Download Two%Sided Markets with a Negative Network Effect: Radio

Two-Sided Markets
with a Negative Network E¤ect:
Radio, Advertisers, and Audiences
Sheila M. Campbelly
Economics Department
Boston College
February 4, 2006
Abstract
Recognizing commercial radio (and advertiser-supported media more
generally) as a two-sided market with a negative network e¤ect presents
a means to evaluate the welfare e¤ects of regulatory and technological
changes. Listeners would prefer to hear fewer advertisements, while advertisers want to reach as many listeners as possible. It is necessary to
consider the actions of all three types of actors to analyze the radio market – individuals who decide what to listen to and what to consume,
…rms that sell goods to individuals and purchase advertising from radio
stations, and radio stations that broadcast programming to attract listeners and sell advertisements to …rms. This rare uni…ed approach provides
a more thorough assessment of the industry’s impact on social welfare.
In this framework, an increase in the number of radio stations – more
competition – does not necessarily improve social welfare. Heightened
competition among radio stations reduces the amount of advertising on
each station, resulting in a lower surplus in the goods market. In general,
the net welfare e¤ect of radio station competition depends on the relative
importance of individuals’listening and consumption choices. In the speci…c case considered here, the market will provide more stations than is
socially optimal when it is costly to broadcast quality programming.
Many thanks are due to Professors Richard Arnott and Frank Gollop for their helpful
comments. All errors are mine.
y Economics Department, Boston College, 140 Commonwealth Ave., Chestnut Hill, MA
02467. E-mail: [email protected]
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1
Introduction
The commercial radio industry in the United States has undergone exceptional
change in the last decade, largely as a result of regulatory reforms. New technologies like digital and satellite radio will require commercial radio to adapt
yet again. The responses of both regulators and broadcasters have a potentially
large e¤ect on social welfare, since the more than 13,800 stations broadcasting
in the U.S. had more than 90% of Americans over the age of 12 tuning in at
least once each week in 2004 (Arbitron 2004). Recognizing the radio industry
as a two-sided market with a negative network e¤ect provides a way to evaluate
the welfare e¤ects of past and proposed regulatory changes and to project how
radio broadcasters might position themselves to compete in the advent of new
alternatives.
In a two-sided market, value can only be created if a …rm sells to two distinct
types of consumers who purchase di¤erent but related goods. Demand by each
customer type depends in part on the other side’s consumption, so that each side
of the market creates a network e¤ect for the other side. Credit card payment
networks are a common example, as they must sell services to both retailers and
consumers. Much of the existing literature on two-sided markets assumes that
they are all like credit cards, where each side of the market generates a positive
network e¤ect for the other side, so that each side’s demand is increasing in the
size of the other group’s customer base, all else equal.
Two-sided markets may also include a negative network e¤ect. The broadcast and print media, and radio in particular, are the primary examples. A
radio station sells to two groups of customers –listeners and advertisers –each
of whose demand depends on the extent of demand on the other side of the market. A larger listening audience creates a positive network e¤ect for advertisers,
who would like to reach as many potential buyers as possible with their commercials. However, when audience members judge advertisements to be a nuisance
(Becker and Murphy 1993, Berno¤ et al. 2003), they will prefer broadcasts that
air fewer commercials, all else equal –the negative network e¤ect.
This paper provides an assessment of commercial radio’s social welfare e¤ects
by examining the industry in the context of two-sided markets. In addition to
the interaction between listener demand and advertiser demand, it also includes
the e¤ects that carry through to the market for consumer goods –the products
featured in the advertisements aired on the radio stations. The existing literatures on two-sided markets, media economics, and the economics of advertising,
treat listeners, advertisers, and radio stations in isolation. The contribution of
this paper is that it uni…es these markets, providing a more complete picture of
agents’interactions and social welfare.
This uni…ed approach that includes all the decision agents –radio stations,
advertisers/goods producers, and listeners/consumers –leads to interesting …ndings on the e¤ects of competition among radio stations. In the symmetric equilibrium developed here, the presence of more radio stations results in fewer
advertisements on each radio station, though this does not necessarily improve
social welfare. More competition may spur stations to improve the quality of
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their broadcasts, which listeners appreciate but is costly for radio stations. The
e¤ects of competition among radio stations carry through to the market for
consumer goods. When there are fewer advertisements to in‡uence consumer
demand, a smaller surplus is generated by the exchange of these products. The
overall e¤ect of increased competition on welfare depends largely on the relative importance of advertising to an individual’s listening and consumption
decisions.
The question of the optimal degree of competition in the market is an important one for the radio industry in the United States.1 There are a limited
number of radio frequencies available in any geographic market, and their usage
is regulated by the Federal Communications Commission. The Telecommunications Act of 1996 relaxed ownership restrictions in radio and other media
markets. Further changes to ownership regulations are now being contested in
the courts. Technology also presses the question of how many outlets are optimal, as the move from analog to digital transmission makes more channels
available to radio broadcasters.
In addition to providing insights on the optimal degree of competition, this
model may, with some extensions, address the question of how …rms in a twosided market with a negative network e¤ect might compete with a one-sided
product market that excludes the side that produces the negative e¤ect. With
dual positive externalities, this would be impossible, since neither side of the
market reaps any bene…t without the other –a credit card is of no use to a consumer if no retailers accept it. In the case of a negative network e¤ect, however,
one group of customers might pay to avoid the others. Some publications are
entirely subscriber-supported. Internet sites like Salon.com and Slashdot.org
o¤er readers a choice between an ad-free paid subscription and viewing advertisements to access content. The emergence of satellite radio and premium cable
TV channels also suggests that there are cases where the customer who produces
the negative network e¤ect may be excluded from the market.
Much of the existing theoretical literature in media economics and two-sided
markets considers only monopoly or duopoly market structures. While this may
be a reasonable …t for some types of two-sided markets, even within the media,
broadcast media markets typically include many more than two …rms.2 Though
there has been a signi…cant concentration of station ownership since passage of
the Telecommunications Act of 1996, there are still many outlets in radio and
television, especially cable television. If advertising-supported Internet sites are
also considered to be two-sided, then the idea of a market dominated by one
or two players appears even less realistic. The model presented here o¤ers the
monopoly case, then generalizes it to allow a large number of …rms.
