RaðÞ¼av aðÞ:
Assume that the corresponding marginal revenue R
0
(a) slopes down in standard fashion.
2.2.3 Media Platforms
Media platforms are assumed to maximize their profits. Abstracting for the moment from
costs (and therefore quality) of providing programming, then under pure advertising
finance (so s
i
¼0 for all i), profit is π
i
¼P
i
a
i
with P
i
the price of an ad on platform i. With
mixed finance, profit is π
i
¼P
i
a
i
+ s
i
N
i
. We unpack these profit functions and draw out
tractable ways to deal with them in oligopolistic platform competition in the next section.
2.2.4 Other Players
To be sure, there are many other agents interacting in the production of the final product
(such as ad agencies, content producers like journalists and program producers, cable pro-
viders and distributors, and the ilk—see especially
Chapter 7 (this volume)). These are
often set aside in the analyses in order to concentrate on the major market interaction
we focus upon here, namely, the two-sided market interaction between advertisers
and consumers as arbitrated by the platforms.
2.3. EQUILIBRIUM ANALYSIS OF SINGLE-HOMING VIEWERS/READERS/
LISTENERS/SURFERS
We start out with the analysis of pure advertising finance. For technological reasons in the
difficulty of excluding and pricing access to a pure public good (the TV or radio signal,
say), the early days of broadcasting involved such a business model. Only fairly recently,
with the advent of signal scramblers and descramblers, did it become economically viable
to have viewers pay for platform access. The case of pure ad finance is also one type of
equilibrium regime in the panoply of broader tariff choices, as seen below.
The key step in finding an equilibrium is to use the structure imposed above in order
to regroup and rewrite the platform’s profit:
π
i
¼P
i
a
i
¼va
i
ðÞN
i
γa
i
;γa
i
ðÞa
i
¼Ra
i
ðÞN
i
γa
i
;γa
i
ðÞ:
That is, the profit which is the product of the price per ad times the volume of ads aired
can be split up and repacked as profit per ad per viewer times ad volume, and then recon-
stituted as the ad revenue per viewer times the number of viewers. We can thus find an
equilibrium to the game between platforms by treating the a values as strategic variables.
Notice that this means that the platforms can be viewed as choosing the amount of air
time (or newsprint pages) to devote to ads, and then selling the ad time (or space) at the
price the market will bear. Equivalently, because v(a) is monotonically decreasing, we can
47Two-Sided Media Markets
treat prices per ad per viewer as the “strategic” variable. Alternatives, such as choosing ad
prices per se, are discussed below.
The first-order condition for the ad-finance game is then readily expressed (by max-
imizing ln π
i
) as the equality between two elasticities (Anderson and Gabszewicz, 2006),
those of revenue per viewer and viewer demand. Equivalently, letting a prime denote a
derivative with respect to own advertising,
R
0
R
¼γ
N
0
i
N
i
; (2.1)
where N
0
i
< 0 denotes the derivative of the demand function with respect to its first
argument (i.e., the full price). This equation underscores a crucial distinction between
cases when ads are a nuisance and when they are desirable to viewers. To see it, assume
first that viewers are ad-neutral, so they are indifferent between having an extra ad or not.
Then platforms set ad levels such that marginal revenue per viewer (R
0
) is zero. When ad
levels do not affect viewer levels, platforms simply extract maximal revenue from their
viewer bases. Otherwise, there is a two-sided market effect, and platforms internalize
the ad effect on viewer participation. For γ > 0 (ad nuisance), they restrain ad levels
below the level at which marginal revenue is zero. This entails ad prices above the
“monopoly” level even when there is competition among platforms. Conversely, for
γ < 0, they sacrifice some revenue per viewer by expanding ad levels in order to entice
viewers and so deliver more of them and consequently charge advertisers less per ad. That
is, the ads themselves are used as part of the attraction to the platform, though the plat-
form does not expand ad levels indefinitely because then the revenue per viewer would
fall too much as more marginal willingness-to-pay advertisers would have to be attracted.
The RHS of
(2.1) can readily be evaluated for standard symmetric oligopoly models
with n platforms, to deliver some characteristic properties of the solution. For the
Vickrey
(1964)
10
and Salop (1979) circle model, it is γ(n/t)(Anderson and Gabszewicz, 2006;
Choi, 2006
), where t is the “transport cost” to viewers. For the logit model
(
Anderson et al., 1992), it is γ n 1ðÞ=μnðÞ, where μ is the degree of product heteroge-
neity.
