Beyond the spectrum constraint: Concentration and entry in the broadcasting industry, M Motta, M Polo

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Content: Beyond the Spectrum Constraint: Concentration and Entry in the Broadcasting Industry
Massimo Motta Universitat Pompeu Fabra Barcelona - Spain
Michele Polo IGIER and Universita' Bocconi Milan - Italy
August 1997
Abstract The broadcasting industry is still very concentrated all over the world, after 15 years in which new technologies and public policies allowed to overcome the constraint of limited availability of frequencies on the radio spectrum. We argue that the monopolistic competition set up, traditionally used to analyze the broadcasting industry, does not t the empirical evidence. Instead we analyze the free entry equilibrium in a multistage game in which the decision on program quality attractiveness is crucial and the associated xed costs are endogenously determined. We show that concentration might arise in the long run even in large markets despite entry is free. JEL Classi cation: L10, L82
We thank for helpful discussions and suggestions Damien Neven, Fausto Panunzi, Piero Tedeschi, Jean Tirole, Thomas von Ungern-Sternberg and seminar participants at IGIER, Padua, Naples, Lausanne, Wien 1996 EARIE Conference, Bologna, LSE. financial support from MURST and IGIER are gratefully acknoledged. Usual disclaimers apply. 1
1 Introduction Up to the Seventies, the broadcasting industry was dominated in each country by few national over-the-air networks: in most cases they were state-owned, with the notable exception of the United States. The uniform picture was that of a very concentrated industry all over the world. The traditional explanation referred to the so called spectrum constraint: the broadcast signals were delivered over-the-air from terrestrial transmitters for reception by individual homes. The frequencies available on the radio spectrum were limited, restricting the number of television channels that might be transmitted over-theair. Therefore, the very high industry concentration was determined by a technological constraint. During the last 15 years, alternative technological solutions have developed in order to overcome the spectrum constraint: cable and satellite broadcasting, often combined, have o ered new entry opportunities in the industry, while the development of digital technologies in the over-the-air transmission will multiply in the early future the number of signals that can be delivered on the radio spectrum. In some countries, as the United States, Canada, Germany and Japan, a relevant percentage of households is cabled; in the UK and Japan direct satellite broadcasting services are well developed; in other cases scrambled over-the-air transmission allowed to introduce pay-TV services within the traditional broadcasting support. The pattern of industrial structures is now much more diversi ed than two decades ago, and a very active role of private rms has emerged both in the traditional over-theair transmission and in alternative broadcasting supports. In Europe and Japan private commercial broadcasters now compete on equal grounds with the long-standing stateowned networks. In the United States cable TVs have partially eroded the dominant position of the three commercial networks: the new scenario that tends to emerge is a dual market structure, with the major networks still maintaining a large share of the audience and the residual viewers spread over a huge number of small channels. Another interesting piece of evidence that springs out of the US experience, where heterogeneous operators compete in the same market, refers to the di erent importance of the costs related to the production of programmes and the purchase of transmission rights. This component becomes extremely important for the more popular channels, covering up to 3 4 of the budget, while it is much less relevant for small operators. The intense entry process of the last two decades has undoubtly led to a decrease in concentration. A crucial question, which is relevant also from a policy perspective 1, is whether this process will continue over time with a progressive fragmentation of the industry, or whether there exist reasons that will help a small number ot operators to maintain their market dominance. The aim of this paper is to o er new insight on the determinants of market structure in the long run in the broadcasting industry. The way in which we model market competition is crucial to construct our predictions. The monopolistic competition and horizontal di erentiation approach has been tradition- 1On Public Policy in the broadcasting industry see OECD 1993 and Motta and Polo 1997. 2
ally applied to the broadcasting industry: the associated view of the long run market structure would suggest a very fragmented industry with no dominant TV-channel. However, we argue that horizontal product di erentiation captures only part of the story, and that the monopolistic competition model does not t some of the evidence that today is characterizing the industry both in terms of market and cost structure. In particular, the patters of programming costs associated with the success of a TV-channel seems to suggest an important role of investments in the attractiveness of programmes. This important feature of the industry is better expressed in terms of vertical product di erentiation. A richer modelling of the broadcasting market requires therefore to combine horizontal and vertical di erentiation, an approach that, to the best of our knowledge, has not been developed in the literature on this industry. The two main elements of our analysis are related to programming. The most relevant strategic tool in this perspective is identi ed in the design of the program schedules, by which horizontally di erentiated TV-channels can improve their audience and consequently the willingness to pay of advertisers. However, improving the program schedule requires higher xed costs, related to the production and or acquisition of better more popular programs. Our analysis is reminiscent of the endogenous sunk cost paradigm proposed by Sutton 1991 to explain patterns of persistent concentration in food and beveradge industries: successful, dominant rms have higher xed costs, related to their e ort to maintain and strengthen their market position; larger markets, ensuring higher gross pro ts to the dominant rms, determine an increase in their e orts for leadership but at the same time in the related xed costs. The main result of this literature, known as the Finiteness Property, states that the number of rms does not depend on market size, but can be explained according to the distribution of the willingness to pay and the shape of the xed costs associated to quality improvements2. In our setting, the number of rms sustainable in a free entry equilibrium becomes independent of the market size as the market becomes larger and larger, as occurs according to the Finiteness Property. Concentration in this limiting case is determined only by the degree of horizontal di erentiation among TV-channels, a higher di erentiation being consistent with a more fragmented structure3 Hence, the free entry equilibrium may be consistent with a very fragmented structure if the TV-channels specialize in different programme types. But it also shares some features of the Finiteness Property: in particular, concentration might arise despite free entry as the long run equilibrium if TV rms choose relatively similar programme schedules, attracted by viewers' bias toward a limited number of program types. The paper is organized as follows: section 2 presents some stylized facts on the broadcast industry in the main developed countries; in section 3 we set up a model with private, advertising nanced, TV rms; the equilibrium is analyzed and discussed in 2See Shaked and Sutton 1982 and 1983 and Sutton 1991. 3This characterization of the equilibrium number of rms in terms of horizontal product di erentiation seems new with respect to the existing literature on the Finiteness Property. 3
