copying, superstars, and artistic creation
TRANSCRIPT
Information Economics and Policy 22 (2010) 365–378
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Information Economics and Policy
journal homepage: www.elsevier .com/ locate / iep
Copying, superstars, and artistic creation
Francisco Alcalá a,b,*, Miguel González-Maestre a
a Departamento de Fundamentos del Análisis Económico, Universidad de Murcia, Campus de Espinardo, 30100 Murcia, Spainb Ivie, Calle Guardia Civil 22, 46020 Valencia, Spain
a r t i c l e i n f o
Article history:Available online 17 July 2010
JEL Classification:L10L82Z1
Keywords:Artistic creationSuperstarsPrivate copyPiracyLevies
0167-6245/$ - see front matter � 2010 Elsevier B.Vdoi:10.1016/j.infoecopol.2010.05.001
* Corresponding author. Address: DepartamentoAnálisis Económico, Universidad de Murcia, CampusMurcia, Spain. Tel.: +34 868883767; fax: +34 86888
E-mail addresses: [email protected] (F. Alcalá), mGonzález-Maestre).
a b s t r a c t
We provide a new perspective on the impact of unauthorized copying and copy levies onartistic creation. Our analysis emphasizes three aspects of artistic markets: the predomi-nance of superstars, the important role of promotion expenditures, and the difficulties oftalent-sorting. In the short run, piracy reduces superstars’ earnings and market shareand increases the number of niche and young artists. In the long run, copying can also havea positive effect on high-quality artistic creation by helping more young artists start theircareers, which increases the number of highly talented artists in subsequent periods. Thelong-term impact of levies on copy equipment on artistic creation depends on whethertheir yields primarily accrue to superstars who already receive rents or are allocated tohelp young artists.
� 2010 Elsevier B.V. All rights reserved.
1. Introduction taxes and levies on copy equipment and electronic de-
The music industry and other artistic markets areexperiencing profound changes as a result of digitalrecording, Internet file-sharing, and new electronic de-vices. This has launched a far-reaching debate on theconsequences of new technologies for artistic creationand the possible need to redefine intellectual propertyrights.
According to some individuals and companies in theartistic industry, file-sharing and unauthorized copyingare bound to have a very negative impact on artistic crea-tion. These individuals have asked for controls and restric-tions on the use of the Internet for copying and for levieson copy equipment that would restore incentives forartistic creation. Their arguments have led many countriesin Europe and other parts of the world to implement new
. All rights reserved.
de Fundamentos delde Espinardo, [email protected] (M.
vices.1 Revenues from levies tend to be allocated to copy-right holders, performers, and publishers according to theirsales in the market.
In contrast, it has also been argued that current copy-rights are excessive in most Western countries and thattheir yields mostly accrue to a relatively small number ofsuperstars and artistic firms that obtain economic rents.New communication technologies and file-sharing mayhelp the careers of young and niche artists and reducethe concentration of sales in artistic markets. Restrictionson file-sharing and the implementation of levies on copyequipment may revert this process and harm the generalpublic.
This paper explores some of these questions. Can file-sharing and copying really favor niche and young artists?Can they do this without hampering high-quality artistic
1 The average copy tax implemented in Western European countries is0.17 euros for blank data-CDs and 0.45 euros for blank DVDs. Copy taxes ondevices such as Mp3 players, memory cards, and hard-disk DVD recordersdepend on their GB memory and range from 4 to 50 euros (see DeThuiskopie, 2009).
366 F. Alcalá, M. González-Maestre / Information Economics and Policy 22 (2010) 365–378
creation? Even more, might it be possible that file-sharingand copying enhance high-quality creation in the long run?This paper analyzes the short- and long-term conse-quences of unauthorized copying for artistic creation andthe effects of implementing different types of copy levies.It does so within a theoretical framework that emphasizesthree key aspects of artistic markets that have largely beenneglected in the conventional analyses: the predominanceof superstars, the important role of promotion expendi-tures, and the dynamics of talent-sorting. These threeaspects of artistic markets can be briefly explained asfollows.
First, artistic creation is intensive in an innate input: tal-ent. Rosen (1981) shows that this factor, combined withthe scale economies associated with the joint consumptionof artistic goods, leads to the superstar phenomenon: theconcentration of output and extremely large rewards forthe most talented artists.2 Second, promotion costs are acrucial ingredient in explaining the demand for artistic prod-ucts and greatly affect the division of market shares betweensuperstars and niche as well as young artists.3 Third, there isa dynamic positive link between the current number ofyoung artists and the future number of highly talentedsuperstars. As pointed out by MacDonald (1988), talentand charisma are not easily detected. As a result, to have alarge number of highly talented artists in the future, oneneeds to have many young artists starting an artistic careertoday (even though most of them will not succeed).4
Consistent with these circumstances, our analysismakes an explicit distinction between superstars (orhigh-type artists) and niche and young artists (or low-typeartists). First, we consider the short-run equilibrium inartistic markets. In the short run, the number of superstarsis exogenously given whereas there is free entry into thesub-market of niche and young artists. Piracy reducessuperstars’ earnings and the incentives to invest in theirpromotion. This tends to increase the number and marketshare of niche and young artists.
Second, one must analyze the dynamics of the marketand its long-run equilibrium. We build a simple overlap-ping-generations model of artists in which only a fraction
2 Several papers provide evidence of the strong concentration of sales inthe market for popular music. See Rothenbuhler and Dimmick (1982), Crainand Tollison (2002), and Krueger (2005), among others. Krueger (2005), forexample, reports that in 2003, the top 1% of artists obtained 56% of concertrevenues, with the top 5% taking in 84%. Similarly, there is evidence of theextremely skewed distribution of copyright yields across artists, even ifdata about these earnings are not easily accessible (they are privately heldby collecting societies). For example, Kretschmer and Hardwick (2007)report data on the distribution of payments in 1994 by the UK PerformingRight Society. This society distributed £20,350,000 among 15,500 writersfor the public performance and broadcasting of their works. The top 9.3% ofwriters earned 81.07% of the total. Ten composers earned more than£100,000, whereas 53.1% of the composers earned less than £100. Theseauthors’ estimations for the period 2004–2005 show similar results. Forevidence on superstars’ rents in the motion picture industry, see Chisholm(2004).
3 For example, Peitz and Waelbroeck (2005) cite several sources showingthat marketing and promotion are the main costs of making and selling arecorded CD.
4 See Terviö (2009) for a general analysis of the market’s failure todiscover talent and how this leads to inefficiently low output and higherearnings for known talents.
of young artists starting an artistic career show talentand become superstars later in their careers. This endoge-nizes the number of superstars. Piracy may help moreyoung artists to start their careers, which in turn mayincrease the number of highly talented artists in the longrun.
Third, policy issues are important to consider. We com-pare the consequences of different levies on copy equip-ment and analyze alternative schemes for allocating theiryields. We find that taxes on copying may hinder the pro-motion of niche and young artists and hamper artistic cre-ation in the long run. Moreover, the most common policyin Western countries of distributing levy yields in propor-tion to market sales strongly favors superstars. This in-creases the incentives to promote superstars, therebyfueling market concentration, which in turn reduces artis-tic diversity in the short run and high-quality artistic crea-tion in the long run.5 We find that artistic creation can bestimulated more effectively in both the short and long termby allocating levy yields using non-linear (concave in sales)schemes that favor young artists.