11
In both cases (as long as R
0
(a)/R(a) is decreasing, as implied by the marginal ad
revenue decreasing), a higher ad nuisance causes lower ad levels per platform. More pref-
erence heterogeneity (t or μ respectively) raises ad levels as platforms have more market
power over their viewers. Increasing the number of platforms, n, decreases the ad level.
The analogy is that advertising is a “price” to viewers, so naturally such prices go down
with more competition. Because the advertising demand curve slopes down, this means
that the ad price per viewer exacted on the advertiser side actually rises with competition
10
The relevant analysis is republished in Vickrey et al. (1999).
11
Similar properties hold for other discrete-choice models with i.i.d. log-concave match densities in that the
corresponding expression is increasing in n: see
Anderson et al. (1995).
48
Handbook of Media Economics
(though the ad price itself may not because viewer bases per platform contract). This
result may reverse when viewers multi-home, as discussed in
Section 2.4 on multi-
homing and competition for advertisers.
The oligopoly analysis can also be readily extended to allow for asymmetric platforms,
with asymmetries in viewer demand functions allowing for “quality” differences such
that higher qualities are associated with higher numbers of viewers for any given vector
of ad levels.
Anderson and Peitz (2014) engage the structure of aggregative games (which
encompasses logit, among other demand structures) to deliver a number of characteriza-
tion results for market equilibrium. For example, higher quality channels carry more ads,
but nonetheless serve more viewers.
12
The profit function formulation above readily extends to when subscription fees are
charged to, e.g., magazine readers. Then there are two sources of revenue from each
reader, the direct fee and the ad revenue. The profit expression becomes
π
i
¼ s
i
+ Ra
i
ðÞðÞN
i
f
i
; f
i
ðÞ:
The solution (assuming that the s and a values are determined in a simultaneous move
Nash equilibrium between platforms with consumers observing subscription prices
and ad levels
13
) can be determined recursively by first showing the optimal split between
s
i
and a
i
while keeping readership constant. This device will allow us to tie down equi-
librium ad levels and then determine subscription prices. That is, fix f
i
¼
f
i
, and so max-
imize total revenue per reader, s
i
+ Ra
i
ðÞ, under the constraint that
f
i
¼s
i
+ γa
i
,so
a
s
i
¼ argmax
f
i
γa
i
+ Ra
i
ðÞ. Then a
s
i
0 solves R
0
a
s
ðÞ¼γ (Anderson and Coate,
2005
).
14
This means that marginal ad revenue should equal the reader nuisance cost:
if it were lower, then total revenue could be increased by decreasing ads and monetizing
the subsequent nuisance reduction into the subscription price, and conversely. This rela-
tion embodies the two-sided market phenomenon mentioned by
Rysman (2009), that a
stronger advertising side (a rise in the revenue per visitor) implies less is earned on the
other side because then there is more incentive to attract viewers.
One immediate conclusion is that pure subscription pricing prevails if R
0
0ðÞγ,
which occurs if the ad demand is weak, and/or if ad annoyance costs are strong. In this
case, subscription prices are given by the standard Lerner/inverse elasticity conditions for
oligopoly prices—the standard “one-sided market” analysis applies.
12
This analysis is discussed at more length below (Section 2.3.4) when we discuss see-saw effects in media
markets.
13
For magazines, for example, subscription prices are likely determined in advance of advertising rates: it
might be worthwhile to develop the analysis for the corresponding two-stage game. Another theme
to develop is price discrimination between newsstand and yearly subscription prices.
14
The result is generalized in Crampes et al. (2009) to a circle market structure and a general advertising
annoyance function.
Anderson and Gans (2011) extend the result to a distribution of γ in the viewer pop-
ulation: then the average γ determines a
s
.
49
Two-Sided Media Markets
Note that if ads are desirable to readers (γ < 0) then ad levels are above the
“monopoly” level (defined as a
m
¼R
0
1
0ðÞ).
The constraint that s
i
be non-negative is imposed because, if not, readers would be
paid for getting magazines, and would then get lots of them and throw excess copies away
to collect the subsidies, which would be untenable. Assuming for the moment that s
i
> 0,
and that R
0
0ðÞ> γ so that there is at least some ad financing, the profit function is given as
π
i
¼ s
i
+ Ra
s
ðÞðÞN
i
f
i
; f
i
ðÞ; (2.2)
where a
s
solves R
0
a
s
ðÞ¼γ for all i and f
i
¼s
i
+ γa
s
. As pointed out by Armstrong (2006),
the problem then has a familiar structure, though with an interesting twist. The profit
function above, and therefore the game and its solution, is just like a standard oligopoly
problem with R(a
s
) entering as if it were a negative marginal cost!