section 4. Section 5 concludes the paper. 2 Concentration in the broadcasting industry: some international evidence Table 1 presents some data on market dimension and industry structure for the largest European countries - France, Germany, Italy, Spain and United Kingdom - the United States, Canada and Japan. The rst two rows show the potential dimension of the market in terms of viewers and advertising investment4. Three groups of countries can be identi ed according to both measures of market size: the largest - US and Japan - an intermediate group Germany, UK, Italy and France - and two smaller countries - Spain and Canada. While considering only the main developed countries, our sample presents a very signi cant range of values, i.e. a range of very di erent market sizes. Table 1: Concentration in the broadcasting industry 1992-93 F D I E UK J USA CAN 1 20448 31860 20304 11350 22088 42500 93053 9993 2 2674 3127 3882 2127 4247 14300 29375 1459 3 6.4 43.9 0 6.6 3.8 21.9 61.8 80.0 4 1.6 10 0 1.3 13.6 16.3 4.8 5.1 5 91 73 69 89 94 77 70 n.a. 6 80 60 93 78 83 40 39 n.a. 1: TV households x 1000; 2: TV ads expenditures million $; 3: Subscribers Cabled households ; 4: Satellite households TV households ; 5: Concentration ratio C4 audience by channel; 6: Concentration ratio C2 audience by group. ||||||||||||||||||||||Sources: TBI Yearbook 1994, The Media Map 1994 The penetration of distribution supports alternative to the over-the-air broadcasting one are shown in rows 3 and 4 for cable and satellite: although the picture is very di erent from country to country, in Germany, Japan, US and Canada cable TV services are chosen by a very large percentage of potential subscribers; direct satellite distribution is still relatively limited, probably due to the cost of the reception equipment for private viewers. 4These two variables are typically used to determine market size and the corresponding fees in international transmission rights contracts for television programs. 4
Finally, the last two rows show the concentration ratios for the industry in terms of audience 5 computed by taking the rst four channels row 5 and the rst two rms row 6. It is convenient to present both measures because the natural index for concentration - aggregate market share of the rst n rms - is strongly in uenced from country to country by the regulatory environment and the ceilings on ownership and multi-licences; on the other hand, the aggregate share of the rst n channels, although not immune from regulatory in uences, tends to re ect more closely the number of products sustainable in the market and therefore the economic tendency towards concentration. Concentration by channel is extremely high in all countries, showing that a small number of programs is chosen by most viewers; moreover, even if a certain increase in concentration can be identi ed moving from larger to smaller countries, this pattern is not very pronounced6. Concentration by television group rm is particularly high in Europe, due to the role of public and private multichannel TV rms. The changing environment of the broadcast industry can be further illustrated by referring to the United States case: until the late Seventies the three major commercial networks reached a 90 per cent viewing audience; the expansion of cable systems in the last fteen years and the emergence of a fourth over-the-air national network7 have partially eroded this dominant position. The over 100 cable system operators today in the market o er a very high number of channels to their subscribers in basic and premium packages8, including the over-the-air networks program schedules. However, if we compute the audience of the cable systems net of the programs of the over-theair networks, their importance is relatively limited 9, with an aggregate audience of around 25, slightly above that of a single over the air network. The combined national advertising revenues - around $ 2.3 billion in 1994 - is far below the 10.9 $ billions of the four major networks .10 The slight decrease in concentration experienced in the last decade in the major countries, taking the US as the leading case, suggests the emergence of a dual structure, where the major TV-broadcasters remain very few while many small operators ll the 5While audience is not the only relevant variable for industry analysis, it is probably the one which is less in uenced by the di erent ways of nancing of the broadcasting rms - public funds, advertising, subscription fees and several combination of these. Moreover, the audience distribution is the most important element of industry performance for public policy issues. 6Germany and Italy, which can be considered medium size markets, have a relatively low concentration ratio - in terms of the rst four channels - as compared to the other European countries. The critical role of multichannel broadcasters in these two countries could explain this pattern. 7More recently two new over-the-air networks, United Paramount's UPN and Warner Bros' WB entered. 8The penetration ratio subscribers cable households of basic packages in 1994 was 65.2 while that of premium services was 28.1. The packages o ered seem to be very similar: the 15 more popular programming services are o ered by almost all the cable system operators - see FCC 1995, appendix H, tab.6. 9In cable homes around 2 3 of the viewing time is spent watching programs originating from the major over-the-air networks. 10On the situation in the US market see FCC 1995. 5
market niches. The main e ect of entry in the broadcast industry seems a strong increase in the variety of programs available to the households, but not a corresponding diversi cation in the actual choices of the viewers. A further piece of evidence which is useful in motivating our approach is related to the cost structure of TV rms. Although reliable and comparable data on costs are not available for TV rms across countries, some evidence from the US market suggests that the cost structure varies considerably across di erent types of TV operators. In particular, the share of costs for programming, including home production and purchase of transmission rights, seems crucially related to the success of the rm in terms of audience. In the US market, programming costs reached in 1993 74 of the balance sheet in a typical television network, 33 for cable system operators and only 23 for the local programming of television stations11. This ranking corresponds to the relative audience of these types of operators, very large for networks, lower for cable operators and local for TV stations. Hence, it seems that the share of programming costs increases sharply with the audience. 