A growing body of economic literature is graduallyaddressing the effects of the new information and copyingtechnologies on artistic markets and other industries (seePeitz and Waelbroeck, 2006, for a survey). Alcalá and Gon-zález-Maestre (2009) and Zhang (2002) are the closest pa-pers to this one. Alcalá and González-Maestre (2009) builda model with the three aspects of artistic markets empha-sized here and analyze the optimal length of the copyrightterm. Nonetheless, they do not consider the possibility ofunauthorized copying and do not explore its consequences.Zhang (2002) considers the role of promotion costs andcopying in artistic markets using a duopoly model in whichdigital copies help to reduce the distortionary effects of thelarge-audience artist’s persuasive advertising. However, inZhang’s (2002) model there is no entry into the low-typesub-market, or to the high-type artistic sub-market. In con-trast, analyzing entry into each of these markets is crucialto our investigation of how unauthorized copying and copylevies may affect artistic creation in the short and in thelong run.6
Two final notes on the scope and the limitations of thispaper are the following. First, the paper mostly concernsthe music and recording market. However, similar mecha-nisms are present in most activities to which creative workis important and in which it can be easily copied, as in themovies. Second, a key assumption throughout the paper isthat superstars’ earnings are above their opportunity cost,i.e., that they obtain rents. This seems a reasonable hypoth-esis and is motivated by the empirical evidence regardingthe concentration of market share and of revenues tosuperstars. Moreover, the dynamic model in Section 3, inwhich the number of superstars is endogenized, shows
5 Moreover, as long as not all of the equipment subject to copy levies isused for copying artistic material (as happens with many data-CDs, hard-disks and pen drives), this scheme for allocating copy levies may involve atransfer of resources from the rest of the economy to superstars.
6 Other papers such as those by Gayer and Shy (2003) and Kinokuni(2005) have analyzed the effects of copy levies on technological markets.However, to our knowledge, this is the first paper analyzing the effect ofthese levies on artistic creation.
F. Alcalá, M. González-Maestre / Information Economics and Policy 22 (2010) 365–378 367
that superstars can indeed obtain rents in equilibrium(even if there is free entry into the artistic market as youngartists and all talented young artists become superstars la-ter in their careers).
The rest of the paper is organized as follows. Section 2lays out the static version of the model and analyzes theshort-run equilibrium of artistic markets with and withoutpiracy. Section 3 introduces the dynamic version of themodel and investigates the long-run impact of copyingon artistic creation. Section 4 considers different types oflevies on copy equipment and analyzes their impact onartistic creation. Section 5 concludes.
8 Usually, consumers buy at most one unit of each artistic good. This isthe case for the symmetric equilibrium of this model if we assume that S islarge enough so that the number of artists will be large with respect to theconsumer’s expenditure. In such a case we have xi 6 1 and yj 6 1(i = 1,. . . n;j = 1,. . .m). Then, xi (resp. yj) should be interpreted as the probability thatthe representative consumer will buy the work of artist i (resp. j). Becausethere is a measure-S continuum of identical consumers, these probabilitiestranslate into certain aggregate sales Xi = xi�S and Yj = yj�S. Also note thatthis consumer problem could be framed in a more general two-stagebudgeting model with a general consumption good in addition to artisticgoods.
9 The relationship between creators and artistic firms (such as labels and
2. Superstars and niche artists: the short run
In this section, we introduce the static version of themodel and analyze the short-run equilibrium of artisticmarkets. Artists may be either high-type (superstars) orlow-type (niche and young artists). In the short run, thenumber of high-type artists is exogenous, whereas thereis free entry into the sub-market for low-type artists. Theexogeneity of the number of high-type artists capturesthe idea that the set of superstars changes with lower fre-quency than the set of niche and young artists. The numberof high-type artists is endogenized in the dynamic modelin Section 3 in which we analyze artistic markets in thelong run.
Each active artist creates a single artistic good (such as asong, novel, and movie). Therefore, artistic creation is pro-portional to the number of artists, though we may distin-guish between high-quality artistic creation (whichresults from high-type artists’ work) and low-quality artis-tic creation (low-type artists’ work). Being active as an art-ist involves opportunity costs Fl for low-type artists and Fh
for high-type artists.7 As discussed in the Introduction, weassume throughout the paper that superstars’ earnings areabove their opportunity cost Fh, i.e., they obtain rents.
Once an artistic good is created, it can be infinitelyreproduced at some constant marginal cost. Consumerscan consume artistic goods by buying original reproductions(originals for short), which pay copyrights, or unauthorizedcopies (copies for short), which do not. We first analyzeartistic markets when piracy does not exist; i.e., when indi-viduals can only buy originals. Then, we introduce piracyand consider the case in which all artists are copied. Weend this section by addressing the possible intermediatecases in which superstars are affected by copying butlow-type artists are not.
Introducing and solving a model with different types ofartists whose work has imperfect substitutes (unautho-rized copies) that are valued differently across heteroge-neous groups of consumers and in which advertising anddynamics play an important role, can be complicated andtedious. In the main text, we simplify a number of issues
7 Fl and Fh can be interpreted as the fixed cost of creating a low- and ahigh-type artistic good, respectively. In addition to including the artists’time opportunity cost, these parameters can be interpreted as alsoincluding the costs of other inputs needed for creation (e.g., recording orfilming equipment).
to make the main argument more transparent. We indicateour generalizations in Appendices A and B.
2.1. The model without piracy
There is a measure-S continuum of consumers. Theyspend an amount of money on artistic goods that is nor-malized to 1. The representative consumer solves the fol-lowing utility maximization problem:
maxxi ;yj
a lnXn
i¼1
xi
!þ ð1� aÞ ln
Xm
j¼1
yj
!" #; ð1Þ
s:t:Xn
i¼1
xiph þXm
j¼1
yjpl ¼ 1;
where xi (respectively, yj) is consumption of superstar i’soriginals (resp., low-type artist j’s originals), ph (resp., pl)is the price of superstars’ (resp., low-type artists’) work,and n (resp. m) is the exogenous (resp. endogenous) num-ber of high-type (resp. low-type) artists.8 In Appendix A, weexplicitly introduce horizontal differentiation (and monopo-listic competition) within each group of artists.
Superstars’ market share a is endogenous and positivelydepends on superstars’ expenditures on promotion andmarketing. Only high-type artists enjoy promotion andmarketing expenditures, which may be thought of as man-aged by competitive artistic promotion firms.9
A firm’s advertising tends to increase both the relativedemand for that firm’s good and the overall demand forthe type of good being advertised (Sutton, 1991). Thissecond effect is the most important one in our argument.Hence, in order to simplify we consider only this secondeffect in the main text, which is captured by a positiveeffect of superstars’ total promotion expenditure on theirmarket share a. In Appendix B we consider a more generalset-up with vertical product differentiation where eachsuperstar’s promotion expenditure also increases con-sumer preference for her specific work.
