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FEDERAL COMMUNICATIONS COMMISSION
MEDIA BUREAU STAFF RESEARCH PAPER Media Ownership Working Group
A Theory of Broadcast
Media Concentration and
Commercial Advertising
By BrendanC. Cunningham and PeterJ. Alexander
September 2002
2002 - 6
1
A THEORY OF BROADCAST MEDIA
CONCENTRATION AND COMMERCIAL
ADVERTISING
Brendan M. Cunningham and Peter J. Alexander
September, 2002
Executive Summary
We analyze a model in which the interaction of broadcasters, advertisers, and consumers
determines the level of non-advertising broadcasting produced and consumed. Our main
¯ndingisthatanincreaseinconcentrationinbroadcastmediaindustriesmayleadtoa
decreaseinthetotalamountofnon-advertisingbroadcasting.Thestrengthofthisinverse
relationship depends, in part, on the behavioral response of consumers to changes in ad-
vertising intensities. We also present numerical general equilibrium solutions to our model
and demonstrate a positive relationship between consumer welfare and the number of ¯rms
in the broadcast industry.
¤ Cunningham: Department of Economics, U.S. Naval Academy, email: bcunning@usna.edu. Alexander: Fed-
eral Communications Commission, email: palexand@fcc.gov. We thank Matt Baker, Jerry Duvall, Jonathan Levy,
and Pam Schmitt and for their insights. We would especially like to thank David Sappington for his unstinting
support, and many thoughtful and useful comments. All errors are our own. The views expressed in this paper
are those of the authors, and do not necessarily represent the views of the Federal Communications Commission,
the Chairman or any of its Commissioners, or other sta®.
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I Introduction
The broadcast industry in the United States is unique in that a unit of broadcast ¯rm output
is imperfectly related to a ¯rm's revenues. That is, broadcast media output is divided between
non-advertising (i.e., programming) and advertising components. The latter generate income
for the ¯rm, while the sum of the components jointly determine a ¯rm's costs. Broadcast ¯rms
must, on a continuing basis, strike a balance between garnering an audience through the supply
of a zero-price output while simultaneously selling di®erent output to a third party. It is this
balance that is the central focus of the model we present.
In this paper, we explore how the interaction of broadcasters, advertisers, and consumers
determines the level of non-advertising broadcast content produced by broadcast ¯rms. We
employ a model of imperfect competition in the advertising market and explore the impact of
the number of ¯rms in the broadcast industry on the distribution of broadcasting between non-
advertising and advertising content. This model di®ers from its antecedents in that the broadcast
market may be populated by an arbitrary number of ¯rms. 1 We ¯nd that the pro¯t-maximizing
response of broadcasters to a change in concentration (i.e., the number of ¯rms) depends, in
part, upon the behavioral response of consumers to a change in the fraction of broadcast time
devoted to advertising.
We consider a full range of values for this response and describe three cases. In the ¯rst
two cases, the broadcaster's pro¯t-maximizing response to increasing industry concentration
is to increase the fraction of broadcasting devoted to advertising. Depending on the precise
behavioral response of consumers (captured by a range of elasticities), we ¯nd an increase in the
1 Moreover, unlike previous work we do not assume that consumers directly dislike advertising.
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3
fraction of broadcast time devoted to advertising leads to a fall (rise) in the overall amount of
advertising and an increase (decrease) in the price of a unit of advertising. In both of these cases,
we ¯nd a reduction in the amount of non-advertising broadcasting consumed and supplied. In
the third outcome we explore, we ¯nd that an increase in concentration results in a reduction
of the fraction of broadcast time devoted to advertising, and a crowding-in of non-advertising
broadcasting.
It is important to distinguish between the amount of advertising and the fraction of broadcast
time devoted to advertising. We ¯nd that, under plausible conditions, the amount of advertising
can fall while the fraction of broadcast time devoted to advertising increases. This result emerges
from our assumption of market clearing in the broadcast market combined with a particular be-
havioral response from consumers that we refer to as \switching-o®." Simply put, switching-o®
may occur as consumers reduce their overall media demand in response to increased advertis-
ing/broadcast ratios. If this behavior is strong enough, higher levels of concentration can result
in lower levels of advertising, higher prices, and a larger fraction of broadcast time devoted to
advertising. In this case, we obtain the \classic" market power result of fewer units sold at a
higher price and a crowding-out of programming by advertising.
The importance of our ¯ndings reside, in part, in the potential welfare e®ects associated
with broadcast media concentration. Closed-form general equilibrium analysis of these e®ects is
intractable. For this reason, we apply numerical techniques to determine the equilibrium values
of the model's key endogenous variables for varying levels of concentration in the broadcast
industry. This approach reveals that the reduction in programming associated with industry
concentration induces indirect utility losses via higher equilibrium prices. Moreover, increasing
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concentration induces direct utility losses due to reduced consumption of overall programming.
The remainder of the paper is as follows. In Section II, we review the existing theoretical
literature relating to broadcast media and detail how our model is distinct from the existing
literature. In Section III, we introduce our model of consumers, advertisers, and broadcasters
and present the conditions which characterize optimal behavior in our model. In Section IV,
we explore the speci¯c conditions under which variations in concentration may induce a change
in the amount of non-advertising broadcasting. In Section V, we specify additional functional
forms and present welfare results from numerical solutions to the model. In Section VI we make
some concluding remarks and suggest areas for future research.