3 Advertising- nanced TV channels: a model The broadcasting industry has been traditionally considered a good example of monopolistic competition 12 or horizontal product di erentiation of the Hotelling type: TV rms design their program schedule by choosing their variety, attracting the viewers according to their heterogeneous tastes and segmenting the market. Unfortunately, the stylized facts we brie y described, namely a very weak relation between market size and market concentration, and a strong correlation between xed costs and rm's performance, do not match the basic predictions of those models13. Therefore we propose an alternative speci cation, by focussing on a di erent dimension in the competition for audience among TV rms, the perceived quality popularity of programs. Modelling the TV sector requires to consider three classes of agents, the TV viewers, the advertisers and the TV rms. The rst type of agents decide whether to watch a TV programme and which channel to patronize, determining the audience distribution. The willingness to pay of advertisers for advertising airtime increases with the audience. Finally, the TV rms in uence the decisions of the other two groups in two ways: through the design of the program schedule, which attracts the viewers and determines the value of the advertising time; through the amount of advertising time within the programs broadcasted, which in uences positively the revenues but discourages the viewers, reducing the value of the advertising slots. 11See Veronis et al. 1994. By local programming we refer to the program schedule of a local TV station when it does not broadcast programs of the a liated network. 12See, for axample, Spence and Owen 1977. 13In horizontal di erentiation models we expect a decrease in concentration an increase in the number of rms as the market size grows, and xed costs una ected by the variety chosen. 6
This complex interaction will be analyzed in a multistage game according to the
following timing of moves: the TV rms decide initially and simultaneously whether to
enter or not the industry; then, being the number n of active rms public information,
they choose the quality of their programs
qtiusianligtyslqoitsanfdaitghegivadenvetrhtiesinqugaslliotytsoafi
the on
fqig; thirdly they select the amount of adver- programs, anticipating the e ect of both the the audience Ai and therefore on the demand
for advertising by the other rms in the economy. The latter choose the amount of
advertising slots bought on the n TVs and nally the TV viewers watch their preferred
if any programs.
According to backward induction, we consider initially the choice of the rst two
groups, the viewers and the advertisers, moving then to the more complex analysis of
the strategies of the TV rms.
Viewers' choice: the audience function
The allocation of TV viewers among the n TV channels is summarized by an audience function which depends on the type of programs and on the amount of advertising slots broadcasted by the n TV rms. The viewers react positively to the quality of the programs and negatively to the amount of advertising slots; moreover, they consider the di erent TV channels as imperfect substitutes, with an own e ect greater than the cross ones. We adopt the following linear speci cation
2
3
Ai = 4 n + n qi , ai , n X qj , aj5
1
j6=i
with n n , 1 n 0 and 1=n; measures the marginal impact of program
qchuaanlintyelqii',s
, a scale parameter, audience, and ai is
measures the size of the population of viewers; the amount of advertising slots of TV-channel
Ai.i
is TVNotice
that each channel competes with all the others on symmetric grounds, with no localized
e ect.
Contrary to the previous formal literature on the broadcasting industry, we consider
the variety of TV-channels as an exogenous variable, and focus on the quality decisions
of rms. We use the term quality as referred to the ability of any type of program
to increase the audience; the complementary dimension of program's variety, which is implicitly given by the direct and cross e ects n and n in the audience function,
pertains to the particular type of program broadcasted. Therefore we can have di erent
varieties as sport or movies and, for each of them, a program which is able to attract
a large or small portion of viewers, as the Superbowl vs. a minor league match or
Jurassic Park vs. a dinosaurs B-movie with very poor special e ects. Notice that even
if several broadcasters o er similar programme schedules, they can still maintain some
limited degree of horizontal di erentiation through the design of the time schedule of
programmes, i.e. avoiding to broadcast a movie at the same time of a rival.
7
Equation 1 can be obtained from di erent models of viewers' behaviour: an exam-
ple derived from a viewers's discrete choice model is presented in the appendix We prefer,
however, not to restrict ourselves to a speci c model of viewers' choice, since our results
can be proved for a wide class of linear functions that meet mild restrictions on the
parameters. In general the parameters n, n and n are related to the number of
rms n, and can be speci ed in di erent ways according to di erent models of individual
viewers' behaviour .14 Some general restrictions can be set for this family of functions;
the aggregate share of active viewers is P When the own e ect is greater than the
Ai= sum
= of
n the
+cross,enec,ts1,i.e.Pqi
,nai,
1. 1 ,
qi , ai 0 implies 1=n. Moreover, a more attractive programming makes some
new viewers entering the market in addition to and total viewership increases .15 Conversely, watch a TV-channel16, which implies = n
those when , 1
PwhAoi and
shift = =
from the other channels, all the potential viewers 1=n, i.e. an increase in
audience can be realized only by subtracting viewers from the other channels.
To simplify notation, we initially refer to those parameters simply as , and ;
their relation to the number of rms will be explicitly consider in the analysis of the
entry stage, in which the number of rms will be determined.
Advertisers' choice: the demand for advertising time The next step requires to derive the demand for advertising slots by the rms in the economy. Since our focus is on the TV sector we simplify this analysis, assuming strong symmetry conditions among non-TV rms that enable us to obtain simple aggregate relations. We require the demand for advertising to have three properties which seem empirically appealing: advertising has diminishing returns; it diminishes rival rms' demand; these strategic e ects tend to decrease as the number of advertisers increases17. All these properties are satis ed by the following, admittedly simple, speci cation. The demand for the product sold by an advertiser k k = 1; ::; K, besides the usual price e ect, is assumed to depend, through a multiplicative demand enhancing e ect tpthhaaarttamaisdevtoeenrritP ziesdiinagbki yh aAsi,awdhe1ec,rreeoanaskiinthigsemtnhauermgaibmneaorluoenftetocimft aoedsnvtdehreetmisaaindngvdeordtfeisriirnvmigngmk feorsonsmaTgetVhiesi.ivnNideouwtceiecdde, 14Linear demand systems as the one adopted for the audience function can be obtained from three di erent models of individual behaviour: the representative agent, the address and the discrete choice approaches. The relations among these three models is further analyzed in Polo 1997. 15Alternatively, the total viewing time of the representative viewer increases, subtracting time to other leisure activities. 16Alternatively, the representative viewer spends all the leisure time watching TV programmes. 17Advertisers are implicitly assumed to operate in a monopolistically competitive market; therefore we consider advertising rms o ering a generic consumer good which is an imperfect substitute of the products o ered by the other advertisers, and which is potentially purchased by a typical viewer. We rule out for simplicity localized e ects among advertisers, as those among producers of music equipment, whose advertising expenditures poorly in uence the demand for food and beveradge, and which are particularly interested in the audience of music events and programmes.