The following section reviews some of the relevant literature. Section 3
outlines a model of a monopoly broadcaster and monopoly consumer goods
1 Other concerns expressed in discussions of media competition include the degree of local
control of media outlets and the value of a diversity of voices in arriving at the truth (Stucke
and Grunes 2001).
2 Local newspaper markets in the United States are increasingly home to only one or two
papers, so that a monopoly or duopoly market structure seems a reasonable match for them.
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producer to highlight the central problem of a two-sided market. A parameterized version of the model is presented next. Section 5 introduces competition
in both broadcasting and consumer goods markets. The …nal section discusses
extensions and concludes.
2
Literature Review
Three distinct areas o¤er insights into the operations of two-sided markets with
a negative network e¤ect. An emerging literature looks at two-sided markets directly, focusing on the dual positive network e¤ects case. The media economics
literature has tended to present advertising as creating disutility for broadcast
media consumers. Finally, the vast advertising literature, which seeks to understand the e¤ect of advertising on consumer utility, suggests a role for advertising
in the market for consumer goods that two-sided markets and media economics
literature have often ignored.
2.1
Two-Sided Markets
Armstrong (2005) and Rochet and Tirole (2003) provide overviews of the twosided markets literature and reach similar results. Armstrong focuses on twosided markets with dual positive network e¤ects. In a competitive two-sided
market, the platform …rm sets prices for each side of the market so that one
group of customers subsidizes the other’s participation. The subsidized type
is the group of customers that generates a larger network e¤ect for the other
side or has a more elastic demand. The presence of two-sided positive network
e¤ects may either push the industry toward monopoly or push prices down on
both sides of the market as …rms struggle to compete with each other.
Rochet and Tirole reach similar conclusions regarding the cross-subsidization
of the two customer groups. Most markets with any network externalities will be
organized as two- (or more) sided markets unless the two sides of the market are
able to coordinate purchases or agree on a contract for side payments between
the two groups. Rochet and Tirole deem such a bypass of the two-sided market
structure unlikely given the transaction costs involved. If either group faces a
…xed cost to access the two-sided market, a two-sided market structure is even
more likely.
Evans and Schmalensee (2005) point out some of the challenges for antitrust
analysis of two-sided markets. Pricing to one side of the market below the
marginal cost of that side is not necessarily predatory in a two-sided market,
and therefore not a relevant standard by which to judge whether the …rm is
acting in an anticompetitive manner. Instead, the nature of a two-sided market
in and of itself may limit the exercise of market power by the platform …rm, as
gains on one side of the market may be competed away on the other side.
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2.2
Media Economics
Much of the media economics literature points to a negative network e¤ect in
a two-sided market by characterizing advertising as a nuisance to media consumers. This arises most often in work on the broadcast media and, more
recently, the Internet. The print media is often excluded from this characterization because print ads may be more easily avoided and need not interrupt
media consumption. In addition, print ads may convey more information than
TV or radio ads, as they can o¤er more detailed information on the price and
characteristics of the product advertised and provide explicit instructions on
how to contact the seller. Becker and Murphy (1993) suggest that advertising
on TV and especially radio should be considered an annoyance to the audience.
Several recent media economics works characterize advertising as a nuisance.
A common feature is to characterize the pro…t-maximization problem in terms
of viewer-advertisement combinations. That is, prices of advertisements are set
per viewer or listener reached, and demand is in terms of viewer- or listener-ad
minutes. Anderson and Coate (forthcoming) model a TV station’s program and
advertising choice under monopoly and duopoly market structures to …nd the
conditions under which the socially optimal levels of programming and advertising will be provided. They …nd that the market may over- or under-provide
both programming and advertising, depending on how the bene…ts to goods
producers from advertising compare to the nuisance cost to the audience.
Masson, Mudambi, and Reynolds (1990) consider audiences as “factors
of production” that are sold to advertisers. They assume there is one market price of advertising per viewer, and allow broadcasters to di¤er only in the
quantity of advertisements aired. Still, they …nd that the negative e¤ect advertising has on audience size will limit the decline in the price of advertising as
competition increases in the industry.
Cunningham and Alexander (2003) present a media market with an arbitrary
number of …rms with no restriction to monopoly or duopoly cases. The audience
is modeled as a representative consumer, indi¤erent between broadcasters that
devote the same fraction of time to advertising. The level of advertising does not
directly enter an individual’s utility function, but is modeled so that an increase
in advertising raises the opportunity cost of consuming non-ad broadcasting.
2.3
Economics of Advertising
There is a vast literature on the economics of advertising. Bagwell (2005) o¤ers
an extensive survey of the literature, highlighting the leading theoretical and
empirical works of the last century. Bagwell sorts the literature into three camps
o¤ering di¤erent views of the e¤ects of advertising on demand, utility, and social
welfare –the informative, persuasive, and complementary perspectives.
Informative advertising serves to let consumers know information about a
good that enables them to make purchases that better match their true preferences. Advertisements, usually provided by producers free of charge to consumers even though they may be willing to pay for them, transmit information
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about a good – its existence, location, quality, price, or other characteristics.
By lowering search costs for consumers (Butters 1977, Stigler 1961), informative advertising tends to improve social welfare, with the post-advertising utility
function used as a metric.
Persuasive advertising is not generally welfare-improving, and may in fact be
anticompetitive. Braithwaite (1928) di¤erentiates between "true" selling costs
that a producer incurs in order to get its product to consumers and spending
on advertisements that aim only to convince consumers the product is more
valuable than it really is, thereby increasing demand for the product. Persuasive advertising may create brand loyalty or spurious product di¤erentiation,
reducing competition (Kaldor 1950) or erecting barriers to entry (Comanor and
Wilson 1967). Dixit and Norman (1978) …nd advertising may be excessive under a range of market structures, even when ex post utility is used to gauge the
welfare e¤ects.