II Broadcast Literature
There are a handful of important contributions to the broadcast literature. Among the seminal
theoretical works on the industry are those of Steiner (1952), Spence and Owen (1977), and
Beebe (1977). Recent theoretical work includes that of Anderson and Coate (2001), Nilssen and
Sorgard (2000), J. Gabszewicz and Sonnac (2000), and Gal-Or and Dukes (2001). 2
Steiner's early article demonstrated that under certain (restrictive) conditions a monopoly
market structure would provide optimal program diversity. Steiner noted that when viewer
preferences were such that a large group of consumers preferred a single program type, and much
smaller groups of viewers preferred other types, a monopolist would have the incentive to provide
each distinct program type (i.e., the monopolist would internalize the business stealing e®ect),
whereas multiple competing ¯rms would have incentives to provide programming for the largest
2 This list is not intended to be exhaustive. Rather, the works cited are among the more in°uential and detailed
extant theoretical studies.
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group of viewers only. Beebe (1977) extended the analysis in Steiner (1952) and Rothenberg
(1962) to include program costs, di®ering distributions of viewer preferences, and unlimited
channel capacity. Beebe concluded that optimal market structure depends on the structure of
viewer preferences and the extent of channel capacity.
Spence and Owen (1977) provide a seminal rigorous analysis of broadcasting. They explore
the welfare implications of program provision under alternative market structures (e.g., competi-
tive advertiser supported and pay television). Their results suggest that the ¯xed costs associated
with program production often result in under-provision of certain programming since the broad-
cast subscription revenues of such programs do not exceed costs. Thus, even in situations where
bene¯ts exceed costs, broadcast television is biased against certain programming. This bias is
reduced under a pure pay-television framework relative to the competitive advertiser-supported
structure, while a monopoly (advertiser supported) market structure exacerbates this bias.
The works of J. Gabszewicz and Sonnac (2000), Nilssen and Sorgard (2000), Anderson and
Coate (2001), and Gal-Or and Dukes (2001), collectively represent the horizon of analytical
work on the broadcast industry. All four works are similar in that they: (1) adopt a two-¯rm
(broadcasters) location-style approach, with each ¯rm carrying one program with advertising,
competing for viewers; and (2) assume consumers dislike advertising. 3 Methodologically these
works share an important lineage that stems from the path-breaking work of Hotelling (1929).
Hotelling's original work suggested ¯rms would minimally di®erentiate (locations), while the
work of d'Aspremont, Gabszewicz and Thisse (1979) demonstrated, under slightly di®erent as-
3 Anderson and Coate (2001) take a relatively novel approach, and assume that there are two types of consumers
for broadcasting: advertisers and viewers, and that advertisers impose a negative externality on consumers and
other advertisers. This `externality' is paid for through the pricing of advertising, which Anderson and Coate note
is equivalent to a Pigovian tax. The idea that advertisers impose costs on each other is an important innovation,
¯rst noted by Berry and Waldfogel (2001).
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sumptions, that ¯rms would maximally di®erentiate. 4; 5
Our model di®ers from the recent literature in at least two important ways. First, we do
not employ a location-style, stage-game approach. While this methodology is productive in
the two-¯rm context, a speci¯c focus of our work relates to a situation in which the number
of broadcast ¯rms is somewhat large. Location models are generally less tractable when the
number of ¯rms is large. The case of many ¯rms is important to consider because, in practice,
the number of ¯rms is often greater than two. Second, the works cited above generally assume
that commercial advertising imposes direct utility costs on consumers. While we also conclude
that consumers reduce their amount of broadcast viewing as the level of advertising relative to
the total broadcast increases, our approach is based on weaker assumptions than straight-forward
disutility, as discussed further below.
4 In the case of modern address theory, location refers to product space or, more generally, the degree of product
di®erentiation among ¯rms. 5
J. Gabszewicz and Sonnac (2000), Anderson and Coate (2001), and Nilssen and Sorgard (2000) are method-
ologically similar to these works in that they structure stage games in which broadcast ¯rms ¯rst choose their
programming type, and then each ¯rm chooses a broadcasting/advertising ratio. In contrast, in the work of
Nilssen and Sorgard (2000), ¯rms ¯rst make the choice of investment in programming and the price of adver-
tising, and then producers choose their level of advertising. Nilssen and Sorgard (2000) suggest that a duopoly
market structure reduces the number of viewers and amount of advertising relative to a monopoly market struc-
ture. Gal-Or and Dukes (2001) (see also Tirole (1988), p. 293) demonstrate conditions whereby broadcasters
minimally di®erentiate their programming. Minimal di®erentiation in turn induces a reduction in advertising
that reduces consumers overall information. Given reduced information is available to consumers, producers have
greater latitude to increase prices. Increased product prices then allow broadcasters to raise the price of advertis-
ing, which increases pro¯tability. In direct contrast to Gal-Or and Dukes' ¯nding of broadcast ¯rms maximizing
pro¯ts via minimal di®erentiation, Anderson and Coate suggest that minimal di®erentiation will minimize pro¯ts
of the broadcast ¯rms. Anderson and Coate's e®ort highlights the trade-o®s inherent in the broadcast industry,
and concludes that programming resources and advertising levels may be too high or too low, contingent upon
the method of aggregating costs and bene¯ts.