Let Ai be artist i’s promotion expenditures (Ai P 0) andA �
Pni¼1Ai. Superstars’ market share is increasing in n
and in promotion expenditures per consumer A/S, boundedabove zero if their total advertising is zero, and equal to 1 iftheir total advertising A is infinite:
publishers) are regulated by contracts that can make artistic firms the mainbeneficiaries of the market. The potential conflict of interest betweencreators and artistic firms has been analyzed in Gayer and Shy (2006). Herewe simplify this issue by assuming that artistic promotion firms areperfectly competitive or, alternatively, by considering each superstar in themodel to be a vertically integrated structure consisting of a high-type artistand a promotion firm.
368 F. Alcalá, M. González-Maestre / Information Economics and Policy 22 (2010) 365–378
a ¼ 1� be�cnA=S; ð2Þ
where b and c are exogenous parameters, 0 < b < 1, c > 0.We consider the following timing of competition:
Stage 1: Each high-type artist chooses simultaneously andindependently her Ai.
Stage 2: Each potential low-type artist decides whether toenter and be active in the low-type artistic sub-market. As noted, entry involves a fixed opportu-nity cost Fl.
Stage 3: All active artists decide how many original repro-ductions of their work to bring to the market(they compete à la Cournot).
We use the following notation: Xi ¼ xiS; X ¼Pn
i¼1Xi;
X�i ¼Pn
k–iXk; Yj ¼ yjS; Y ¼Pm
j¼1Yj; Y�j ¼Pm
k–jYk. Let usconsider the Cournot–Nash equilibrium at Stage 3. Stan-dard calculations yield inverse demand functions ph = aS/X and pl = (1 � a)S/Y. Hence, high-type artist i’s earningsas a function of her output Xi and other high-type artists’output X�i, are
phi ðXi;X�iÞ ¼
aSXi
X� cXi � Ai; i ¼ 1;2; . . . ; n:
Cournot-equilibrium first-order conditions yield ph ¼ nn�1 c;
Xi ¼ ðn�1Þn2
aSc . Hence superstar i’s earnings as a function of
her and other superstars’ advertising are as follows:
phi ðAi;A�iÞ ¼
aSn2 � Ai: ð3Þ
Substituting with (2) and maximizing phi with respect to Ai
yields the subgame perfect equilibrium (SPE) value ofsuperstars’ total market share (which is denoted by a*):
be�cnA=S
nc� 1 ¼ 0! a� ¼ 1� n
c: ð4Þ
Inequality c > n/b must hold to insure Ai > 0. We assumethat c is always high enough to guarantee this condition.Moreover, ph
i > Fh requires n to be small enough or S largeenough.10
In turn, each low-type artist j’s revenues as a function ofher output and other high-type artists’ output, are pl
jðYj;
Y�jÞ ¼ ½ð1� aÞS=Y � c�Yj. Cournot equilibrium in the low-type sub-market yields pl ¼ m
m�1 c; Yj ¼ m�1m2
ð1�aÞSc . The equi-
librium number of active low-type artists m* is then deter-mined by the free entry condition pl
j ¼ Fl, which yields:
m� ¼ nS
cFl
!12
: ð5Þ
2.2. The impact of piracy
We now introduce piracy. Consumers can obtain unau-thorized copies of any artistic good at an exogenous cost pc.The characteristics of market equilibrium may changedepending on the value of pc with respect to the equilib-
10 As discussed in the Section 1, we assume throughout the paper thatsuperstars’ earnings are above their opportunity cost Fh; i.e., they obtainrents.
rium values of ph and pl. Different cases lead to differentcombinations of superstars’ and niche artists’ copies beingblockaded, deterred, or accommodated. In this subsectionwe assume that pc is low enough such that in equilibriumpc < pl
6 ph. As a result, all artists are pirated. This case mayseem the most relevant one from the empirical point ofview and is likely to make the strongest case againstpiracy. In the next subsection, we briefly characterize theother possible cases (copying is deterred, only superstarsare copied, etc.).
Consumers behave heterogeneously with respect totheir attitude towards originals or unauthorized copies(this may be due to differences on several dimensions: val-uation based on quality, moral restraints on copying,opportunity cost of the time needed to search for anddownload files from the Internet, etc.). The theoretical liter-ature has formalized consumer heterogeneity in differentways (see Peitz and Waelbroeck, 2006). In this paper, weconsider a continuum of consumers with different (con-stant) marginal rates of substitution t between copies andoriginals. The consumer problem is now recast as follows:
maxxi ;zi ;yj ;zj
a lnXn
i¼1
xi þ tzi½ � !
þ ð1� aÞ lnXm
j¼1
yj þ tzj� � !" #
;
ð6Þ
s:t:Xn
i¼1
xiph þXn
i¼1
zipc þXm
j¼1
yjpl þXm
j¼1
zjpc ¼ 1;
where zi and zj are respectively consumption of copies ofsuperstar i’s and low-type artist j’s work. Assuming that tis uniformly distributed across individuals along the inter-val [0,1], the fraction d of individuals that buy originals inthe case of high-type goods is d = pc/ph (provided thatpc < ph; otherwise, d = 1). The remaining fraction 1 � d con-sume copies. Hence, if pc < ph, the demand for high-typeoriginals is now X = aSpc/(ph)2. Similarly, if pc < pl, thedemand for low-type artists’ originals is Y = pc(1 � a)S/(pl)2 (otherwise, their demand is Y = (1 � a)S/pl as in theprevious subsection). Thus, demand is more elastic as aresult of competition from copies.
As already indicated, in this subsection we assume thatpc is low enough such that in equilibrium pc < pl
6 phi .
Hence, all artists’ work is pirated (although not all consum-ers buy copies). Using the corresponding new demandfunction at the last stage of the game, Cournot competitionamong high-type artists yields:
ph ¼ 2n2n� 1
c; Xi ¼ð2n� 1Þ2
4n3
pcaSc2 ;
phi ðAi;A�iÞ ¼
2n� 14n3
pcaSc� Ai: ð7Þ
As before, substituting for a with (2) and maximizing phi
with respect to Ai yields the new level of a denoted as ac:
be�cnA=S ¼ 1c
cpc
4n2
2n� 1! ac ¼ 1� 1
ccpc
4n2
2n� 1: ð8Þ
In turn, low-type artists’ profit maximization conditionalon the demand when their work is pirated (i.e., pc < pl),yields equilibrium price pl ¼ 2m
2m�1 c and per artist output
F. Alcalá, M. González-Maestre / Information Economics and Policy 22 (2010) 365–378 369
Yj ¼ ð1� aÞ pc
c2 S ð2m�1Þ24m3 . Then, using the free entry condition,
we obtain the short-run equilibrium number of low-typeartists in the case of piracy:
mc ¼ 2mc � 1mc
n2n� 1
nS
cFl
!1=2
: ð9Þ
Comparing (5) with (9) shows that mc > m* if mc > n (whichis taken for granted).
Proposition 1. Consider the short-run equilibrium in whichthe number of superstars is given. If the parameters are suchthat all artists’ work is pirated, the number of niche and youngartists in the market is larger with piracy than if piracy can becompletely prevented.