The complementary school takes issue with the changing tastes that both
the informative and persuasive perspectives assume (Stigler and Becker 1977).
Tastes are instead assumed to be stable, with advertisements changing the prices
of goods and their value to consumers, as utility is measured with respect to
characteristics, not goods. Advertising enters directly into the consumer’s utility function, and more advertising makes goods more valuable to consumers.
Becker and Murphy (1993) adopt this perspective and recognize that advertisers compensate radio and television audiences with programming but do not
fully integrate this into a welfare analysis of advertising.
3
The Problem of a Two-sided Market
Three sets of agents participate in this market. Radio stations broadcast programming, which appeals to listeners, and sell advertisements to goods producers. Advertisers produce and sell consumer goods and purchase advertisements
to encourage listeners to purchase their goods. Listeners enjoy broadcasting that
is interrupted by advertisements and purchase the goods and services advertised
on the radio. Although radio listeners consider advertisements a nuisance, those
same advertisements do in‡uence listeners’consumption decisions.
The game can be broken down into four stages:
1. Stations choose a location based on the distribution of potential listeners
over the market space.
2. Each station decides how many advertisements to o¤er for sale to goods
producers and the quality of the broadcasting it will air.
3. Each goods-producing …rm maximizes pro…ts by simultaneously setting
the price of the consumer good it sells and purchasing advertising time on
radio stations.
4. Listeners decide whether to tune in to the radio or not. An individual
who opts to listen chooses a station by taking into account each station’s
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set of characteristics and the total amount of advertising on each station.
Listeners are also consumers, and base their demand for consumer goods
on the prices of the goods and the set of goods they hear advertised on
their chosen radio station.
This analysis focuses on stages two through four. The …rst stage, where
stations choose their locations, is not modeled here. The case of one radio
station and one consumer goods producer will be most convenient to highlight
the central points of the two-sided market problem. The more interesting (and
arguably more realistic) case of competition in both broadcasting and consumer
goods markets appears in section 4.
3.1
Listeners/Consumers
With only one radio station to choose from in the monopoly case, an individual
decides to listen to the radio only if the net utility from listening exceeds the
reservation utility, which here is set to zero.
The individual knows how much advertising the station airs. This assumption is not especially unrealistic, as listeners are likely to have good expectations
about the amount of advertising on a radio station based on past experience or
on public claims the station makes (Arbitron and Edison Media Research 2005).
Though the advertising an individual hears will in‡uence consumption behavior, the listening choice and consumption choice are modeled separately.
One explanation is that the listening choice is made according to ex ante preferences, before the individual has been exposed to advertising. Consumption
choices, made after the individual has listened to the radio and heard advertisements, are made according to an ex post utility function. An alternative
interpretation is that although listeners know how many ads they will hear
when tuning in to a station, they do not know what products will be advertised. Though this may be unrealistic in the case of a monopoly consumer
goods producer, it will be more compelling when a large number of consumer
goods producers are purchasing advertisements. Either argument ensures that
an individual’s decision to listen may be modeled without including the utility
she will enjoy from consuming the advertised goods.
3.1.1
Listening Demand
The net utility an individual gains from listening depends on the amount of
advertising heard and on how closely that station’s programming matches the
individual’s ideal set of characteristics. With a monopoly radio station, the
choice is between listening and not listening. An individual will choose to listen,
then, if
V = V (q; a; z) > 0
(1)
where q is a measure of the quality of programming aired on the station, a is
the number of advertisements aired on the radio station, and z is the station’s
distance from the individual’s ideal location in characteristics space. V increases
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in q and decreases in both a and z, since both detract from enjoyment of the
broadcasting.
Given V and the distribution of the potential listeners over the characteristics
space, the number of listeners who tune in to the radio station is de…ned as
L = L(q; a)
(2)
with Lq > 0, Lqq < 0, La < 0, Laa > 0. It is assumed there is no time
constraint for listeners. With the population normalized to a size of one, the
number of non-listeners is 1 L(q; a).
3.1.2
Consumption
Both listeners and non-listeners are consumers, though their consumption patterns di¤er a great deal. Utility from listening, considered in the previous section, is separable from utility from consumption. Two types of consumer goods
are available – the advertised good, x, and all other goods, which here are
condensed into a numeraire good x0 that is provided competitively. The nonlisteners purchase only the numeraire good, while listeners purchase a mix of
the advertised and the numeraire good.
Firms choose to advertise in the expectation that advertising will increase
demand for their products. If this advertising is informative or complementary,
it also has the potential to improve consumer surplus and welfare. Advertising
may instead be distortionary, diverting demand by warping a consumer’s perceived utility to di¤er from his true utility. Bagwell (2005) discusses these cases
in an extensive review of the advertising literature.
Advertising enters the consumer’s perceived utility function in such a way
that more advertising leads to more demand for the advertised good. How advertising does this –whether by better informing the consumer or by distorting
preferences – will eventually be important for social welfare, but is immaterial
at this point. The representative listener’s consumption decision is summarized
as:
max
U
0
x ;x
= U (x0 ; u(x; a)) = x0 + u(x; a)
subject to x0 + px
(3)
I
This money-metric utility function produces no income e¤ects. The resulting
demand function for good x depends on the price of the good, p, and a, the
amount of advertising for the good that the listener hears. Price and advertising
are assumed to in‡uence demand in the following ways, with subscripts denoting
partial derivatives:
x = x(p; a)
xp < 0; xpp 0
xa > 0; xaa < 0
xpa = xap < 0
8
(4)
Individuals who choose not to listen to the radio station also purchase consumer goods. Since they have not heard any advertisements, however, their
purchases are restricted to the numeraire good, x0 . Non-listeners, then, spend
all their income on the numeraire good.