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III The Model
In our model, we explore how the interaction of broadcasters, advertisers, and consumers deter-
mines the level of non-advertising broadcasting under various levels of market concentration. We
assume that broadcasters are also content providers, and that all broadcast content is informa-
tional. Broadcasters are only compensated for the informational content provided by advertisers.
Broadcasters do not charge their viewers, but they do charge advertisers for delivering their mes-
sages to viewers. Additionally, we assume that advertisers are also the producers of the goods
that are advertised, and that advertisers are price takers. Finally, we assume consumers maxi-
mize utility by their consumption of both non-commercial information and goods produced by
advertisers.
A Consumers
We begin by assuming there is a representative consumer that purchases ¯nal goods from adver-
tisers, earns a wage, and consumes broadcasting. The following variables are relevant, from the
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consumer's perspective:
A ¡ total advertising consumed
N ¡ total non-advertising consumed
B ¡ total broadcast time consumed
Q ¡ total quantity of advertised goods consumed
PQ ¡ price per unit of goods
w ¡ wage rate
Y ¡ consumer's \full" income
(1)
By full income, we mean the level of income which would obtain if all of the consumer's time
were spent earning wages. Implicitly, we assume a time endowment in which a unit of time spent
consuming broadcasting reduces household income by w.
We assume there is a function, U(Q; N), that maps goods consumption and non-advertising
consumption to utility,with the standard property of positive and diminishing marginal utilities.
Letting Ux ´ @U=@x and Uxy ´ @ 2 U=@x@y, we assume that Ux > 0 > Uxx for x = Q; N.
There are m broadcast ¯rms in the market, indexed by i = 1; : : : ; m. Variables labelled with
an i subscript represent ¯rm-level quantities. Letting ®i represent the fraction of each ¯rm's
broadcast time devoted to advertising, we have N = P m i=1 (1 ¡ ®i)Bi.
The consumer faces a budget constraint that binds the choice of goods consumption and
non-advertising consumption: PQQ + wB = Y . Consumers choose Q and fBig m i=1 to maximize
the LaGrangian:
L = U (Q; N) + ¸(Y ¡ wB ¡ PQQ) (2)
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with
N =
m
X i=1 (1 ¡ ®i)Bi (3) and
B =
m
X i=1 Bi (4) The ¯rst-order conditions characterizing the solution to this problem are:
UQ = ¸PQ (5)
(1 ¡ ®i)UN = ¸w for i = 1; : : : ; m (6)
Combining these conditions, we obtain:
UN
UQ =
w
(1 ¡ ®i)PQ for i = 1; : : : ; m: (7)
We can see that an increase in ®i will be associated with an increase in the right-hand side of (7).
The assumption of diminishing marginal utility implies that consumers will decrease the ratio of
non-advertising consumption to goods consumption (N=Q) in response to this increase in ®i.
An increase in the fraction of broadcast time devoted to advertising increases the e®ective
price of non-advertising broadcast consumption. To show this, we re-write the budget constraint
to re°ect the price of consuming non-advertising broadcasting:
PQQ +
m
X i=1 w 1 ¡ ®i Ni = Y: (8)
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If an individual broadcaster begins to devote a larger fraction of a unit of broadcasting to
advertising, a consumer must spend additional time consuming broadcasting in order to achieve
the same level of utility from non-advertising consumption, thereby sacri¯cing additional wage
earnings. Thus, the e®ective price (or opportunity cost) of non-advertising consumption has
increased. In other words, the coe±cient on Ni in the budget constraint (8) is increasing in ®i.
We have shown that the consumer will reduce total non-advertising consumption, relative to
goods consumption, in response to a rise in ®i. We can also conclude that, given optimal values
of Q and N, consumers will devote their media demand to the broadcast ¯rm with the lowest
fraction of broadcasting devoted to advertising. This can be seen by inspection of (8), where
the total \expenditure" on non-advertising broadcasting is minimized by devoting all media
consumption to the ¯rm with the lowest value of ®i, thereby allowing maximum consumption of
Q for a given N. Thus, the only outcome in which all m ¯rms face strictly positive demand for
their output is one in which each broadcast ¯rm chooses the same ®i. We demonstrate below
that this symmetry holds in our model and we label this optimal value ® ¤ i . When ¯rms choose
the same value of ®i, the consumer is indi®erent with respect to its distribution of total non-
advertising consumption across broadcast ¯rms. Thus, for simplicity, we assume this total is
distributed evenly among ¯rms, i.e., Ni = N=m.
