0
paywall
Note: In this table, we highlight the difference in readers? consumption behavior under
hard-HL2 and hard-HL paywalls. We discuss the consumption behaviors under other
types of paywall in the appendix.
Table 2.1: Equilibrium Strategy When 0 < ? < 1
61
Figure 2.1: Consumers? Subscription and Reading Decisions
Note: In this figure, V = 1 and ? = 0.25. c = 1.08 when A = 0.
Figure 2.2: Equilibrium Strategy (0 < ? < 1)
62
(a) Price (b) Meter Limit
Figure 2.3: Impact of the Ad Rate (A) on the Firm?s Decisions When c(A) < c <
max c(A)
A?(A,V )
(a) Price (b) Meter Limit
Figure 2.4: Impact of the Upper-bound of Valuation (V ) on the Firm?s Decisions
(a) Price (b) Meter Limit (c) Information Flow
Figure 2.5: Impact of the Light Reader Segment Size (?) When c < c < c??
63
(a) Without PPU Strategies (b) With PPU Strategies
Note: In Panel (b), a no-paywall strategy is equivalent to a PPU strategy with r = 0. In
the purple region, a hard-HL2 paywall is equally profitable as a PPU strategy with
r = ph,HL2. We mark the purple region as Hard-HL2 because a hard paywall should be
easier to implement than a PPU strategy, thus is preferred by the firm.
Figure 2.6: Equilibrium Strategies (V = 1, ? = 0.5)
(a) c = kv (b) c = k(V ? v)
Figure 2.7: Equilibrium Strategies When c and v Are Correlated Among Light
Readers (V = 1, ? = 0.5)
64
Chapter 3: The Accuracy of News1
3.1 Introduction
In April 2014, the city of Flint in Michigan changed its source of drinking water,
which turned out to be the beginning of the ?Flint water crisis.?2 Since August 2014,
residents have been concerned about the discolored tap water and some of them even
experienced unexplained illnesses.3 People wanted to know whether the water was
safe to drink. The city stated, ?the Flint River presented a safe ... water source?
and a review from a third-party company concluded that ?the water is considered
to meet drinking water requirements.?45 More evidence emerged later, suggesting
the water contained an elevated level of lead, and city officials might have known
this risk for months before they publicly admitted it.6 Though the state of Michigan
tells its residents that the water quality has met the federal standard since 2016,
local officials still recommend people to drink only bottled or filtered water.7 Since
this crisis, concerns over water safety also emerged in other cities including Newark,
1This research is conducted with Bo Zhou and Yogesh V. Joshi.
2https://tinyurl.com/czj585e8
3https://tinyurl.com/y4xcegmc
4https://www.cityofflint.com/wp-content/uploads/CoF-Water-System-QA.pdf
5https://www.cityofflint.com/wp-content/uploads/Veolia-REPORT-FlintWater-Quality-
201503121.pdf
6https://tinyurl.com/wny5fmk
7https://www.nytimes.com/2019/04/25/us/flint-water-crisis.html
65
New Jersey; Portland, Oregon; and Pittsburgh, Pennsylvania.8
Since the water crisis in Flint was covered by the media, it has attracted
the attention of the entire nation. During the long process of investigation, news
consumers who follow the development of the water crisis have many questions on
their minds. Should the third-party company or the government officials be held
accountable? Is the water crisis resolved in Flint, Michigan? Do I have to worry
about my local water supply system? Individuals seek answers to these questions by
consuming news from the media. They become more certain about the true state of
the world after news consumption when the news is more informative. Responding
to such consumer needs, media firms engage in investigative journalism and provide
news. When deciding the level of accuracy in its reporting, a media firm needs to
balance between consumers? willingness to pay (WTP) and the cost of investigative
reporting. The cost concern of media firms in the U.S. is partially reflected by
the following observations: the overall newsroom employment in the U.S. decreased
by 26% from 2008 to 2020, and one third of large U.S. newspapers suffered layoffs
between 2017 and 2018.9 Many local news outlets even ended up in closure of
business as their revenues could not cover costs, which raised the concern over ?the
death of local news? among media practitioners.10
In addition to the supply side issue of costs, news media firms also face major
challenges on the demand side. In the U.S., the increasing polarization in public
views has been a concern since the 1980s and has reached an alarmingly high level
8https://www.theatlantic.com/health/archive/2019/09/millions-american-homes-have-lead-
water/597826/
9See https://tinyurl.com/45uud4pd and https://tinyurl.com/k6vmprwu
10https://tinyurl.com/ymauj5t3
66
in recent years (Abramowitz and Saunders 2008; Pew Research Center 2017). As
individuals become more divided in their opinions, their consumption and media
firms? provision of news will be directly affected. While the impact of news provision
on polarization has been studied, there is limited discussion about the impact of
polarization on news provision.
In this paper, we study a media firm?s news provision strategy and consumers?
news consumption decisions. More specifically, we intend to answer the following
research questions: When consumers are seeking the truth, how does their prior
belief influence their news consumption? How would the firm optimally choose its
accuracy of news reporting? What is the impact of polarization in consumers? prior
beliefs on the firm?s news reporting?
We build an analytical model to study the strategic interaction between a
media firm and news consumers. We assume that the underlying state of the world
is a binary random variable. Neither the media firm nor the consumers know the
truth definitively, but they share a common prior belief about its distribution. The
firm decides on its news provision strategy, which is operationalized as the accuracy
with which its report reflects the truth. This strategy is a long-term decision and
is announced before the realization of the true state. In order to uncover the truth
and report the news to consumers, the firm expends efforts in investigating and
learning the state of the world. This process is costly, and a higher level of accuracy
is typically associated with a higher cost. After this decision on its amount of
investigation, the firm announces the price for its news. Then nature decides the
true state, and a news report is generated according to this true state and the firm?s
67
reporting accuracy. Consumers know the firm?s strategy and they want to learn the
truth. They will buy and consume news if their expected benefit is greater than the
price.
Our model generates several interesting results on media accuracy. First, we
find both the cost of providing information and consumers? prior beliefs over the
true state influence the provision of news. When improving accuracy is not very
costly, the firm always provides news. When improving accuracy is sufficiently
costly, the firm is profitable only when consumers? prior belief is not too extreme.
In other words, the media market will fail when consumers? prior belief is relatively
extreme. This happens because consumers? ex ante valuation for news can only
exceed the firm?s cost if their prior uncertainty is sufficiently high. Second, although
consumers are indifferent between different states and obtain no extra utility from
biased reporting, inaccuracies will emerge when news reporting is sufficiently costly.
In order to maximize its probability of offering an accurate report, the firm will
focus on accurately reporting a certain outcome, but spend relatively little resources
on investigating the other possibility. As a result, in equilibrium, the probability
with which the ex-ante more likely state is reported will be greater than the actual
probability with which that state is realized. We label this as the exaggeration
effect.
Third, we discuss the implications of different market characteristics on the
level of reporting inaccuracy. When the cost of news provision increases, reporting
inaccuracy increases. The impact of prior beliefs on reporting inaccuracy is also
interesting. In an environment with higher uncertainty, the journalistic investigation
68
is more costly, so one might expect higher reporting inaccuracy. However, we find
that reporting inaccuracy is independent of the level of prior uncertainty as long as
the firm provides news. Note that higher uncertainty implies not only a higher cost
but also a higher WTP for news. We show that these two effects cancel each other
out in equilibrium, resulting in their independence from the prior belief.
To study the impact of polarization, we next extend our model by incorporat-
ing the heterogeneity in consumers? prior beliefs. Heterogeneous prior beliefs lead
to heterogeneous WTP for news, which makes the demand for news more sensitive
to the price. This limits the firm?s ability to extract consumer surplus and reduces
its incentives to provide accurate news. We find that when consumers? prior beliefs
become more polarized, media accuracy will decrease under moderate costs of news
provision, but does not change under low or high costs. With more polarized beliefs,
consumers become more certain under their priors and tend not to consume news.
To encourage consumers to use news, the firm cuts its price while trying to main-
tain a high accuracy level. Such a strategy is effective under low costs, but higher
levels of costs (i.e., moderate costs) will drive the firm to compromise and lower its
accuracy. Under even higher costs, the cost-saving motivation dominates, and the
firm would provide no news regardless of the degree of polarization. This result is
concerning from a public policy standpoint, because a higher level of polarization,
particularly in intricate and sensitive fields such as politics and healthcare, calls for
more and more accurate news reporting instead of less.
As many consumers rely on news to learn about the state of the world, a
news media firm may consider the public interest in addition to the commercial
69
interests. We further extend our model to incorporate a media firm?s considera-
tion for the public interest. We start our analysis with an extreme case where the
firm only focuses on improving the objective welfare of a society, which increases
with consumers? probability of being correct about the truth. Consumers? expected
probability of being correct increases when consumers learn about the state of the
world from news, and the media firm can improve accuracy and reduce the price to
encourage news consumption. We find that compared with a profit maximizer, an
objective-welfare maximizer is more likely to provide news, and its accuracy is also
weakly higher because it has more incentives to attract extreme consumers than
a profit maximizer. When the degree of polarization increases, a profit maximizer
never increases its accuracy, while an objective-welfare maximizer may increase its
accuracy. Polarization decreases consumers? WTP for news, which discourages a
profit maximizer from raising accuracy. However, an objective-welfare maximizer
expects more gain from improving its accuracy than its profit-oriented counterpart,
because the payoff gain of converting a non-consumer to a consumer does not de-
crease in the degree of polarization.
Finally, we analyze a more general case where the firm has a dual objective
of earning profits and improving objective welfare. We find that if the firm?s profit-
seeking motivation is strong, it never offers news for free. Even if its profit-seeking
motivation is weak, the firm offers news for free only when the cost is sufficiently
high or when consumers are sufficiently polarized. This is because low polarization
means most consumers have a high demand for accurate news, and low costs make
providing such news relatively easy. The firm would charge a price from those high-
70
demand consumers and ignore the extreme consumers. The size of the latter group
is very small under low polarization, so the loss due to leaving them uninformed is
smaller than the revenue gain. If the cost increases, the firm needs to reduce the
accuracy and thus the price till the news becomes free. If the level of polarization
increases, the firm tends to encourage consumption, which also leads to price cutting.
We also study a dual-objective firm?s response to polarization and compare
the results with those of a single-objective firm (i.e., maximizing only profits or
only objective welfare). We find that in the equilibrium where the firm chooses
an interior level of accuracy and a positive price, its accuracy increases in the
degree of polarization only if it sufficiently values objective welfare, and the de-
gree of polarization is sufficiently high. Greater polarization strengthens the firm?s
objective-welfare-improving incentives while weakening its profit-seeking incentives.
The former impact dominates the latter under the specified condition and leads to
higher accuracy.
The rest of the paper is organized as follows. Section 3.2 reviews the relevant
literature, and Section 3.3 introduces the model and presents the analysis. Sec-
tion 3.4 presents the results of the main model. Section 3.5 extends the model to
study the implications of heterogeneous prior beliefs and the media firm?s objective.
Finally, Section 3.6 concludes and discusses future research opportunities.
71
3.2 Related Literature
This paper is related to the theoretical literature on consumers? news con-
sumption and media bias. We analyze the issue of reporting inaccuracy in the
media market, which is related to but also different from media bias. Media bias
is defined as the difference between the news report and the media?s private obser-
vation of the state of the world (Mullainathan and Shleifer 2005, hereinafter MS;
Xiang and Sarvary 2007, hereinafter XS). It describes the extent to which a media
firm distorts its report from its own observation. Such distortion can be a source
of reporting inaccuracy, which we define as the difference between the news report
and the truth. In our paper, we assume that there is no distortion between a media
firm?s observation and its report (i.e., no media bias). As a result, the only source
for reporting inaccuracy is the difference between the firm?s observation and the
truth.
Previous studies suggest media bias as the source of reporting inaccuracy and
provide the following explanations for those biases: biases emerge when consumers
obtain utility from conforming ideas (MS 2005; XS 2007; Gal-Or et al. 2012; Zhu
and Dukes 2015; Godes 2020), or when media firms get a higher evaluation by
confirming consumers? prior (Gentzkow and Shapiro 2006, hereinafter GS; Godes
2020). While the former explanation captures the entertaining value of news, they
do not completely reflect the value of news. Besides the entertainment value, a
critical characteristic of news is its informational value, which is determined by its
accuracy on truthful reporting. GS analyze a model where consumers care only
72
about the informational value. The media firm obtains a private signal related to
the truth and decides on whether to truthfully report it. A medium will be regarded
as a more accurate source by consumers if its report confirms consumers? prior, and
thus it has incentives to misreport. Similarly, in our paper, consumers also only care
about the informational value and we also find that the media firm would confirm
consumers? prior. But the mechanism in our paper is markedly different. In their
paper, the firm?s reporting accuracy is exogenously determined and unknown to
consumers. Consumer inference for the firm?s accuracy is a key driver of the firm?s
misreporting behavior. In our paper, reporting accuracy is endogenously chosen by
the firm and is known to consumers. Reporting inaccuracy emerges because accurate
reporting is costly and uncertainty may never be fully resolved. Moreover, GS shows
that the media firm reports each state with the underlying probability of each state
(i.e., no exaggeration in news content).11 Instead, we find that in equilibrium, the
content of news exaggerates the ex ante more likely state in consumers? prior belief.
More recently, Godes (2020) extends the model in GS and study the impact of
feedback on media bias. While GS suggest feedback reduces media bias, he finds
that feedback can exacerbate media bias in the presence of consumers who seek
conforming news. In contrast, all consumers in our model are truth-seekers, and we
focus on the supply-side factors in news provision.
In contrast with the studies on demand-side factors, Baron (2006) explains the
11In GS, the firm?s report presents each state with the underlying likelihood, regardless of being
from a high-type firm (that honestly reports its observation) or a low-type firm (that pretends to be
a high-type by distorting its observation in news). For example, when the underlying distribution
is Pr(state L happens)=30% and Pr(state R happens)=70%, either firm would reports l in news
30% of the time, while report r 70% of the time.
73
emergence of media bias with supply-side factors. He suggests that journalists would
bias their reports to enhance their career prospects, and a media firm needs to pay
higher salaries to journalists to prevent them from generating bias. In equilibrium,
the firm may tolerate some bias in its news to save on labor costs. By contrast,
our paper provides a more general framework to capture the relationship between
a media firm?s reporting costs and its accuracy. We also explore the impact of
polarization on the firm?s news provision strategy. In a recent paper, assuming the
accuracy to be exogenous, Papanastasiou (2020) studies the spread of inaccurate
news on a social media platform as well as the platform?s intervention decision.
Different from that paper, the accuracy level is endogenous in our paper and we
focus on the production of accurate information rather than the spread of it.
This paper also relates to the research on polarization in public views. Three
types of polarization have been discussed in the literature: [i] belief polarization,
which is also called ?ideological polarization,? refers to an increasing difference be-
tween the stances and policy positions of different people (DiMaggio et al. 1996;
Fiorina et al. 2005); [ii] affective polarization, which means the tendency of peo-
ple to view opposing partisans negatively and co-partisans positively (Iyengar and
Westwood 2015); and [iii] behavior polarization, which means people becoming more
divergent in their behaviors, for example, voting decisions (Jacobson 2000; Fleisher
and Bond 2004). Earlier research suggests the polarization among the American
public is primarily affective but not ideological (Iyengar et al. 2012), but recent
studies show the existence of both and provide evidence on the connection between
these two types of polarization (Rogowski and Sutherland 2016; Pew Research Cen-
74
ter 2017; Webster and Abramowitz 2017). A stream of literature provides economic
explanations for the emergence of belief polarization (Rabin and Schrag 1999; Dixit
and Weibull 2007; Glaeser and Sunstein 2009; Zimper and Ludwig 2009; Baliga et al.
2013; Acemoglu et al. 2016; Nielsen and Stewart 2020). In a recent paper, Iyer and
Yoganarasimhan (2021) explain the emergence of behavior polarization with peo-
ple?s incentive to influence group decision. Different from this stream of literature
that focuses on the antecedence of belief polarization, we take belief polarization as
given, and study its impact on media market outcomes.
Previous research has also investigated the relationship between polarization
and news media. On the one hand, it is shown that exposure to partisan media can
lead to both ideological and affective polarization (Levendusky 2013a, b; Levy 2021).
On the other hand, polarization can also influence news consumption. For example,
Iyengar and Hahn (2009) and Flaxman et al. (2016) find that consumers? ideological
leanings influence their consumption of news. Our analysis not only captures the
impact of consumers? beliefs on their news consumption decision, but also reveals
the implication of polarization for news provision. We model polarization as an
increase in the heterogeneity in consumers? beliefs. Previous theoretical papers find
that an increase in heterogeneity has no impact on media bias (MS; Zhu and Dukes
2015). In our paper, we find polarization either has no impact or decreases media
accuracy, depending on the cost of reporting. Interestingly, when the media firm
intends to improve consumers? understanding of the truth rather than maximize its
profits, we find it may even increase accuracy in response to polarization.
Our research also adds to a fast-growing stream of literature on Bayesian per-
75
suasion and information design (Kamenica and Gentzkow 2011; for a review, see
Kamenica (2019) and Bergemann and Morris (2019)). The framework of Bayesian
persuasion/information design analyzes the game between a Sender and a Receiver
of information in a world with an unknown state. Sender and Receiver have sym-
metric information. Sender?s payoff depends on both the true state and Receiver?s
action. However, Sender can only influence Receiver?s action by providing informa-
tion. Specifically, Sender designs an information structure and commits to it, from
which Receiver can obtain information about the truth and act accordingly. We
apply this framework to the media market. Although consumers in our setting take
no explicit action and their belief determines their utility, the firm?s payoff from
selling news can still be written as a function of consumers? posterior belief like in
Kamenica and Gentzkow (2011). Note that Bayesian updating plays an important
role in consumers? interpretation of news. Consumers understand that media firms
take stances and may generate inaccurate news, so they will not take the news
content literally. Their prior beliefs influence their interpretation of a given news
report. Consumers with a more extreme prior are less likely to change their belief
over the default state (i.e., the more likely state under their prior).
Our model can be categorized as the ex ante pricing of information (Berge-
mann and Bonatti 2019). Bergemann et al. (2018) study the optimal menu design
by a monopolist information seller. Assuming costless information provision, they
characterize the properties of any revenue-maximizing menus. On the contrary, in
our model, it is costly for the media firm to provide information, and this cost plays a
major role in its reporting accuracy. Another related paper in terms of model setup
76
is Jerath and Ren (2021). They study consumers? attention allocation between pos-
itive and negative product information and assume the cost of information to be
incurred by homogeneous consumers. In our model, we assume the cost to be born
by the information provider, as Gentzkow and Kamenica (2014). As mentioned in
the introduction, the cost concern widely exists among U.S. newspapers. The cost
of investigating plays an important role in how much information it can provide.