3.2
Advertisers
The goods producer maximizes its pro…ts by jointly setting the price of its good
and choosing how much advertising to purchase. The pro…t function of the
producer of the advertised consumer good di¤ers from the traditional expression
in two fundamental ways. The total quantity of goods the producer sells is
L(q; a)x(p; a), or the number of listeners who hear the advertisement times the
demand by a representative listener. There are two components to the …rm’s
costs –the traditional production costs, C(Lx), and the cost of advertising –the
number of ads, a, times the price charged by the radio station, r. The marginal
cost of production is constant or increasing. The advertiser’s objective is to set
a price and purchase advertisements to maximize pro…ts:
max
= pL(q; a)x(p; a)
p;a
C(L(q; a); x(p; a))
ra
(5)
The advertiser’s …rst-order conditions implicitly de…ne the optimal price and
advertising combination.
p
C0
p
ra
pLx
=
=
x
1
=
pxp
"x:p
p C0
("x:a + "L:a )
("x:a + "L:a ) =
p
"x:p
(6)
(7)
The …rst-order condition for price (6) is the standard pro…t-maximization
condition for a monopolist. In (7), the …rst-order condition for advertisements,
the expression ("x:a + "L:a ) is the elasticity of total demand (Lx) for the advertised good. This term is positive, as it corresponds to the …rm choosing to
operate and advertise such that total demand is increasing in advertising, where
@(Lx)
@a > 0.
While the …rst-order conditions will determine the optimal solution to the
advertiser’s problem –the pro…t-maximizing levels of p and a to choose –comparative statics show how the advertiser will respond to changes in the radio
ln g
station’s pricing of advertisements. Let bgb = dd ln
h and de…ne
h
D
"C 0 :Lx "x:p (1 "x:p ) 2"x:p "xp :p
h
i
2
"x:a "xa :a + "L:a "L0 :a + 2"C 0 :Lx (1 "x:p ) ("x:a + "L:a )
"x:p "x:a
"xp :a
"C 0 :Lx (1
"x:p ) ("x:a + "L:a )
2
According to second-order conditions, D > 0.3
3 Under
the assumption that second-order terms are relatively small, the second-order con-
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As a result,
pb
rb
b
a
rb
("x:a + "L:a ) "x:a
=
=
"xp :a
("x:a + "L:a ) "C 0 :Lx "x:p (1
D
"C 0 :Lx (1 "x:p ) ("x:a + "L:a )
< 0 (8)
D
"x:p ) 2"x:p "xp :p
<0
(9)
Both expressions are negative with the assumption that second-order elasticities
("xp :a and "xp :p ) are small in absolute terms and therefore do not dominate.
Starting with (9), an increase in r, the price of advertising, prompts …rms to
reduce their ad purchases, all else equal, much as one would expect. The price
of advertising also has a negative e¤ect on price in (8), even though advertising
is a factor of production for the goods producer, and an increase in a factor price
would generally cause an increase in the price of the good. Here, advertising also
has another role, as a driver of demand. With the increase in r causing a drop
in advertising, the per-listener demand x falls. Though some gain in listeners
should be expected with the lower advertising level, this drop in advertising
would bring about lower total sales for the good since ("x:a + "L:a ) > 0. The
pro…t-maximizing goods producer will try to stem some of the sales losses from
the drop in advertising by cutting the price of the good.
3.3
Radio Stations
Radio stations maximize pro…ts over the two sides of the market – listeners
and advertisers. They raise revenues by selling advertisements to the consumer
goods producer. These same advertisements make the station less attractive to
listeners. As listeners turn o¤ the station, demand for advertising decreases,
taking a bite out of radio station revenues. This balancing act between the two
groups highlights the two-sided nature of the radio station’s pro…t maximization
problem.
It is costly for the radio station to broadcast. It must incur costs to build the
station and the technology necessary to broadcast the radio signal. FCC licenses
to broadcast are costly to acquire, with the cost varying with the type of signal
(AM or FM) and its strength. In addition, there are ongoing costs to broadcast
ditions for pro…t maximization are satis…ed so that the …rst-order conditions describe a unique
local interior local maximum:
@2
@p2
=
p
C 0 Lxpp + 2Lxp
@2
@a2
=
p
C 0 (Lxaa + 2La xa + Laa x)
C 00 (Lxp )2 < 0
C 00 (Lxa + La x)2 < 0
The Hessian is negative de…nite, as its determinant may be reduced to
h
i
p C 0 xpp + 2xp C 00 L (xp )2
p C 0 (Laa x + 2La xa + Lxaa )
C 00
p
C 0 xpp + 2xp (La x + Lxa )2 > 0
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programming and to get listeners to tune in to the station – labor costs for
on-air and technical sta¤, promotional materials to make the community aware
of the station, licensing fees to musicians and other content providers, and the
power to fuel the radio signal.
Though radio stations have high …xed costs, they still have an interesting
pro…t maximization problem to consider.4 Higher quality programming will
lead to higher costs for the radio station, as it recruits more talented and more
costly on-air sta¤, o¤ers more tempting promotions, and improves the strength
and clarity of its broadcasting signal. Quality helps to draw listeners, and more
listeners boost the producer’s demand for revenue-producing advertisements.
The amount of advertising should have no e¤ect on radio station costs. A
station needs the same licenses, towers, etc., to broadcast either advertisements
or programs. Programming costs will feel little, if any, e¤ect from advertisements, so that the marginal cost of advertising is assumed to be zero.
The radio station is a quantity setter. It is not practical to think of a station
setting a price and then selling all the advertisements the market desires at
that price. Practices in the radio industry (and in broadcasting more generally)
suggest that stations set quantities rather than prices. Clear Channel, owner of
more than 1,200 radio stations in the United States, announced in July 2004 that
it would cut back on advertising minutes at its stations in a bid to improve their
performance (Ives 2004).5 In the previous section, the goods producer chose the
level of advertising that would maximize its pro…ts. The solution for a implied
by (6) and (7) can be transformed into an inverse demand function r(L(q; a); a)
that indicates the goods producer’s willingness to pay for advertising given the
number of listeners on a station and the number of advertisements it airs. The
radio station takes this as given in its own pro…t-maximization problem
max
q;a
RS
= r(L(q; a); a)a
F (q)
(10)
This leads to …rst-order conditions that express the familiar monopoly result for
the optimal markup over marginal cost:
(rL La + ra ) a + r
rL Lq a Fq
= 0
= 0
(11)
(12)
Combining the …rst-order conditions for advertising and quality shows that the
radio station chooses a quality level and an advertising level such that the price
of advertisements is equal to the marginal cost of quality times the rate at which
advertisers are willing to trade o¤ broadcasting quality for advertising quantity
– the two variables that in‡uence the number of listeners who will be exposed
4 This paper takes up the question of pro…t maximization for a radio station after it has
decided to enter the market. Fixed costs that would be important to entry decisions are
therefore ignored.