8
reduction in the audience. The demand Dk of advertiser k is therefore:
Dkp; a = dkp X n aki Ai i=1
where dkp shows the price e ects at the individual level and measures the impact of advertisings messages on individual demand18. The pro t function of an advertiser is therefore:
k = pk , ck dkp X n aki Ai , X n piaki
i=1
i=1
where pi is the unit price of advertising on TV-channel i. From rm k's rst order
conditions it can be easily checked that the nal product price pk does not depend on
the total channel i
amount of advertising can be written as:
ak
;19
the
optimal
amount
of
advertising
aki
on
TV-
8
9
pk , ckdkp + :
qi ,
X qj , j6=i
X ali + 2aki + l6=k
X j6=i
Xalj l6=k
+
2akj
= ;
=
pi
In order to obtain a manageable expression of the demand for advertising slots we
assume symmetric advertisers, i.e. ck = c and dkp = dp implying pk = p. In the
symmetric ai=K, i.e.
equilibrium of we observe the
the advertising same amount of
game among the K advertising across the
rKmsa,dtvheernti,searkis
= on
aeliac=h
individual TV-channel, although not necessarily across each TV-channel. From the rst
order conditions we can write:
8
9
p , c dp :
+
qi ,
X qj , j6=i
K+ K
1
ai
+
K+ K
1
X j6=i
aj
= ;
=
pi
Hence, being K very large, we can approximate the demand for advertising slots by
2
3
pi = S 4 + qi , ai , Xqj , aj5
2
j6=i
where S = p , cdp is a scale parameter that measures the economic pro t
dimension of the economy for an advertiser: it can increase because the number of con-
sumers increases , because the advertising messages are more e ective in stimulating purchases or because the pro t that can be extracted from a single consumer is greater. Di erent values of S can therefore be interpreted as due to di erent market
18This parameter would be important in evaluating advertising on di erent media - as TV-channels, radio or newspapers - as well as in comparing of TVs nanced through advertising vs. subscription fees. 19This is because we assume that advertising has only a scale e ect upon demand.
9
sizes, di erent media and advertising techniques and di erent phases of the business
cycle.
It is worth noting that, although the demand for slots might seem very similar to
the audience function, there exists a fundamental di erence between the two: while
the TV viewers look at the channels as substitutes, in the demand for advertising slots
the j's
quantities advertised on the n TV-channels enter as complements: if audience falls while i's audience increases: the willingness to pay for
aj a
increases, spot in i's
programs increases as well, i.e. i's demand for slots shifts to the right.
TV rms
We consider now the pro t function of the TV rms. In the TV business, most of
the costs do not depend on the number of viewers that watch the programs, and are
therefore xed, while the costs of broadcasting the programs including the advertising
messages to an additional viewer are negligible. The nature of xed and variable costs
is therefore very similar to a public good case.
Within the xed costs, we can distinguish between two broad subsets: a rst class is
basically determined by technological or institutional reasons, as the cost of the cable or
transmitters network and that of the broadcasting equipment, or the cost of a licence.
Those xed costs, that we label as , are exogenous with respect to market size and do
not depend on the nature of market competition.
The second class of costs refers to programming and includes production costs and
the purchase of transmission rights: those costs are very sensitive to market size and the
degree of competition, due to technical and, more substantially, quasi-rent reasons. A
very popular program costs more because the cost of the scarse input needed talent is
pushed up by competition among TV-channels. Those xed costs F are endogenous and
will be assumed to be increasing and convex in the level of quality of the programmes,
i.e. F = Fqi, F0 0 and F00 0. As will be clear later on, in our model the simplest
speci cation consistent with a nite level of quality in equilibrium is a cubic function,
i.e.
Fqi = Finally,
wqie3=s3h.all
assume
constant
zero
marginal
costs.
The
current
pro
ts
of
TV
i
can be written as
2
3
i = S 4
+
qi , ai ,
Xqj , aj5 ai ,
,
q3 i
=3
3
j6=i
4 Equilibrium
We are now able to analyze the broadcasters decisions. In the third stage, the TV rms choose simultaneously the amount of advertising slots. Standard computations allow to establish the following result.
10
Lemma 1 In the third stage of the game there exists a unique subgame perfect equi- librium in advertising time characterized by
a^i = 2
+

+ h,2
2 , n , 2 2 + 2
, n , 1 2 qi , , n , 1
q P
i
j6=i j
4
Substituting the equilibrium expression in the demand function, it is easy to check that
2
3
pi = S 4 + qi , a^i , Xqj , a^j5 = S^ai j6=i
In the second stage of the game the TV rms choose the quality of their programs. The net pro ts of a TV rm can be written as
i =
S a^2i ,
,
1 3
q3 i
5
The equilibrium level of qualities is described in the following proposition. We identify
the conditions that ensure existence and uniqueness, and we shall check that they are
met in the free entry equilibrium of the overall game.
Proposition 2 If 2 + p2H2 , n , 1 2 + 4 H ,Hn,1 0 there exists a symmetric subgame perfect equilibrium in qualities characterized by
q^ = H
, n , 1
+ p2H2 2
, n , 1
2 + 4
H
6
where H = 2 1 0 the
. S 2 2,n,2 ,n,1 2 , , 2 + 2 n 1 2 equilibrium is unique.