In addition, we also consider the heterogeneity in consumers? beliefs and study its
implication for market outcomes.
3.3 Model
In our main model, there are a monopoly media firm and a group of homoge-
neous consumers. There is a true underlying state of the world, t. The state is either
L or R. Ex ante neither the firm nor consumers know the true state with certainty,
but they have a common prior belief over the distribution of the true state. We
denote ? = Pr(t = R) as the belief that the true state is R with probability ?, and
the common prior belief is denoted by ? 120. In the main model, this common prior
belief is assumed to be consistent with the underlying distribution of t. The media
firm decides on its reporting strategy ? and price p, which will be described in detail
in Section 3.3.1. Consumers know ? before deciding whether to purchase the news
or not. If they purchase the news, they will observe the news content and update
their belief about t. At the end of the game, consumers still don?t know the true
state with certainty (unless the news is fully accurate) and their expected utility
12Since no one knows the true state with certainty ex ante, ?0 ? (0, 1).
77
will be determined by their belief. In general, consumers? expected utility is higher
if they feel more certain about their belief, which will be elaborated in Section 3.3.2.
In the rest of this section, we describe the media firm?s strategy, consumers? decision
and utility, the timing of the game, and then the analysis of the game.
3.3.1 Media Firm
The media firm provides a news report to consumers. Though the firm cannot
directly observe the true state, it can collect information to construct an informative
news report. We use s to denote the firm?s observation from information gathering,
and assume that this observation (s) is reported to consumers without distortion.
The media firm?s reporting strategy is defined as the probability with which the
collected information is consistent with the true state, ? = (?L, ?R), where ?L =
Pr(s = l|t = L) is the probability of reporting l when the true state is L and
?R = Pr(s = r|t = R) is the probability of reporting r when the true state is
R. Higher values of ?L and ?R indicate higher levels of reporting accuracy. In
particular, ?L = ?R = 1 means completely accurate reporting. The reporting
strategy is decided by the firm before its production of news. For example, when
a media firm is producing a news report about the impact of lockdown policies on
people?s life, the true state can be the benefits of those policies are greater than
their costs (L), or vice versa (R). The firm implicitly chooses its reporting accuracy
by deciding how many and which journalists to assign for this report. Specifically,
it can increases ?L by assigning journalists with expertise on public health, and
78
increases ?R by assigning those with expertise in economics.
To achieve higher levels of reporting accuracy, the firm needs to recruit qual-
ified journalists, interview relevant parties, and collect and analyze information.
This process can take a substantial amount of time and effort. In our model, we
use a function, C(?), to capture the firm?s news production costs when its report-
ing strategy is ?. C(?) is proportional to the amount of information included in
the firm?s news report, which is measured by the expected amount of uncertainty
reduction caused by this report (Gentzkow and Kamenica 2014). Therefore, C is
proportional to the expected uncertainty reduction, as Equation (3.1). c > 0 rep-
resents the unit cost of providing information, which depends on the characteristics
of the information environment and the firm (e.g., the availability of evidence in the
environment, the firm?s capability to collect relevant information). H(?) is residual
variance, which measures the amount of uncertainty under a belief ? (Ely et al.
2015; Augenblick and Rabin 2021).13 ?s is the media firm?s posterior belief after
observing s.
C(?;?0) = c(H(?0)? Es[H(?s)]),
???? ?R?0
Pr(s|R)? ? ? if s = r0 (1 ?L)(1??0)+?R?0
whereH(?) = (1? ?)?; and ?s = Pr(R|s) = = .
Pr(s) ???? (1??R)?0 if s = l
?L(1??0)+(1??R)?0
(3.1)
13We tried different specifications for the measure of uncertainty (e.g., an entropy function used
by Sims (2003)). For the findings in Proposition 1-3, we obtained qualitatively similar results when
using an entropy function to measure uncertainty.
79
This cost function has several desirable properties. First, this cost function is
non-negative. Blackwell?s theorem suggests that Es[H(?s)] ? H(?0) for all ? and ?0
if and only if H is concave (Blackwell 1953; Gentzkow and Kamenica 2014). Second,
2
it is a convex function of reporting accuracy (? C2 > 0) and is an increasing function??t
of accuracy under certain constraints ( ?C > 0 when ?L + ?R > 1).
14 Therefore, it
??t
is always more costly to pursue higher reporting accuracy conditional on any given
prior belief. When ?L = ?R = 1, the report is fully accurate so that the uncertainty
is reduced to zero, H(?s) = 0, and the cost of providing such news is proportional
to the prior uncertainty. Third, the cost is zero when ?0 = 0 or ?0 = 1. Under these
prior beliefs, the true state is certain ex ante, so no information is needed to further
reduce uncertainty. In the model, we assume that there is uncertainty under the
prior, so the cost is always positive when the firm provides information.
The media firm chooses its reporting strategy ? based on the prior belief ?0,
and then it chooses the price, p, for its news. The price is also chosen before the
completion of the news report so that it is not influenced by the firm?s observation
s. The firm maximizes its profit, p?C, and it would provide news only if p?C > 0.
3.3.2 News Consumers
Consumers have the same prior belief as the firm. With the Bayesian approach,
they update their prior belief of ?0 to the posterior belief, ?s, upon observing s in
the news report. The reporting strategy of the firm, ?, is known to consumers before
they purchase and consume news. As a result, they can incorporate this knowledge
14We discuss the implication of this constraint in Section 3.3.4.
80
when interpreting the signal/content s in the news. For example, if a firm chooses
?L = Pr(s = l|t = L) = 1 and ?R = Pr(s = r|t = R) < 1, it always reports l when
t = L and would report r only when t = R. Therefore, consumers receiving a report
of r will update their posterior belief to ?r = 1. In contrast, a report of l from this
firm has lower credibility. Consumers receiving l would update their posterior belief
to ? = (1??R)?0l ? ? > 0, which implies that consumers would discount the l report1 ?0+(1 ?R)?0
from this firm.
Consumers? objective is to seek the truth.15 They will obtain a higher utility
if the state they believe in turns out to be the truth, but a lower utility otherwise.
We model the truth-seeking consumers with the utility function in (3.2). I is the
indicator function which is 1 when the conditions in its parentheses hold and is 0
otherwise.
( ) ( ) ( )
1 1 1 v
u(?, t) = I ? < , t = L ? v + I ? > , t = R ? v + I ? = ? (3.2)
2 2 2 2
We denote the more likely state in consumers? beliefs as ? . When consumers
believe state L is more likely than state R (i.e., ? < 1), then ? = L; similarly, when
2
consumers believe state R is more likely than state L (i.e., ? > 1), ? = R. When
2
consumers believe the two states L and R are equally likely (i.e., ? = 1), ? is L with
2
probability 1 and is R with probability 1 . According to Equation (3.2), consumers?
2 2
utility is v > 0 when the more likely state in their beliefs is consistent with the true
15Based on the literature in communication and journalism, informational gain is one of the
fundamental motivation for news consumption (Lee 2013). News satisfies the ?surveillance? needs
of individuals by improving their knowledge about the environment (Diddi and LaRose 2006;
Shoemaker 1996).
81
state (i.e., t = ?). Their utility when they believe in a wrong state (e.g., t = L but
? = R) is assumed to be zero. When ? = 1 , believing in either state will lead to v
2
with probability 1 and 0 with probability 1 , therefore consumers? (expected) utility
2 2
is v .16 Therefore, Equation (3.2) can also be written as u(?, t) = v ? I(t = ? |?).
2
Although we specify consumers? utility based on their belief and the true state,
in reality, the true state may not be observable to consumers (at least not within
a certain period of time). For example, to fully understand the impact of a water
pollution crisis or a lockdown policy, a long-term evaluation of its effect on people?s
health and life quality will be needed. Those evaluations and evidence can help
consumers update their posterior beliefs, in a way that could potentiallyreverses
the more likely state in their belief. However, the true state is never known with
certainty unless ?L or ?R is 1. As a result, at the end of the game, consumers
may not know the utility u(?, t) but only know the expected utility, as Equation
(3.3). Note that ? can be either ?0 or ?s in Equation (3.3). Hereinafter, we refer
to Et[u(?s, t)] as consumers? conditional expected utility after observing news s (i.e.,
the expected utility conditional on observing s).
Et[u(?, t)] = u(?, L)(1? ?) + u(?,R)? = v ?max{1? ?, ?} ? v ? Pr(t = ? |?) (3.3)
The last part of Equation (3.3) shows that consumers expected utility depends
on their certainty about the true state. Specifically, consumers? expected utility
16This utility framework is fairly flexible. For instance, if a priori consumers prefer one state
over the other, vL and vR can be different. In our setting, consumers only care about knowing the
truth, so without loss of generality we assume vL = vR = v.
82
increases when they believe t = ? with a higher probability. Figure 3.1 below
illustrates a consumer?s expected utility given her belief. A consumer has a higher
expected utility when she is more certain about the true state (i.e., ? gets closer to
0 or 1), but a lower expected utility when she feels both states may happen with a
similar likelihood (i.e., ? gets closer to 1).
2
???????????????
Insert Figure 3.1 about here
???????????????
To maximize their expected utility at the end of the game, consumers decide
whether to purchase the news report from the firm. They know the firm?s reporting
strategy (?) and price (p), but they do not observe the content of the news report
before paying the price. Only after purchase can they observe the news content (s)
and update their belief (from ?0 to ?s). If consumers do not purchase the report,
they will maintain their prior belief till the end of the game.
3.3.3 Timing of the Game
The sequence of the media firm?s and consumers? decisions is summarized
below.
1. Media accuracy : based on the prior belief ?0, the cost coefficient c, and con-
sumer preference for believing in the true state (v), the firm announces its reporting
strategy (?L, ?R);
2. Media pricing : the firm announces the price (p) for its news report;
83
3. Nature chooses the true state: the true state t is realized;
4. News report generation: the firm incurs the cost C to obtain a signal s
based on the true state (t) and the reporting strategy (?); then it reports s in the
news;
5. Consumers? purchase and consumption of news : consumers decide whether
or not to purchase the news based on the firm?s strategy (?, p) and their preference
(v); if they purchase the news report, they observe s and update their belief to ?s.
3.3.4 Model Analysis
We analyze the game by backward induction. We first discuss consumers?
belief updating process and several constraints on reporting accuracy. Then we
analyze consumers? purchase decisions, followed by the firm?s profit maximization
problem.
Consumers update their belief following the Bayes rule when they receive a
news report. Though Blackwell?s (1953) theorem implies that a news report always
leads to an uncertainty reduction regardless of the firm?s reporting strategy ? (or at
least remain at the original level of uncertainty), an additional constraint is needed
for the posterior and prior beliefs to ensure meaningful information transmission
(alternatively, informative communication): ?l ? ?0 ? ?r. This constraint means
that the belief of R becomes weaker when l is observed and becomes stronger when
r is observed.17 It ensures that the news report is either informative (?l < ?0 < ?r)
17Jerath and Ren (2021) analyze this constraint in a context where consumers allocate limited
attention to positive and negative product information before making a purchase. They derive the
same constraint, which is required to make an ?information structure? (report) informative.
84
or uninformative (?l = ?0 = ?r), but never nonsensible (?l > ?0 > ?r). Solving
these inequalities leads to ?L + ?R ? 1. Note that ?l = ?0 = ?r if and only if
?L + ?R = 1, which is the condition for uninformative reporting.
Consumer?s ex ante expected utility from purchasing the news depends on the
extent of their belief change upon consuming the news. One particularly important
change is consumers believing L to be more likely under the prior (?0 = L) shift
to believing R to be more likely after consuming news (?s = R), or vice versa.
Formally, we define consumers? ?belief change? based on the relationship between
their prior and posterior beliefs as follows.
Definition 1. A belief change over which state is more likely is defined as
(1) ?s >
1 when ? 1 1 1 10 < ; (2) ?s < when ?0 > ; or (3) ?s 6= when ?0 = 1 .2 2 2 2 2 2
Mathematically, this is equivalent to ? + ? > 1 and 1??L < ? < ?L .18L R 1??L+? 0R ?L+1??R
Note that any change that leads to ? = 1s , which means that consumers?2
posterior belief is that L and R are equally likely, does not qualify a belief change
in our context. With this definition, we can analyze consumers? ex ante expected
utility when they purchase news, given by Equation (3.4).
18When the news is informative (as defined in this subsection), the constraint for a belief change
is equivalent to the obedient constraint in the Bayesian games of communication (Myerson 1982;
Bergemann et al. 2018). Specifically, a belief change happens if and only if the more likely state
in consumers? posterior beliefs (?s) is consistent with the news content (s), i.e., ?l = L and ?r = R.
85
Es[Et[u(?s, t)]] = P?r(l) ? Et[u(?l, t)] + Pr(r) ? Et[u(?r, t)]?????v(?L(1? ?0) + ?R?0) if news may lead to a belief change,= ???v ?max{1? ?0, ?0} if news never lead to a belief change.
(3.4)
By comparing a consumer?s ex ante expected utility with and without consum-
ing news, we can see that a news report leads to a strictly higher ex ante expected
utility if and only if it may lead to a belief change. This relates to a key insight
of Blackwell, that information is valuable only if it changes the recipient?s optimal
actions. Bergermann and Morris (2019, Proposition 1) also show this point in a
general model of information design. In our model, consumers don?t explicitly take
action after receiving the news report and their expected utility depends on their
posterior belief. The value of information (i.e., the net gain in expected utility from
information consumption) depends on whether it leads to a belief change. From the
firm?s viewpoint, it should choose ? to make the news valuable to consumers, i.e.,
the new report needs to satisfy the conditions presented in Definition 1.
From the viewpoint of consumers, given ?, the news report is more valuable
when their prior belief is closer to 1 . As their prior gets closer to 1 , the prior
2 2
uncertainty is higher and then consumers have a higher WTP for news. If consumers?
prior belief is so extreme that there is no belief change from news consumption, then
their WTP becomes zero. In the rest of the paper, we assume that consumers will
86
consume news only when consumption leads to a positive ex ante surplus (i.e., their
WTP is greater than the price, Es[Et[u(?s, t)]] ? Et[u(?0, t)] ? p =WTP ?p > 0).
This implies that news consumption will happen only when consumers expect a
potential belief change from news, even if the price is zero. As a result, the firm
needs to increase its reporting accuracy to induce consumers to purchase its news
report. Lemma 1 presents the relationship between consumers? WTP and the firm?s
reporting accuracy.19
Lemma 1. Consumers? WTP for news weakly increases as ?0 ? 1 . WTP =2
v(?L?1+(1??L+?R)?0) when 1??L? < ?0 <
1 , WTP = v(?L?(?L+1?? )? )1 ?L+? R 0R 2
when 1 ? ? ?L0 < ? , and WTP = 0 when ? ?
1??L ?L
2 ?L+1 ? 0R 1?
or ?
? 0
? .
L+?R ?L+1??R
As the monopolist in this market, the media firm can always charge (slightly
below) consumers? WTP. To increase its price, the firm needs to raise the accuracy
of reporting. However, the cost of news provision also plays an important role
and needs to be accounted for. In the next section, we analyze the firm?s optimal
strategies under different cost structures and discuss the impact of the prior belief.
3.4 Results
In this section, we examine the impact of costs on the media firm?s reporting
strategy. We start with the condition for news provision, then discuss the optimal
accuracy levels chosen by the firm. We also construct a measure of the overall
reporting inaccuracy and study how it changes with market circumstances. Our
19Bergemann et al. (2018) obtain similar results in Section III.A of their paper.
87
first finding is that consumers? extreme prior beliefs can discourage the provision of
news when reporting costs are sufficiently high. The proposition below summarizes
the results.
Proposition 1. Under low reporting costs (c ? v), the media firm provides
news as long as consumers have prior uncertainty (0 < ?0 < 1). Under high report-
ing costs (c > v), it provides news if and only if consumers have sufficiently high
prior uncertainty ( c?v < ?0 <
v+c).
2c 2c
In our model, we assume that consumers do not know the truth with certainty
under their prior belief. If they do, i.e., ?0 = 0 or ?0 = 1, the firm would not
provide news because news does not create value for any consumer. Proposition
1 suggests that as long as uncertainty exists under consumers? prior belief, i.e.,
0 < ?0 < 1, the firm will always provide news when reporting is not too costly.
This corresponds to situations where information on the focal issue can be easily
collected, such as the price changes of a specific stock in a day. When reporting
becomes sufficiently costly, consumers? prior belief plays a more important role in
the firm?s news provision decision. If consumers? prior belief is sufficiently extreme
(? < c?v0 or ?
v+c
0 > ), their ex ante expected utility without news consumption2c 2c
is already high under the prior. As a result, their WTP will be too low to cover
the firm?s cost, and news provision becomes unprofitable. With priors ?0 =
c?v or
2c
?0 =
v+c , consumers? WTP becomes just high enough to cover the cost, so news
2c
provision is still not strictly profitable for the firm. However, when the prior belief
is relatively moderate ( c?v < ? < v+c0 ), i.e., consumers are fairly uncertain about2c 2c
88
the true state of the world. their WTP for a news report becomes high enough and
the firm finds it profitable to produce news.
We now elaborate on the equilibrium level of accuracy chosen by the firm when
news is provided. The results are presented in Proposition 2.
Proposition 2. When the media firm provides news, it chooses a full-accuracy
strategy under low reporting costs (c ? v):
?L = ?R = 1, p = v ?min{?0, 1? ?0},
and a partial-accuracy strategy under high reporting costs (c > v):
( )
? (v + c)(v ? c(2?0 ? 1)) (v + c)(v + c(2?0 ? 1)) c+ v?L = , ??R = , p = v ?max{?0, 1? ?0} .4vc(1? ?0) 4vc?0 2c
As a result, under high costs, the news report exaggerates the presence of the ex ante
more likely state.
When the cost of news provision is low, the firm will choose full accuracy.
After purchasing and consuming the news, consumers will know the true state with
certainty, and their posterior belief is either ?l = 0 (if the news is l, the probability
that the true state is R is zero) or ?r = 1 (if the news is r, the probability that the
true state is R is one). Because news is more valuable to consumers when they have
higher prior uncertainty, the firm?s price increases in prior uncertainty and reaches
the highest level under the prior ?0 =
1 .