With these observations, we conclude that (8) becomes
PQQ + w 1 ¡ ® ¤ i N = Y: (9)
From this expression, we can see that an increase in the fraction of broadcast time devoted to
advertising must be matched by a fall in non-advertising consumption. By way of illustration,
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suppose this constraint is satis¯ed for some initial ® ¤ i . If the advertising share of broadcasting
increases to ~ ® ¤ i , the second term on the left-hand side of (9) increases. In this case, the ratio
Q=N must also increase. If Q were to increase by itself, the budget constraint would not be
satis¯ed since the left-hand side of (9) would exceed the right-hand side. Thus, N must display
an inverse relationship with ® ¤ i , implying that Ni displays an inverse relationship with ®i. Since
Bi = Ni + Ai, we can conclude that the demand for total broadcasting is decreasing in the
fraction of broadcasting devoted to advertising. Therefore, we write the consumer's demand
for broadcasting as a general, decreasing function of the fraction of broadcasting devoted to
advertising: Bi = B(®i) with B 0 < 0. This result will be employed below.
B Advertisers
We assume that there is one advertiser that purchases advertising from the m broadcasters and
produces the ¯nal good Q. This advertising ¯rm acts in a perfectly competitive manner in all
markets. 6 The advertiser's objective is to maximize pro¯ts from selling the ¯nal good Q. We
model the advertiser's revenue function as multiplicative in production of Q and the purchase of
a bundle of advertising, ~ A, from the m broadcasters. Thus, total revenue for the advertiser is:
PQQ ~ A ¯ where 0 < ¯ < 1 (10)
The parameter ¯ induces concavity of the ¯rm's revenues with respect to the advertising bundle
so that total revenues increase at a decreasing rate with respect to overall advertising. 7 While
6 The simplifying assumption of one advertising ¯rm is equivalent to assuming ultra-free entry.
7 While stylized, this simply assumes that to sell more, ¯rms must advertise more.
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revenue scales linearly with production of Q, our assumption of convex production costs ensures
the advertiser's problem is well-behaved.
We next specify the manner in which purchases of advertising from individual broadcasters
are aggregated into the advertising bundle ~ A. As in Blanchard and Giavazzi (2001), we assume a
Dixit-Stiglitz aggregator in which the marginal rate of substitution between advertising purchased
from di®erent broadcasters, ¾, is increasing in the number of broadcasters. Speci¯cally:
~ A = "
m
X i=1 A ¾¡1 ¾ i #
¾
¾¡1
(11)
with ¾ = ¾g(m); g 0 (m) > 0. The assumption that ¾ is rising in the number of ¯rms captures
the idea that a broadcast market populated by a larger number of ¯rms is one in which the
individual advertising supplies of broadcasters are closer substitutes.
Given these speci¯cations, an advertiser's pro¯ts may be written as:
¼A = ~ PQQA ¯ ¡ CQ(Q) ¡
m
X i=1 PiAi (12) We assume positive and increasing marginal costs of production: C 0 Q ; C 00 Q > 0 with C(0) = 0. The
advertiser seeks to maximize pro¯ts with respect to production levels and advertising purchases.
There are m + 1 ¯rst-order conditions which characterize the solution to this maximization
problem:
~ PQA ¯ ¡ C 0 Q = 0 (13)
~ ¯PQA ¯¡1 ~ A 1=¾ A ¡1=¾ i ¡ Pi = 0 for i = 1 : : : m: (14)
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These two conditions respectively equate the marginal revenue from production/advertising to
the relevant marginal cost. Note that (14) implies an inverse relationship between demand for
advertising from an individual broadcaster and that broadcaster's price.
If we de¯ne the price aggregator as:
P ´ "
m
X i=1 P 1¡¾ i #
1
1¡¾
: (15)
we can derive a simpli¯ed expression for advertising demand that each individual broadcaster
will face. Using (15), we see that (14) is equivalent to:
Pi = P( ~ A=Ai) 1=¾ (16)
Observe that (16) is an inverse demand function for a given broadcaster's advertising, where
demand for a given broadcast ¯rm's advertising is decreasing in price. 8
C Broadcasters
We begin by de¯ning the following variables for broadcaster i:
Pi ¡ price per unit of advertising
Bi ¡ broadcasting supply
C(Bi) ¡ total cost of producing broadcasting
(17)
8 It is important to note that this derivation of the inverse demand function illustrates that an individual
broadcaster's demand is a®ected by behavior of other ¯rms in the broadcast industry. For expositional simplicity,
we omit industry-level variables from the inverse demand function presented here since we assume that each
individual ¯rm is taking the industry-level outcome as independent of its own choices.
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We assume the cost function C(Bi) has the standard feature of positive and increasing marginal
costs: C 0 ´ @C=@B > 0; C 00 ´ @ 2 C=@B 2 > 0. 9 We further assume the broadcaster operates in
an imperfectly competitive market in which it considers the inverse demand function (16) when
maximizing pro¯ts, i.e., Pi = P(Ai). This inverse demand function was derived in (16) and
demand was shown to be the level of advertising / broadcast ratio of ¯rm i.
We also assume that the market for broadcasting clears. 10 The market clearing condition
allows us to equate supply to the demand function described in Section A: Bi = B(®i). Finally,
it is trivially clear that Ai = ®iB(®i).