If
2
+ p2H2
, n , 1 2 + 4
H,2Hn,
Proof: By deriving the pro t function we get the rst order condition
2
3
@i @qi
=
2
H +
42
+
+ 2 2 , n , 2
, n , 1 2qi ,
X
qj
5
,
q2 i
=
0
j6=i
7
which, in a candidate symmetric equilibrium, can be rewritten as H + H , n ,
1 q , q2 = 0. Solving for q gives the expression above. The second order conditions
require
11
@2i
@
q2 i
=
2
H +
2 2 , n , 2
, n , 1
2
,
2qi
0
8
Evaluated at the equilibrium point, after rearranging, 8 gives the rst condition
above, which sets a constraint in the n; S; ; ; ; space. We shall check once solved
for the equilibrium number of rms if the concavity conditions hold.
Finally, uniqueness can be established by noting that equation 7 is a quadratic
mfmSuueanbnxcsttitmiitothunuemtiicnn,ogtnqhida;einttbdiroeenrasettafionrrerrgpaunlqny,giiiqfnuuagnellncwteteiososgonebctaithsaneidnrbe,[email protected][email protected]@@[email protected]@[email protected]@[email protected]@froqgrjuja-.
2
It is worth noting that, for any given level of n, the equilibrium quality and advertising levels are increasing in the size of the market S. Since n , 1 when the market is not covered, an increase in the size of the market, allowing to nance better programs, determines an expansion in the individual and overall audience in equilibrium. This process continues until all the market is covered20, or, equivalently, until market size reaches a level S. Fron that level on, no further expansion in aggregate audience is possible: the parameters of the audience function become = n , 1 and = 1=n21. It is easy to check that all the equilibrium expressions obtained so far remain valid, with the additional restriction on the parameter values described above.
We can now consider the entry decisions of the rms in the rst stage game and the long run equilibrium structure of the market. To simplify the analysis, we treat n as a continuous variable. The pro ts evaluated at the subgame perfect equilibrium in a^ and q^ are
= S
+ 2
, n , 1 , n , 1
q^ 2
2
,
, 1=3q^3
9
We proceed in the analysis as follows: rst of all we prove in the following proposition that the concavity and uniqueness conditions hold in a free entry equilibrium. Then we characterize the equilibrium number of rms as the market size increases, focussing on the asymptotic market structure, and showing its relationship to the degree of substitutability among channels.
Proposition 3 In a free entry equilibrium the conditions for concavity and uniqueness speci ed in Proposition 2 hold.
20This occurs when all the potential viewers watch a TV channel and or all the viewers spend all the leisure time watching television. 21This change in parameters is not determined by a shift in tastes, but simply by the fact that the viewers' choice problems shifts from an internal to a corner solution.
12
Proof: The rst order conditions FOC in the quality stage, evaluated at the symmetric equilibrium, can be written as + , n , 1 q^ = q^2=H. Set initially = 0 and evaluate the free entry condition FEC:
+
, n , 1
q^ 2 = 2
, n , 1 3S
2 q^3
Substituting the FOC in the FEC we obtain, after rearranging,
q^ = H2 2
, n , 1 3S
2
=
2H ,2
2 , n , 2 32 +
, n , 1
2
Equating it to the expression of the symmetric equilibrium qualities 6 we obtain, after
rearranging
32 + p , H ,2 2 + 2n , 1 62 +
, n , 1 2 = 0
10
whpere=p H==3p22H2+22n,,n1,
1 2 + 4 ,n,1
H. Hence in a free entry equilibrium 2 + 2. Substituting in the condition for uniqueness
speci ed in Proposition 2 we obtain H=32 2+ ,n,1 2 which always holds for
n , 1 . Finally, if the uniqueness condition holds, the concavity condition holds
as well. It is easy to check that if the exogenous sunk costs are positive, i.e. 0, the
same results hold good.
2
Once established that the free entry symmetric equilibrium exists and is unique, we can characterize the number of rms sustainable in the market. Looking at the expression of the zero pro t condition 9, it turns out that the number of rms n should depend on ; ; ; ; S; , a rather long list to expect a clearcut result. However, when market sizes become large, the zero pro t condition is governed by the behaviour of the higher degree terms. Moreover, the zero pro t locus becomes asymptotically independent of S, what is usually associated with the Finiteness Property. Finally, we shall prove that this limiting number of rms is entirely explained by a combination of parameters and of the audience function which can be interpreted as the degree of substitutability among channels.
Proposition 4 When S ! 1 the equilibrium number of rms in a free entry equilibrium n^1 does not depend on S. Proof: Remember that q^ = q^S and H is linear in S; when S becomes very large, q^ becomes almost linear in S, since the highest degree of S in q^ is 1, i.e.
q^S ' , n , 1 H
11
In this limiting case the zero pro t condition is governed by two terms of the third degree in S
13
'
2
, n , 1 , n , 1
2 2
S q^S 2 , 1=3 q^S 3 = 0
12
Substituting the simpli ed expression of the equilibrium quality 11 in the simpli ed
expression of the zero pro t condition 12, the and S terms cancel out. The free
entry condition reduces, after rearranging, to 0 if 2 2 , 4n , 5 , n , 1 2 0,
which is a function of and only. n^1, the free entry equilibrium number of rms when
S ! 1, solves this expression as an equality.