2
Compared with the low-cost case, the prior belief over the true state has a
larger impact on the accuracy of reporting under high costs. Figure 3.2(a) shows
89
an example of the firm?s optimal reporting strategy captured by the y axis as a
function of the prior belief ? captured by the x axis. The regions to the left of c?v0 2c
and to the right of v+c represent for the range where no news is provided, while an
2c
intermediate ?0 allows for the existence of the news market.
???????????????
Insert Figure 3.2 about here
???????????????
Figure 3.2(a) illustrates how the optimal reporting accuracy changes with the
prior belief when news is provided. When L is believed to be more likely than R
under the prior, the media reports L with higher accuracy than R. When the prior
belief favors R rather than L, reporting accuracy for R is higher than that for L. In
the example of the water pollution crisis, if the prior is that the pollution has a large
impact on local residents? life, the media firm will put more resources on accurately
reporting a large impact with high accuracy, but only limited resources on collecting
evidence to accurately reflect a small impact. In other words, the media firm will
allocate more resources toward accurately reporting the more likely state based on
the prior belief. Upon observing this, consumers expect to see an accurate report
under the majority of circumstances and are willing to pay for the news.
Panel (b) of Figure 3.2 illustrates the news content resulting from the optimal
accuracy. Interestingly, as the firm tries to build an image of being accurate under
most circumstances, its news content, measured by the probability of reporting l or
r, always exaggerates the ?default? state (i.e., the more likely state) in consumers?
prior. For example, in Panel (b), when state R happens with a probability of
90
70%, the firm reports r in 90% of the time (i.e., Pr(r) = 0.9 when ?0 = 0.7).
Such an exaggeration makes the less likely state even harder to be found in news.
From consumers? perspective, this is similar to the effect of an ?echo chamber,?
because they are largely exposed to conforming opinions in equilibrium. What?s
striking about this result is that it does not arise due to the media firm?s intentional
misreport such that media bias emerges (i.e., the firm does not truthfully report the
signal it receives during investigation). Instead, the reporting inaccuracy completely
stems from the firm?s strategic trade-off between its production costs and consumers?
willingness to pay for information to reduce their uncertainty.
After consumption, consumers? posterior belief is c?v if they receive l, or v+c
2c 2c
if they receive r. Note that the posterior belief is independent of the prior belief.
They are exactly the belief thresholds under which the firm would not provide news.
The intuition is as follows. Suppose the firm chooses (??L, ?
?
R) 6= (?? ?L, ?R) that leads
to different posteriors. On the one hand, if those posteriors are between c?v and
2c
v+c , the firm could have earned more profit by increasing its reporting accuracy.
2c
On the other hand, if those posteriors don?t fall between c?v and v+c , then the
2c 2c
firm?s marginal investment in reporting accuracy is above consumers? WTP for it.
Consequentially, choosing the accuracy level (?? ?L, ?R) that leads to the threshold
(for news provision) posterior beliefs is optimal for the firm.
Compared with the low-cost scenario (c ? v), consumers? posterior belief
is less extreme under high costs (c > v). There is remaining uncertainty after the
report?s realization because the high cost deters the firm from choosing full reporting
accuracy. As the unit cost of news provision (c) increases, the remaining uncertainty
91
under the posterior belief increases, and the range of ?0 under which news is provided
shrinks.
???????????????
Insert Figure 3.3 about here
???????????????
Figure 3.3 illustrates the relationship between equilibrium outcomes and the
prior belief, ?0. In Panel (a), the vertical axis represents the ex ante expected
utility. The dashed line shows that consumers? ex ante expected utility without news
consumption is lower under moderate priors (i.e., when ?0 is closer to
1). However,
2
by consuming news, their ex ante expected utility can increase to a constant level.
The firm earns revenue by charging the difference between the ex ante expected
utility with and without news. Its revenue, as shown in Panel (b), is higher under
higher prior uncertainty, so are the cost and the profit (i.e., the difference between the
revenue and the cost). Panel (c) shows the levels of prior and posterior uncertainty,
H (multiplied by c). Prior uncertainty is higher under moderate ?0, so the firm
needs to incur more cost to reduce uncertainty. The expected remaining uncertainty
after news consumption is constant. If the uncertainty is above this level, the firm
would provide more accurate news to earn a profit until the uncertainty achieves
this constant level. Once the news can help consumers reach this particular level of
uncertainty, the firm has no incentives to provide any further improvement over its
accuracy.
Our model also allows us to study the level of reporting inaccuracy. In the pre-
vious literature such as MS and XS, media bias is defined as the expected difference
92
between the raw information and the news, where the collected raw information is
assumed to accurately present the truth in expectation. By contrast, the concept of
media bias does not apply in our context. Instead, we focus on reporting inaccuracy
and define it as the expected difference between the true state and the reported
news. As discussed in Section 3.2, media bias can be one source of reporting in-
accuracy. In our paper, we assume there is no systematic distortion from the raw
material in the news report, and we focus on another source of inaccuracy: the
inaccuracy in the process of investigation and information collection. We formally
define reporting inaccuracy (RI) as the following.
Definition 2. RI = E[|I(t = R)? I(s = r)|] =Pr(l, R) + Pr(r, L)= (1 ?
?R)?0 + (1? ?L)(1? ?0).
Specifically, reporting inaccuracy is the sum of the probabilities of two types
of misreporting. One is the probability of reporting l when the true state is R, and
the other is the probability of reporting r when the true state is L. Intuitively, RI=0
when ?L = ?R = 1, and RI=1 when ?L = ?R = 0. RI can also be viewed as a
weighted sum of the probabilities of type 1 and type 2 statistical errors. Suppose
the null hypothesis is t = R. If the true state is indeed R, then the firm reports l
(type 1 error) with probability 1 ? ?R; if t = L, the firm reports r (type 2 error)
with probability 1 ? ?L. The weights of these two probabilities are the underlying
probabilities that the corresponding state is the truth.
We measure the amount of reporting inaccuracy in equilibrium based on the
definition above. Next, we describe the equilibrium reporting inaccuracy under
93
different cost structures in the following proposition.
Proposition 3. When the media firm provides news, the reporting inaccuracy
(RI) increases when the cost of information provision (c) increases, but it remains
unchanged when the prior uncertainty level (H) increases.
Proposition 3 states that when the firm provides news, the cost of news provi-
sion leads to higher reporting inaccuracy. High costs prohibit the firm from choos-
ing high accuracy, which leads to an increased probability of misreporting, and
consumers are more likely to end up in a wrong posterior belief. Surprisingly, the
amount of prior uncertainty does not influence reporting inaccuracy. One may
expect there to be more inaccurate reporting in a murkier environment because
evidence collection will be more difficult. However, consumers? higher valuation
for accurate reporting in such an environment also incentivizes the firm to invest
more. As a result, those two forces exactly cancel each other out so that reporting
inaccuracy is invariant in prior belief.
Note that the results in this section show that consumers? prior beliefs play an
important role in the media firm?s optimal reporting strategy. To further understand
the impact of prior beliefs, we consider heterogeneity in consumers? prior beliefs in
the next section.
3.5 Extensions
Over a wide range of topics, consumers have heterogeneous prior beliefs about
the true state of the world. For example, consumers who have had negative experi-
94
ences with tap water tend to believe in the existence of water pollution. Furthermore,
the degree of heterogeneity among consumers? beliefs can change over time. Sur-
veys show that during the past two decades, Americans have become more divided
in their attitudes towards political values and policy issues, such as immigrants
and government regulation of business (Pew Research Center 2017). Polarization
in individuals? opinions directly influence their consumption of news, and thus the
media firms? provision of news. To understand the impact of polarization on news
accuracy, we analyze an extension of the main model that incorporates consumers?
heterogeneity in their priors.
In addition to the heterogeneity among consumers, the firm?s objective be-
hind news provision also drives its strategy. For media firms, tension always exists
between profits and the public interest (Croteau and Hoynes 2006). In a second
extension, we assume that the firm is a social planner that aims at improving con-
sumers? probability of being correct about the true state. We analyze the firm?s
response to polarization and compare it with that of a pure profit maximizer. Fi-
nally, in a third extension, we analyze a firm with a dual objective (of obtaining
profits and improving consumers? probability of being correct), which illustrates how
the trade-off between a firm?s commercial interest and the public interest drives the
accuracy of news.
95
3.5.1 Impact of Polarization on News Accuracy
To study the impact of polarization, we first introduce an approach to capture
polarization, then analyze its impact on the firm?s choice of accuracy. Suppose
consumer i has a prior belief that Pr(R) = ?i0 ? [0, 1]. We use a linear probability
density function to represent a family of distributions of consumers? beliefs, as given
in Equation (3.5).
??
??
??
4(1? ?)?+ ? if ? ? 1 ;
? 2f(?; ?) = ?? (3.5)4(1? ?)(1? ?) + ? if ? > 1 .
2
where 0 ? ? ? 2.
???????????????
Insert Figure 3.4 about here
???????????????
This density function is flexible and can describe a wide variety of distributions.
Figure 3.4 displays three examples with different values of ?. When the parameter
? is small, the majority of consumers believe L and R are similarly likely (i.e., their
? are close to 1). An increase in ? will move consumers towards both ends of the
2
spectrum, which means their beliefs become more polarized. As ? approaches to 2,
the majority of consumers believe that one state is much more likely than the other.
Note that previous research has suggested using variance as a measure of polarization
(DiMaggio et al. 1996). In our context, the variance of ?, Var(?; ?) = 1+? , is a linear
24
96
function of ?, which also shows that ? captures the degree of polarization in beliefs.
Further, the true underlying distribution of t is assumed to be Pr(R) = 1 . Re-
2
call that in the main model, consumers? prior belief, ?0, is assumed to be consistent
with the underlying distribution. On the contrary, there are discrepancies between
consumers? priors and the underlying distribution when we incorporate heteroge-
neous priors into the model. The assumption Pr(R) = 1 means that the median
2
consumer?s prior belief is consistent with the true underlying distribution. We also
assume that the prior belief of the medium, ?m0 , is consistent with the underlying
distribution of t (i.e., ?m = 10 ), as in the main model.2
We now consider the impact of consumer heterogeneity on the consumption
and provision of news. To simplify the analysis, we assume that the firm needs to
maintain ?L = ?R. To facilitate exposition, we omit the subscripts and use ? to
represent the firm?s accuracy in the rest of this section. We first analyze consumers?
purchase decisions to derive the total demand for news, then discuss the firm?s trade-
offs when deciding on its accuracy. Next, we study the firm?s equilibrium strategy,
compare it with that in the main model, and finally discuss the implication of
polarization for news provision.
Recall that news consumption happens only when it leads to a strict increase
in a consumer?s ex ante expected utility. In other words, consumer i purchases
news when WTP i > p. where WTP i can be derived based on Lemma 1 in Section
(3.3.4). Corollary 1 below formally summarizes the relationship between consumers?
consumption of news, their prior beliefs, and the reporting accuracy in the presence
of heterogeneous prior beliefs. Though consumers with more extreme prior beliefs
97
see relatively little value in news and generally tend not to consume news, they
would still use it when the news is sufficiently accurate.
Corollary 1. Extreme prior beliefs (?i0 ? 1??+
p or ?i ? ?? p0 ) discouragev v
news consumption. However, as the media becomes more accurate, more consumers
start consuming news.
Aggregating all con?sumers? decisions leads to the total demand as a func-?? p
tion of price, D(?, p) = v? p f(?; ?)d?, with which we can obtain the optimal1 ?+
v
price, p?het(?), where the subscript ?het? denotes ?heterogeneous beliefs? among
consumers. The next step is to find the optimal accuracy that maximizes the firm?s
profit. When the firm decides its accuracy, it needs to account for several effects of
accuracy on its profit, summarized in Equation (3.6) below.
?
d(D ? p? C) ??
d? ?
( )
?p? ?
= het ? ?
?D ?D ?p
D(p ) + p + het
?C
het het ? (3.6)
p=p?het(?) ????? ? ? ?? ???p ?? ? ??????
price effect demand expansion effect cost effct
Equation (3.6) shows the three effects of accuracy on the firm?s profit. First, for
each consumer of the media firm, news of higher accuracy is ex ante more valuable,
so the firm can charge a higher price. This is the price effect of accuracy. Second, as
shown in Corollary 1, higher accuracy will attract consumers with relatively extreme
beliefs to consume news, which leads to a higher demand (captured by ?D ). A higher
??
demand gives the firm an incentive to raise the price, so the demand increase induced
?p?
by the higher accuracy is attenuated (by the size of ?D het ). The total impact of
?p ??
accuracy on demand is positive, which can be viewed as a demand expansion effect.
98
Finally, increasing accuracy also has a cost effect, because the firm needs to expend
more resources in collecting information and reducing uncertainty. To summarize,
the price and demand expansion effects incentivize the firm to increase accuracy,
but the cost effect drives the firm to decrease accuracy.20
Recall that in the main model, only the price and cost effects play a role
in the firm?s decision of accuracy, because the demand function D(?, p) is a step
function of ? and p under a homogeneous prior belief. In other words, as long as
accuracy (price) is sufficiently high (low), all consumers would consume news, and
the demand is not sensitive to a change in accuracy (price). This property allows
the firm to capture a large amount of consumer surplus. We will further elaborate
on this point when comparing the results of the case of heterogeneous priors with
those in the main model.
Accounting for the heterogeneity in consumers? prior beliefs, we solve the profit
maximization problem with Equation (3.6) and summarize the results in Lemma 2.
We assume that the firm favors providing news at its breakeven point.
Lemma 2. A profit-maximizing media firm chooses a full-accuracy strategy
(? = 1, p = p?het(? = 1)) when c ? c?; it chooses a partial-accuracy strategy (? =
??het < 1, p = p
? ?
het(? = ?het)) when ? < 1 and c? < c <
v(2??) , and does not provide
2
news otherwise.21
Figure 3.5 illustrates the results in Lemma 2. Similar to the case with homo-
( ? ?20 ?p ?pThe indirect e)ffects in Equation (3.6) sum up to zero: het?? D(p? ) + p? ?D hethet het ?p ?? =
?p?
D(p? ) + p? ?D het = ?(D?p?C)
?p?het
het het ?p ?? ?p ?? = 0, because
?(D?p?C)
?p = 0 when p = p
? (?).
? ? het
2
21 2 v(4 (?
2?3?+3)3?4?3+18?2?18?)
c? is v(? ?6?+6?? ? ?3?+3)9(1??) when ? < 1, is
v
2 when ? = 1, and is 27(??1)2
when ? > 1. ?? ?het and phet(?) are given in Appendix B.
99
geneous priors, the firm provides full accuracy under low costs but no news under
high costs. When the unit cost of providing information is relatively low compared
to consumers? valuation, the price and demand expansion effects dominate. As a
result, the firm chooses the highest accuracy to create a strong demand and then
charges a high price. However, under high costs, consumers? WTP can no longer
cover the cost. The cost-saving motivation drives the firm to choose lower accuracy
despite the resulting decrease in price and demand. Consequently, news becomes
uninformative and no one will purchase it, leading to a failure of news provision.
When the degree of polarization is low and the cost level is intermediate,
partial accuracy is offered by the firm. Interestingly, partial accuracy is never chosen
by the firm when the degree of polarization is high. We explain the intuition by
considering the firm?s response to a cost change. When the cost level (c) increases,
the marginal cost of accuracy becomes higher. In response to this change, the firm
tends to reduce the accuracy and focus on the high-valuation consumers (i.e., those
with higher prior uncertainty). If the polarization level is low (i.e., ? < 1), reducing
accuracy can effectively cut the cost while only drives a limited number of consumers
away. The firm is able to find an accuracy level to balance the three effects (defined
in Equation (3.6)). However, when consumers become sufficiently polarized (i.e.,
? ? 1), saving cost by reducing accuracy can end up like a downward spiral: a small
decrease in the accuracy can lead to a significant drop in demand, which forces the
firm to cut the price to retain consumers. However, a lower price means an even
lower return to accuracy, so that the firm would further reduce its accuracy to save
costs. As a result, providing no news is optimal for the media firm when the cost is
100
above a threshold.22
???????????????
Insert Figure 3.5 about here
???????????????
By comparing the results of the main model with those of Lemma 2, we identify
the impact of consumers? heterogeneous prior beliefs on news provision. In the main
model, the firm pursues a full-accuracy strategy when c < v, and a partial-accuracy
strategy otherwise. In Lemma 2, the range of costs for a full-accuracy strategy
is narrower, and the range for no news expands. This is because the firm loses
part of its ability to extract consumer surplus when consumers have heterogeneous
prior beliefs. Heterogeneous prior beliefs imply heterogeneous WTP for news, which
means that the demand becomes more sensitive to a price change. Therefore, for
the same reporting accuracy, the optimal price under a heterogeneous prior is lower
than that under a homogeneous prior. Furthermore, this price decreases in the
degree of polarization. As a result, the return to investing in accuracy improvement
decreases, which incentivizes the firm to choose lower accuracy.
While polarization can drive the firm to choose lower accuracy levels, Lemma
2 also reveals that its impact critically depends on the level of costs. We summarize
the finding formally in the following proposition.
Proposition 4. When consumers? prior beliefs become more polarized, a
profit-maximizing media firm?s accuracy does not change under low costs (c ? 8v )
27
or high costs (c ? v), and weakly decreases under moderate costs (8v < c < v).
27
22The threshold for cost is v(2??)2 when ? < 1, and c? when ? ? 1.
101
Proposition 4 shows that an increase in polarization influences media accu-
racy only when the cost is at a moderate level. First, under low costs (c ? 8v ),
27
polarization does not influence the firm?s accuracy. Under this condition, accurate
information about the true state is readily accessible and can be collected with
low expenditure, such as reporting today?s temperature in a particular zip code or
describing the functions of a newly-released smartphone, etc. The firm can easily
obtain an accurate signal and report it in its news. Its decision is driven by the
price and demand expansion effects of accuracy. In this case, the firm provides full
accuracy.
Second, when the cost is sufficiently high (c ? v), the firm chooses the min-
imum accuracy (? = 1). No one would consume news when it is of the minimum
2
accuracy, so the market for news fails. This corresponds to the issues where accurate
reporting is extremely challenging, such as examining the overall impact of a gov-
ernment policy or explaining the debate around a thousand-page bill in Congress.
Under this condition, the cost effect is the dominant factor for choosing accuracy
regardless of the degree of polarization.