5 The announcement makes no mention of corresponding increases in the price of advertisements, though it is di¢ cult to imagine why a pro…t-maximizing …rm would restrict quantity
without expecting a rise in prices.
11
to an advertisement on a station:
r=
rL La + ra
Fq
rL Lq
(13)
The market for advertising clears in equilibrium. The demand for advertising by
goods producers, summarized in the expression for barb in (9), equals the quantity
of advertising supplied by the radio station according to its …rst-order conditions
(11) and (12).
4
Parameterized Model
The general model above describes how the agents on each side of the radio
market optimize. In particular, it gives insight into how a change in the price
of a radio advertisement will a¤ect the market for consumer goods. It will not,
however, allow welfare comparisons. In order to obtain a better understanding
of the welfare e¤ects of the radio industry, it is necessary to adopt a more
parameterized speci…cation of the model.
4.1
Listeners
The radio station chooses a location at any point along a circle of circumference
one. Each point on the circle can be denoted by z. Potential listeners/consumers
are distributed uniformly around the circle. Without loss of generality, then,
the monopoly station may choose to locate at a point zRS = 0 on the circle. A
listener located at point z then faces a distance of z from her ideal location. If
an individual tunes in the radio, the utility from listening is
V (q; a; z) = q
a
(zRS
z)2
(14)
Assuming a reservation utility of 0, the individual will only tune in if listening
generates positive utility, if V > 0. As a result, individuals located within the
range
1
q
a 2
jzj <
will listen, producing a total audience for the radio station of size
L(q; a) = 2
q
a
1
2
(15)
As discussed in section 3.1.1, higher quality programming will draw more listeners, while more advertisements will shrink the listening audience.
4.2
Consumers
An individual who chooses to listen to the radio hears all a advertisements, and
therefore makes consumption choices based on an ex post utility as described in
12
section 3.1. In the decision of whether to listen or not, an individual does not
consider which advertisements the radio station airs or how those advertisements
will in‡uence consumption behavior. Once an individual has tuned in to the
radio, however, the advertisements heard in‡uence the choice of consumer goods
when maximizing utility
U = x0 + (xa )
(16)
subject to the budget constraint
x0 + px
I
(17)
This produces a demand function for the advertised consumer good that is not
unfamiliar
1
1
a
(18)
x(p; a) =
p
Both the price-elasticity of demand and the advertising-elasticity of demand for
the advertised consumer good are constant in this case:
"
"x:p =
"x:a =
1
1
1
>1
(19)
1
(20)
To simplify notation, de…ne an intermediate parameter
k=(
"
)
and rewrite (18) as
x(p; a) = ka p
4.3
"
(21)
Consumer goods producer
The consumer goods producer sets the price of the good and chooses how much
advertising to purchase from the radio station. The marginal cost to produce
the good is non-decreasing according to the cost function:
C(Lx)
=
(Lx)'+1
'+1
> 0; ' 0
(22)
The goods producer knows that the radio station has L(q; a) listeners from (15)
and that advertising on the radio station will generate demand for its good of
x(p; a) from (18) by each of those listeners. Keeping these in mind, the goods
producer maximizes pro…t
max
= pLx
'+1
13
(Lx)'+1
ra
(23)
The …rst-order conditions for pro…t maximization, corresponding to (6) and (7),
are
[p
(Lx)' ] xp + x = 0
(Lx)' ] (Lxa + La x) = r
[p
(24)
(25)
Using (21), the …rst-order conditions reduce to
p
r
'
=
=
1
1+"'
(kLa )
(26)
1 "
1+"'
1
"
1+'
(ka ) 1+"' L
'(1 ")
1+"'
L
a
2
L
(27)
Since the number of listeners, L, is a function of both the quality of the broadcast
and the amount of advertising on the radio station, both p and r, the inverse
demand for advertising, are in terms of q and a.
Using the intermediate parameter g, de…ned as
"
g
k
;
in the special case of a constant marginal cost of production of
…rst-order conditions reduce to:
p
=
r
=
(' = 0), the
(28)
g
L
a
a
2
L
(29)
The goods producer takes advantage of its market power to set the price of the
good above its marginal cost of production. With a constant marginal cost,
the pro…t-maximizing price of the consumer good is de…ned entirely in terms
of parameters. The …rst-order conditions implicitly de…ne the demand for
advertising, a, in terms of r and q, since the total number of listeners to the
station, L, is a function of the quality of programming, q, and the amount of
advertising, a (see (15)). The expression in (29) shows the goods producer’s
willingness to pay for advertising on the radio station is increasing in the number
of listeners to the station and decreasing in the number of advertisements.
4.4
Radio Station
The radio station maximizes pro…t by setting the quality of its programming
and the amount of advertising to air. The station’s costs, F (q), are increasing
in quality. The marginal cost of quality is also increasing, as increases in signal
strength or the improvements in the quality of on-air sta¤ are likely to grow
ever more expensive:
F (q) = q 2
(30)
14
As in (10), the radio station’s objective is to
q2
(31)
= 0
= 0
(32)
(33)
max r(L(q; a); a)a
q;a
leading to …rst-order conditions,
(ra + rL La )a + r
rL Lq a 2 q
which, in the constant marginal cost of production case described in (28) and
(29), result in
2
L
a
4.5
2 (1 + 2 )
4 2
2 L3
L
g
2
4
a
+ 2 3
La
L
=
0
(34)
=
2 q
(35)
Social Welfare
The social welfare produced in this two-sided market is a combination of the
listener and consumer surpluses and the pro…ts of the goods producers and radio
stations.