The intuition behind this result is that superstars’ pro-motion expenditures act as a barrier to entry againstlow-type artists. Copying reduces the profitability ofsuperstars’ promotion, thereby leaving a larger marketshare for low-type artists (compare (8) with (4)).11 This po-sitive effect is large enough to compensate for the fact thatlow-type artists are also copied. Copying also brings abouta reduction in the prices of both high- and low-type artisticgoods, which benefits consumers.12 In Appendix A we showthat the same qualitative result is obtained in a Dixit andStiglitz (1977) model of monopolistic competition withhorizontal differentiation. In Appendix B we show that thesame qualitative result is obtained in a model with verticaldifferentiation in which each superstar’s advertising has aspecific effect on the demand for her work.
2.3. The general case: from blockaded copying toaccommodation
In general, there are several possible scenarios for thevalue of pc with respect to the equilibrium levels of ph
and pl. This leads to different characteristics of equilibrium.We briefly describe the different cases here and refer to theAppendix C for a detailed analysis. Denote by ph the priceof high-type originals as obtained in Subsection 2.1 forthe case in which there is no piracy, ph � n
n�1 c, and by ph
the price of high-type originals when high-type work iscopied, as computed in Subsection 2.2: ph � 2n
2n�1 c. Simi-larly, denote by pl the price of low-type work when itsmarket is not affected by piracy and by pl its price whenlow-type work is copied. The possible cases dependingon the exogenous level of pc are as follows13:
11 Empirical evidence regarding the market for rock concerts seems to beconsistent with the model’s prediction regarding the decreasing marketshare of superstars. According to Pollstar (an industry trade magazine),ticket revenues from concerts in North America in 2007 rose to $3.9 billion,which represents about an 8% increase over 2006 with $3.6 billion and theninth consecutive year with increasing revenues. However, the top 20 tourscombined saw a 15% decline in ticket revenues from that of the top 20 toursfrom 2006.
12 The effect of copying on CD prices has been openly recognized by theRecording Industry Association of America. See RIIA (2007).
13 See the Appendix A, where it is also shown that pl ¼ mm�1 c and
pl � 2m2m�1 c. It could also be the case that ph � pl . In such a case, the analysis
is somewhat simpler because case (iii) is replaced by a different case inwhich both high- and low-type artists fix the same price pc for theirproducts thereby both deterring piracy.
(i) pc > ph;(ii) ph P pc P ph;
(iii) ph > pc > pl;(iv) pl P pc P pl; and(v) pl > pc .
These cases correspond to: (i) (all copies are blockaded)(ii) (all copies are deterred) (iii) (copies of superstars’work are accommodated whereas copies of low-typework are blockaded) (iv) (copies of superstars’ workare accommodated whereas copies of low-type artists’work are deterred) and (v) (copies of superstars’ workand that of low-type artists’ work are accommodated).This last case was the one analyzed in the previoussubsection.
Fig. 1 depicts m as a function of pc based on the anal-ysis in Appendix C. The key result is that m is larger inall cases in which the market is affected by piracy (cases(ii)–(v)) than when it is not (case (i)). The followingproposition characterizes m as a function of pc in the fivecases.
Proposition 2. Consider the short run when the number ofsuperstars is given. The number of niche and young artists mis a continuous function of the price of copies pc, which ischaracterized as follows. There is a critical value po < ph thatmaximizes m. This value po is the lowest value of pc such thatsuperstars are pirated but low-type artists are not affected bypiracy, which occurs for pc ¼ pl. For pc > po, m is monoton-ically decreasing, whereas for pc < po, m is monotonicallyincreasing. Moreover, m is constant for small values of pc suchthat all artists are copied, and for values such that none arecopied. In all cases, the number of niche and young artists islarger when the market is affected by piracy than when it isnot.
Proof. See Appendix C. h
As noted, the key result is that m is larger in all casesin which the market is affected by piracy than when it isnot. Still, there are quantitative differences betweencases (ii) through (v) that will be of interest in discussingpolicy alternatives in Section 4. Thus, it is useful tobriefly discuss which cases may be most relevant. Be-cause casual observation indicates that the work of mostartists is copied, it seems that the most relevant case isthat analyzed in Section 2.2. Still, the case in which onlysuperstars are copied may be of particular interest.Superstars’ work is more likely to be copied, not only be-cause their originals tend to be more expensive but alsobecause their larger market makes their work more eas-ily available in P2P networks. However more importantlyin the case of the music industry, revenues from records(as opposed to revenues from concerts) are relativelymore significant for superstars than for young and nicheartists. There is an important reason for this: the econo-mies of scale of joint consumption that give rise to thesuperstar phenomenon entail a limitation on the numberof live performances but no limitations on the number ofrecords sold. In fact, the main goal of superstars’ concerttours, at least until the advent of the Internet, was topromote new records. This is not the case for niche
Fig. 1. The short run number of low-type artists m as a function of the cost of unauthorized copies pc.
370 F. Alcalá, M. González-Maestre / Information Economics and Policy 22 (2010) 365–378
and young artists, some of whom are willing to providerecords on the Internet even for free as a way to becomepopular and increase demand for their live performances(see Peitz and Waelbroeck, 2005).14
The model can account for these circumstances bymeans of a reinterpretation. In the simplest reinterpreta-tion, it can be assumed that the consumption of high-type artists’ work entails buying or copying records, asbefore, whereas consumption of low-type artists’ workentails attending live performances. (Now, in the caseof low-type artists, Y represents concert ticket salesand c represents the marginal cost of using a venue withone more seat). Under this interpretation, which empha-sizes the different origin of the main source of revenuesfor each group of artists, only superstars can be copied.The results of case (iii) are then the most interesting toconsider.
3. Piracy and artistic creation in the long run
In this Section, we analyze the long-run conse-quences of piracy for high-quality artistic creation. Todo so, we endogenize the number of high-type artistsin a dynamic model. The number of highly talented ar-tists in the market at a given point in time depends onthe available opportunities for starting an artistic careeras a young artist in the previous periods. Young poten-tial artists may or may not be talented, but their talentand charisma can only be ascertained if they actually
14 At any rate, the importance of live performances is increasing for alltypes of artists. For example, according to the Music Managers Forum (atrade group in London) musicians derived two-thirds of their income in2000 from record labels, with the other one-third coming from concerttours and merchandise. In 2007, this proportion reversed. Still, consumers’total expenditure on music seems to be roughly the same. According tosome concert promoters, music lovers seem to have a mental budget tospend on music and have switched their spending from CDs to tickets andmerchandising (see The Economist, July 5th 2007). This suggests that ourassumption of a constant consumers’ budget in the artistic market may bereasonable even when the nature of thegood being bought changes, with ashift from recorded music to concerts.
enter the artistic market and perform for the public.After some period in the market, only a small fractionof them show talent and become superstars.15 The restof the young artists eventually drop out of the artisticmarket. In this context, the high earnings and marketshare associated with stardom have a conflicting impacton new artistic careers. Superstars’ large earnings attractyoung potential artists and push them to start an artisticcareer. However, the larger the market share absorbed bythe current generation of superstars, the smaller theroom for a new generation of talents to be tested and re-vealed. This reduces the future number of highly talentedartists. Piracy weakens superstars’ position, which canthen help young artists and, in the long run, increasehigh-quality artistic creation.