Finally and interestingly, under moderate costs (8v < c < v), stronger polar-
27
ization drives the media to choose lower accuracy. At these levels of costs, providing
full accuracy is more costly than that under low costs, but not large enough to
prevent news provision. In other words, none of the three effects in Equation (3.6)
dominates so that the degree of polarization drives the firm?s decision. When the de-
gree of polarization increases, consumers become more certain about the state under
their priors and thus have lower WTP for news. Lower WTP weakens the price effect
102
of raising accuracy, because it not only leads to lower demand for news (in Equation
(3.6), D(p?het) decreases), but also implies the firm cannot raise its price as much as
?p?
it could for the same increase in accuracy (in Equation (3.6), het decreases). Under
??
this condition, the firm needs to decrease price (p?het in Equation (3.6)) to attenuate
the decline in demand, which results in a lower return on investment in improving
accuracy.23 All in all, under higher degrees of polarization, the firm is less likely to
provide news, and is less accurate upon news provision. From a societal perspective,
this result is significant because polarization should call for more accuracy so that
consumers with different opinions ex ante can collectively move closer to the truth
upon news consumption. However, Proposition 4 demonstrates that in equilibrium,
the profit-maximizing media firm either decreases or makes no change to its accu-
racy as polarization increases, which may further discourage the consumption of
news. This outcome suggests that there will be scope for third-party intervention,
especially when the underlying issues are important political or economic ones. In
the next subsection, we furthur extend the model to study how the firm?s objective
influences its response to polarization.
3.5.2 Media Firm As An Objective-Welfare Maximizer
In addition to generating revenues for media firms, news also has educational
and public service functions for society (Croteau and Hoynes 2006). In this subsec-
tion, we first discuss how to measure social welfare from an objective perspective
23Greater polarization may increase or decrease the demand expansion effect of accuracy in
Equation (3.6), depending on the level of reporting cost. Compared with the changes in other
parts of Equation (3.6), this change has less impact on the firm?s decision on accuracy.
103
(i.e., objective welfare) and then analyze the game assuming that the media firm
intends to maximize objective welfare. Finally, we compare the results with those
in Section 3.5.1 to understand how the firm?s objective (i.e., maximizing profits
vs. maximizing objective welfare) influences the market outcome in the presence of
polarization.
To ensure a fair comparison between the results in this subsection and those
in Section 3.5.1, we retain three assumptions made in Section 3.5.1. First, the
distribution of consumers? prior beliefs is described by f(?, ?), as defined in Equation
(3.5). Second, the true underlying distribution of t is Pr(t = R) = 1 , and the media
2
firm?s prior belief is consistent with the underlying distribution (i.e., ?m = 10 ). Third,2
the media firm maintains ?L = ?R = ? >
1 when news is provided.
2
When consumers and the firm have different beliefs about the true state of
the world, they have different evaluations of consumers? probability of being correct
about the truth, and thus different evaluations of welfare. From consumer i?s per-
spective, her probability of being correct is Pr(t = ? i|?i), which is evaluated based
on her belief ?i. We refer to Pr(t = ? i|?i) as consumer i?s subjective probability of
being correct, which is her expected utility when v = 1 (see Equation (3.3)). By
contrast, from the firm?s perspective, consumer i?s probability of being correct is
ki = Pr(t = ? i|?m), which is evaluated based on the media firm?s belief ?m. For a
media firm that cares about consumers? objective welfare, ki is a more reasonable
measure to rely on than Pr(t = ? i|?i). ki is consumer i?s objective probability of
being correct, because the firm?s prior is consistent with the underlying distribution
of the truth. To best serve the public interest, a media firm should (in expectation)
104
use news to lead consumers objectively closer to the truth, rather than merely let
consumers subjectively believe that they are closer to the truth. In the rest of the
paper, we simply use ?consumer i?s probability of being correct? to refer to ki, unless
otherwise specified.
To aid the discussion, we use Figure 3.6 to illustrate the relationship between
consumers? subjective and objective probabilities of being correct, and how they re-
late to subjective and objective welfare. We normalize v = 1 so that each consumer?s
expected utility equals her subjective probability of being correct. In Figure 3.6(a),
the V-shape line is each consumer?s expected utility (and subjective probability of
being correct) without news consumption, which is a function of one?s prior belief,
?i0. For example, if consumer i believes R happens with a probability of 0.6 under
the prior (i.e., ?i0 = 0.6), then the more likely state in her mind is ?
i
0 = R, and she
subjectively believes that she is correct 60% of the time (i.e., Pr(t = R|?i0) = 0.6).
The area below the V-shape line represents the baseline level of subjective welfare
enjoyed by all consumers without consuming news.
If the firm provides news with accuracy ? and price p, consumers with prior
beliefs 1??+ p < ?i p0 < ?? will consume news (see Corollary 1). These consumersv v
pay p to access news, and their ex ante expected utility is v? = ? (based on Equation
(3.4)). Consumer i?s ex ante expectation of her (subjective) probability of being
correct becomes Es[Pr(t = ?
i|?is s)] = ? if she consumes news.24 After paying p,
those consumers expect a surplus from news consumption (blue triangle), while the
24When n[ews may l]ead to consumer i?s belief change, based on Equation (3.3), Es[Pr(t =
i
i| i Et[u(?s,t)] Es[Et[u(?
i
? ? )]= E = s
,t)]]
s s s v v . Based on Equation (3.4), Es[Et[u(?
i
s, t)]] = v(?(1??i0) +
??i0)= v?, so Es[Pr(t = ?
i
s|?i v?s)] = v = ?.
105
firm obtains revenues (red rectangle), and the sum of these two parts is the ex ante
expectation of the increase in gross subjective welfare due to news consumption.
Specifically, consumer i?s ex ante surplus from news consumption is the difference
between her WTP and the price, given in the following equation.
CSi = E [E [u(?is t s, t)]]? Et[u(?i0, t)]? p
= ?v(E [Pr(t = ? i|?i )]? Pr(t = ? i|?is s s 0 0))? p???
??v(?? (1? ?
i
0))? p if ?i < 10 ,2
= ??? (3.7)v(?? ?i )? p if ?i? 10 0 .2
In Equation (3.7), consumer i?s ex ante surplus depends on the increase in
her expected (subjective) probability of being correct because of news consumption,
Es[Pr(t = ?
i
s|?is)]?Pr(t = ? i0|?i0). For example, in Figure 3.6(a), if a consumer with
prior ?i0 = 0.6 consumes the news of accuracy ? = 0.9, her expected (subjective)
probability of being correct will increase by 0.3(= 0.9? 0.6). Her ex ante consumer
surplus will be v(? ? ?i0)? p = 1(0.9? 0.6)? 0.2 = 0.1. In our analysis in Section
3.5.1, a profit-maximizing firm optimizes its producer surplus, which equals to its
revenue (red rectangle) less its cost (which is not plotted in Figure 3.6). By contrast,
a subjective-welfare-maximizing firm optimizes the total surplus, i.e., the sum of the
producer surplus (red rectangle less the cost) and the (ex ante) consumer surplus
(blue triangle). Importnatly, in our model, the firm focuses on improving objective
welfare, which is different from the expected total surplus because the latter depends
on consumers? subjective probability of being correct. We will further elaborate on
106
this difference in the subsequent discussion about Figure 3.6.
???????????????
Insert Figure 3.6 about here
???????????????
Figure 3.6(b) shows consumers? (ex ante) gross objective welfare, which is the
multiplication of consumers? value of being correct (v, which is 1 in this figure)
and their ex ante objective probability of being correct (E[ki]). Without news, the
expected probability of being correct (E[ki]) is 0.5 for all consumers. Given that the
truth is either state with equal likelihood, all consumers are expected to be correct
half of the time. The area below the horizontal line at 0.5 represents the baseline
level of objective welfare. Comparing these two figures, we see that without news, a
consumer subjective probability of being correct (the V-shape line in Figure 3.6(a))
is weakly higher than the objective probability (0.5, as in Figure 3.6(b)). This is
because the prior biases in consumers? beliefs give them a false sense of certainty
and make them overestimate their probability of being correct.
When consumers with prior beliefs 1??+ p < ?i < ?? p0 consume news, theirv v
ex ante objective probability of being correct (Es[k
i i m 25
s] = Es[Pr(t = ?s|?s )]) is ?.
Note that this equals to their ex ante expectation of the (subjective) probability
of being correct in Panel (a). The intuition is as follows. As discussed in Section
3.3.4, consumers would consume news only when news may lead to a belief change.
Under this condition, the state which is more likely under consumer i?s posterior
25When news may lead to consumer i?s belief change, there are ? il = L and ?
i
r = R. Under this
condition, consumer i?s ex ante probability of being correct is E is[ks] = Es[Pr(t = ?
i m
s|?0 )]= Pr(s =
l, t = ? il |?m0 ) + Pr(s = r, t = ? ir|?m0 )= Pr(s = l, t = L|?m0 ) + Pr(s = r, t = R|?m0 ) = ?.
107
(? is) always depends on the news content (s) that she observes (i.e., ?
i
l = L and
? ir = R). Furthermore, the news content (s) is consistent with the true state (t)
with a probability of ? (i.e., Pr(s = l|t = L)= Pr(s = r|t = R) = ?). As a result,
? is is expected to be consistent with t with a probability of ?, regardless of being
evaluated based on the consumer?s belief or the firm?s belief.
By comparing Figures 3.6(a) and 3.6(b), we observe that news consumption
has a greater impact on consumers? objective probability of being correct than on
their expected subjective probability. Recall that in the example, when ? = 0.9,
a consumer with ?i0 = 0.6 will get an increase of 0.3 in her ex ante subjective
probability of being correct. From the firm?s perspective, consumer i?s objective
probability of being correct increases by 0.4(= 0.9? 0.5) because of news consump-
tion. In Figure 3.6(b), the gray rectangle represents the increase in consumers? ex
ante gross objective welfare. This increase in objective welfare can be interpreted
as the (objective) value of moving consumers closer to the truth. It is greater than
the increase in subjective welfare, i.e., the sum of the ex ante consumer surplus and
the firm?s revenue. The is because when consumers overestimate their probability
of being correct, they will underestimate the value of information in news.
Next, we analyze the game assuming that the firm?s objective is to maximize
objective welfare. Consumers consume news only when it strictly increases their ex-
pected utility, which requires p < WTP i for con?su(mer i. Ac)counting for consumers?
consumption decisions, the?fir(m solves)max
i
?,pv E[k ]? 1 ?C.26? Lemma 3 belowi 2
26Note that solving max?,pv E[k
i]? 12 ? C and solving max v E[k
i
?,p ] ? C will generatei i
the same solution. To be consistent with Figure 3.6(b), we use the former one.
108
describes the firm?s optimal strategies.
Lemma 3. An objective-welfare-maximizing media firm chooses a full-accuracy
strategy (? = 1, p = 0) when ? < 1 and c ? v(1 + ?), or ? ? 1 and c ? 2v;
it chooses a partial-accuracy strategy (? = ??het,k < 1, p = 0) when ? < 1 and
v(1 + ?) < c < 2v(2? ?), and does not provide news otherwise.27
Figure 3.7 illustrates the results in Lemma 3. The overall pattern is similar to
that of a profit-maximizing firm: the firm offers full accuracy under low costs, offers
partial accuracy under moderate costs if polarization is low, and offers no news un-
der high costs. Notable differences from comparing Figures 3.5 and 3.7 are that an
objective-welfare maximizer is more likely to provide news than a profit maximizer,
and its accuracy is weakly higher than that of a profit maximizer. This is because
the payoff gain from raising accuracy for an objective-welfare maximizer is larger
than the profit gain from raising accuracy for a profit maximizer. First, when a
firm raises its accuracy, the gain in objective welfare (viewed from the firm?s per-
spective) is larger than the increase in subjective welfare (viewed from consumers?
perspectives), because consumers? incorrect prior beliefs make them underestimate
the benefit of news. Second, only part of the increase in subjective welfare trans-
lates into the firm?s profit, because the firm cannot fully capture consumer surplus
when charging a uniform price from heterogeneous consumers. Consequently, an
objective-welfare maximizer tends to choose higher accuracy levels than a profit
maximizer. Importantly, this result illustrates that financial incentives alone may
27??het,k =
v(7?5?)?c
6v(1??) .
109
not be sufficient to generate news reports that maximize objective welfare under
relatively high costs of reporting.
???????????????
Insert Figure 3.7 about here
???????????????
Lemma 3 also shows how an objective-welfare maximizer responds to polariza-
tion and how costs influence the equilibrium strategy. We summarize those findings
in the following proposition.
Proposition 5. When consumers? prior beliefs become more polarized, an
objective-welfare-maximizing media firm?s accuracy does not change under low costs
(c ? v) or high costs (c ? 4v). Its accuracy weakly increases under moderately low
costs (v < c < 2v), and weakly decreases under moderately high costs (2v ? c < 4v).
Fundamentally different from that of a profit-maximizing firm, the social
planer media firm may increase its accuracy when consumers become more po-
larized. Specifically, this happens when v < c < 2v. The intuition is as follows.
An objective-welfare maximizer firm offers the news for free to encourage news con-
sumption, and consumers with relatively high prior uncertainty (i.e., those with
1 ? ? < ?i0 < ?) consume the news. When polarization increases, consumers be-
come more extreme, and some of them would stop consuming news, leading to a
decline in objective welfare. In response to such a decline, the firm would raise its
reporting accuracy when the cost of reporting is not prohibitively high. Two factors
strengthen the firm?s incentives to choose higher accuracy. On the one hand, under
110
higher degrees of polarization, the firm can achieve a larger increase in demand from
2
the same increase in accuracy (i.e., ? D(?,0) > 0) as long as the level of accuracy is
????
sufficiently high.28 On the other hand, when the firm raises accuracy to convert non-
consumers, each conversion generates a payoff gain of v(?? 1), which is invariant in
2
how extreme the converted consumer?s prior belief is. Overall, the objective-welfare
maximizing firm has stronger motivations to convert extreme consumers in the pres-
ence of polarization, so it would raise accuracy levels when reporting costs are not
too high (c < 2v).
For a profit-maximizing firm, the benefit from raising accuracy is different,
which depends on its financial return. Polarization decreases consumers? WTP for
news. As we pointed out in the discussion following Proposition 4, consumers?
extreme prior beliefs make them see less value in news. Holding everything else
constant, when polarization increases, the demand decreases so that the firm is
only able to charge a lower price for the same accuracy level. Moreover, for the
same increase in accuracy, the additional price the firm can charge is smaller under
greater polarization. In summary, polarization weakens the profit-maximizing firm?s
incentives to improve accuracy, so the firm reduces its accuracy and saves costs.
Again, consumers? underestimation of the benefit of news (because of their incorrect
prior beliefs) is the key driver behind the difference between a profit maximizer and
an objective-welfare maximizer. It limits the profit maximizer?s ability to extract
consumer surplus, which in turn hurts consumers? probability of being correct.
28Please see Appendix B for details.
111
3.5.3 Media Firm with Dual Objectives
In the two previous extensions, we assume that the media firm either max-
imizes profits or objective welfare. In practice, many media firms may need to
balance between the two distinctive objectives instead of completely focusing on
one. To capture this feature, in this subsection, we consider the case where the
media firm has a dual objective of ear?nin(g profits a)nd improving objective welfare,
solving max?,p ? = ? ?D ? p+ (1? ?)v E[ki]? 1 ?C. In the objective function,i 2
? ? [0, 1] is the weight of the profit-seeking objective, and 1 ? ? is the weight of
the objective-welfare-improving objective. The two previous extensions are special
cases of this function: ? = 1 corresponds to a profit maximizer and ? = 0 corre-
sponds to an objective-welfare maximizer. To provide more generalized insights, in
this extension, we focus on the case where the firm accounts for both objectives,
i.e., 0 < ? < 1.
We first analyze consumers? decisions on news consumption. They consume
news when their WTP is above the price of news. Then we solve the firm?s optimal
price and optimal accuracy level. We summarize the firm?s equilibrium strategies in
the lemma below.
Lemma 4. When the media firm has a dual objective of earning profits and
improving objective welfare, its equilibrium strategies are summarized in Table 3.1,
where p?het,d(?) is uniquely determined by
??(?, p) = 0, ??het,d is uniquely determined?p
??(?, p?
by het,d
(?))
= 0 on ? ? (1 , 1), and ???het,d = 5 +
2v(1??)?c
? ? . The expressions of?? 2 6 6v(1 ?)(1 ?)
cd and cd are given in Appendix B.
112
???????????????
Insert Table 3.1 about here
???????????????
???????????????
Insert Figure 3.8 about here
???????????????
The results in Lemma 4 are illustrated by Figure 3.8(a). Intuitively, the firm
chooses full accuracy under low costs and weakly reduces its accuracy as costs in-
crease. The level of accuracy also decreases in the strength of the firm?s profit-seeking
motivation (?). As in our discussion about Lemma 3, an objective-welfare maximizer
experiences a larger payoff gain from raising its accuracy than a profit maximizer.
Therefore, a media firm?s accuracy decreases when it weighs more heavily towards
earning profits. By contrast, a less profit-seeking firm tends to encourage the con-
sumption of news. When ? is sufficiently low, it can even offer news for free. We
summarize a media firm?s equilibrium pricing strategy in the proposition below.
Proposition 6. In the equilibrium where a media firm provides news, it always
provides news with a positive price if its profit-seeking motivation is sufficiently
strong (2 < ? ? 1). If its profit-seeking motivation is weak (0 ? ? ? 2), it provides
3 3
news for free under high costs (c ? cd) or high polarization (? ? ?? ), but with a1 ?
positive price otherwise.
In Figure 3.8(b), we provide an example with ? = 0.25, which allows us to
visually compare a dual-objective firm?s equilibrium strategy with that in the two
113
previous extensions. A profit maximizer always sets a positive price for news, while
an objective-welfare maximizer always offers news for free. By contrast, a dual-
objective firm?s pricing strategy is more nuanced: it only provides news for free
when its profit-seeking motivation is weak. Under this condition, it provides news
for free under high costs or high polarization, but with a positive price otherwise.
We first explain why the firm charges a positive price under low costs and
low polarization. On the one hand, low costs mean that it is relatively easy for
the firm to offer high accuracy. On the other hand, under low polarization, most
consumers are highly uncertain about the truth and thus they have a high demand
for accurate news. If the firm charges a small price for news, most consumers will
pay to get news, except for a small group of extreme consumers. Compared with
providing news for free, charging a small price leads to a gain in revenue and a loss
in objective welfare, the latter of which is due to the extreme consumers who do
not consume news. Under low polarization, the gain outweighs the loss so the firm
provides news with a positive price.
Now, we discuss what happens if the degree of polarization or the cost changes.