2
The proposition above shows that the zero pro t locus in the S; n space is asymptot- ically horizontal; its behaviour for small market size depends on the relative importance of the demand intercept , which enables more rms to coexist given their captive market share, and of the exogenous sunk costs , which make it more di cult to survive in a fragmented market. Hence, the zero pro t locus when = 0 gives the upper bound on the number of rms sustainable in the market. Moreover, the intercept tends initially to determine a negative relationship between the number of rms and market size, the opposite being true for the e ect of the xed entry costs . Figure 1 shows the two di erent cases: the downward sloping line22 corresponds to the zero pro t locus when = 0, i.e. the case in which only matters, while the upward sloping lines might be the zero pro t loci when the exogenous sunk cost are positive. Hence, the downward sloping curve gives the highest number of rms for given market size which are sustainable in a free entry equilibrium. It is immediate to notice that all the curves tend asymptotically to squeeze around the value n^1. The equilibrium industry structure as determined by the zero pro t condition is strongly in uenced by the competition for audience among TV rms, which is primarily realized through an increase in the quality of programs. If the market size S increases, current pro ts tend to increase: they are reduced, restoring the zero pro t condition, not through further entry but through an increase in the quality of programs and in the corresponding xed outlays. This result reminds the Finiteness Property that characterizes natural oligopolies23 in which competition in quality is crucial. Notice that the negative relation between market size and the number of rms that can initially emerge clearly shows the increasing importance of the xed endogenous outlays for programming that are pushed up as the market grows: for small market size, programme quality and the associated xed costs are negligible, while when the market becomes larger and larger quality and costs increase even faster, inducing an increase in concentration. We are now interested in determining the equilibrium number of rms when market size becomes larger and larger. Since the entire map of isopro t curves lies around the asymptotic horizontal line that identi es the limiting number of rms sustainable when 22The plot is drawn using the discrete choice speci cation of the audience function presented in the appendix. 23See, for instance, Shaked and Sutton 1983.
14
the market becomes very large, n^1, we focus on the determinants of that value, i.e. on the position of this at line. As shown above, in the limiting case of S very large, the zero pro t condition is de ned in the ; ; n space: the equilibrium number of rms n^1, therefore, is expected to depend on the degree of substitutability among TV channels, i.e. on the features of horizontal product di erentiation. It must be reminded that the parameters of the audience function depend in general on the number of rms, i.e. = n and = n .24 Su cient conditions for characterizing the free entry equilibrium can be given by using the expression
d
;
;
n
=
n
,
n 1
n
13
which is the ratio of the own e ect and the sum of the cross e ects in the audience function and in the demand for advertising time; d generalizes to the n products case the usual index of product substitutability in linear demand models25. This index d depends on the particular functions n and n, which derive from di erent micro models of viewers' behaviour, and, through those expressions, on n. Therefore it can vary because the functions n and n change for any value of n, what we de ne a variation in the degree of di erentiation; alternatively, d changes when n varies given the functions and : we shall refer to this second source of variation as the pattern of di erentiation. Figure 2 shows two examples in which the pattern of di erentiation is decreasing, the former implying a higher degree of di erentiation than the latter: the curves are decreasing26, showing that the pattern of di erentiation is consistent with a negative relation between the number of TV channels and their di erentiation; moreover, for each n one curve is always above the other, since its degree of di erentiation is higher.
Figure 1 and 2 about here
The following proposition establishes a su cient condition for the equilibrium number of rms being increasing in the degree of di erentiation without restricting us to a speci c expression of n and n, i.e. to a speci c micro model of viewers' choice.
Proposition 5 If the pattern of di erentiation d for given functions n and n is
non increasing in n, the maximum number of rms sustainable in a free entry equilibrium
when S becomes very large, n^1, is increasing in the degree of di erentiation d ; .
If a su cient degree of di 1, while if limn!1 d
erentiation 2, then n^1
is feasible is nite.
such
that
limn!1 d = 2,
then
n^1
!
24We omitted in the equilibrium analysis so far to write down explicitly this functional relation to save notation, since the number of rms was given in the second and third stage of the game. 25Notice that d is strictly related to the importance of the expansion e ect with respect to the displacement e ect: with no entry of new viewers d = 1, while with no displacement e ect . d ! 1 26The two curves are obtained from the discrete choice speci cation of viewers' behaviour discussed in the appendix, by choosing di erent values of the parameter f.
15
Proof: The free entry condition in the limiting case S ! 1 reduces to 2 2 , 4n , 5 , n , 1 2 0. Dividing by n , 12 2 it can be rewritten as
2d2
,
4n , 5 n,1
d
,
n
1 ,
1

0
14
Totally di erentiating this expression we obtain
dn dd
=
d
,
1
4d , 1n , 12 + n , 1 , 4d , 1n , 12 + n , 1
@[email protected]
15
which is positive if @[email protected] 0, being d 1 by assumption. Taking the limit of the free
entry condition as n tends to 1 we obtain 2dd , 2 0. Since d increases, for any n,
as the degree of di erentiation increases, the condition above determines the degree of
di erentiation su cient to induce the entry of an in nite number of rms. If d 2 as
n ! 1 the pro ts would be negative and the entry process ends up with a nite number
of rms.