Given these observations, the broadcaster's pro¯t function is as follows:
¼i = P(®iB(®i))®iB(®i) ¡ C(B(®i)): (18)
A pro¯t maximizing broadcaster will choose ®i to maximize this expression. The ¯rst-order
condition characterizing pro¯t maximization is:
P 0 i ®iB 2 i + P 0 i ® 2 i B 0 i Bi + PiBi + Pi®iB 0 i = C 0 i B 0 i : (19)
or:
Pi ¢ Bi ¢ µ 1 + P 0 i Ai Pi + P 0 i Ai Pi B 0 i ®i Bi + B 0 i ®i Bi ¶ = C 0 i ¢ B 0 i (20)
Let the elasticity of advertising price with respect to total advertising supplied be ´Pi;Ai ´ P 0 i Ai Pi .
9 The presence of ¯xed costs has no qualitative e®ect on the predictions of the model since ¯xed costs have no
e®ect on the ¯rst-order conditions describing pro¯t maximization. 10
Market clearing in this model implies that the amount of broadcasting falls either absolutely or relatively, or
both. An absolute reduction in broadcasting implies a shortening of the broadcast period. A relative fall in the
amount of broadcasting implies that broadcasters produce output where marginal costs are zero, e.g., re-runs.
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Let the elasticity of broadcasting supplied and consumed with respect to the fraction of broadcast
time devoted to advertising be ´Bi;®i ´ B 0 i Bi ®i .
Then (20) becomes
Pi ¢ Bi ¢ (1 + ´Pi;Ai + ´Pi;Ai ¢ ´Bi;®i + ´Bi;®i ) = C 0 i ¢ B 0 i (21)
Finally, multiplying both sides by ®i=Bi, we ¯nd:
®i ¢ P ¢ (1 + ´Pi;Ai + ´Pi;Ai ¢ ´Bi;®i + ´Bi;®i ) = C 0 i ¢ B 0 i ¢ ®i Bi (22)
so that ¯rm i's pro¯t-maximizing share of broadcasting devoted to advertising, ® ¤ i , satis¯es:
® ¤ i ¢ P(® ¤ i ¢ B(® ¤ i )) = 1 ´ ¡1 Bi;®i (1 + ´Pi;Ai + ´Pi;Ai ¢ ´Bi;®i + ´Bi;®i ) C 0 (B(® ¤ i )) (23)
Inspection of (23) reveals that the e®ective price of a unit of broadcasting (®i ¢ Pi) is optimally set
equal to a markup (the fraction on RHS of (23)) over marginal cost. Alternatively, the average
revenue from a unit of broadcasting is a markup over marginal cost. In subsequent sections,
this expression will be used to assess the impact of market concentration (the level of m) on a
broadcaster's optimal advertising share.
IV Concentration and Broadcast Behavior
We now characterize the manner in which broadcast ¯rms optimally adjust the fraction of broad-
cast time devoted to advertising as the number of ¯rms in the industry changes. The discussion
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in this section is conducted in a partial equilibrium framework, and consideration of indirect,
secondary e®ects of consolidation among broadcast ¯rms is evaluated in a subsequent section.
The results of the analysis are presented graphically in Figure 1. From condition (23), it is
apparent that the impact of concentration on ® ¤ i depends upon the values of the elasticities. For
this reason, the elasticity values are marked on the axes of Figure 1.
A The Case of Strong Switching-O®
To begin our analysis of broadcasters' behavioral response to a change in the number of ¯rms,
we ¯rst describe the e®ect of ®i (the fraction of broadcast time devoted to advertising) on
the average revenue from a unit of broadcasting (i.e., ®iPi on the left hand side of (23)). In
this model, the impact of variations in ®i on average revenues is fundamentally tied to the
behavior of consumers, as captured by the value of ´Bi;®i . If the response of broadcast demand
to advertising's share is relatively strong, i.e., ´Bi;®i < ¡1, we say that consumers are engaging
in strong switching-o®. In Figure 1, this case corresponds to the unshaded area to the left of the
vertical line intersecting the horizontal axis at -1. Given that @(®iPi)=@®i = 1 +´Pi;Ai (1 +´Bi;®i )
and, per (16), ´Pi;Ai < 0, when consumers engage in strong switching-o® the left hand side of
(23) is rising in ®i since @(®iPi)=@®i > 0. An increase in the fraction of broadcasting devoted
to advertising increases the average revenue from a unit of broadcasting. Note that when strong
switching-o® occurs, an increase in ®i is associated with a decrease in the level of advertising
since @Ai=@®i = Bi(1 + ´Bi;®i ) < 0.
When ´Bi;®i is less than one, the markup term in (23) is positive if
1 + ´Pi;Ai + ´Pi;Ai ¢ ´Bi;®i + ´Bi;®i < 0 (24)
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It can be shown that when (24) holds, ´Pi;Ai > ¡1. Thus, in the case of strong switching-o®,
pro¯t-maximizing behavior by an individual broadcaster entails positive values of ®i and Pi when
the elasticity of price with respect to advertising volume is greater than negative one but less
than zero. This condition ensures that the model's predictions are sensible. Hence, the leftmost
shaded region of Figure 1 is the region of elasticity values such that markups are negative (in the
strong switching-o® case), while the non-shaded region immediately above this area corresponds
to the set of elasticities which generate an economically meaningful result (i.e., non-negative
mark-ups).