When the degree of polarization increases, the firm gradually decreases its price until
it becomes zero. First, in terms of revenue, greater polarization means consumers
become more certain and less willing to pay for news, so the firm needs to cut
the price. Second, in terms of objective welfare, polarization raises the benefit of
converting non-consumers?the same price cut can attract more consumers under
higher ??as long as the level of accuracy is sufficiently high (see the discussion
following Proposition 5). Both factors drive the firm to reduce its price. Likewise,
114
an increase in the cost also leads to a drop in price. Under higher costs, the firm saves
production costs by reducing its accuracy, which decreases consumers? demand. As
a result, the firm lowers its price.
In addition to the pricing strategy, we are also interested in the firm?s choice
of accuracy. Recall that in the presence of polarization, a profit-maximizing firm
always weakly decreases its accuracy, while an objective-welfare-maximizing firm
may increase or decrease its accuracy, depending on its cost level. The following
proposition presents our finding on a dual-objective firm?s accuracy.
Proposition 7. In the equilibrium where offering partial accuracy with a
positive price is optimal, greater polarization (a higher ?) leads to higher accuracy
when the dual-objective firm sufficiently values (? < 3) objective welfare and the
4
degree of polarization is sufficiently high (? > ??). Otherwise, greater polarization
leads to weakly lower accuracy.29
Proposition 7 suggests that when a dual-objective firm offers partial accuracy
with a positive price, it may increase its accuracy in response to stronger polar-
ization. This happens when the firm sufficiently values objective welfare and the
degree of polarization is sufficiently high. As we noted in the discussion follow-
ing Proposition 5, greater polarization strengthens an objective-welfare maximizer?s
incentives to raise accuracy but weakens a profit maximizer?s incentives to do so.
When the firm accounts for both incentives, its response to polarization depends
on the weight it puts on each objective, ?. If it sufficiently values making more
29 ??
?
?? is uniquely determined by het,d?? = 0.
115
consumers better-informed, it will react more like an objective-welfare maximizer,
raising its accuracy.
For a given firm (i.e., fixing the value of ?), greater polarization leads to
higher accuracy when the degree of polarization is already sufficiently high. The
intuition is as follows. Under low degrees of polarization, most consumers have
high uncertainty and are willing to pay for news. In this case, the decrease in the
profit-seeking incentives caused by greater polarization (i.e., not able to raise the
price as much for the same increase in accuracy, lower demand, and lower price, as
mentioned in the discussion following Proposition 4) is larger than the increase in
the objective-welfare-improving incentive caused by it (i.e., demand become more
sensitive to accuracy). Consequently, the equilibrium level of accuracy decreases.
As the degree of polarization (?) increases from low( to high, the)demand?s sensi-
?D(?,p?
tivity to accuracy not only increa(ses in ? (i.e.,) ? het,d
(?))
> 0), but also
?? ??
2 ?D(?,p? (?))
increases at a faster rate (i.e., ? het,d2 > 0). When ? is above a thresh-?? ??
old, the decrease in the profit-seeking incentives caused by greater polarization is
dominated by the increase in the objective-welfare-improving incentive, so the accu-
racy level rises. To summarize, when the degree of polarization in the environment
becomes sufficiently high, the objective-welfare-improving objective dominates the
firm?s decision-making. The firm, therefore, raises its accuracy to counter the greater
division among consumers? prior beliefs.
116
3.6 Concluding Remarks
In this paper, we study a media firm?s news provision strategy. Specifically, we
conceptualize the news provision strategy as the firm choosing reporting accuracy
in a world with a binary state. Consumers want to learn about the true state, which
cannot be directly observed. By consuming news from the firm, they can update
their beliefs and possibly obtain a higher utility from a better understanding of the
true state. We analyze the firm?s optimal news provision strategy under different
cost levels. First, news provision depends on both the cost of reporting and the
prior beliefs of consumers. When the cost of reporting is sufficiently high, consumers?
extreme prior beliefs can discourage news provision. Second, conditional on the firm
providing news, it allocates more resources to accurately reporting the state that is
ex ante more likely so that consumers expect an accurate report under the majority
of circumstances. As a result, the relatively more likely state is exaggerated in the
news report.
Interestingly, as one may expect more reporting inaccuracy in an environment
with higher prior uncertainty, we find that reporting inaccuracy does not depend on
prior beliefs. This is because consumers? valuation for news is higher under greater
prior uncertainty, which then drives the firm to invest more in news provision. In
equilibrium, the overall impact of the prior beliefs on reporting inaccuracy nets out
to be zero.
Our analysis also sheds novel light on the impact of polarization in consumers?
prior beliefs on news provision. We find that the firm becomes less likely to provide
117
accurate news in a more polarized environment. Importantly, the impact of polar-
ization is most pronounced when the cost of news provision is at an intermediate
level. This is because the firm tends to respond to polarization by cutting the price
under low costs, and by not providing news under high costs. On the contrary, if
the firm aims at moving consumers closer to the truth rather than earning higher
profits, it may increase the accuracy of reporting when polarization increases. This
is because the firm evaluates social welfare from an objective viewpoint, which is not
influenced by consumers? subjective beliefs over the state of the world. If the firm
has a dual objective of earning profits and improving objective welfare, its strategy
depends on its value for each objective and how polarized consumers are. Under
high polarization, the incentive to make consumers better-informed drives the firm?s
decision, so the firm tends to provide news for free and to raise accuracy in response
to greater polarization.
Our research provides important insights for several groups of stakeholders.
For information providers, especially news media firms and platforms, our analysis
shows that their brand positioning and objective have important implications for
market outcomes. A media firm that puts more emphasis on moving consumers
closer to the truth is more likely to supply accurate information, especially in the
presence of consumer polarization. Our findings also highlight the undesirable con-
sequences of polarization, which should put consumers on notice and be cautious
about the influence of extreme opinions and beliefs. For policymakers, our study
shows that the cost of providing information influences the equilibrium outcome,
such that polarization may not lead to a drop in reporting accuracy if reporting
118
cost is sufficiently low. As one of the important sources of information, if policy-
makers can improve the consistency and transparency in their communication to
media, they can reduce the cost of reporting and thus help improve the accuracy of
news. In addition, the government can support organizations and campaigns that
advocate media literacy. Improving consumers? media literacy will raise their valua-
tion for learning about the true state, which encourages the production of accurate
information. Finally, for advertisers that advertise in media markets, our analysis
shows that a more accurate media outlet attracts a more diverse audience, which
also has implications for targeted advertising.
Our model builds on the existing framework of information design and offers
new insights into the relationship between news provision strategy and market con-
ditions. There are several paths to extend our research. First, it would be interesting
to consider the impact of competition on reporting inaccuracy. In previous studies,
when the provision of accurate news is costless, competition can decrease reporting
inaccuracy when consumers want accurate information (GS), but increase reporting
inaccuracy when consumers prefer like-minded news (MS; XS). In our model, con-
sumers seek the truth, but the accuracy of news is costly. The introduction of cost
makes the impact of competition on reporting inaccuracy less clear. Suppose two
firms?a low-cost incumbent and a high-cost entrant?are competing for consumers
with heterogeneous prior beliefs. When both firms are in the market, it is likely
that the low-cost firm targets consumers with high uncertainty under the prior,
while the high-cost firm serves news to those with lower uncertainty. On the one
hand, competition can drive the incumbent to offer higher accuracy, which leads
119
to lower inaccuracy. On the other hand, consumers served by the high-cost firm
may encounter more inaccuracy than before. As a result, a priori, the impact of
competition on reporting inaccuracy under costly news provision is ambiguous and
merits further studies.
Second, there is a growing discussion on echo chamber and news polarization
(Boxell et al. 2017; Flaxman et al. 2016). Echo chamber describes an information
environment in which individuals are largely exposed to conforming opinions. This
can result from selective exposure to like-minded news (Iyengar and Hahn 2009),
limited attention (Che and Mierendorff 2019), and a platform?s curation algorithm
(Berman and Katona 2020). We find an exaggeration effect that is similar to echo
chamber in our current model, and some further exploration can deepen our un-
derstanding. For example, does competition increase or decrease this effect? When
consumers have low heterogeneity in prior beliefs, we expect that competition will
increase accuracy and thus decrease the level of exaggeration. When consumer het-
erogeneity is high, we expect the opposite to happen, because firms will have enough
differentiation and don?t need to compete on accuracy.
120
Accuracy Price
Parameter Range Strategy
(?) (p)
? ? Full accuracy? and c ? min{v(1? ?)(1 + ?), 2v(1? ?)} 1 0
1+? for free
? > ? and c ? Full accuracyc ?
1+? d
1 p
with a positive price het,d
(? = 1)
? < 1, ? ? ? and v(1? ?)(1 + ?) < c < 2v(1? ?)(2? ?),
1+? Partial accuracy ??? 0
or ? < 1, ? < ? < 1 and cd ? c < 2v(1? ?)(2? ?) for free het,d1+? 2
Partial accuracy
? < 1, ? > ? and c < c < c ?? p? (??d d )1+? with a positive price het,d het,d het,d
Otherwise No news ? ?
Table 3.1: Equilibrium Strategy When 0 < ? < 1
121
Figure 3.1: Consumer?s Expected Utility Under A Given Belief (v = 1)
(a) Reporting Accuracy (b) Reported Content
Figure 3.2: Reporting Accuracy and Reported Content in Equilirbium (v = 1, c = 2)
122
(a) Ex Ante Expected Utility (b) Revenue and Cost (c) Uncertainty
Figure 3.3: Equilibrium Outcomes (v = 1, c = 2)
(a) ? = 0 (b) ? = 1 (c) ? = 2
Figure 3.4: Examples for f(?; ?)
Figure 3.5: The Firm?s Equilibrium Strategy (v = 1)
123
(a) Ex Ante Consumer Surplus (b) Change in Gross
(Blue) and Revenue (Red) Objective Welfare
Note: These two figures show the gross welfare because the costs of news provision are
not plotted. In Panel (a), the solid line is consumers? ex ante expected utility if they do
not consume news, or consumers? ex ante expected utility less the price if they consume
news. In Panel (b), the solid line is consumers? ex ante probability of being correct.
Figure 3.6: Alternative (Gross) Objective Functions of the Firm (v = 1, ? = 0.9,
p = 0.2)
Figure 3.7: An Objective-Welfare-Maximizing Media Firm?s Equilibrium Strategy
(v = 1)
124
(a) When ? = 0.5 (b) When ? = 0.25
Figure 3.8: A Dual-Objective Media Firm?s Equilibrium Strategy (v = 1)
125
Chapter 4: Conclusion
In this dissertation, we study media platforms? digital content provision and
consumers? consumption decisions. We analyze platforms? pricing strategy in the
presence of consumers? endogenous content consumption in the first essay. Our
analysis contributes to the literature on paywall strategies. First, our paper is the
first to endogenize content consumption in the presence of paywalls. Second, we
incorporate consumers? heterogeneity in consumption costs, which provides a novel
explanation for the existence of metered paywalls and generates new insights into
the optimal paywall design.
We investigate media firms? product design strategy when consumers are truth-
seeking in the second essay. Our research on the accuracy of news adds to the lit-
erature on the news consumption and information design. We show that reporting
inaccuracy can be a result of media firms? unbalanced resource allocation in the
presence of costly news provision, and it will lead to the exaggeration of the de-
fault state. Moreover, while polarization among consumers calls for more accurate
reporting, the profit-seeking motivation may drive a firm to reduce its investment
on the accuracy, leading to more inaccuracies.
There are several future directions to extend the research in this dissertation.
126
First, the impact of competition on media firms? strategies is an important issue.
Under competition, it is more difficult for media firms to charge a price for their
content. It is not clear whether media firms should respond to competition by
cutting price or providing more content for free. The implications of competition
for the accuracy of news also merit further study. As consumers become more
polarized, competing media firms may differentiate on their reporting strategies,
especially in the presence of reporting costs.
Second, the firm?s content production and consumers? preference for content
in the first essay can be further explored, for example, allowing the media firm
to endogenously decide the quantity and quality of its content. Moreover, all the
content provided by the firm is assumed to be of the same category and thus has
the same value for consumers. Incorporating multiple categories of content and
consumers? heterogeneous taste will allow us to study richer designs of paywalls
(e.g., freemium paywalls).
Finally, the phenomenon of echo chamber can be incorporated in the model of
the second essay. We find an effect similar to echo chamber in our current frame-
work, and further exploration can deepen our understanding of this phenomenon.
Depending on the extent of consumer heterogeneity, competition may increase or
decrease this effect. It will also be interesting to incorporate some behavioral factors
of consumers (e.g., confirmation bias) and see how this effect will be affected.
127
Appendix A: Proof of Lemmas and Propositions in Chapter 2
A.1 Proof of Lemmas and Propositions
A.1.1 Proof of Lemma 1
When ? = 0, all consumers are heavy readers. We first analyze consumers?
utility maximization problem. Consumers decide whether to read for free or pay to
subscribe. The heavy reader who is indifferent between the free version and the paid
version has a valuation of vH =
p
? . Next, we analyze the firm?s profit maximization1 f
problem. We consider the two following cases:
1. To make some readers subscribe (vH ? (0, V )), the firm needs to set the price
p ? (0, (1?f)V ). In this case, ?? < 0, which leads to a corner solution, f = 0.
?f
This is a hard paywall. Solving the first-order condition for price (FOCp)
with f = 0, we can obtain ph,H =
V?A . This price falls in (0, (1? f)V ) when
2
A < V .
2. If all readers read for free, the firm only earns advertising revenue. This
happens when p ? {0} ? [(1 ? f)V,?). In this case, ? = Af , which always
increases in f . The firm would choose f = 1, which is a no-paywall strategy.
128
Comparing the profits from these two strategies, we can find: the hard paywall with
p = ph,H is optimal when A ? [0, V ); and no-paywall is optimal when A ? [V,?).
A.1.2 Proof of Lemma 2
When 0 < ? < 1, if the firm earn both subscription and advertising rev-
enues, it can obtain subscriptions from both heavy and light readers or only from
heavy readers. Besides, it can also choose to only earn advertising revenue. In the
following, we analyze each case separately.
A.1.2.1 If the Firm Obtains Subscriptions From Both H and L Seg-
ments
We now consider a case where some heavy readers subscribe (vH ? (0, V )) and
some light readers subscribe (vL ? (0, V )). While it is easy to derive vH = p? , we1 f
need to solve u(f ; v, c) = u(min{v , 1}; v, c)? p to derive vL. To determine the valuec
of min{v , 1}, we should consider whether the marginal subscriber (whose v = vL)c
finishes all the content (i.e., reads 1).
1. If she does not finish reading all the content (vL < 1 so that min{vL , 1} = vL ),
c c c
?
then vL = fc + 2pc. The demand and impressions are Equations (2.3)
and (2.4) respectively. In this case, ?? < 0, so the corner solution f = 0
?f
is optimal (i.e., a hard paywall). Solving FOCp with f = 0, we can obtain
?
9c?2?3? 16c(1??)(V?A)+9c2?2
p = V?Ah,HL ? + ? 2 . This price satisfies v2(1 ?) 16(1 ?) H ? (0, V ),
vL ? (0, V ), and vL < 1 in the following parameter ranges: ? ? (0, 2 ],A ?c 3
129
[ ) ( ) [ )
(2?3?)V 2(V?A) 2(1??)V 20, ( , and c)? (, ?) ; or ? ? (0,
2 ],A ? (2?3?)V , V ,
2 2+? (2 3?)V?2A (3 )2
and c ? 2(V?A) ,? ; or ? ? 2 , 1 ,A ? [0, V ), and c ? 2(V?A) ,? .
2+? 3 2+?
2. If she finishes reading the whole newspaper (vL ? 1 so that min{vL , 1} = 1),
c c
2
then v = 2p+(1?f )cL ? . The demand is Equation (2.3) and the impressions are2(1 f)
Equation (2.4). In this case, we also find that ?? < 0, so a hard paywall (f = 0)
?f
is chosen. Solving FOCp with f = 0, we can obtain p
2V?2A?c?
h,HL2 = . This4
price satisfies vH ? (0, V ), vL (? (0, V ), a]nd vL ? 1 in the following parameterc
ranges: A ? [0, V ) and c ? 0, 2(V?A) . In this case, all subscribers finish
2+?
reading the whole newspaper (i.e., reads 1 unit of content). By contrast, in
the case of a hard-HL paywall, the marginal subscriber only reads vL unit of
c
content.
A.1.2.2 If the Firm Obtains Subscriptions Only From the H segment
Similar to previous, heavy readers subscribing means that vH ? (0, V ). Light
readers don?t subscribe, which means that vL ? [V,?]. In this case, D = DH . The
calculation for impressions is more nuanced, because no light readers would hit the
paywall if the meter limit is sufficien[tly h)igh (i.e., f
V
[ > )). Therefore, we separatec
the analysis into two subcases: f ? 0, V and f ? V , 1 .
c c
[ )
1. W(h?en f ? 0,
V
? , som)e light readers hit the paywall. In this subcase, Ic L =fc V
? v dv + f dv . Solve the first-order condition(s, we obtain the opti)-0 cV fc V
2 2
mal paywall design, f = V ? (1??)(V?A)m and p V?A Vm (= ) 1? +
(1??)(V?A) .
c 4c?A 2 c 4c?A
? 2
Denote A = (1? ?) V? . The meter limit falls in 0,
V when A ? (A, V ). Be-
1 ? c
130
sides, the pri(ce satisfies]vH ? (0, V[) and vL ? [V,?] in the following parameter )
3 2 2 3 2 2 3
ranges:(A ? A, (1??)V) and c ? [ (V?A) ?2?(V+A)(V?A) +?)(V +AV +11A V+3A ) ,? ;1+3? 16?2A2
2
or A(? (1??)V , (1??)V and c)? (V?A)(??(V+A)(V)?3A) ,? ;[or A = (1??)V and1+3? 1+? 4?A 1+? )
c ? (V?A)
2??(V+A)(V?3A) ,? ; orA ? (1??)V , V and c ? ?(V?A)
2+?(V+A)2 ,? .
4?A 1+? 4?A
When A ? [0, A], fm ? 0 so that the firm would choose a hard paywall (f = 0).
Solving FOCp with f = 0, we can obtain p
V?A
h,H = . This is a hard paywall2
targ[eting hea)vy readers. The price satisfies vH ? (0, V ) and vL ? [V,?] when
c ? V 2? ,? .V A
[ ) ?
2. When f ? V V, 1 , no light reader hits the paywall. Thus, I = ? vL dv.c 0 cV
We find that ?? < 0, so the corner solution f = V is optimal. Solving FOC
?f c p
with f = V , we obtain p = (c?V )(V?A) . This price satisfies vH ? (0, V ) andc 2c
vL ? [V,?] when A ? [0, V ) and c ? (V,?).