SWM ON = (1
L)CSN L + L(V + !CSL ) +
GP
+
RS
(36)
Utility from listening to the radio is measured as V , or the average utility across
all the individuals tuning in to the radio station. Non-listeners consume only the
numeraire good (see section 3.1.2). Assuming that good is sold competitively
according to its constant marginal cost, it produces no consumer surplus for the
non-listener and zero pro…t for the goods producer. This allows the non-listener
term to fall out. Taking into account the components of pro…t and consumer
surplus, social welfare reduces to
SWM ON = L(V + !U )
C(Lx)
F (q)
(37)
The parameter !, 0 < ! < 1, indicates how closely the listener’s perceived utility
from consumption matches the true utility – recall the discussion from section
3.1. For ! closer to 1, the advertising may be considered more informative and
less distortionary.
5
Multiple Radio Stations
Transforming the model to accommodate multiple radio stations requires some
revision of notation, though the general structure is maintained. The subscript
i denotes the radio station, while the relevant consumer goods producer appears
J
P
in the superscript j. In addition, Ai =
aji , or the total amount of advertising
j=1
on station i by all J of the goods producers.
15
5.1
Listener Demand
Individuals choose whether to listen to the radio or not much as before, but
may now choose between several radio stations that compete in the quality of
their programming and in the amount of advertising they air. Listeners opt for
the station that generates the largest utility, described as
Vi = q i
Ai
zi )2
(z
(38)
All individuals are assumed to listen to one radio station. With listeners distributed uniformly around the unit circle, the radio stations locate at equal
distances around the circle. With M stations, each one is located at a distance
1
from its neighbors. This symmetry results in listeners tuning in to each
of M
station according to the demand function
Li =
5.2
M
1
+
[qi
M
qi+1
(Ai
Ai+1 )]
(39)
Consumer Demand
As in the monopoly case, listeners’ preferences over consumption goods are
in‡uenced by the advertisements they hear on the radio. Non-listeners again
limit their consumption solely to the numeraire good since they do not hear any
advertisements. Notation has changed slightly, according to the following:
x0i
xji
= consumption of numeraire good by station i listener
= consumption of good j by station i listener
aji
Ui
= number of ads for good j on station i
= utility from consumption by a listener to station i
Listeners may consume the numeraire good as well as a set of J di¤erentiated products. Dixit-Stiglitz preferences over the di¤erentiated products are
modi…ed to account for the e¤ect of advertising. A listener to station i, then,
seeks to
2
3
J
X
5
max Ui = x0i + 4
xji aji
(40)
x0i ;xji
j=1
subject to the budget constraint
x0i +
J
X
pj xji
I
(41)
j=1
Notice that (40) is identical to the utility speci…cation in the monopoly case
in (16) when J = 1. Utility functions for listeners are symmetric, so that the
objective function of a listener to station 1 has the same structure as that of a
listener to station 2.
16
Assuming that = , so that demand for each of the J goods is independent
of demand for the other advertised goods, the utility-maximizing consumer who
listens to station i will demand each of the goods she hears advertised on the
radio in the amounts
2
311
j
ai
"
6
7
= k aji
pj
(42)
xji = 4
5
pj
5.3
Advertisers/Goods producers
Advertisers seek to maximize their pro…ts by setting the price of the goods
they sell and choosing the level of advertising to purchase. Each advertiser
or goods producer makes and sells one good, which it may advertise on more
than one radio station. The market for consumer goods is characterized by
monopolistic competition along the lines of Dixit-Stiglitz. Goods producers
know how consumers respond to the prices they charge and the advertising
they broadcast on the radio stations –they know (42).
With a constant marginal cost of production , as in section 4.3, the producer
of good j aims to
maxj
j
= (pj
)
pj ;ai
M
X
Li xji
i=1
M
X
ri aji
(43)
i=1
Two related assumptions are made about how the goods producers or advertisers operate. First, there is no strategic interaction between the goods
producers in setting prices or advertising demand. Second, with many producers of consumer goods (large J), each producer does not internalize the e¤ect of
its own advertisement on listenership at a radio station. That is, the goods proi
ducers take Li as given, believing @L
= 0. The resulting …rst-order conditions
@aj
i
reduce to
pj
=
(44)
"
aji
=
k
1
Li
ri
1
= g
Li
ri
1
1
8i
(45)
Producer j’s demand for advertising on station i is responsive to the number of listeners to the station, Li . If more people tune in to the station, each
producer’s demand for advertising on that station increases. Demand for advertising also depends predictably on the price of advertising.
Each of the J producers of consumer goods has an identical demand for
advertising on station i. As a result, the total demand for advertisement on
any station i is
1
Li 1
Ai = J g
8i
(46)
ri
17
The symmetry built into the consumer’s choice and the goods producers’costs
results in symmetric demand for advertisements from each station. Inverse
demand for advertising is
5.4
1
J
Ai
ri = g
Li
8i
(47)
Radio Stations
Radio stations act simultaneously in setting advertising prices and broadcast
quality given their locations around the circle. Each seeks to maximize pro…ts
by choosing the quality of its broadcasting and the number of advertisements
to sell and air. As before, the radio stations’locations and entry choices have
1
from neighboring
already been made, with M stations each at a distance of M
stations. A radio station i seeks to maximize pro…ts
i
qi2
= r(L(qi ; Ai ); Ai )Ai
(48)
The radio station knows the goods producers’ willingness to pay, or inverse
demand, that results from solving their own pro…t-maximization problem (46).