From (16), we can see that if the e®ect of an individual advertiser's production on the ag-
gregate advertising bundle is negligible, the elasticity of price with respect to an individual
advertiser's supply is a function of the elasticity parameter:
´Pi;Ai = @ ln Pi @ ln Ai = ¡(1=¾): (25)
If the number of broadcasting ¯rms falls due to consolidation, since g 0 > 0, ¾ falls and the
elasticity of price with respect to advertising supply becomes more negative. Inspection of (23)
will con¯rm that any given broadcast ¯rm will optimally increase its markup in response to this
fall in the elasticity of substitution. 11 An increase in ® ¤ i is clearly the pro¯t-maximizing response
to consolidation since such an increase will: (1) increase the average revenue from a unit of
broadcasting (the left hand side of (23)), and, (2) reduce the marginal cost of broadcasting (this
follows from the combination of switching-o® behavior and the assumption of increasing marginal
11 This observation follows if ´Bi;®i does not endogenously respond to ¾. As discussed above, this assumption
will be made for this section and will be loosened in the subsequent section.
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costs).
Thus, our model predicts that under strong switching-o®, consolidation of the broadcast
industry will induce a larger share of broadcasting devoted to advertising, a fall in the amount of
advertising supplied, and a fall in the amount of broadcasting consumed. We refer to this result
as crowding-out. The elasticity values that generate this outcome are identi¯ed in Figure 1.
B The Case of Weak Switching O®
Next, we determine the generality of the result described above by analyzing the e®ect of broad-
cast industry consolidation when the demand for broadcasting responds to ®i in a weaker manner:
¡1 < ´Bi;®i < 0. We refer to this as the case in which consumers engage in weak switching-o®.
In this case, the level of advertising rises with ®i. Inspection of (24) con¯rms that under weak
switching-o®, the pro¯t-maximizing values of Pi and ®i will be positive only when ´Pi;Ai < ¡1.
The range of elasticities which produce economically meaningful results in the case of weak
switching o® are contained in the rightmost non-shaded region of Figure 1.
In the case of weak switching-o®, the broadcaster's average revenue (the left hand side of
(23)) is rising in ®i only when ´Pi;Ai < ¡(1 + ´Bi;®i ) ¡1 . The right-hand side of this inequality
is depicted as a dashed curve in Figure 1. Provided this condition holds, the crowding out
of N associated with consolidation in the case of strong switching o® continues to emerge in
the case of weak switching o®. Consolidation still induces larger markups of average revenue
over marginal cost; markups that are attained by an increase in the fraction of broadcast time
devoted to advertising. The region below the dashed curve in Figure 1 identi¯es the elasticities
that generate this result.
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19
The e®ects of consolidation on broadcaster behavior are ambiguous when ´Pi;Ai > ¡(1 +
´Bi;®i ) ¡1 . In this case, average revenue declines as ®i increases. As a result, the rising markups
associated with increased concentration in the broadcast industry will require a reduction in ® ¤ i
and a crowding-in of non-advertising broadcasting, provided the average-revenue e®ect of a fall
in ® ¤ i is greater than the the marginal cost e®ect of such a reduction. This particular result
emerges only when ¡1 < ´Bi;®i < 0 and ¡1 > ´Pi;Ai > ¡(1 + ´Bi;®i ) ¡1 and corresponds to the
region above the dashed curve in Figure 1.
In sum, the behavioral impact of an alteration in the number of broadcast ¯rms depends
on a range of elasticity values associated with consumer and advertiser behavior. Inspection of
Figure 1 con¯rms that, if all elasticities in the relevant range are equally likely, crowding-out
will be the most frequent outcome. Note that there is an unbounded region of elasticities for
which the model predicts an inverse relationship between the number of broadcast ¯rms and
the pro¯t-maximizing fraction of broadcast time devoted to advertising. In contrast, since the
region above the dashed curve is asymptotically bounded, a direct relationship between these
two variables is the least likely prediction of the model.
V Welfare and Consolidation
As noted above, our model does not admit a simple closed-form solution. In order to assess the
general equilibrium and consumer welfare impact of variations in the number of broadcast ¯rms,
we utilize numerical solution techniques. To do so, we must ¯rst supply speci¯c functional forms
for the set of key relationships in the model.
We begin with the consumer utility function. We employ a function that is quasi-linear in
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20
the consumption of the advertised good and non-advertising broadcasting:
U = Q + ° ° ¡ 1
m
X i=1 N °¡1 ° i (26) where ° > 1. The parameter ° captures the curvature of the utility function with respect to
each broadcaster's non-advertising content.
We also assume exponential cost functions for the representative advertiser and the m broad-
casters:
CQ = KQQ ¹Q (27)
Ci = KBB ¹B i (28)
where ¹Q; ¹B > 1 and KQ; KB > 0. These cost functions were initially introduced in (12) and
(18). Both (27) and (28) are consistent with positive and rising marginal costs of production
for all ¯rms. Finally, we specify a functional form for g, the mapping from the number of ¯rms
to the inverse of the elasticity of price with respect to a given advertiser's production level. We
choose a linear function:
¾ = ¹¾m ¡ K¾ (29)
with ¹¾ > 0 and K¾ > 0.
Having established a full set of functional forms, we calibrated the exogenous variables to
produce a baseline set of results that seem intuitively plausible. These parameter values are
listed in Table 1.