A.1.2.3 If the Firm Only Earns Advertising Revenue
If no consumer subscribes (vH ,vL ? [V,?)), the firm only earns advertising
revenue (i.e., D = 0). Similar to the case where the firm obtains sub[scrip)tions
only [from) the H segment, we separately discuss the subcases of f ? 0,
V and
c
f ? V , 1 . We also discuss f = 1 because it is also a subcase where all revenues
c
are from advertising.
[ ) (? ? )fc V
1. When f ? 0, V , some light readers hit the pay[wall)and I = ?
v dv + fL dv .c 0 cV fc V
In th[is su
??
)bcase, > 0, so that any f ? 0,
V is strictly dominated by
?f c
f ? V , 1 .
c
131
[ ) ?
2. When f ? V V, 1 , no light reader hits the paywall and I v
c L
= ? dv. In
0 cV
this subcase, we also find that ?? > 0, so the firm would deviate to f = 1.
?f
3. When f = 1, the firm chooses a no-paywall strategy pn = 0.
Given any combination of parameters (V, ?,A and c), we can compare the profits
earned by the strategies in all the cases above. The one that earns the highest profit
is the equilibrium strategy. The results of the comparison are:
( ]
1. A hard paywall with p = ph,HL2 is optimal whenA ? [0, V ) and c ? 0, 2(V?A) ;
( 2+? ]
2. A hard paywall with p = ph,HL is optimal whenA ? [0, V ) and c ? 2(V?A) , c ;12+?
3. A hard paywall with p = ph,H is optimal when A ? [0, A] and c ? (c,?);
4. A metered paywall with f = fm and p = pm is optimal when A ? (A, V ) and
c ? (c,?);
5. No-paywall is optimal when A ? [V,?).
6. A metered paywall with f = V and p = (c?V )(V?A) is never optimal.
c 2c
A.1.3 Proof of Lemma 3
When ? = 1, all consumers are light readers. The firm may choose to earn
revenues from both subscription and advertising or only earn advertising revenue.
Similar to the proof of Lemma 2, we also need to consider whether the marginal
subscriber (whose v = vL) finishes all the content.
1c(V, ?,A) is the value of c such that ?h,HL(V, ?,A, c) = ?m(V, ?,A, c) when A ? (A, V ), and
the value of c such that ?h,HL(V, ?,A, c) = ?h,H(V, ?,A, c) when A ? [0, A].
132
1. If some light readers subscribe (vL ? (0, V )) and the marginal subscriber does
?
not finish all the content (vL < 1), then vL = fc + 2pc. In this subcase,c
?? < 0, so the firm chooses a hard paywall (f = 0). Solving FOCp with f = 0,?f
2
we can o[btain ph,L =) 2(V?A) . This price satisfies v ? (0, V ) when A ? [0, V )9c L
and c ? 2(V?A) ,? .
3
2. If some light readers subscribe and the marginal subscriber finishes all the
2
content (vL ? 1), then v = 2p+(1?f )c . In this subcase, ??L ? < 0 so that thec 2(1 f) ?f
firm would choose a hard paywall (f = 0). Solving FOCp with f = 0, we
can(get p = p]h,HL2. This price satisfies vL ? (0, V ) when A ? [0, V ) and
c ? 0, 2(V?A) .
3
3. In the subcase where no light reader subscribes (vL ? [V,?)), the firm only
earns advertising revenue. The profit always increases in f when c ? (0, V )
and f ? [0, 1]; or when c ? [V,?) and f ? [0, V ]. As a result, a no-paywall
c
strategy is chosen.
Comparing these solution(s, we can ]find: a hard paywall with p = ph,HL2 is optimal
when A ? [0, V ) an[d c ? 0, 2()V?A) ; a hard paywall with p = ph,L is optimal when3
A ? [0, V ) and c ? 2(V?A) ,? ; and no-paywall is optimal when A ? [V,?).
3
A.1.4 Proof of Proposition 1
As we find in Lemma 2, the boundary between a hard-HL paywall equilibrium
and a metered paywall equilibrium is c = c (when A? (A, V )). An increase in A
could make the firm shift from a metered paywall to a hard-HL paywall under the
133
( )
following condition: V ? (0,?), ? ? (0, 1), and c ? c(A), max c(A) , where
A?(A,V )
c is uniquely determined by ?h,HL = ?m. We illustrate the existence of such a
strategy shift with the following numerical example: V = 1, ? = 0.25. In this case,
c(A) = 1.85 and max c(A) = 2.08. When c = 2, ?m > ?h,HL when A = 0.38,
A?(A,V )
but ?m < ?h,HL when A = 0.40. Hence, the firm launches a metered paywall when
A = 0.38 but a hard-HL paywall when A = 0.40. Figure 2.2 in the paper illustrates
the equilibrium strategies.
A.1.5 Proof of Proposition 2
2
(Based on L)emma 2, f = V ? (1??()(V?A)m , so) ?fm = ?(1??)V+(1+?)A . Whenc 4c?A ?V 2c?A
A ? A, (1??)V , ?fm < 0; when A ? (1??)V , V , ?fm > 0. Under a metered
1+? ?V 1+? ?V
paywall, when there is an increase in V , less content will be provided for free under
low ad rates, while the opposite is true under high ad rates. The intuition behind
this result is discussed in Section 5.1.
A.1.6 Proof of Lemma 4
2 2
Based on Lemma 2, f = V ? (1??)(V?A) , so ?fm = (V?A)m 2 > 0. This impliesc 4c?A ?? 4c? A
that under a metered paywall, the amount of free content increases in ?. The
intuition behind this result is discussed in Section 5.1.
134
A.1.7 Proof of Proposition 3
In Lemma 2, we obtain fm and pm, based on which we can calculate the size
of information flow under a metered paywall (Im). Since Equation (2.8) is helpful
with the explanation, we copy it here again:
( )
?I ( )m
= ?? 1?? ??? pm ? ?fm(2V??? fmc) (1? ?)(V ? A) ? (V ? fmc) ?fm+ + +V 2V ? ? 2V ?? V ???
smaller H segment size (-) larger L segment size (+) paywall-hitting readers get more free content (+)
.
Under a metered paywall, the exact condition for ?Im > 0 can be obtained
??
by plugging in p , f , and ?fmm m . After simplifying the inequality, we can find that??
?Im > 0 when ? < ?? and c < c? , and ?Im? ? 0 otherwise. ??(V,A, c) is the minimum?? ??
between the two following values: the value of ? such that ?Im = 0, and ?(c), which
??
is the inverse function of c(?). When ? ? ?(c), the firm no longer chooses a metered
2
paywall but adopts a hard-HL paywall. c? (V,A) = V (V+A)? ? .2(V A)A
A.1.8 Proof of Proposition 4
?
9c?2?3? 16c(1??)(V?A)+9c2?2
Based on Lemma 1 to Lemma 3, p V?Ah,HL = ?( +2(1 ?) 16(1? )2 ,?)
p = 2V?2A?c? , p = V?A
2
h,HL2 h,H , and pm =
V?A 1? V + (1??)(V?A) . We can
4 2 2 c 4c?A
obtain that: ( )
?p 2( h,HL?=
3?
? 2 3?? ?
8(1??)(V?A)+9c? < 0, because
?c 16(1 ?) 16c(1??)()V?A)+9c2?22
2
3? 16c(1? ?)(V ? A) + 9c2?2 ? (8(1? ?)(V ? A) + 9c?2) = ?64(1 ?
?)2(V ? A)2 < 0;
135
?ph,HL2 = ?? ?p< 0; h,H = 0; ?pm = (V?A) fm > 0.
?c 4 ?c ?c 2 c
A.1.9 Proof of Lemma 5
When the price for each unit of content is r, a light reader?s utility maximizes
at n = v?r , so she would consume min{v?r , 1}. The media firm?s profit function is
c c
?(r) = (r + A)(IH + IL), where Ii is the impressions from segment i = H,L.
?
1. If r ? V0, then IH = ? and IL = (1? ?) min{v?r , 1} 1 dv;0 c V
?
2. If 0 < r ? V , then IH = ?(1? r
V
) and IL = (1? ?) min{v?r , 1} 1 dv;V r c V
3. If r > V , IH = IL = 0.
The next step is solving the profit maximization problem and identifying the pa-
rameter range where the optimal price holds. We first focus on the case where
?
(A?c)2? +6V c/??A?2c0 < ? 1. We can obtain that r = < 0 is optimal when
3
A > max{2V?c? , 2c(1+?)?3V ?}, and r = V?2A?2c(1?1/?) < 0 is optimal when A ?
2? 2? 4
(2c(1??)+V ? , 2c(1+?)?3V ? ]. Denote A = max{2V?c? , V ?+2c(1??)}, we can rewrite
2? 2? PPU 2? 2?
?
(A?c)2+6V c/??A?2c
the firm?s negative PPU strategy as r = max{ , V?2A?2c(1?1/?)}
3 4
when A > APPU .
We can also obtain that r = 2V?2A?c? > 0 is optimal when c ? 2V? and A <4 4 ?
2V?c? , or 2V? < c < V and
(4??)c?2V < A < 2V?c? , and r = r? = (2V?A)?+2c(1??) ?
2 4 ? 2 2 3?
?
((V+A)?+2c(1??)2)?2c(V+A)?(1??)
> 0 is optimal when 2V? < c < V and A ?3? 4 ?
(4??)c?2V , or c ? V andA < V (V ?+2c(1??)) . DenoteA = max{2V?c? , V (V ?+2c(1??))},
2 2(V ?+c(1??)) PPU 2 2(V ?+c(1??))
we can rewrite the firm?s positive PPU strategy as r = max{2V?2A?c? , r?} > 0 when
4
A < APPU .
136
When APPU ? A ? APPU , r = 0 is the most profitable and thus the equilib-
rium strategy.
When ? = 0, all consumers are heavy readers. By solving the profit maxi-
mization problem, we can obtain r = V?A when A < V , and r = 0 when A ? V . A
2
negative PPU strategy is never used.
Proof of Proposition 5
To find the equilibrium strategy, we compare the profit obtained from the
optimal paywall strategy (as described in Lemma 1-3) and that obtained from the
optimal PPU strategy (as described in Lemma 5). As mentioned in Section 2.6.1, a
PPU strategy with r = 0 is equivalent to a no-paywall strategy, while a PPU strategy
with r = 2V?2A?c? earns the same profit as a hard-HL2 paywall. Next, we compare
4
a hard-H paywall with a PPU strategy with r = r?. Under the condition where a
hard-H paywall is chosen (as in Lemma 2), ?(f = 0, ph,H) is always dominated by
?(r = r?). Define A?PPU as the value of A such that ?(f = 0, p = ph,HL) = ?(r = r?)
when c ? c, and the value of A such that ?(fm, pm) = ?(r = r?) when c > c.
Due to the complexity of equations, we haven?t analytically solved A?PPU , and only
numerically show the results in Proposition 5.
137
A.2 Other Results and Proof
A.2.1 Free Content Provision
Lemma 5. Under a metered paywall, the amount of free content increases in
the ad rate (A), but decreases in light readers? consumption cost (c).
2
Proof: Based on Lemma 2, fm =
V ? (1??)(V?A) . We can obtain that:
c 4c?A
?f (1??)(V 2 2m = ?A ) > 0 when A < V ;
?A 4c?A2
?fm = ?fm < 0.
?c c
Discussion: First, if an increase in the ad rate does not shift the type of
paywall (as in Proposition 1), then a firm that operates a metered paywall would
increase the meter limit. Because it wants to increase the consumption of content
by providing more free content. Second, when light readers? consumption costs
increase, they would consume less and generate fewer ad impressions. Hence, the
firm has a smaller incentive to offer free content and would lower the meter limit.
A.2.2 Information Flow
Lemma 6. Under a metered paywall, the size of information flow increases
in the ad rate (A), but decreases in light readers? consumption cost (c).
Proof: Based on Lemma 2, we know fm and pm, so we can calculate the size
of information flow, Im. We can obtain that: ( )
?Im = ?(1??) 1 ?pm+?V?fmc ?fm > 0, where ?pm = 1 ?(1? f )? (V ? A)?fm <
?A V ?A V ?A ?A 2 m ?A
0, and V ? fmc > 0.
138
( )
?Im = ?(1? ?) (V?A) f
2
m ? ? fm + fm(V?fmc) < 0.
?c 2V c 2V cV
when A < V ; ?fm = ?fm < 0.
?c c
Discussion: Under a metered paywall, when the ad rate increases, the firm
gives more content for free (Lemma 5) and reduces its subscription price (Lemma
8). A lower price can convert more readers to subscribers, which leads to a larger
subscription demand. After becoming subscribers, those consumers read more than
they would with a free version, resulting in a larger information flow.
When light readers? consumption costs increase, they have a weaker appetite
for content. In response to it, the firm decreases the amount of free content (Lemma
5), and raises the price accordingly (Proposition 4). As a result, the consumption by
non-subscribers decreases while that by subscribers remains the same, so the total
consumption declines.
Lemma 7. Under a metered paywall, the size of information flow may de-
crease in the upper-bound of consumer valuation for content (V ). This happens
under a low ad rate and a large difference in consumption costs.
Proof:
?I 2m
= (1? ?)( ??(1??V ?2?fm)A? ?V ??A? ?fm V ? fmc ?fm f c+ ) + ?( + m )V 2 2V ?V? ? V ?? ?V? ?2?V?2?
H,cancel subscription (-) H,hitting L,hitting L,not hitting (+)
Based on Proposition 2, whether the second and the third terms in the above
equation are positive depends on the ad rate, as the conditions for ?fm < 0 and
?V
?fm ? 0. After plugging in ?fm , we can find that ?Im < 0 when A ? (A, V ) and
?V ?V ?V
139
c ? (max{c, c?V },?
?
), where c?V (V, ?,A) is the value of c such that
?I = 0. Denote
?V
A?V (V, ?) as the value of A such that c?V = c.
???????????????
Insert Figure A.1 about here
???????????????
Discussion: Im decreases in V when the difference in consumption costs is high,
as shown in Figure B.1 above. Based on the expression of ?Im above, an increase in
?V
V leads to changes in Im to four different groups of consumers. The first term is the
decline in the information flow due to the heavy readers that cancel the subscription
and only read the free version because the subscription gets more expensive when
V increases (Lemma 8). The changes in consumption by paywall-hitting heavy
readers (of size V?A , captured by the second term) and paywall-hitting light readers
2V
(of size V?fmc , captured by the third term) depend on the change in the meter limit.
V
The last term is the additional consumption from light readers who did not hit the
paywall.
When the ad rate is sufficiently low, i.e., A < min{ (1??)V , A?V }, the information1+?
flow decreases in V .2 As V increases, the firm would decrease the amount of free
content, which results in a decline in consumption from all paywall-hitting readers
(?fm < 0, so the second and third terms in ?Im are negative). Under low ad rates,
?V ?V
these two losses are signifi(cant: The )size of paywall-hitting readers in the H segment
2For the case where A ? (1??)V1+? , A?V , as V increases, the information flow decreases even
though the firm offers more free content. This happens when the light reader segment is small. In
this case, the amount of free content is small and the first term in the expression of ?Im?V is large.
It dominates all the other three effects so that overall the information flow decreases.
140
(V?A in the second term) is large under low ad rates, and so is the size of paywall-
2V
hitting light readers (V?fmc in the third term), because the meter limit is low under
V
2
low ad rates. A low meter limit also implies that the only gain in consumption ( fmc
2V 2
,
the last term) from light readers who do not hit the paywall, is small. As a result,
the three losses (the first, the second, and the third terms) in ?Im dominate the gain
?V
(the last term), and the information flow drops.
When the ad rate is high, the change in Im from a change in V depends on
the difference in consumption costs. First, Im increases in V under a high ad rate
and a low difference in consumption costs (?high A, low c?), the latter of which
means that even light readers want to read a lot. Under a metered paywall, these
conditions imply a large amount of free content. To take advantage of the strong ad
market, as V increases, the firm would offer even more content for free (?fm > 0), so
?V
paywall-hitting readers have more to read and contribute more ad revenues. From
the expression of ?Im , all terms except the first are gains and the total gain in
?V
Im outweighs the loss from subscribing heavy readers (the first term). Second, Im
decreases in V under a high ad rate and a high difference in consumption costs
(?high A, high c?). Compared with the case of ?high A, low c,? the amount of free
content becomes smaller, so the loss from subscribing heavy readers? cancellation
(? (1?fm)A2 in the first term) becomes more prominent, while the gain from light2V
2
readers who do not hit paywall (captured by the last term, fmc2 ) decreases. Further,2V
the gain in ad impressions from all paywall-hitting readers (the second and the third
terms) also become smaller under a high difference in consumption costs. This is
because light readers have a weaker desire for content under this condition, and the
141
amount of free content is small and becomes less responsive to the upper-bound
change (?fm becomes smaller when c is high). In summary, once the difference in
?V
consumption costs is above a certain threshold, the loss from one group (subscribing
heavy readers) will dominate the gains from the other three groups of readers, which
leads to a smaller amount of information flow.
A.2.3 Subscription Price
Lemma 8. Under a metered paywall, the subscription price decreases in the
ad rate (A) and the size of the light reader segment (?), but increases in the upper-
bound of consumer valuation for content (V )(. )
2
Proof: Based on Lemma 2, pm =
V?A 1? V + (1??)(V?A) . We can obtain
2 c 4c?A
that: ( )
?pm = 1 ?(1? f ?fmm)? (V ? A) < 0 when A < V , because ?fm > 0?A 2 ?A ?A
(Lemma 5);
?pm = ? (V?A)
3
< 0 when A < V ;
?? 8(c?2A )
?p 1 2 2m = (1? f )? (V ? A)?fm = (3+?)(V?A) +4?(cA?V )m > 0 when A ??V 2 ?V 8c?A
(A, V ) and c ? (c,?).
Discussion: Following the discussion of Lemma 5, when the ad rate increases,
the firm offers more free content under a metered paywall. The availability of free
content weakens the demand for subscriptions, so the firm has to cut the price.
Similarly, based on Lemma 4, the amount of free content increases when the pro-
portion of light readers increases. That would also result in a lower subscription
142
price. Finally, when consumers? valuation for content increases, they have a higher
WTP for subscription, so the firm increases the price.
A.2.4 Correlation between c and v
A.2.4.1 Positive Correlation between c and v
When c = kv, all light readers want to consume 1 unit of content. When
k
k > 1 and f < 1 , they would subscribe if u( 1 ; v, kv)? p > u(f ; v, kv). When k ? 1,
k k
they would subscribe if u(1; v, kv) ? p > u(f ; v, kv). Heavy readers? decisions are
similar to those in the main model. The firm chooses (p, f) to maximize its profit.