3.1. A model of overlapping generations of artists
We consider an overlapping-generations extension ofMacDonald’s (1988) model of artistic markets. Thisextension is similar to the one in Alcalá and González-Maestre (2009). The key difference is that here we intro-duce piracy and consumer heterogeneity. Artists live fortwo periods. Every period, there is an infinite pool of po-tential young artists in the population. The probabilitythat young artists are talented is q, but neither theynor artistic promotion firms can observe their talent le-vel until after they complete a period as active artistsin the market. Individuals entering the artistic professiondo so in their first period of existence as young artists.Only the fraction q of young artists that reveal them-selves to be talented in this first period continue theartistic career in their second life period as high-type ar-
15 Some economists have raised doubts about superstars necessarilyhaving above average talent (see for example Adler, 1985). If superstars donot have more talent than the average artist, the arguments in this papercan be simplified and the results will be reinforced. In fact, our short-termstatic model would suffice to show that piracy increases overall artisticcreation if there is no distinction between high- and low-quality creation.
F. Alcalá, M. González-Maestre / Information Economics and Policy 22 (2010) 365–378 371
tists and receive advertising. Non-talented artists dropout of the artistic market at this point.16
Thus, during every period, the artistic market looks likeit does in Section 2 except that low-type artists are nowonly interpreted as young artists, with the number ofhigh-type artist at time t, nt, given by
nt ¼ q �mt�1: ð10Þ
Every period, a new generation of potential young artistsdecide whether to enter the artistic market (in which casethey create an artistic good) or to stay out of the market.We denote by Fl the income that potential artists can earnoutside the artistic market and assume a constant relativerisk aversion utility function with coefficient r. Then, thepresent discounted value of not embarking on an artisticcareer is U ¼ ð1þ hÞ 1
1�r ðFlÞ1�r, where h is the discount fac-
tor for second-period earnings. In turn, the present dis-counted expected utility of beginning an artistic career attime t as a young artist is
Ut ¼1
1� rpl
t
� �1�r þ h q phtþ1
� �1�r þ ð1� qÞðFlÞ1�rh ih i
:
Because there is free entry to the market for young artists,the following expression will determine the number ofyoung artists at time t:
11� r
plt
� �1�r þ hq phtþ1
� �1�r � ð1þ hqÞðFlÞ1�rh i
¼ 0: ð11Þ
In the following, we directly solve for the steady state equi-librium, which is obtained by taking n = q�m.
3.2. The long-run impact of piracy
As in the previous section, we first compare the case inwhich there is no piracy with the case in which all artistsare pirated. Then, we briefly consider all of the intermedi-ate cases of piracy.
3.2.1. The case in which all artists are copiedConsider first an economy in which unauthorized copy-
ing is not possible. In the short run, the SPE revenues forhigh and low-type artists are, respectively,
ph ¼ Scn
cn� 1� 1
nln
cbn
� �� ; ð12aÞ
pl ¼ Sq2
cn: ð12bÞ
16 The details of the process of how artists with heterogeneous andunknown talent are sorted by the market through information accumula-tion are analyzed in MacDonald (1988). Assuming that future performanceis correlated with past performance, MacDonald shows that individualsenter the artistic career only when they are young (i.e., during the first life-period) and remain in the artistic market for the second period if and only ifthey receive a good review of their performance in the first period. If thishappens, their performances in the second life-period are attended by alarger number of consumers who pay higher prices (i.e., the artist becomesa superstar). Our setting is intended to indicate a reduced form of thisprocess.
Substituting these expressions into (11) yields
V�ðnÞ � 11� r
Scn
� �1�r
q2ð1�rÞ
1þ hq2r�1
"
� cn� 1� 1
nln
cbn
� �� 1�r!� ð1þ hqÞðFlÞ1�r
#¼ 0:
ð13Þ
The value of n solving this expression determines the stea-dy state number of high-type artists n�ss when there is nopiracy.
Similarly, from the previous analysis of the short-runequilibrium in the case where all artists are copied, wehave the following:
ph ¼ Scn
cn
2n� 14n
pc
c� 1� 1
nln
cbn
pc
c2n� 1
4n
� �� ; ð14aÞ
pl ¼ Sq2
cn2n� q2n� 1
: ð14bÞ
Hence, substituting into (11) yields:
VcðnÞ � 11� r
Scn
� �1�r
hq
� cn
2n� 14n
pc
c� 1� 1
nln
cbn
pc
c2n� 1
4n
� �� 1�r
þ 11� r
Scn
� �1�r
q2ð1�rÞ 2n� q2n� 1
� �1�r"
� ð1þ hqÞðFlÞ1�ri¼ 0 ð15Þ
The value of n solving this expression determines the stea-dy state number of high-type artists nc
ss under piracy.Now, we have:
VcðnÞ � V�ðnÞ > 0() 11� r
2n� q2n� 1
� �1�r
� 1
" #
þ hq2r�1 11� r
cn
2n� 14n
pc
c� 1
�
�1n
lncbn
pc
c2n� 1
4n
� �1�r
� hq2r�1 11� r
cn� 1� 1
nln
cbn
� �� 1�r
> 0:
Thus, Vci ðnÞ � V�i ðnÞ > 0 can be ensured if hq2r�1 is small
enough, which in turn is the case if h is small enough orif r > 1/2 and q is small enough. Under these conditions,this inequality is satisfied for any n, and, in particular, forn ¼ n�ss. Because both Vc
i ðnÞ and V�i ðnÞ are strictly decreas-ing in n, it follows that h or q being small enough (ifr > 1/2) is a sufficient condition for nC
ss > n�ss. Furthermore,n = qm also implies that mC
ss > m�ss. Hence, we have thefollowing.
Proposition 3. Consider the case in which all artists arepirated. In the long run, if high-type artists obtain rents andhq2r�1 is small enough (that is, if the time discount factor orthe probability of becoming a star is sufficiently low, with
Fig. 2. The long-run number of high-type artists nss as a function of the cost of unauthorized copies pc.
372 F. Alcalá, M. González-Maestre / Information Economics and Policy 22 (2010) 365–378
r > 1/2), piracy increases the number of low- and high-typeartists.
Thus, the reduction in the superstars’ earnings thatresults from piracy does not necessarily reduce the numberof young artists starting an artistic career. In fact, the oppo-site is true if the time discount factor or the probability ofbecoming a superstar is sufficiently low. Piracy shifts rev-enues from superstars to young artists (piracy reducesthe profitability of superstar promotion, which thereforedecreases thereby raising young artists’ market share).This, from a young artist’s perspective, implies the trans-formation of future potential earnings into actual currentones. Hence, the present discounted value of starting anartistic career increases. Furthermore, because the numberof talented high-type artists in the long run depends on theabundance of young artists trying to develop an artisticcareer, piracy increases the long-run number of high-typeartists.