The ¯rst step in the simulations is to employ the ¯rst-order conditions from the consumer's
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21
problem (7) and the functional form for consumer utility (26) to derive an explicit expression for
consumer broadcast demand. This expression is provided in the Appendix. Consumer broadcast
demand is then combined with the expression for advertiser's demand (16) and the cost function
(28) to arrive at a pro¯t function for broadcasters. Maximization of this function with respect
to the fraction of broadcast time devoted to advertising, ®i, is carried out numerically.
Simultaneously, the market-clearing price of goods is determined. The ¯rst-order condition
(14) is combined with advertiser's cost function (27) to arrive at an expression for goods supply.
This expression is presented in the Appendix. The consumer's goods demand can easily be
derived from the budget constraint and the expression for broadcast demand. Equating goods
demand to goods supply yields a market clearing condition which is non-linear in the price of
goods, PQ. In addition, in the symmetric equilibrium in which all broadcast ¯rms adhere to (19)
the advertising aggregator (11) implies that ~ A = Ai .
This condition, the broadcaster's ¯rst-order condition, and the market clearing goods mar-
ket condition represent three non-linear expressions in three unknowns: ®i; PQ, and ~ A. These
three expressions are simultaneously solved and the remainder of the endogenous variables are
calculated from the relationships and identities described in Section III. 12 The solution values
are calculated for each value of m in the interval [20; 30]. The results of this approach are pre-
sented in Table 2. We identify the twenty-four ¯rm case as a baseline. The table presents prices,
quantities, and consumer utility (the last seven columns) as a percentage of the baseline case. 13
The ¯rst three columns represent unaltered values of the respective variable.
The numerical general equilibrium results reported in Table 2 do not contradict the partial-
12 The solution is obtained via the fsolve routine in Maple 7.00
13 Note that quantities in this table are industry totals.
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22
equilibrium predictions in Section IV. In the twenty-four ¯rm baseline, the model predicts that
broadcasters devote 33% of broadcast time to advertising. When twenty ¯rms operate in the
broadcast market, this ratio rises to 42%. The switching-o® e®ect of this higher advertising
ratio is evident in the fourth column of the table, where total broadcasting in the twenty ¯rm
equilibrium is 25% lower than the baseline case. Simultaneously, in the twenty ¯rm equilib-
rium, total non-advertising broadcasting is 35% below baseline due to the joint switching-o® and
crowding-out e®ects.
Although broadcasters devote a larger share of their output to advertising in the twenty
¯rm case, the switching-o® e®ect implies these ¯rms are essentially creating a larger advertising
slice from a shrinking broadcasting pie. The net result is a 7% decline of the total volume of
advertising when the pool of broadcast ¯rms shrinks from twenty-four to twenty. As indicated
in the eighth column of the table, the relative scarcity of advertising in this situation leads to a
8% increase in advertising relative to the baseline. In column eight, we see that advertisers pass
along this price increase in the form of a 7% increase in goods prices.
Along with this increase in the price of the advertised good Q, there is a simultaneous
17% increase in consumption of this good. This is largely a result of the increase in ®i; as
described above this increase boosts the price of non-advertising broadcasting for consumers.
The income and substitution e®ects associated with the increase in ®i induces consumers to
shift their expenditures away from broadcasters and towards advertisers. While this behavioral
change might mitigate some of the impact of consolidation on consumer welfare, the net result of
the higher prices and lower quantities in the twenty ¯rm equilibrium is a 10% decline in utility.
In contrast to the twenty ¯rm equilibrium, the thirty ¯rm equilibrium displays the opposite
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23
pattern relative to the baseline. A broadcast sector populated by thirty ¯rms displays a lower
fraction of broadcast time devoted to advertising (30%) and higher quantities of broadcasting,
advertising, and non-advertising broadcasting. The quantity of goods purchased decreases in
the thirty ¯rm equilibrium as consumers shift their expenditures towards broadcasters and away
from advertisers. Prices are also lower in the thirty ¯rm equilibrium. The net result of the
more competitive equilibrium is increased consumer welfare: utility increases by 8% relative to
baseline.
The numerical results reported in Table 2 suggest there is a positive relationship between
the number of ¯rms in the broadcast industry and consumer welfare. These results also reveal
a diminishing marginal impact of the number of ¯rms on consumer utility. A drop of four ¯rms
from the baseline induces an 10% decrease in U while an increase of six ¯rms from the baseline
increases U by just 8%. This diminishing impact of m repeats itself across the quantities in
columns (4) - (7) and the prices in columns (8) and (9). Thus, this model also predicts a
diminishing marginal welfare impact of competition.
VI Conclusion
This paper presents a positive model in which the interaction of broadcasters, advertisers, and
consumers determines the level of non-advertising broadcast content. The model illustrates the
e®ect of market concentration on the broadcast industry's decision to supply non-advertising
content. We demonstrated that the pro¯t-maximizing response of broadcasters to increasing
concentration depends, in part, upon the behavioral response of consumers to a change in the
fraction of broadcast time devoted to advertising.
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24
In the ¯rst two cases we examined, the broadcaster's pro¯t-maximizing response to increas-
ing industry concentration was to increase the fraction of broadcasting devoted to advertising.