However, the model does not generate closed-form solution when being solved with
general values of ?. In the following, we present the results when ? take two special
values: ? = 1 and ? = 1.
2
When ? = 1 , the firm?s equilibrium strategy is summarized in Table B.1, where
2
? ?
2 3 2 2
k = ((3k?2) 1+2k?2k +k?2)V when A ? A, = ( 2k ?k ?k+2k ?7k?1)V? 2? when A < A <
2V ,
2(4 k)k 2k 10k?1 3
and = 1 when 2V ? A < V . The equilibria are very similar to those in the main
3
model.
???????????????
Insert Table A.1 about here
???????????????
When ? = 1, c and v are perfectly positively correlated, and either a hard
paywall or no paywall will be chosen. Specifically, the firm launches a hard paywall
with p = (2?k)V?2A when k ? 1 and A < (2?k)V , or a hard paywall with p = V?2A
4 2 4k
143
when k > 1 and A < V , and no paywall otherwise. When the consumption cost is
2
relatively low (k < 1), the area for a no-paywall strategy expands with k. This is
because consumers want more content than the total amount of available content
(i.e., 1 > 1) under this condition. Consequently, an increase in k has no impact
k
on the amount of content consumed (and thus the ad revenue from a no-paywall
strategy). On the other hand, an increase in k leads to a drop in consumers? WTP.
As the ad revenue remains invariant and the WTP decreases, the firm shifts from a
hard paywall to no paywall.
A.2.4.2 Negative Correlation between c and v
When c = k(V?v), light readers want to consume k(V?v) . The consumer who is
v
indifferent between the free and paid versions has u(min{ v? , 1}; v, k(V ?v))?p =k(V v)
u(f ; v, k(V ?v)). Denote the valuation of this consumer as v?L. Among light readers,
those with v ? [0, fkV ) would read for free, those with v ? [ fkV , v?L] would read f ,1+fk 1+fk
while those with v ? (v?L, 1] would pay and read min{ v? , 1}. The next step is tok(V v)
solve the firm?s profit maximization problem. Numerical analysis suggests metered
paywall can still emerge in equilibrium (as in Figure B.1(b)).
When ? = 1, c and v are perfectly negatively correlated, and a metered
paywall does not earn more profit than a hard paywall or no paywall. Specifically,
when A ? V , a hard-H paywall (with p = V?A) is the most profitable. When
1+k 2
V 2<( A < V , a] hard-H paywall with p = (V?A) and a metered paywall with1+k 2kA
f ? 0, A(1+k)?V and p = (1+fk)(V?A)
2
are equally profitable. If we assume that
kV 2kV
144
operating a metered paywall is slightly more costly than a hard paywall (e.g., a very
small cost for tracking how much content each consumer already consumed), then
a hard paywall is preferred by the firm. When A ? V , the firm chooses no paywall
in equilibrium.
A.2.5 Heterogeneity in v
In this subsection, we discuss the role of heterogeneity in v. First, we show the
existence of a metered paywall assuming consumers have heterogeneous valuation
and homogeneous consumption costs. Second, we prove that the heterogeneity in v
alone cannot support a metered paywall in equilibrium.
In the main model, we assume that consumers have heterogeneous v ? U [0, V ]
and heterogeneous c, where ? proportion of the consumers with c > 0 and 1 ? ?
proportion of them with c = 0. Here, we consider an alternative distribution for
valuation: v = vL for ? ? (0, 1) proportion of the consumers and v = vH > vL
for 1 ? ? proportion of the consumers. All consumers have the same consumption
cost c ? (vL, vH). In this setting, consumers with vL would consume min{1, vL} ifc
they subscr[ibe. T) hey would pay to subscribe when u(
vL ; vL, c) ? p ? u(f ; vL, c),c
where f ? 0, vL . Consumers with v
c H
would consume 1 if they subscribe, which
happens when u(1; vH , c)?p ? u(f ; vH , c), where f ? [0, 1). Solving the firm?s profit
maximization problem using the approach in Lemma 2, we can obtain the following
table.
145
???????????????
Insert Table A.2 about here
???????????????
Figure B.2 illustrates the results with a numerical example. We find that a
metered paywall can be the equilibrium strategy when consumers have sufficiently
large heterogeneity in valuation, the size of the low valuation segment is small, and
the ad rate is sufficiently high.
???????????????
Insert Figure A.2 about here
???????????????
Next, we assume that consumers have no cost for consuming content and
examine whether heterogeneity in valuation leads to metered paywalls.
Theorem 1 below presents the result. We find that a metered paywall strategy
is never more profitable than a hard or a no-paywall strategy. The intuition is the
following: when consumers have heterogeneity in valuation and zero consumption
cost (only heavy readers exist in the market), they display no heterogeneity in the
amount of content desired. In this case, when the firm gives some content for free, it
can earn more profits either by reducing the amount of free content and raising the
price when ad rates are low, or by giving more content for free when ad rates are
high. When the ad rate is at a threshold level, a metered paywall earns the same
amount of profit as a hard paywall. In summary, heterogeneity in v alone does not
make a metered paywall more profitable than a hard paywall or no paywall.
146
Theorem 1. When consumers have heterogeneous valuation for content and
no cost of consumption, a metered paywall strategy is never more profitable than a
hard paywall or a no-paywall strategy.
Proof: We separately prove this theorem for two cases: v discretely distributed
and continuously distributed.
(i) Suppose v ? V = {v1, ..., vn|vi < vi+1}. Assume that Pr(v = vi) = ?i ? 0
(i = 1, 2, ..., n) and ?ni=1?i = 1. For each given pair of (f, p) that satisfies 0 ? f < 1
and 0 < p ? vn(1 ? f), there exists j ? {1, 2, ..., n} such that vj?1(1 ? f) < p
? vj(1 ? f) (define v0 = 0). All consumers with vi ? vj would pay the price
p and consume all content, while all consumers with vi ? vj?1 do not pay and
consume f . Let Dj = ?
n
i=j?i, then the profit function can be written as ?(f, p) =
pDj+A(f(1?Dj)+Dj) for p ? (vj?1(1?f), vj(1?f)]. This is a increasing function
of p on p ? (vj?1(1 ? f), vj(1 ? f)], therefore ?(f, vj?1(1 ? f) < p ? vj(1 ? f)) ?
?(f, vj(1? f)). We rewrite ?(f, vj(1? f)) as the following:
?(f, vj(1? f)) = vj(1? f)Dj + A(f(1?Dj) +Dj) (A.2.1)
= (vj + A)Dj + (A(1?Dj)? vjDj)f
?(f, vj(1 ? f)) is function of vj and f . Based on the equation above, it is a
v D
linear function of f . If A > j j? , then ?(f, vj(1 ? f)) increases as f ? 1, so it1 Dj
is less profitable than a no-paywall strategy (which earns a profit of ?(1, 0) = A).
v
If A < j
Dj
? , then ?(f, vj(1 ? f)) optimize at f = 0, which corresponds to a hard1 Dj
v D
paywall strategy which earns a profit of ?(0, vj) = (vj +A)Dj. If A =
j j
? , then f1 Dj
147
has no impact on the profit, which means a metered paywall is not more profitable
than a hard paywall. To summarize, ?(f, vj(1 ? f)) ? max{A, (vj + A)Dj}. Note
that at j = 1, there is Dj = 1 so that ?(0, v1) = v1 +A > A = ?(1, 0). Therefore, a
no-paywall strategy is always dominated by a hard paywall with p = v1.
Based on the analysis above, the firm would always choose a hard paywall for
given i ? {1, 2, ...n}. In equilibrium, it chooses a hard paywall with p? = vi, where
i = arg maxi?{1,2,...,n}(vi + A)Di.
(ii) Suppose v ? G(v), which is defined on v ? [0,?). The firm?s profit is
?(f, p) = pD + A(f(1?D) + D), where D = 1?G( p? ). Denote the valuation of1 f
the indifferent consumer as v?, then there is p = v?(1? f). We can then rewrite the
profit function as a function of v? and f .
?(f, v?(1? f)) = v?(1? f)D(v?) + A(f(1?D(v?)) +D(v?)) (A.2.2)
= (v? + A)D(v?) + (A(1?D(v?))? v?D(v?))f
In the equation above, D(v?) = 1 ? G(v?). Now, we can consider the firm?s
problem as choosing v? and f to maximize ?. Equation (A.2.2) is a linear function
of f . Therefore, for a given v?, it either optimizes at f = 0 (if A < v?D(v?)? ), or is1 D(v?)
dominated by f = 1 (if A > v?D(v?)? ). f has no impact on ? if A =
v?D(v?) . In
1 D(v?) 1?D(v?)
other words, a metered paywall does not earn more profits than a hard paywall or
no paywall. Similar to the proof in (i), in equilibrium, the firm chooses a paywall
strategy with p? = arg maxp?[0,?)(p + A)D(p), where p > 0 corresponds to a hard
paywall and p = 0 corresponds to no paywall.
148
Readers? Consumption
Parameter Range Paywall Source of Meter Limit Subscription
Behavior
Strategy Sub- (f) Price (p)
scribers
A < 2V and k ? All subscribers read the1, or Hard-HL2 H, L 0 (2?k)V? ?
A
3 4 k 2
2V ? whole newspaperA < V and
3
k < 4(V?A)
2V?A
Some subscribers only
A < 2V and 1 < k ? k Hard-HL H, L read part of the 0 2V?3A
3 4k+2
newspaper
A ? A and k > k Hard-H H 0 V?A
2
A < A < V and k > k Metered H 1 (V?A)(1?1/k)
k 2
2V ? A < V and No- - 1 0
3
4(V?A) ? k ? 1, or A ? V paywall
2V?A
Note: In this table, we highlight the difference in readers? consumption behavior under
hard-HL2 and hard-HL paywalls. The consumption behaviors under other types of
paywall are similar to those discussed in the proof of Lemma 1-3.
Table B.1: Equilibrium Strategy When c = kv among Light Readers (? = 1)
2
Parameter Range Paywall Source of Meter Limit Subscription Price
Strategy subscribers (f) (p)
{ ? v
2
max 1 L
(c?vL)(2vH? ?
, 0} < ? ? 1 and 2
c vL) v
? ? ? 2 Hard Both 0
L
{ c(2v c)(1 ?) v 2cA > max H L , 0}
2vL?
2
? ? 1? vL? , andc(2vH c)
2 Hard High value 0 v
c
H ?
A ? min{ (2vH?vL)(1??) c(2v ?c)(1??)?v 2, H L}
2? 2vL?
v < c(2v
2
H?c) v
L , ? ? 1? L , and2vH (c?vL)(2vH?c?vL)
? ? Metered High value
vL (vH ? c+vL )(1? vL )
A > (2vH vL)(1 ?)
c 2 c
2?
Table B.2: Equilibrium Strategy Under Heterogeneous v and Homogeneous c (vL <
c < vH)
149
(a) Information Flow
Figure B.1: Impact of the Upper-bound of Valuation (V ) When c > max{c, c?V }
Figure B.2: Equilibrium Strategy Under Heterogeneous v and Homogeneous c (? =
0.5,c/vH = 0.5)
150
Appendix B: Proof of Lemmas and Propositions in Chapter 3
B.1 Proof of Lemmas and Propositions
B.1.1 Proof of Lemma 1
To prove Lemma 1, we need to derive Equation (3.2) first. Et[u(?, t)] =
u(?, L)(1 ? ?) + u(?,R)?. When ? < 1 , Et[u(?, t)] = I(? < 1 , t = L) ? v(1 ? ?) =2 2
v(1 ? ?); when ? > 1 , E[u(?, t)] = I(? > 1 , t = R) ? v? = v?; when ? = 1 ,
2 2 2
E[u(?, t)] = v . Thus we can rewrite Et[u(?, t)] = v ? max{1 ? ?, ?}. We can also2
prove Et[u(?, t)] = v ? Pr(? = t|?). When ? < 1 , there is ? = L, and Et[u(?, t)] =2
I(? < 1 , t = L) ?v(1??)= v ?I(? = L, t = L) Pr(t = L|?)= v ?Pr(t = ? |?). Similarly,
2
Et[u(?, t)] = v ? Pr(t = ? |?) when ? > 1 and ? = 1 , so Et[u(?, t)] ? v ? Pr(t = ? |?).2 2
Now consider consumers? WTP for news, which depends on the difference
between the expected (gross) utility without and with news consumption (Equation
(3.4)). When consumers do not use news, their expected utility is Et[u(?0, t)] =
v ?max{1? ?0, ?0}.
When consumers use news, Es[Et[u(?s, t)]] = Pr(l) ? Et[u(?l, t)] + Pr(r) ?
Et[u(?r, t)].
(i) When ? < 10 , consumers believe L to be more likely, a belief change implies2
151
that ? > 1r . The expected utility from news consumption becomes Pr(l) ? v(1 ?2
?l) + Pr(r) ? v?r = v(?L(1? ?0) + ?R?0). The expected utility from no purchase is
v(1? ?0). Compare these two expected utility:
? ? ? ?R?0 ? (1? ?L)(1? ?0)v(?L(1 ?0) + ?R?0) v(1 ?0) = v Pr(r)
Pr(r)
= v Pr(r) (?r ? (1? ?r)) (B.1)
1
= v Pr(r) (2?r ? 1) > 0 when ?r >
2
If no belief change happens after consuming news, consumers expected utility
is Pr(l) ? v(1? ?l) + Pr(r) ? v(1? ?r)= v(1? ?0).
(ii) when ? > 10 , a belief change implies that ? <
1
l . The expected utility2 2
from news consumption is also v(?L(1??0)+?R?0), and the expected utility from no
purchase is v?0. Similarly, v(?L(1? ?0) + ?R?0)? v?0= v Pr(l) (1? 2?l) > 0 when
?l <
1 . If no belief change happens, the expected utility is Pr(l) ? v?l + Pr(r) ? v?r =2
v?0.
(iii) when ? = 10 , a belief change means that ? 6= 1s and the informative2 2
constraint implies that ?L + ?R > 1. The expected utility from news consumption
is v(?L+?R) . The expected utility from no purchase is v . The informative constraint
2 2
suggests that the signal is valuable.
By combining (i)-(iii), we obtain Equation (3.4). Now we can compare the
difference between consumers? expected utility with and without consuming news.
(i) when ? 10 < , a belief change implies that ? >
1
r , which is equivalent to2 2
? > 1??L0 . WTP = v(? ? 1 + (1? ? + ? )? );1?? +? L L R 0L R
152
(ii) when ?0 >
1 , a belief change implies that ? 1l < , which leads to ?2 2 0 <
?L
? . WTP = v(?? +1 ? L ? (?L + 1? ?R)?0);L R
(iii) when ?0 =
1 , a belief change implies that ? 1s 6= . WTP = v(?2 2 L ? (?L +
1? ?R)?0).
Combining (i)-(iii) leads to Lemma 1.
B.1.2 Proof of Proposition 1
The cost function C(?;?0) = c(H(?0) ? Es[H(?s)]), where Es[H(?s)] =
Pr(l)H(?l) + Pr(r)H(?r).
Properties of the cos(t function: (i) co)nvexity in ?t (t = L,R):
2 ?2? C 2= 2c?2(1? ? )2 R (1??R)2 0 0 ( 3 + 3 ) > 0;??R Pr(r) Pr(l)
?2C ?
2 2
2 = 2c?20(1? ? )2 L +
(1??L) > 0;
?? 0L Pr(l)
3 Pr(r)3
where Pr(r) = (1? ?L)(1? ?0) + ?R?0, Pr(l) = (1? ?R)?0 + ?L(1? ?0).
(ii) increase in ?t when ?L + ?R > 1:
?C = c?2(1? ? )?, where ? = (?R Pr(l)+(1??R) Pr(r))(1??0)(?L+?R?1)0 0 > 0.??R Pr(r)2 Pr(l)2
?C = c? (1? ? )2?, where ? = (?L Pr(r)+(1??L) Pr(l))?0(?L+?R?1)
?? 0 0
> 0.
L Pr(r)2 Pr(l)2
The firm?s problem is max?WTP (?, ?0)?C(?, ?0). The first order condition
for ?L is:
?WTP?C = c(1??0)(v??20?). We can prove that ?2? < 1? ?20 0 Pr(l)2?2??L c R?
?2 Pr(r)2(1? ? )2 < Pr(l)2 Pr(r)20 R
? ??2 Pr(r)2(1? ? )2 < Pr(l)2(Pr(r)2 ? ?2?20 R 0 R)
? ??20 Pr(r)2(1? ? )2R < Pr(l)2(Pr(r) + ?0?R)(1? ?0)(1? ?L).
When c ? v, we can obtain that ?(WTP?C) > 0 because ?2? < 1. Similarly,
??L 0
153
?(WTP?C) > 0. In this case, the firm would choose ?L = ?R = 1. Consumers???R
posterior belief after news consumption is ?l= 0 or ?r = 1. Therefore, as long as
consumers? prior belief ?0 6= 0 or 1, the firm is able to charge a positive price for
news. So news is provided when 0 < ?0 < 1.
When c > v, there exist interior solutions to the first order conditions (FOC):
?(WTP?C) = 0 and ?(WTP?C) = 0. Note that the firm?s strategy needs to ensure a
??L ??R
positive profit (i.e., p= WTP (?, ?0)?C(?, ?0) > 0) and the provision of informative
news (i.e., ?L +?R > 1). With these constraints, the firm can earn a positive profit
only when c?v < ? v+c0 < . No news is provided when ? ? c?v or ? ? v+c .2c 2c 0 2c 0 2c
B.1.3 Proof of Proposition 2
In the proof of Proposition 1, we show that the firm chooses ?L = ?R = 1 when
c ? v and 0 < ?0 < 1. Consumers? expected (gross) utility from news consumption
is v, so the firm can charge p= WTP ? v ?max{1? ?0, ?0}= v ?min{1? ?0, ?0}.
When c > v, solving the firm?s problem leads to ? = (v+c)(v?c(2?0?1))L and4vc(1??0)
? = (v+c)(v+c(2?0?1))R . The posterior beliefs caused by the news is ?l =
c?v or
4vc?0 2c
?r =
v+c . When news is provided ( c?v < ? < v+c0 ), it charges p= WTP ? v ?2c 2c 2c
max{1 ? ?0, ?0}= v( c+v ? max{?0, 1 ? ?0}). For news consumers, the probability2c
of receiving news l is Pr(r) = v+c(2?0?1) ; and Pr(l) = 1? Pr(r). When ?0 > 1 , the2v 2
degree of exaggeration is Pr(r)? ? = (c?v)(2?0?1)0 .2v
154
B.1.4 Proof of Proposition 3
RI =(1? ?L)(1? ?0) + (1? ? c?vR)?0 = .2c
We can find that ?RI = v2 > 0 and
?RI = 0.