15
The idea is that each
reader carries with her an associated revenue. Hence solutions can be found from solu-
tions to standard oligopoly models with differentiated products, modulo the caveat that
subscription prices be non-negative. Indeed, while standard oligopoly models return
prices above marginal cost, here an (unconstrained) solution would only return prices
above Ra
s
ðÞ, which might well entail negative solutions for subscription prices. There-
fore the subscription price non-negativity constraint might well be binding. If so, the
solution is pure ad finance. This happens when a
s
is above the level of advertising that
would be chosen for a free service,
16
and the outcome is described already above as
the elasticity equality between ad revenue per reader and reader demand.
The logic above can also explain the coexistence of pay and free services in the same
market as a function of platform content. Loosely, media platforms with the highest elas-
ticity of subscription demand would be free while others would have pay-walls. It follows
also that those services charging subscription prices would have a lower advertising level
(i.e., a
s
) than the free services.
17
Using a model of vertical product differentiation,
Gabszewicz et al. (2012) show that a free-to-air low-quality media platform may coexist
with a subscription priced high-quality media platform.
Anderson and Peitz (2014) use an
aggregative game formulation to determine when and which platforms use pay, free,
or mixed finance, based on program “quality” (by which we mean a favorable
demand-shifter). Low-quality platforms are more likely to be ad-financed, and high-
quality ones to use subscription pricing.
15
And modulo the inclusion of γa
s
in the full prices in demands, which is like a quality decrement to all
platforms.
16
Assuming quasi-concavity, the service is free if the slope RN
0
i
+ N
i
is negative at a
s
, which can be written as
R
0
a
s
ðÞ
R a
s
ðÞ
< γ
N
0
i
a
s
; f
i
ðÞ
N
i
a
s
; f
i
ðÞ
.
17
Recall that all media audiences are here assumed equivalent for advertisers. The conclusion would be
modified if the consumers of the paid media were more attractive for advertisers.
50
Handbook of Media Economics
We have treated so far the marginal cost to reaching consumers as zero. While this
fits radio, TV, and the Internet, for magazines and newspapers there are newsprint costs.
The analysis so far is readily adapted to these cases. Indeed, it suffices to include a cost c
i
per reader for the basic entertainment pages, and a further cost per reader per page c
a
for
the ad pages, and so the profit function becomes
π
i
¼ s
i
c
i
+ Ra
i
ðÞc
a
a
i
ðÞN
i
f
i
; f
i
ðÞ:
Thus the analysis above goes through replacing R(a
i
)by
e
Ra
i
ðÞ¼c
i
+ Ra
i
ðÞc
a
a
i
.
18
In
particular, the ad level is now determined by
e
R
0
a
s
ðÞ¼γ. When γ < 0, this may mean pric-
ing below cost, as developed in the next section.
2.3.1 The Ad Revenue/Subscription Revenue Balance
This section both delivers a description of equilibrium finance model for a calibrated
example for monopoly and illustrates some key features of pricing in two-sided markets.
It also delivers results about how the market business model responds to changes in the
demand strengths on the two sides of the market.
19
Suppose that ad market demand is linear, so vaðÞ¼1 a and hence R
0
aðÞ¼1 2a.In
any equilibrium involving ads and subscriptions, then a
s
¼ 1 γðÞ=2, so that
Ra
s
ðÞ¼1 γ
2
=4, and the subscription price solves 1 + Ra
s
ðÞ+ sðÞN
0
fðÞ=NfðÞðÞ¼0.
Now specify too a linear consumer demand function for the medium, NfðÞ¼1 f ,
with f ¼s + γa. Then s > 0 solves 1 s γa
s
Ra
s
ðÞ+ sðÞ¼0, or
s ¼
1
8
3 2γ +3γ
2
:
When s ¼0 we have the pure ad-finance regime which solves R
0
=R ¼γ N
0
i
=N
i
(see
2.1), so
1 2a
a 1 aðÞ
¼
γ
1 γa
:
Whenever γ 1, the equilibrium is in subscriptions only. Then, given the linear demand,
s ¼f ¼1=2. The solutions for the equilibrium values as a function of γ are given in
Figures 2.1 and 2.2. Figure 2.1 shows equilibrium participation on the two sides of
the market, namely, advertiser and consumer levels. Both of these are decreasing in γ
up to γ ¼1, whereafter there are no advertisers and subscriber numbers are constant
in the subscription-only regime. Put the other way, the more consumers like
ads—negative γ is ad loving, so that then the market interaction involves bilateral
18
One might also include some fixed cost as an increasing function of the number of advertisers (sales force
effort finding advertisers, etc.), which might be important empirically.
19
This material is based on Anderson and Shi (2015).
51
Two-Sided Media Markets
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