Depending on the precise behavioral response of consumers (captured by a range of elasticities),
we found an increase in the fraction of broadcast time devoted to advertising led to a fall (rise)
in the overall amount of advertising and an increase (decrease) in the price of a unit of advertis-
ing. In both of these cases, we found a reduction in the amount of non-advertising broadcasting
consumed. In the third outcome we explored, we found that an increase in concentration results
in a reduction of the fraction of broadcast time devoted to advertising, and a crowding-in of
non-advertising broadcasting.
This paper also presented the model's welfare predictions. Speci¯cally, to the extent increased
concentration in broadcast media does result in higher goods prices and the crowding out of non-
advertising broadcasting, welfare losses for consumers may obtain. Empirical work that estimates
the values of the key parameters would suggest which of the model's predictions are most relevant,
as well as shed light on the robustness of our numerical general equilibrium evidence. Finally,
a fully general equilibrium version of the model, in which the merger activity of ¯rms is more
explicitly treated, would prove a welcome extension of the current framework.
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25
VII Appendix
The ¯rst component to the numerical analysis contained in Section V is an expression for the
consumer's demand for an individual ¯rm's broadcast. Employing the LaGrangian (2) and the
utility function (26), the demand expression is:
Bi = µ PQ w ¶
°
(1 ¡ ®i) °¡1 : (30)
This expression can be derived from the from the ¯rst-order condition with respect to broadcast-
ing (Bi).
Moreover, if we combine (13) and (14) and then apply the aggregators (11) and (15) we
obtain:
P = ¯¹QKQQ ¹Q ~ A ¡1 : (31)
If (14) is combined by itself with the aggregators (11) and (15) we ¯nd a supply function for the
quantity of advertised goods:
Q = P ~ A
1¡¯
PQ¯ : (32)
When (31) is combined with (32) we obtain a mapping from the price of goods and the aggregate
advertising bundle to the aggregate price of advertising:
P = ¯(¹QK)
1
1¡¹ Q P
¡¹ Q
1¡¹ Q
Q ~ A
¡ (1¡¹ Q (1¡¯))
1¡¹ Q : (33)
When this expression is then combined with (30), (28) and the identities from Section II we
obtain broadcaster's pro¯ts as a function of three unknowns: ®i; PQ and ~ A. The ¯rst-order
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26
condition associated with maximization of these pro¯ts is the ¯rst equation in our system.
In order to determine the equilibrium value of the price of goods, the demand for Q is derived
from the broadcast demand expression (30) and the consumer's budget constraint. The resulting
expression is:
Q = Y PQ ¡ w 1¡° P ° Q m(1 ¡ ®i) (34)
When this expression is combined with (32) we obtain a marking-clearing condition which de-
termines PQ. This is the second equation in our system. Once combined with (33) the only
unknowns in this expression are PQ and ~ A.
The ¯nal equation in our system is the equality between the aggregate bundle of advertising
and individual advertising levels in the symmetric equilibrium, ~ A = Ai. Combining this equality
with (30) we obtain an expression whose unknowns are ®i; PQ and ~ A. Given these three unknowns
and the three non-linear relationships outlined above, we employ the fsolve routine in Maple 7.00
to solve for the numerical value of our unknowns. Our ¯rst pass occurs with an assumption of
twenty ¯rms.
The remaining endogenous variables are then calculated from identities and other relation-
ships. Once the value of all the endogenous variables has been calculated, a loop is executed in
which the number of ¯rms is increased incrementally by one. The fsolve routine is called again,
the equilibrium is calculated, and the loop repeats until the ¯rm number reaches thirty.
25
27
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29
Table 1: Parameter Values
w 25 KB .75
Y 10,000 K¾ 4.95
¯ .75 ¹Q 2
° 3.75 ¹B 2
KQ .75 ¹¾ .025
Table 2: Numerical Welfare Results
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Relative to Baseline
m ¾ ® ¤ i B A N Q P PQ U
20 1.050 0.417 0.746 0.935 0.652 1.168 1.085 1.072 0.897
21 1.075 0.381 0.836 0.956 0.776 1.115 1.041 1.043 0.934
22 1.100 0.359 0.902 0.972 0.868 1.071 1.020 1.025 0.961
23 1.125 0.344 0.955 0.986 0.940 1.033 1.008 1.011 0.982
24 1.150 0.333 1.000 1.000 1.000 1.000 1.000 1.000 1.000
25 1.175 0.325 1.039 1.014 1.052 0.970 0.995 0.990 1.016
26 1.200 0.319 1.074 1.027 1.097 0.944 0.990 0.982 1.030
27 1.225 0.314 1.105 1.040 1.138 0.919 0.987 0.974 1.043
28 1.250 0.310 1.134 1.053 1.174 0.896 0.985 0.967 1.055
29 1.275 0.306 1.161 1.066 1.208 0.874 0.983 0.961 1.067
30 1.300 0.303 1.186 1.078 1.239 0.854 0.981 0.954 1.078
28
30
Figure 1: Results
´B; ®i
´P; Ai ´P; Ai
-1
-1
²Strong Switching O®
²Crowding Out
²Weak
Switching
O®
²Crowding
In??
²Weak
Switching
O®
²Crowding
Out
Negative Markup
Negative Markup
¡(1 + ´B; ®i ) ¡1
29
31