The model with two firms delivers two key results. First, we see an across-group pref-
erence externality: having more W-type consumers delivers such consumers better
choices in the aggregate but makes the others worse off. Second, merger tends to spread
the two products apart. Adding more firms to the linear depiction of preferences rapidly
encumbers the structure, so we eschew further development of this model in order to
elaborate more subtle and intricate patterns of preference structures (albeit with signifi-
cant simplifications).
1.3.3 Market Size and Equilibrium Media Diversity
Above we considered product positioning, consumption, and the well-being of market
participants in contexts with small and fixed numbers (1 or 2) of products. Here we shift
the analysis to the number of firms or products operating. The first question to address is
the determination of the number of entering products which, as we have suggested
above, has an important impact on the way that preference externalities operate.
The logit model gives us a simple setup for illustrating this relationship. We begin
with one category of products targeting the single group of consumers. Products are dif-
ferentiated but symmetrically so. Hence, additional products will expand the market, but
all varieties attract identical shares. Suppose the group has “economic mass” M, which is
the product of the number of consumers and their economic weight to advertisers. Each
product has entry cost F, and we define n as the number of products that enter. The share
of the population consuming any particular product i is then
i
¼
e
s
1+ne
s
:
This is the classic symmetric logit with an outside option, and s represents the attractive-
ness of listening.
Under free entry, products enter until profit opportunities are dissipated. Ignoring
integer constraints, the free entry condition is M
i
¼F,orM
1
n +e
s
¼F, which deter-
mines the number of products as:
n ¼
M
F
e
s
:
The resulting equilibrium number of firms is the integer component of n. Hence, we
have monopoly if
M
F
e
s
2 1,2ðÞ, etc.
This simple setup yields a number of predictions relevant to preference externalities.
For a given positive value of potential consumers to advertisers, a larger population gives
rise to a larger economic mass M. So, first, as M rises, the number of products that can
profitably operate (modulo integer constraints) rises as well. Second, consumption also
rises with M (and with n). Note that overall revenue is
Mne
s
1+ne
s
. Finally, given that per capita
consumer surplus is proportional to log(1 + ne
s
Þ, then consumer welfare also rises with
20 Handbook of Media Economics
the population size. That is, this simple entry model delivers a positive within-group pref-
erence externality: consumers benefit one another by bringing forth additional products
which, in turn, attract a larger share of consumers to consume.
The equation n ¼
M
F
e
s
delivers another set of insights. As written it implies a par-
ticular relationship between market size (M) and entry. If the fixed costs associated with
entry are constant across markets of different sizes, then for markets with many entrants,
the relationship between M and n is nearly linear. On the other hand, if the fixed costs are
higher in larger markets, then the number of products available will rise more slowly.
Fixed costs may be higher in larger markets for two broad reasons. First, input prices
may be higher in larger markets for cost-of-living reasons. Second, if quality is produced
with fixed costs—as is plausible for media products—then firms in larger markets may
have incentives to spend more in an attempt to attract a larger share of a larger market
(see
Sutton, 1991). The general point is that while entry grows in market size across a
range of plausible models, the positive relationship may be tempered by other factors
affecting the determinants of fixed costs.
1.3.4 Optimum Media Diversity
The (first-best) optimum problem is to choose the set of products to maximize social sur-
plus. As long as private and social marginal benefits coincide, this is the sum of all agents’
surpluses. In particular, we shall assume for the present argument that social and private
benefits from advertising coincide (the analysis is readily amended if there are advertising
spillovers). Hence social surplus is equal to the sum of consumer surplus, advertiser net
surplus, and firm profits. We can in general write the last two terms as advertiser gross
surplus minus total fixed costs, because the price paid for advertising is a transfer from
advertisers to firms. Moreover, for simplicity we assume that the advertiser willingness
to pay is fixed at w per listener reached (and so advertiser net surplus is zero).