?c 2c ??0
B.1.5 Proof of Corollary 1
Consumers only consume news when WTP>0, so the consumers who are in-
different between consuming news or not satisfies 1? ? + p < ?i0 < ??
p . We can
v v
find that consumers with extreme prior beliefs do not consume news. Define the
demand in the presence of heterogeneous beliefs as the following:
? ?? p
v
D(?, p) = ? f(?; ?)d?1??+ pv1 ? ?? p
2 v
= (4(1? ?)?0 + ?)d?0 + (4(1? ?)(1? ?0) + ?)d?0 (B.2)
1??+ p 1
v 2
(v(2?? 1)? 2p)(v(2?(? ? 1)? 2? + 3)? 2p(? ? 1))
=
v2
If p = 0, the demand is D(?, 0) = (2? ? 1)(3? 2? + 2?(? ? 1)), which increases in
?: ?D(?,0) = 8? 6? + 8?(? ? 1) > 0 when 1 < ? < 1 and 0 ? ? ? 2.
?? 2
B.1.6 Proof of Lemma 2
As we calculate in the proof of Corollary 1, the demand is
(v(2?? 1)? 2p)(v(2?(? ? 1)? 2? + 3)? 2p(? ? 1))
D(?, p) =
v2
155
?
? v(4?(??1)?3?+4)?v 4?2(??1)2?2?(??1)(3??4)+3?(??3)+7. Solving the FOC for p leads to phet = ? .6(? 1)
The next step is finding the optimal accuracy. The news needs to be informative (i.e.,
?
2 2 2 2
1 v (2??) +4vc(4?3?)?9c +(v(2??)?3c) v (2??)2?2vc(2??)+9c2? > ). Solving the FOC for ? leads to ?? = .
2 het 16vc(1??)
?
2 2
This is an interior solution when ? < 1 and v(? ?6?+6?? ? ?3?+3) < c < v(2??)? . When9(1 ?) 2
?
? < 1 and c ? v(?
2?6?+6?? ?2?3?+3)
? , the firm makes the highest profit from ? = 1.9(1 ?)
When ? < 1 and c ? v(2??) , the firm would not make a positive profit from news,
2
so no news is provided.
?2(D(p? )p? ?C)
When ? ? 1, the second order condition for ?, het het2 > 0 always??
hold when D(p?het)p
?
het ? C > 0, so the firm chooses either ? = 1 or ? = 1 . In2
the latter case (? = 1), the firm would rather not provide news because no one
2
?
v(4 (?2?3?+3)3?4?3+18?2?18?)
would use news. ? = 1 is chosen when c < . When c ?
27(??1)2
? ?
v(4 (?2?3?+3)3?4?3+18?2?18?) 2 2
? 2 , no news is provided. We define c?=
v(? ?6?+6?? ? ?3?+3)
27(? 1) 9(1??)
?
v(4 (?2?3?+3)3?4?3+18?2v ?18?)when ? < 1, c? = when ? = 1, and c? = when ? > 1.
2 27(??1)2
B.1.7 Proof of Proposition 4
Based on the definition of c? (in the Proof of Lemma 2), we can find that ?c? < 0.
??
Since the firm chooses ? = 1 when ? < 1 and c ? c?, or ? ? 1 and c < c?, we can
obtain that ? = 1 is optimal when c ? min?c? = c?(? = 2) = 8 . Similarly, the firm27v
would not provide news when ? < 1 and c ? v(2??) , or ? ? 1 and c ? c?. We can also
2
obtain that no provision is optimal when c ?v(2?0) = v. To summarize, the optimal
2
level of accuracy is not influenced when c ? 8 or c ? v.
27v
When 8 < c < v, as ? increases, the firm may shift from ? = 1 to not
27v
156
providing news, or first shift from ? = 1 to ? = ??and then to not providing news.
From consumers? perspective, not providing news and providing uninformative news
(i.e., ? = 1) are effectively equivalent, because no one would use news in the latter
2
?
case. When the firm choose ? = ??, the accuracy decreases in ? (?? < 0). In
??
summary, in this range of costs, the accuracy of the firm weakly decreases in ?.
B.1.8 Proof of Lemma 3
Compared with Lemma 2, the only difference here is the firm?s objective func-
tion. Therefore, consumers? demand is still
D= (v(2??1)?2p)(v(2?(??1)?2?+3)?2p(??1))
? ( )
2 . The firm?s problem is max??,p(v E[k
i])?
1 ?
v i 2
C( , whe)re the aggregate level of consumers? probability of being correct, E[k
i]? 1 =
i 2
?? 1 D, always increases in D. This is because ? > 1 when news is provided.
2 2
When the firm chooses a price to maximize the aggregate level of consumers? prob-
ability of being correct, it will chooses the price that maximizes D, which is p = 0.
The next step is finding the optimal accuracy. The news needs to be infor-
mative (i.e., ? > 1). Solving the FOC for ? leads to ?? v(7?5?)?c
2 het,k
= ? . This is6v(1 ?)
an interior solution when ? < 1 and v(1 + ?) < c < 2v(2 ? ?). When ? < 1 and
c ? v(1 + ?), the net expected welfare is maximized at ? = 1. When ? < 1 and
c ? 2v(2? ?), providing news always lead to a decrease in the net expected welfare,
so no news is provided. ?
2
? ? (v i(E[k
i]? 1)?C)
When ? 1, the second order condition for ?, 2? ( ) 2 > 0 always??
hold when v E[ki]? 1 ? C > 0. Under this condition, the firm would choose
i 2
157
either ? = 1 or ? = 1 . ? = 1 is chosen when c < 2v. When c ? 2v, ? = 1 is chosen,
2 2
which is equivalent to no provision of news.
B.1.9 Proof of Proposition 5
Based on the results of Lemma 3, the firm always chooses ? = 1 when
c ? min(min??[0,2]{v(1 + ?), 2v}) = v. Similarly, the firm would not provide news
when c ? max(max??[0,2]{2v(2 ? ?), 2v}) = 4v. To summarize, the optimal level of
accuracy is not influenced when c ? v or c ? 4v.
When v < c < 2v, as ? increases, the firm chooses ? = ?? chet,k when ? < ? 1,v
???
and ? = 1 when ? ? c?1. Under this condition, het,k > 0 , so the accuracy weakly
v ??
increases in ?. To understand the intuition behind the increase of accuracy, we can
analyze the firm?s incentive for increasing accuracy using the following equation:
? ( )
d(v E[ki]? 1 ? C)
i 2 = v
d? ????
( )
? 1 ?D(?, 0) ? ?CD(?, 0)+v ?
2 ? ???? ? ???incremental accuracy effect ???
demand expansion effect cost effct
(B.3)
The interior optimal accuracy, ??het,k, makes Equation (B.3) equal to zero,
which means the first and second terms (incremental accuracy and demand expan-
sion effects) cancel out the third term (cost effect). When ? increases, the first
term decreases (i.e., ?D(?,0) < 0), the second term increases when ? is sufficiently
??
large (?
2D(?,0) > 0 when ? > 3), while the third term remains constant. Under the
???? 4
condition of v < c < 2v, there is ?? > 3het,k . Under such a high accuracy level, an4
increase in ? will enlarge the demand expansion effect, which dominates the decrease
158
in D(?, 0). As a result, the firm is incentivized to raise its accuracy.
When 2v ? c < 4v, as ? increases, the firm shifts from ? = ??het,k to not
???
providing news. Under this condition, het,k < 0 when , so the accuracy weakly
??
decreases in ?.
B.1.10 Proof of Lemma 4
? ( )
A dual objective firm solve?s m( ax?,p ? =)? ?(D ? p+)(1? ?)v E[k
i]? 1 ?C.
i 2
Based on the proof of Lemma 3, E[ki]? 1 = ?? 1 D. The first step is solving
i 2 2
for the p?(?) that maximizes ?. Solving the FOC for price, we can obtain
p?
1
het,d(?) = (v((? ? 1 + ?(5? 4?) + 2?(3? ? 1)(? ? 1))?6?(? ? 1)
? ?2(? ? 2)2 + ?(? ? 2)(? ? 1) + (1 + 4?2)(? ? 1)2 ? 2?(? ? 1)((? + 2)? ? 2(? + 1))).
Note that this price needs to satisfy p?het,d(?) ? 0 and D(p?het,d(?)) ? 0.
Next, we solve for the optimal level of ?. It is worth noting that both p ? 0
and ? ? 1 can be binding. We separately analyze the following cases: [i] Neither
constraint binds; [ii] p > 0 and ? = 1; [iii] p = 0 and ? < 1; [iv] p = 0 and ? = 1.
??(p=p? (?),?)
1. When neither constraint binds, we solve the FOC het,d = 0 and ob-
??
?
2 2 2
tain ? = ?? = 9c ? ?v (2??)
2+4cv((?+2)??2(?+1)) (3c?+v(??2)) 9c2?2+2cv?(??2)+v2(??2)2
het,d ?16cv(??1) 16cv(1? .?)
The corresponding optimal price is p?(??het,d). The solution (?
?
het,d, p
?
het,d(?
?
het,d))
is an interior solution when ? < 1, ? > ? and cd < c < cd, where cd is the1+?
value of c such that ??het,d = 1 if ? ? [0, 1); c =
v(1??)(2??)
d 2? if ? ? [0, 1) and3?
159
? ? ( ? , 1), and = v(2??) if ? ? [0, 1) and ? ? [1 , 1].
1+? 2 2? 2
2. When p > 0 and ? = 1: in this case, the optimal price is p?het,d(1) =
?
v(1????+2??? ?2(??2)2+(??1)2??(2?3?+?2))
? . This is a postiv?e price when ? > ? .6?(? 1) 1+?
??(p? (?),?) ?
To make the constraint bind, we also need het,d ? > 0. It is also nec-?
?=1
essary that providing news leads to a (weak) improvement in ?: ?(p?het,d(1), 1) ?
?(0, 1). These constraints are satisfied when c ? cd , where c vd = if ? = 1,2 2?
and is the value of c such that ?(p? (1), 1) = ?(0, 1het,d ) if ? ? (1, 2].2
3. When p = 0 and ? < 1: in this case, we solve the FOC ??(0,?) = 0 and obtain
??
? = ??? 5 2v(1??)?chet,d = + ? ? . This is an interior solution (i.e., ?
??
het,d ? (1 , 1))6 6v(1 ?)(1 ?) 2
when ? < 1, ? ? ? and v(1 ? ?)(1 + ?) < c < 2v(1 ? ?)(2 ? ?), or ? < 1,
1+?
? < ? < 1 and cd ? c < 2v(1? ?)(2? ?).1+? 2
??
4. When p = 0 and ? = 1: in this case, we need ??(0,?) ? > 0 and ?(0, 1) ??
?=1
?(0, 1), which are satisfied when ? ? ? and c ? min{v(1? ?)(1 + ?), 2v(1?
2 1+?
?)}.
For the parameter range that is not covered by any of the cases above, no news is
provided.
B.1.11 Proof of Proposition 6
Consider the conditions for each case in Lemma 4 and focus on the case where
p = 0, we can find that p = 0 is never chosen when ? > 2 . When 0 ? ? ? 2 , the
3 3
firm chooses p = 0 only when c > cd (i.e., choosing (p = 0, ? = ?
??
het,d)) or when
160
? ? ?? (i.e., choosing (p = 0, ? = 1)).1 ?
B.1.12 Proof of Proposition 7
Consider the area where (p? ? ?het,d(?het,d), ?het,d) is the equilibrium strategy. We
??? ???
can find het,d < 0 always hold when ? ? 3 . When ? < 3 , there is het,d < 0 when
?? 4 4 ??
???
? < ??, and het,d > 0 when ? > ??.
??
B.2 Other Results and Proof
B.2.1 Asymmetric Value for States
In many cases, consumers may put more value on being correct about one
state than the other. For example, having the correct understanding about the
existence of a high pollution (state R) is more important than that of a low pollution
(state L). In other words, being correct about the existence of a high pollution is
more valuable (vR > vL). In the main model, we assume vL = vR = v. In this
subsection, we relax this assumption and analyze the game. The following lemma
summarizes the conditions for news provision and equilibrium accuracy levels under
this situation.
Lemma 5. The conditions for news provision and the corresponding lev-
2 2
els of accuracy are summarized in Table B.1, where c? = max{ (vL+vR) , (vL+vR) },
4vL 4vR
? = vL and ? = c . The price is always p = vL?L(1 ? ?0) + vv +v v R?R?0 ?L R L
161
??????vL(1? ?0) if ?0 ?
1
? 2?? .vR?0 if ?0 > 12
???????????????
Insert Table B.1 about here
???????????????
The first two columns of Table B.1 shows the condition for news provision.
The results under low (c ? min{vL, vR}) or high (c > c?) costs are similar to those
in Proposition 1. The result under moderate costs (min{vL, vR} < c ? c?) is more
interesting. Under this condition, news provision happens when consumers do not
have sufficiently strong belief on the more valuable state. In the main model, con-
sumers see little value in news if they have extreme beliefs. When knowing the
two states have different values, an extreme belief about the more valuable state
will discourage learning more than an extreme belief about the less valuable state.
Consumers an extreme belief about the more valuable state expect a smaller loss
from being wrong about the true state, so they have less incentive to learn. As a
result, news provision is less likely when consumers have an extreme belief about
the more valuable state.
The third column of Table B.1 presents the equilibrium levels of accuracy,
which depend on both the cost and the prior belief. To compare these results
with those in the main model, we illustrate the equilibrium accuracy under c > c?
using a numerical example, as in Figure B.1. Figure B.1(a) shows that news is
provided when consumers believe the less valuable state (L) to be more likely, or
162
believe the more valuable state (R) to be a little more likely. Compared with
the case of vL = vR = 1, the increase in vR makes news provision possible when
consumers have relatively extreme beliefs in L. As learning about R becomes more
valuable, consumers have stronger demands for information if they have relatively
extreme beliefs in L, but weaker demand for it if they have relatively extreme beliefs
in R. In response, the firm increases the accuracy of reporting R and decreases
that of reporting L. Consequently, the news report will overproportionally presents
the more valuable state. However, if consumers have sufficiently extreme beliefs
about the less valuable state (e.g., low pollution), the news report may downplay
the likelihood of the more valuable state (e.g., high pollution). In other words,
consumers? extreme beliefs make the media firm underreport the relatively more
important state, which can potentially result in serious consequences.
???????????????
Insert Figure B.1 about here
???????????????
B.2.2 Ex Post Polarization and the Impact of News
In Section 3.5.1, we use ? to measure the level of polarization in consumers?
prior beliefs. If we generate a measure for the ex post (expected) level of polarization,
we can quantify the impact of news on the level of polarization. In this subsection,
we extend the analysis in Section 3.5.1 to find the impact of news on polarization.
Since the variance of consumers? posterior beliefs is mathematically complex, we
163
use another measure to reflect the level of polarization among consumers? beliefs.
Under the prior, the shape of consumers? belief distribution is symmetric around
1 . By measuring the average belief of consumers who believe L to be more likely
2
(i.e., consumers whose prior belief ?i < 10 ) and examining how it changes with news2
consumption, we can also find the impact of news on the level of polarization.
? Under the prior, the average prior belief of consumers whose prior belief ?
i < 10 2
1/2
is 2 ?(? + (4 ? 4?)?)d? = 1 ? ? . The integral is multiplied by 2 because the
0 3 12
probability density function needs an adjustment when calculating the average of
half of the market. To calculate the average posterior belief, we need to consider
consumers? news consumption behaviors as well as the content of news. Based on
Corollary 1, only the consumers with 1 ? ? + p < ?i0 < ? ?
p consume news.
v v
If s = ?l, the average posterior belief of consumers whose prior belief ?
i 1
0 < is2
? ?
1??? phet(?+ het) ?
? = 2 het
1/2
v
l ?(? + (4 ? 4?)?)d?+20 p? (?? ) ?l(? + (4 ? 4?)?)d?.1??? het hethet+ v
The counterpart under s = r, ?r, can be calculated in a similar way, with ?l being
replaced by ?r. We use the expected value, ? = Pr(s = l)?l+ Pr(s = r)?r, to
measure the ex post level of polarization. The following figure illustrates the results
using three numerical examples.
???????????????
Insert Figure B.2 about here
???????????????
In the figure above, the horizontal axis is ?, which measures the level of polar-
ization under the prior. The black line denoted by ?c > 1? represents the average
posterior belief of consumers whose prior belief ?i0 <
1 when no news is provided,
2
164
which is the equilibrium outcome under high costs (i.e., c > 1). In this case, their
average posterior belief is the same as their average prior belief. As ? increases, the
average belief becomes closer to 0, which corresponds to a relatively high level of po-
larization. The blue line represents the case where c = 0.7, where news is provided
under low polarization (i.e., ? < 0.6). The provision and consumption of news make
the average posterior belief closer to 1 . The blue dashed line represents the case
2
where c = 0.3, where news is always provided with full accuracy. Compared this
case with c = 0.7, we can find that the average posterior belief is closer to 1 with
2
when news is more accurate. Moreover, as ? increases, the average posterior belief
under fully accurate news also gets closer to 0, but the distance between the line
with fully accurate news and that without news becomes larger under high values
of ?. In other words, as ? increases, fully accurate news has more impact on po-
larization when the level of polarization under the prior is sufficiently high. This is
because under higher levels of polarization, the firm lowers down the price to attract
consumers with more extreme prior beliefs, which resulting in having more impact
on the average posterior belief.
165
Cost Level Prior Belief Accuracy
c ? min{vL, vR} 0 < ?0 < 1 ?L = ?R = 1
? ?1??0 c/vL
{ } ? 0 <??0 < vL/c if vL < vR, or ?L = ? , ?R =?1 if v1 ? L < vR, ormin v , v < c c? 0L R
1? vR/c < ?0 < 1 if vL > vR, 1?(1??0) c/v? = 1, ? = RL R ( if v > v? L R0 )
v ? v +v ? = 1+4??(1??)L L R 1< ?0 < L + ?? ? ,
c > c? vL+vR 4c 2(1??0) 4??
0
vL + vL+v
( )
R
? = 1+4??
2
v +v 4c 1L R R ? ?+ ?2?0 4?? 0
Table B.1: Conditions for News Provision and Equilibrium Accuracy
166
(a) Reporting Accuracy (b) Reported Content
Figure B.1: Reporting Accuracy and Reported Content in Equilirbium (vL = 1,
vR = 1.5, c = 2)
Figure B.2: Expected Ex Post Polarization (v = 1)
167
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