2
Proposition 5 shows that the industry might be highly concentrated despite free entry even for very large market size. But it also establishes that the market, whatever its size, is not necessarily concentrated if there exists a su cient degree of di erentiation. For example, higher di erentiation, by reducing the extent to which viewers switch from one channel to another, also reduces the incentive to invest in quality; quality and advertising would decrease in equilibrium, and so would advertising revenues and programming costs. In turn, lower xed outlays would allow more rms to enter the industry. The su cient condition for this result requires that the pattern of horizontal di erentiation is non increasing in the number of rms. This amounts to saying that the degree of substitution among products does not decrease as the number of products rises. Such a condition is very natural in the literature of horizontal product di erentiation. With reference to the oligopoly theory literature, proposition 5 suggests a trade o between di erentiation by variety and by quality: if the former is poor d low the latter is very e ective, while a higher degree of horizontal di erentiation among channels decreases the equilibrium quality of the programs. This kind of trade-o emerges also in models of di erentiated duopolies in which rms have to choose both their variety and quality27: in these models, if the fundamentals allow a signi cant horizontal di erentiation the equilibrium con guration entails divergent varieties and similar low quality, while if the scope for horizontal di erentiation is limited similar varieties and di erent qualities are selected in equilibrium. Entry and the equilibrium with n rms, however, are not addressed in these papers. In our setting, the market structure arising at the long run equilibrium depends crucially on the degree of horizontal product di erentiation, which we treat as exogenous. This result calls for some comments. 27See Neven and Thisse 1988 and Ireland 1987. See also Irmen and Thisse 1996 for a situation where two rms decide on n characteristics. 16
If we extended the model such as it stands and allowed for an additional stage of the game where rms decide upon some variable which decreases the degree of substitution, they would exploit this possibility as much as the cost of such a strategy permits28. In turn, if the scope for horizontal di erentiation would be su ciently high, this would imply that the number of rms which could coexist in the industry becomes large. Horizontal di erentiation in the broadcasting industry o ers a rich set of opportunities, because the programme schedule can contain di erent types of programmes and, for each variety, a characterization di erent from that of the other channels. However, the possibility of increasing product di erentiation depends on the distribution of consumers' preferences for the di erent types of programmes. Consider a situation in which consumers' preferences are biased towards only a small subset of program types, as for instance sport events and movies. Even if TV rms tried to characterize their programme schedules with respect to the rival channels, the scope for di erentiation would be limited if the programme schedules were mainly designed for these large potential audiences. The endogenous increase in programme quality and programming costs would be the result: few TV rms providing the popular types of programmes would have large market shares, whereas a large number of TV channels providing programmes devoted to minorities would have a small share of the audience. These features might explain why few TV rms are still dominant in all countries, and might allow for a dual market structure to arise as an equilibrium where few TV rms o er relatively similar and popular programmes and have most of the market while a large number of more specialized or local TV channels cover programme types patronized only by minorities. However, we feel that to deal with such extensions we would need a model where viewers' preferences for di erent varieties of programs are accounted for in a more sophisticated way than our model allows to do. Our main objective in this paper was to enphasize the importance of the quality choice of TV channels and its possible implications upon the structure of the market. A model which combines in a careful way the endogenous sunk cost paradigm we propose with the horizontal product di erentiation approach traditionally suggested by the previous literature on the TV industry is beyond of the scope of this paper and is left for future research. 5 Conclusions Traditionally the monopolistic competition paradigm, focussed on the design of the variety of program schedules, has been considered as the appropriate framework to analyze the broadcasting industry. However, the persistence of concentration which can be ob- 28For instance, if we specify the audience function according to the discrete choice model of viewers' behaviour described in the appendix and we assume that rms are able to determine, through the variety of their programme schedule, the percentage of idiosyncratic viewers who like their channel, we would obtain that rms choose a corner solution, i.e., they choose the maximum di erentiation allowed. This corner solution reminds the maximum di erentiation result of the Hotelling type literature. 17
served in larger and smaller countries can not be explained within that paradigm. In this paper we have developed a model of the broadcasting industry which suggests that the persistence of a high degree of concentration might arise in the industry even in the absence of the spectrum constraint or any other factor which prevents entry. Our central assumption is that competition among broadcasters is on the perceived quality of the programs, i.e. on their ability, for given variety, to capture a high audience. Since a more popular program also tends to cost more, due to technological and quasirent arguments, the broadcast industry seems to be a good example of the endogenous sunk cost paradigm as proposed in Sutton 1991. We model the interaction among viewers, advertisers and TV rms that characterizes the broadcast industry, proving that the maximum number of rms sustainable is independent of market size as this latter becomes larger and larger. We also show that the minimum degree of concentration depends on the degree of horizontal substitutability among TV channels. This is a somehow new result in the natural oligopoly literature. Our results seem relevant in addressing regulatory issues. Public policy in the broadcast industry has been traditionally designed to promote variety of programmes and to foster pluralism of views. Our result that persistent concentration might arise despite the possibility of free entry and the absence of any technological or institutional contraint suggests that public policies in the broadcasting industry might still be needed in the future. References 1 Anderson S. ,De Palma A. Thisse J.-F. 1993, Discrete Choice Models of Product Di erentiation, MIT Press. 2 Dunnet P. 1990, The World Television Industry: an Economics Analysis, London, Rourledge. 3 Federal Communications Commission 1995, 1995 Report. 4 Ireland N. 1987, Product Di erentiation and Non Price Competition, Oxford, Basil Blackwell. 5 Irmen A., Thisse J.-F. 1996, Competition in Multi-Characteristics Spaces: Hotelling Was Almost Right, CEPR Wp n.1446. 6 Media Map 1994 The Media Map 1994, CIT Publications Ltd. 7 Motta M., Polo M. 1997 Concentration and Public Policies in the Broadcasting Industry, forthcoming Economic Policy. 8 Neven D. Thisse J.F. 1988, On Quality and Variety Competition, mimeo. 18
9 Noam E. ed. 1985, Video Media Competition: Regulation, Economics and Technology, New York, Columbia U.P. 10 OECD 1993 Competition Policy and Regulation in a Changing Broadcasting Industry. 11 Owen B. and Wildman S. 1992, Video Economics, Cambridge, Harvard U.P. 12 Polo 1997, Discrete Choice Models of Product Di erentiation: the n Products Linear Case, IGIER wp. 13 Shaked A. Sutton J. 1983, Natural Oligopolies, Econometrica, 51:1469-84. 14 Spence M. Owen B. 1977, Television programming, Monopolistic Competition and Welfare, Quarterly Journal of Economics, 2:103-26. 15 Steiner 1954, Program Patterns and Preferences and the Workability of Competi- tion in Radio Broadcasting, Quarterly Journal of Economics, 66:194-223. 16 Sutton J. 1991, Sunk Costs and Market Structure, MIT Press. 17 Television Business International 1995, Yearbook 1994, 21st Century Business Publications Ltd. 18 Vaglio A. 1995, A Model of Audience for TV Broadcasting: Implications for Adver- tising Competition and Regulation, Rivista Internazionale di Scienze Economiche e Commerciali, 42:33-56. Appendix: the audience function from a discrete choice model of viewers' behaviour We brie y sketch how to derive a system of audience functions for the n channels from a discrete choice model of viewer's behaviour. Obviously this is not the only way to o er a micro-foundation to the audience function, and alternative speci cations can be obtained from the representative consumer and the address approaches of product di erentiation: the former, however, o ers poor insights on the parameters' restrictions when dealing with a n products model, while the latter becomes relatively messy when allowing for a change in the total numer of active consumers total demand for the n products, as admitted in our model 29 The utility of a viewer watching a programme with quality qi and advertising time ai is 29The literature on dicrete choice models of product di erentiation has almost neglected the linear demand model, although most of the applications in oligopoly theory still use this friendly speci cation; moreover, it is usually claimed that it is not possible to generalize the linear two-products model to the n goods case. See for example Anderson, De Palma and Thisse 1991 p.120. In this appendix we show, with reference to the audience function, how pairwise comparisons of n products allow to solve the problem. See also, for linear demand systems, Polo 1996. 19
Ui = qi , ai + i = si + i
16
for i = 1; ::; n, where term with zero mean
sainids
thneitedveateriramnicnei,sdtircawnnetfrsoumrpalucsofmrommotnhdeipstrroigbruatmiona,nrdepireisseanrtainngdovmiewi.ei.rds'.