Unlike the goods producers, the radio station is aware of how the total amount
of advertising Ai in‡uences listening. Using the inverse demand for advertising,
the …rst-order conditions for qi and Ai , respectively, are
@ri @Li
@Li @qi
@ri @Li
@ri
+
+ ri
@Ai
@Li @Ai
Ai
Ai
=
2 qi
(49)
=
0
(50)
Substituting using the inverse demand for ri from (47), the expression for Li
from (39), and Li ’s partial derivatives with respect to Ai and qi gives expressions for Ai , qi , and Li entirely in terms of exogenous parameters. To simplify
notation, de…ne an additional composite parameter
d
Ai
=
qi
=
Li
=
M
g
2
1
;
M
Li =
J1
M2
=
MA =
d
M2
gd
2
8i
8i
J
(51)
1
M1
2
8i
(52)
(53)
Advertising on each station is linear in the number of listeners. For a given
number of listeners, the level of advertising on a station decreases in the number of radio stations. With more competitors, radio stations air fewer advertisements to prevent listeners from defecting to the closer substitutes. With
18
listeners distributed evenly across the number of stations in this symmetric
equilibrium, the number of listeners per station also decreases in the number of
radio stations, so that demand for ads on a station also falls. In equilibrium,
then, the level of advertising on a station decreases in the square of the number
of stations.
The number of radio stations exerts two con‡icting e¤ects on the quality of
broadcasting on a station – what may be termed a competition e¤ect and an
advertising e¤ect. The competition e¤ect would increase broadcasting quality in
the number of radio stations, as each station seeks to maintain its attractiveness
in the face of closer neighbors. The advertising e¤ect pushes quality in the
opposite direction. Quality increases in advertising – to retain listeners when
airing more advertisements, stations must compensate them with higher quality
broadcasting. As described above, when the number of radio stations in a
market increases, the amount of advertising on each station falls. With fewer
advertisements to interrupt the broadcast, a radio station may reduce quality
– and therefore costs – without losing listeners. Whether the competition or
the advertising e¤ect prevails depends on the elasticity of consumer demand
with respect to advertising. If consumption demand is not very responsive to
1
advertising (
2 ), the competition e¤ect dominates and more radio stations
translate to higher quality programming. When demand is more responsive to
advertising, the level of advertising on a station falls o¤ quickly as the number
of stations increases so that the advertising e¤ect dominates and radio stations
broadcast at a lower quality.
With qi and Ai expressed entirely in exogenous parameters, the results may
be fed back through the model to …nd the equilibrium price of advertising on
each station.
1
J
ri = gd 1
M1 2 ; i = 1 : : : M
(54)
Radio station pro…ts, then, are
RS
i
=g
J
d
1
M
1 2
"
d
M2
gd
2
J
1
M
1 2
#2
(55)
When there are more radio stations, each one collects smaller revenues because each sells fewer ads. The change in costs depends on whether the competition or the advertising e¤ect dominates. If the advertising e¤ect is more
important, then radio stations reduce broadcast quality and each station’s profits may increase when there are more stations. A stronger competition e¤ect
means an increase in quality and therefore higher radio station costs for a larger
M.
With free entry, radio stations enter the market until there are zero pro…ts.
The number of radio stations that would result with free competition is
M=
4
J
gd
19
1 2
3
1
2
(56)
The more costly it is for radio stations to attract listeners, the more stations
there will be in the market and the smaller each station’s audience share will
be. A larger makes it more expensive for a radio station to provide quality.
In equilibrium, the lower quality provided reduces stations’costs so that more
stations may earn non-negative pro…ts. Higher makes listeners less willing to
travel far from their preferred location to a radio station. To be able to sell
advertisements to reach those listeners, a radio station will have to locate closer
to them, resulting in more stations in the market.
For a larger , or marginal disutility of advertising for a listener, listeners
to a radio station tolerate fewer advertisements. Each station sells fewer advertisements and revenues fall, but costs decrease more quickly. Radio stations
provide lower quality broadcasting since advertisements take on relatively more
importance in listening choices. Any of these cases would lead to an increase in
M , as more stations are able to achieve non-negative pro…ts.
5.5
Social Welfare
The radio station’s pro…t-maximizing solution for Ai , taken together with the
solution to the consumer goods problem from sections 5.2 and 5.3 allows consumer demand and utility to be expressed entirely in exogenous parameters.
Since the solution is symmetric, the subscripts i and the superscripts j are
suppressed from this point forward.
a =
x =
u
=
d
=
JM 2
JM 2
d
g
JM 2
d
gJ
Jx
= 2
2
JM 2
(57)
(58)
(59)
When there are more consumer goods (larger J), each producer purchases a
smaller share of the advertisements on any given station and each consumer purchases less of that good. Consumer surplus increases with the greater variety,
but each goods producer sees his pro…ts decrease when he has more competitors. As demand for consumer goods is more responsive to advertising (larger
), goods producers purchase more advertisements on each station.
More radio stations produce a lower perceived consumer surplus from the
consumption of the goods x.
CS
= u pJx
d
gJ
=
JM 2
1
1
(60)
When there are more stations, each listener hears fewer advertisements for each
good and therefore consumes less of the advertised goods. The resulting utility
20
loss is larger than the decrease in an individual’s expenditures since utility
depends on both xji and aji , dealing it a double blow when there are additional
stations.
Consumer goods producers see a decline in pro…ts when there are more radio
stations.
=
(p
= g
)x
raM
1
d
JM 2
1
(61)
As mentioned above, demand for their goods falls with the lower advertising levels that result from a higher M . Because the di¤erentiated products are priced
above marginal cost, as in (44), revenues fall o¤ more quickly than production
costs do. Any fall in demand for the good j would result in lower pro…ts for
producer j. At the same time, goods producers also see their spending on advertising decrease as there are more stations. Each station decides to air fewer
ads due to the heightened competition for listeners (51), and the decrease in a
goods producer’s total ad purchases on all stations exceeds any increase in the
willingness to pay for advertisements. The net e¤ect is a decline in advertising
spending by each goods producer, but the fall in production pro…ts is larger than
the drop-o¤ in advertising expenditures, generating lower pro…ts from consumer
goods when there are more stations.