Then, given a mass of M listeners worth w each to advertisers, the social surplus (SS) is
SS ¼M ln 1 + nexpsðÞ+ wM 1
0
ðÞnF:
Here the middle term is the advertiser revenue (all those listening times w) and
0
is the
non-listening probability, and so for the logit model we use
1
0
¼
nexps
1+nexps
:
Differentiating with respect to n to find the optimal variety yields a quadratic function of
the form
Mw exps + ZM exps Z
2
F ¼0,
where we have set Z ¼ 1+nexpsðÞ. The relevant root is the positive one.
21Preference Externalities in Media Markets
It is readily shown that the optimal number is increasing in w, which makes sense
because then it is more important to ensure more communication from advertisers to
listeners. Moreover, we can draw some pointers by comparison with the equilibrium
solution we derived above, namely n ¼
wM
F
exp s
ðÞ
: First notice that if w is too
low, then the market solution is zero, while the optimum can have positive numbers.
This feature is just the point that an ad-financed system needs a strong enough ad demand
to be viable, but the optimum also figures in the consumer benefits.
Indeed, the current example always involves under-entry in the equilibrium (this can
be seen by inserting the equilibrium number into the expression for the optimum above).
We should note that this is one theoretical solution to the question of whether free entry
delivers the right amount of entry. Other models, e.g.,
Mankiw and Whinston (1986),
with homogeneous products and Cournot competition, deliver excess entry; their model
with differentiated products delivers ambiguous results. In the end whether entry is
excessive is an empirical question, but it is one that can only be addressed using some
explicit modeling framework.
1.3.5 Cross-Group Externalities
Individual consumers may consume the content targeted mainly at others, and may ben-
efit correspondingly, but not as much as if the content were targeted at their own type.
Indeed, it may be that more individuals of the other type—even if there is some chance
that the stations provided would be consumed—actually cause own-side welfare to fall.
That is, there may be negative preference externalities from other-side participation. This
would stem from crowd out of own-side media offerings. We now make these claims
precise by showing them in a rigorous model (although it is clearly highly specific and
parametric).
To this end, suppose that there are two types of individual (i.e., two groups) and two
basic program types. Let the economic masses of the W- and B -types be M
W
and M
B
,
respectively. Stations/firms take one of two basic types. Listening to an “own-side” sta-
tion is associated with an attractivity measure s > 0; listening to an “other-side” station
garners attractivity s. This symmetry assumption will be clear in the choice probability
formulae below and is a sort of normalization: negative values are not negative utilities,
and still have positive choice probabilities, although lower than own-side stations. The
formulation will generate “cross-over” across programming. The larger s (and hence the
smaller is s), the fewer people listen to other-side stations. Notice too that the formu-
lation implies that the chance of listening to one’s own side increases in the number of
own-side stations available, and decreases in the number of other-side ones.
Specifically, suppose that n
w
denotes the number of w -type stations available, and
similarly for n
b
. The logit formulation gives us the chance that a W -type listens to a par-
ticular w station as:
22 Handbook of Media Economics
W
w
¼
exps
1+n
w
exps + n
b
exp sðÞ
,
and the chance a W listens to a given b station is
W
b
¼
exp sðÞ
1+n
w
exps + n
b
exp sðÞ
:
From these we can calculate various statistics of interest. For example, the ratio of W’s
listening to b stations to those listening to w stations is
n
b
exp sðÞ
n
w
exps
¼
n
b
n
w
exp 2sðÞ,
which is small if s is large, but increases in the number of opposite-side stations, and
decreases in own-side ones. Indeed, here the number of cross-overs is proportional to
the relative number of stations on the “other” side. The more variety there is, the more
likely the listener finds something that resonates.
The next key step is to find out how many stations of each type there are in the mar-
ket, and how this depends on the numbers of listeners of each type. That is, we take the
analysis of the single type we had earlier, and now we use the central ideas to find the
breakdown of numbers of each station stripe.