3.2.2. Considering all casesIf pc < pl and pc < ph all artists are pirated, which is the
case considered so far. We now briefly consider all possiblecases of pc with respect to pl and ph (see Appendix C fordetails). The results of Proposition 3 are conditional onthe discount factor or the probability of becoming a super-star being low. The same is true for the remaining results.Bearing this in mind, in what follows we concentrate onthe case h = 0, which greatly simplifies the exposition. Forh = 0, (13) and (15) simplify to
n�ss ¼ q2 S
cFl; ð16Þ
ncss ¼
2ncss � q
2ncss � 1
q2 S
cFl: ð17Þ
Clearly, because q < 1, we have n�ss < ncss. Furthermore, nc
ss isa continuous function of pc, which we denote as nss(pc).Fig. 2 illustrates this function. The results are summarizedin the following:
Proposition 4. In the long run, if high-type artists obtainrents, piracy increases the number of low- and high-typeartists. Moreover, the number of both types of artists isconstant as a function of pc for both small and large pc,increasing for intermediate-low values of pc and decreasingfor intermediate-large values of pc. The maximum level forboth types of artists is reached when pc equals the critical levelpl below which low-type artists are not affected by piracy.
Proof. See Appendix C. h
Thus, nss follows the same pattern, as a function of pc, asdoes m(pc) in Fig. 1. Again, as in Section 2, the differencesbetween cases (ii)–(v) do not affect our key result that pi-racy always leads to a larger number of artists. Notwith-standing, these differences will be of some interest whenwe discuss policy alternatives in the next section.
3.2.3. Superstars’ rentsAs with the short-run analysis, the results in this
section are conditional on superstars obtaining rents:ph > Fh. It is thus important to show that superstars canindeed obtain rents in the long run, even if there is free en-try to an artistic career for young artists. The intuition isthat artists must go through a young-artist period in whichthey show their talent as a prerequisite to becoming asuperstar. However, the market for young artists may besmall. In fact, the more resources that superstars spendon their promotion, the smaller the market is. As a result,superstars’ promotion expenditures may create a bottle-neck and limit access to superstar status.
Formally, consider the case in which all artists are cop-ied. For every pc(and every set of parameters), there is amaximum number of superstars such that they obtainnon-negative profits. Using (14a), the set of pairs (pc,n) sat-isfying ph(pc,n) = Fh is given by the following:(ðpc;nÞ : c
pc
c2n� 1
4n2 þ 1n
ln1bc
cpc
4n2
2n� 1
� �
� 1þ ncFh
S
!¼ 0
): ð18Þ
F. Alcalá, M. González-Maestre / Information Economics and Policy 22 (2010) 365–378 373
This schedule is also illustrated in Fig. 2. A higher pc
involves less piracy, so that the market can support a largernumber of superstars. The pairs (pc,n) such that superstarsobtain rents are those below the schedule. Depending onthe value of parameters such as S and Fh, this schedule willcross the m(pc) schedule at different points (e.g., a largermarket or lower opportunity costs shift the ph(pc,n) = Fh
schedule upwards). Superstars obtain rents in equilibriumwhenever this crossing occurs to the left of the relevantvalue of pc (which is never smaller than c).
4. Levies on copying equipment: facilitating artisticcreation?
As noted in Section 1, the policy response to file-sharingand copying in most European countries has been toimplement levies on recording equipment and electronicdevices such as CDs, DVDs, hard disks, and MP3s. Mostrevenues from these levies are then allocated among writ-ers, performers, and copyright holders in proportion totheir legal sales. In this section, we discuss the implicationsfor artistic creation of these and other alternative policies.To analyze the impact of different policy alternatives, it isuseful to think about copy levies as involving two separatepolicies: a tax on copy equipment and a subsidy for artists.We first discuss the impact of different copy taxes and thenconsider the impact of different schemes for allocating taxrevenues across artists. When the different cases outlinedin the previous sections lead to different results here, wefocus on the case in which all artists are copied and onthe case in which only superstars are copied because theseare the two most relevant cases as indicated by the discus-sion at the end of Section 2.
4.1. Taxes on copy equipment
Note first that taxes on copy equipment may or may notbe proportional to the amount of the material being cop-ied. For example, levies on CDs and DVDs may be roughlyproportional to the amount of copying. In contrast, levieson electronic devices such as MP3 players and last-generation cell phones, are not. Levies on electronicdevices instead represent a fixed cost on copying. We musttherefore distinguish between proportional copy taxes (e.g.,taxes on CDs and DVDs) and fixed copy taxeswith respect tothe amount of copying (e.g., taxes on MP3 players, cellphones, and the like). These two policy alternatives caneasily be mapped in terms of the model in this paper. Aproportional copy tax is equivalent to a rise in pc. In turn,a fixed tax is equivalent to a reduction in the amount Sto be spent on artistic goods.
According to expressions (9) and (17), which are validfor the case in which all artists are copied, larger numberof consumers S increases m and nss. The same occurs forcases (ii)–(iv) (see expressions (C.1), (C.3) and (C.4), and(C.5), (C.6), (C.7) in Appendix C). Therefore, given theequivalence between the policies and the parameters inthe model, fixed taxes on electronic devices reduce mand nss. On the other hand, Figs. 1 and 2 show that a smallincrease in pc (which, as we have noted, is equivalent to
implementing a proportional copy tax) has no effect onm and nss if all artists are copied (i.e., for pc < pl). The reasonis that these taxes have two opposing effects on low-typeartists’ revenues: a positive effect on low-type artists’ earn-ings given their market share and a negative effect due totheir market share loss in favor of superstars. However,when only superstars are affected by copying (i.e., ifpl < pc < ph), a proportional copy tax (which is equivalentto increasing pc) has a negative effect on m and nss. The fol-lowing proposition summarizes these results.
Proposition 5. Fixed taxes on electronic devices reduce theshort-run number of niche and young artists, and the long-runnumber of high-type artists. If only superstars are affected bycopying, proportional copy taxes also have a negative impacton the short-run number of niche and young artists and thelong-run number of all artists.
4.2. Allocating the revenues from copy levies
The allocation of levy revenues across artists may ormay not be in proportion to their legal sales (e.g., nicheand young artists could receive a share of levy revenueslarger than their share of sales). We will distinguishbetween a proportional-to-sales allocation of levy revenues(in which revenues are allocated across artists in propor-tion to their legal sales) and a lump-sum allocation (inwhich artists receive a fixed amount that is independentof their sales). Clearly, there may also be many intermedi-ate policies involving revenue allocations that are non-linear in sales, which would be roughly equivalent to acombination of these two policies.