The utility from listening (38) in equilibrium is
V =
gd
2
J
1
M1
2
d
M2
(62)
12M 3
The utility from listening depends on the number of radio stations in several
ways. The quality of broadcasting changes with the number of radio stations as
described in the previous section. With more stations, the level of advertising
on any given station falls, so listeners face fewer interruptions while enjoying
the broadcast, improving utility from listening. More stations also means that
listeners have a shorter distance to "travel" from their preferred station –with
more listening options it is more likely that one will be closer to an individual’s
1
ideal. If more stations lead to higher quality broadcasting (
2 ), listeners
always achieve higher utility when there are more stations.
As in (37), social welfare can be measured as the following, where ! is
the measure of how closely this ex post utility matches the consumer’s true
preferences, and subscripts are left o¤ due to symmetry:
SW
= M L(V + !u)
=
q
M q2
J M Lx
A
12M
M F = V + !u J x
!
+
1 Jx
2
3
MF
(63)
(64)
The …rst term gives the surplus from quality. As there are more stations, the
quality of broadcasts may rise or fall, depending on whether the competition
or advertising e¤ect on quality dominates, as described in the previous section.
21
Except for very large , total radio station costs, M q 2 , will tend to increase
when there are more stations, leading to a decrease in social welfare.
The loss to social welfare from advertising is in the second term. As the
number of stations increases, each station airs fewer advertisements, costing less
in listener utility terms. Similarly, the surplus lost from mismatches between
listener preferences and station locations is smaller when there are more stations,
since listeners have a shorter distance to travel from their ideal.
The …nal term is the social surplus provided by the advertised good. An
increase in M , and the drop in advertising for each product that ensues, results
in less consumption of the consumer goods x. The e¤ect on surplus depends
on !, which reveals how much advertising has distorted consumers’utility from
their true preferences. When ! is close to one, it suggests that this ex post
utility is a good proxy for the consumer’s true preferences, and so an increase
in the number of stations and the drop in advertising that follows are surplusdecreasing. For ! closer to zero, however, the reduction in advertising that
results from more stations improves the surplus from consumer goods, as the
lower level of advertising is less distortionary.
The number of radio stations a¤ects both sides of the market. Advertisers or goods producers su¤er smaller pro…ts when there is more competition
between radio stations. If the utility function in (40) represents a consumers’
true preferences, consumer surplus also shrinks when there is more radio station
competition. However, if advertisements are especially distortionary, consumer
surplus may improve due to the fewer advertisements that result. The e¤ects
of increased competition on both listening utility and on radio station pro…ts
depend on how much advertising can move demand.
To compare the competitive outcome with the social welfare optimum, consider the speci…c case where = 1=2 and ! = 2 . While this simpli…es the algebra signi…cantly (M falls out from the expression for q and the social surplus
from consumption of the advertised good disappears), it also focuses attention
solely on the radio market and the surplus created directly by listening to and
advertising on the radio. Social welfare is maximized when
@SW
=
@M
q2 +
M3
+
4M 4
=0
(65)
M , the socially optimal number of radio stations this returns, is unique.6 When
evaluated at M (56), the number of stations that result in competition, the
di¤erential of social welfare with respect to M is
@SW
j
= q2
@M M =M
6 The
+
M
1
+
64
16
second-order condition is negative
@ 2 SW
=
@M 2
3
M4
22
M5
<0
(66)
1
For any M , this sum is positive for < 16
. When the cost to provide quality
is low (small ), M < M , competition provides fewer than the socially optimal
number of stations. Though stations broadcast at a high level of quality, they
neglect the bene…ts that more radio stations hold for listeners. With more
radio stations, listeners would have a smaller utility loss due to advertising
and to location mismatches. Radio stations instead prefer fewer stations in the
market so they can earn higher revenues by selling more advertisements.
The sum in (66) is negative for > 4 + M =64, resulting in more radio
stations in competition than is optimal when is large. With operations more
costly, stations broadcast at a lower level of quality to try to control costs. With
low-quality broacasting, some listeners may …nd that tuning in gives them only a
very low utility. This leaves room for additional stations to position themselves
on the circle so that the utility loss from location mismatches is smaller for
those listeners. Though these stations are able to sell enough advertisements to
at least break even, the resource costs of broadcasting by this large number of
stations exceed the bene…ts to listeners from more stations –fewer ads on each
station and smaller location mismatches.
6
Conclusions and Extensions
In general, the free entry number of stations M is not expected to be the social
welfare optimum. Both customer groups – listeners/consumers and advertisers/goods producers – fail to take into account the external e¤ects of their
actions on the other type of customer. This suggests there may be cause for
a regulator to act to limit the number of stations in a market, provided the
regulator takes into account the impact the radio market has on the surplus
created in the market for consumer goods. Both quality and advertising are
also potential policy tools, as regulators may set quality standards or limit the
number of advertisements to achieve the social optimum.
These results taking into account the e¤ects of competition on broadcasters,
listeners, consumers, and advertisers, may be particularly relevant to the new
possibilities opened up by the transition to digital radio transmission. The
frequencies available for broadcasting in any given geographic market have been
limited, due in large part to the spacing needed between frequencies to prevent signal interference. Digital transmission of radio broadcasts eases this
constraint, so the question of determining the optimal number of stations in a
given market has newfound importance for regulators.
Changes to media ownership limits, some of which are now being contested
in the courts, may also be analyzed using this two-sided market framework.
Since the 1996 Act, there have been fewer independently-owned radio stations.
In any geographic market, several radio stations may have the same owner.
When these stations jointly choose the number of advertisements and quality of
broadcasting it is likely to have an e¤ect on social welfare. This scenario may
also be compared to joint marketing agreements, in which two or more stations
plan advertising together but choose programming individually.
23
The model can also be extended to allow listeners to pay some positive price
to tune in to a radio station. If listeners may pay to avoid advertising, will they
be better o¤? Will society? The answers are likely to depend again on how
informative advertising is and the advertising-elasticity of consumer demand. A
hybrid model may also be considered, where some listeners pay for radio, while
others hear advertisements while listening. This hybrid model may be the most
easily translated to other media, especially newspapers and magazines and the
Internet, and will be useful in considering the impact of satellite radio on both
the traditional broadcasters and on welfare generally.
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