1.3.6 Variety
Before getting to “thick” markets with many stations of each type, we first look at “small”
markets that can support one or two stations, and we ask what determines whether and
when the market gets a station for each type, or if only one type is represented (so that
here we are paying special attention to integer numbers of stations). Then we draw out
the implications for the preference externalities.
To trace out a coherent picture, we shall fix M
B
and vary M
W
up from nothing to see
how market provision changes. We concentrate on endogenously small station numbers,
and this will ensue if fixed costs are quite high. Accordingly, assume that the entry cost,
F 2 M
B
exps
1 + exps
, M
B
. This will ensure that there is no station at all without at least some
W’s, and that there is at least one station when W’s and B’s have equal market weight.
The lower bound condition already makes a useful point. In weak markets, even if
they are preponderantly of one type, sometimes enough of the other type is needed
to support a single station for the majority. Of course, some part of the minority needs
to be willing to listen to an other-side station (i.e., s should not be too large). But here
is an elementary preference externality. If enough own-side listeners are not available,
then the other side can exert a positive influence by enabling service when none
would be forthcoming in their absence. As one might expect, we cannot have too
23Preference Externalities in Media Markets
much of a good thing: if the minority gets too powerful, it may cause the market to tip to
the other station type. Or indeed, in the benign case, it may simply lead to a station of its
own type being added.
There are thus two cases of interest. As we show, which one holds depends on
whether F is larger or smaller than M
B
exps + exp sðÞ
1 + exps exp sðÞ
(note that this expression is larger than
M
B
exps
1 + exps
, which is the stand-alone profit from the B’s). Even if the s taste parameter were
the same across markets, the numbers of each type are not, and so we can see various
different patterns in a cross-sectional analysis.
Consider first the case F 2 M
B
exps
1 + exps
, M
B
exps + exp sðÞ
1 + exps exp sðÞ
. For low enough M
W
there
is no station at all, because there are not enough B ’s to cover the fixed cost on their own.
As M
W
rises, it becomes profitable to have a single station, and it is a b type (because the
B’s carry more economic weight). As M
W
rises further, but still is below M
B
, there is
enough profit in the market for a station of each type to survive.
28
To summarize, the
progression as M
W
rises is no firm, then a b -type, then a w -type too.
29
The preference externalities for this case are all positive (at the switch-point bet-
ween regimes—and zero elsewhere) for both types. The B’s need enough W’s to
float a first station. Adding further W’s enables another station to enter. It is a w-type,
and this benefits both groups, though the W’s benefit more than the B’s for the addi-
tion. The next (complementary) case highlights the possibility of negative preference
externalities.
Now consider the case F 2 M
B
exps + exp sðÞ
1 + exps exp s
ðÞ
, M
B
. Again, think of raising M
W
; the
first threshold crossed is again the market’s ability to support a firm, and it is a b-type.
However, now as M
W
rises further, the fixed cost is quite large, and indeed (from the
condition given) there is no room for two firms for M
W
< M
B
(and for M
W
at least a
bit above M
B
). However, once M
W
passes M
B
,aw-type is more profitable than a b-type.
Thus, the b-type is displaced. The equilibrium sequence (as a function of increasing M
W
)
is then no firm, b-type only, w-type only.
The preference externality is clearly beneficial to both types as M
W
rises above the first
threshold, and the market is served. However, the second threshold is where the b-type
gets replaced by a w-type, and the market retains a single firm. This favors the W-types,
28
To see that both survive, note indeed that the market can support one firm of each type (but no more) at
M
W
¼M
B
, where profit of each firm (by symmetry) is then M
B
exps + exp sðÞ
1 + expsexp sðÞ
, which is below the entry cost
by assumption in this case.
29
What happens if M
W
increases further? More and more ws enter, and at some point (depending on param-
eter values) the b actually switches type. This is the pattern suggested in the analysis below of the contin-
uous case. In the next case considered, the type-switching occurs immediately (in the sense that there is no
intervening regime where both types coexist).
24
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