Again, these two policy alternatives can easily bemapped in terms of the model in this paper. A lump-sumallocation of levy revenues across artists is equivalent toa reduction in artists’ opportunity costs Fh and Fl. In thecase where all artists are copied, expressions (9) and (17)show that lower Fl increases m and nss. Therefore, lump-sum payments to artists increase m and nss. The same oc-curs for cases (ii)–(iv) (see expressions (C.1), (C.3) and(C.4), and (C.5), (C.6), (C.7) in Appendix C). On the otherhand, a proportional allocation of levy revenues across ar-tists is equivalent to a subsidy that reduces the cost c ofeach original reproduction. To ascertain the impact of thispolicy, note that whenever c or pc enters any expressiondetermining the number of artists, the ratio at play is c/pc. Hence, a proportional-to-sales payment to artists hasthe same effect as a proportional copy tax. Therefore, thesame analysis carried out for proportional copy taxes(summarized in the second part of Proposition 5) holdsfor proportional-to-sales allocations of levy returns. Insummary, we have the following:
Proposition 6. Allocating the revenues from levies as lump-sum payments to artists increases the short-run number ofniche and young artists and the long-run number of high-typeartists. However, allocating the revenues from levies acrossartists in proportion to their legal sales may reduce the short-and the long-run number of artists. This will in fact be the caseif only superstars are affected by copying.
374 F. Alcalá, M. González-Maestre / Information Economics and Policy 22 (2010) 365–378
Propositions 5 and 6 warn about the risks for artisticcreation of a policy based on levies that are allocatedaccording to legal sales. These policies may only favorsuperstars. If levy revenues are allocated in proportion toofficial sales, they raise the incentives to invest in the pro-motion of superstars, which offsets the effect of piracy inloosening market concentration.17
Proposition 6 suggests that the most effective policyfrom the point of view of artistic creation would be touse the yields from levies to help young artists. Of course,any lump-sum-like scheme for allocating levy revenuesshould ensure that artists are indeed active. This mayrequire conditioning payments on a minimum thresholdof output in terms of sales or live performances. Non-linearstrongly concave schemes linking levy payments receivedby artists to their sales may constitute an effective com-promise between strictly proportional schemes andlump-sum schemes. Moreover, resources allocated toyoung artists need not to be implemented as direct pay-ments but can also take the form of subsidies for youngartists’ production costs and live performances or canotherwise be used to reduce general taxes on theseactivities.18
5. Concluding comments
New communication and copy technologies are affect-ing artistic industries in many different ways. This paperfocuses on these effects in a setting that emphasizes threecentral aspects of artistic markets: the difficulties of talent-sorting, the importance of promotion expenditures, andthe predominance of superstars. Under reasonable condi-tions, we find that piracy may lower superstars’ marketshare, which may make entry and survival by niche andyoung artists easier. As a result, the number of artistsand therefore artistic diversity may increase.
Furthermore, the chances of discovering a new talentdepends on how much room there is in the market foryoung artists. Hence the number of highly talented super-stars at a given point of time depends on how manyyoung artists were able to start an artistic career in previ-ous periods. By providing more market opportunities foryoung and niche artists, piracy may enhance high qualitycreation in the long run. Superstars’ market concentrationand profits have a conflicting impact on new artistic ca-reers. The large profits of superstars push young potentialartists to start artistic careers. However, if superstars con-centrate too much of the revenues in the market, therewill be little room for new generations of talent to be
17 Also note that in principle, levies are such that the total revenues beingcollected equal the total payments to the beneficiaries of the levy. Hence,the total amount of resources allocated to the artistic industry remainsconstant. However, it has been argued that not all the equipment subject tocopy levies is used for copying artistic material. If this is so, copy levies willinvolve a transfer of resources from the rest of the economy to the artisticindustry. More specifically, levies with proportional-to-sales allocation ofrevenues that are raised from taxing equipment not used for copyingartistic material entail a subsidy to superstars from the rest of the economy.
18 For related literature discussing alternative mechanisms to financecreation that may be more efficient than granting monopoly rights seeShavell and van Ypersele (2001) and Romer (2002).
tested and revealed. These conflicting effects of stardommay lead to a conflicting long-run impact of piracy onartistic creation.
It follows from the analysis that it cannot be takenfor granted that copy levies recently implemented inmany Western countries, whose revenues are mostlyallocated in proportion to sales, will favor artistic crea-tion. These levies on copy equipment and other possiblerestrictive policies may reinforce the already-strongmarket position of top artists and hinder the promotionof new talent.
As noted throughout the paper, these results are condi-tional on the premise that superstars obtain rents. Is thishypothesis reasonable? Many people may consider it obvi-ous that this is the case. However, economists are rightlyskeptical of anything taken for granted. Our model showsthat superstars can indeed permanently obtain rents.Moreover, we cite empirical evidence that is consistentwith this hypothesis. Still, more detailed data on the distri-bution of artists earnings would be useful. Collecting soci-eties do not readily share data on the distribution ofcopyright earnings. Because collecting societies now bene-fit from the legislative and administrative capacities ofgovernments to implement levies, it would seem reason-able that the statistics on the distribution of levy yieldsacross artists and copyright holders be made public. Thisinformation would help us to assess how skewed the dis-tribution of payments is in favor of a small number ofsuperstars and how reasonable the hypothesis is thatsuperstars obtain rents.
During the last century, technological progress in thedesign of communication and recording devices (such asradio, TV, records, and tapes) greatly skewed some artisticmarkets in favor of a small number of top artists whoobtained increasingly larger revenues. This process is notover, with recent changes in the economic and politicalenvironment continuing to facilitate the globalization ofculture, thereby increasing cultural uniformity and favor-ing the further concentration of revenues in artistic mar-kets. However, communication and copy technologies cannow also have a counterbalancing effect. To borrow fromTom Friedman’s (2005) metaphor, new communicationand copy technologies are flattening the artistic marketby leveling it in favor of the long tail of young and nicheartists. Governments should make sure that policiesintended to favor artistic creation do not hinder this recentdevelopment.
Acknowledgements
We thank Luis Corchón, the editor Martin Peitz, and ananonymous referee for very helpful comments, and semi-nar participants at U. Carlos III de Madrid, Bellaterra sem-inar, U. de Málaga, and U. de Valencia. Francisco Alcalá alsothanks the Economics Department at NYU, which he vis-ited while conducting part of this project, for the generoushospitality. We acknowledge financial support from theSpanish Ministry of Education and Science under projectsECO2008-02654/ECON and ECO2009-07616/ECON, andfrom the Fundación Séneca de la Región de Murcia underproject 11885/PHCS/09.
F. Alcalá, M. González-Maestre / Information Economics and Policy 22 (2010) 365–378 375
Appendix A. Horizontal differentiation
In this appendix we show that the same centralqualitative results can be obtained in an explicit modelof monopolistic competition with horizontal differentia-tion. To make the model easy to manage, we considera Dixit and Stiglitz (1977) model in which the amountof each artist’s work that consumers want to consumemay be any real number and in which the number ofartists is large enough so that their individual pricedecisions do not affect the average product price inthe market. Consumers now solve the following maxi-mization problem:
maxxi ;yj
a lnXn
i¼1
ðxiÞg1
!1=g1
þ ð1� aÞ lnXm
j¼1
ðyjÞg2
!1=g224
35;ðA:1Þ
s:t:Xn
i¼1
ðxiphi Þ þ
Xm
j¼1
ðyjpljÞ ¼ 1:
It is assumed that 0 < g1 < g2 < 1; that is, the elasticity ofsubstitution within the set of superstar artistic goods,1/(1 � g1), is lower than within the group of low-type ar-tists (as a result of higher differentiation). All other compo-nents in the model are the same as in the main text. Also,the timing is similar to in the main text except that now inStage 3, artists do not play a Cournot game but insteadsimultaneously choose the price that they will charge fororiginal reproductions of their work.