heterogeneity on a horizontal di erentiation dimension. The outside utility is U0 = s0 + 0.
nhperaorngTcrdhahomteihrcmeee eeobxu1yitssatcinodnmdenp2o,pa+rtwii1nohngi=l.2epVtrthoyiegepwresaseumrbosmf'sevhetieeittw0ea;renonrgsdidetnejin;ejoittifnyoleryis.si;ttFjhhoe=errvei0infe;osw1rte;ae:rn:rs;cenefwe,arharnoeddtc1hi;t2o6=oovtsjihee:ewbaeperttaiwic;rjheeovonfioesawpelrsteoerbgrdnreaeatwcmtiiedvmeeensse
they consider and to the random components in the preferences on each of the two alternatives
considered.
and
It is convenient to addicted viewers:
de the
fnoer,mreesrpwecatticvhelya,ttympoesstt0t;hi eainrdprtei;fje,rri;ejd
= 1; ::; n, channel,
i 6= j, while
as idiosyncratic the latter watch
in any case a programme, chosen between their two elected channels. We have therefore n subsets
of idiosyncratic viewers and nn , 1=2 subsets of addicted ones.
A viewer of any type knows the realizations of the random terms which characterize her
preferences. An outside observer knows only the distribution of the di erence in the random
terms, which is uniformly
2 x
=
L2=3,
density
f
x
=
distributed 1=2L and
on the support ,L; L cumulative density Fx
, with = 1=2
+mxe=an2Lx.
=
0,
variance
There exists a large number of is f=nn + 1, f 2 0; n + 1 , while f=nn + 1n , 1. Notice that if
viewers; the the share of f = 2 we are
seihanachsryeomofmftheeaetcrihacdocdaficstethe,edinitdywipohesiyscnhtci;rajalltiistch2teynpvie+esw1teir,;0s
types are equally important, while if f = 0 f = n + 1 only addicted idiosyncratic viewers are
represented. Finally, the aggregate size of all the idiosyncratic types is f=n + 1 while that of
the addicted types is n + 1 , f=n + 1.
chosAentib;jy
viewer, j = 0; ::; n, j 6= i a ti;j viewer is therefore
patronizes F si , sj
programme or
i
if
Ui

Uj .
The
probability
that
i
is
80
1
, si sj
P r i = 1 + i;j
:2
2L
if si , sj ,L
if if
,L si , sj
si
, L
sj

L
17
Aggregating individual choices over viewers' types we obtain the linear audience function.
8
9
Ai =
f :nn +
1
P
ri;0i
+
2n + 1 , f n + 1nn , 1
X n 6 j =1;j =i
P
=
ri;j
i ;
18
Substituting the corresponding expressions30 we obtain:
8
9
Ai =
n + :
n qi , ai ,
n
Xqj 6j=i
,
=
aj
;
19
30We explicitly represent the aggregate audience when P ri;j i 2 0; 1 for all the viewers' types; the extension to the corner solutions is trivial.
20
where
=
2n
+
2 , f , nfs0w 2nn + 1
=
2n + 2 , 2nn +
fw 1
=
n + 1 , fw n + 1nn , 1
and where w = 1=L. Two parameters are related to the degree of horizontal di erentiation
among channels. The rst parameter is w, which is inversely related to the degree of horizontal
heterogeneity in tastes at the individual level: a higher w implies that the variance in the random
component decreases, and determines a more elastic individual and aggregate schedule. The
second relevant parameter is f, which measures the relative importance of idiosyncratic viewers
in the population: a higher f implies that when programme i becomes more attractive a higher
vsiie,wtehrse
increase in - expansion
audience e ect and
is determined relatively relative less by the shift
more by the of addicted
entry of new idiosyncratic consumers from other goods
- displacement e ect. The degree of di erentiation among channel i and the remaining n , 1
channels, dn = =n , 1 , is
dnf
=
2n + 2 , f 2n + 2 , 2f
20
For given f, the degree of horizontal di erentiation is decreasing in n; moreover, it is equal to 1 when f = 0 no audience expansion e ect and tends to 1 when f ! n+1 no displacement e ect, i.e. when there is no competition among channels. Finally, it is worth noting that w does not in uence the degree of di erentiation at the aggregate level.
21

M Motta, M Polo

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