Let us consider the equilibrium at Stage 2. The demandfunction for artist i’s output is Xi ¼ Sa � ðph
i Þ1=ðg1�1Þ
=Pni¼1ðph
i Þg1=ðg1�1Þ.19 The same is true for low-type artists.
Then, standard calculations under the usual Dixit–Stiglitzassumptions yield
phi ¼ c=g1;p
lj ¼ c=g2; Xi ¼ a
Sn
g1
c; Yj ¼ ð1� aÞ S
ng2
c:
Hence, high-type artist i’s revenues as a function of her andother superstars’ advertising are ph
i ðAi;A�iÞ ¼ a Sn ð1� g1Þ�
Ai. Maximizing phi with respect to Ai after plugging in
expression (2) yields the superstars’ total marketshare:
a� ¼ 1� 1cð1� g1Þ
: ðA:2Þ
In turn, low-type artist j’s revenues are pljðYj;Y�jÞ ¼
ð1� aÞ Sm ð1� g2Þ. Hence, because there is free entry in this
market at cost Fl, the equilibrium number of low-typeartists is as follows:
m� ¼ S
cFl
1� g2
1� g1: ðA:3Þ
19 Note that the first-order conditions of (A.1) yield aðxkÞg1�1=Pni¼1ðxiÞg1 ¼ ph
k , k = 1, . . . ,n. Hence, for any two high-type artists i and k,we have ðxi=xkÞg1�1 ¼ ph
i =phk ) ðxiÞg1 ¼ ðph
i =phkÞ
g1=ðg1�1ÞðxkÞg1 )Pn
i¼1ðxiÞg1 ¼ðxkÞg1
Pni¼1ðph
i Þg1=ðg1�1Þ=ðph
kÞg1=ðg1�1Þ . Substituting this into the previous
expression yields xk ¼ aðphkÞ
1=ðg1�1Þ=Pn
i¼1ðphi Þ
g1=ðg1�1Þ .
With piracy, the consumer’s problem is the following:
maxxi ;zi ;yj ;zj
a lnXn
i¼1
xi þ tzi½ �g1
!1=g124
þð1� aÞ lnXm
j¼1
yj þ tzj� �g2
!1=g235; ðA:4Þ
s:t:Xn
i¼1
xiphi þ
Xn
i¼1
zipc þXm
j¼1
yjplj þXm
j¼1
zjpc ¼ 1:
Assuming as in the main text that t is uniformly distrib-uted across individuals along the interval [0,1], the fractionof individuals that buys superstar i’s originals and low-typeartist j’s originals is, respectively, dh ¼ pc=ph
i and dh ¼ pc=plj
(provided that pc < phi and pc < pl
j). As a result, demand be-comes more elastic and mark-ups will be lower.
The number of consumers buying superstar i’s originalsis now Spc/pi. Hence, the demand function for i’s originals is
Xi ¼ ðpc=phi ÞSa � ðph
i Þ1=ðg1�1Þ
.Xn
i¼1
ðphi Þ
g1=ðg1�1Þ:
The same is true for low-type artists. Then, standard calcu-lations yield
phi ¼ cð2� g1Þ; pl
j ¼ cð2� g2Þ; Xi ¼ aSn
pc
ð2� g1Þ2c2
;
Yj ¼ ð1� aÞ Sn
pc
ð2� g2Þ2c2
:
Hence, high-type artist i’s revenues as a function of her andother superstars’ advertising are
phi ðAi;A�iÞ ¼ a
Sn
1� g1
ð2� g1Þ2
pc
c� Ai:
As before, maximizing phi with respect to Ai after plugging
in expression (2) yields the new equilibrium total super-star market share:
ac ¼ 1� ð2� g1Þ2
cð1� g1Þcpc: ðA:5Þ
In turn, low-type artist j’s revenues are pljðYj;Y�jÞ ¼
ð1� aÞ Sm
1�g2
ð2�g2Þ2
pc
c . Using the free entry condition yields
the equilibrium number of low-type artists in the case ofpiracy:
mc ¼ S
cFl
1� g2
1� g1
ð2� g1Þ2
ð2� g2Þ2 : ðA:6Þ
Because g1 < g2, we have mc > m*. Therefore, the number ofniche and young artists in the market is larger with piracythan if piracy could be completely prevented.
Similar qualitative results hold for the long-run equilib-rium of the dynamic model. Under the simplifyingassumption h = 0 and using n = qm, the long-run numberof high-type artists assuming that there is no piracy isn�ss ¼ q S
cFl1�g21�g1
. With piracy, the number is ncss ¼
q ScFl
1�g21�g1
ð2�g1Þ2
ð2�g2Þ2. Hence, again, g1 < g2 implies nc
ss > n�ss.
376 F. Alcalá, M. González-Maestre / Information Economics and Policy 22 (2010) 365–378
Appendix B. Vertical differentiation and individualeffects of advertising
In this appendix we introduce vertical differentiationand a more general role for advertising. We show thatthe same central qualitative results hold as in the maintext.
21 Note that we ignore the (reasonable) possibility that the vs are alsoincreasing in Ai. In such a case, advertising will increase the willingness to
B.1. No piracy
Consider the following utility maximization problemwhere ui is the relative valuation of superstar i’s artisticwork within superstars’ work:
maxx1 ;::;xn ;y
a lnXn
i¼1
uixi
!þ ð1� aÞ ln
Xm
j¼1
yj
!" #; ðB:1Þ
s:t:Xn
i¼1
phi xi þ pl
Xm
j¼1
plyj ¼ 1:
There is a continuum of consumers of measure S. Super-stars’ total market share a and individual valuations ui
are endogenous and depend on expenditures on promo-tion. As before, superstars’ total market share a dependson the sum of superstars’ promotion expenditures accord-ing to expression (2). Moreover, the individual valuation ofsuperstar i’s work ui depends on i’s individual promotionexpenditure Ai. To simplify the computations, we assumea functional form for ui similar to (2). The additionalparameter k P 0 in the next expression calibrates promo-tion expenditures’ impact on individual valuations ui (thecase analyzed in the main text corresponds to k = 0):
ui ¼1n
1� be�cn2Ai=S �k
; i ¼ 1;2; ::;n: ðB:2Þ
Competition takes place according to the same three-stagegame as in the main text. Consider first the Cournot–Nashequilibrium in Stage 3. Note that optimal consumer choicesimply ph
k ¼ ukphi =ui. Then, standard calculations yield
inverse demand functions phi ¼ uiaS=
Pnk¼1ukXk
� �; i ¼
1; . . . ;n, and pl = (1 � a)S/Y. Hence, each high-type artist’searnings are ph
i ðXi;X�iÞ ¼ uiaS=Pn
k¼1ukXk
� �� c
� �Xi � Ai. To
compute firm i’s optimal Xi in a symmetric SPE, weconsider a common uk = u
0for all k – i. From the Cournot-
equilibrium first-order condition we have the following:20
phi ¼
1n� 1
þ ui
u0
� �c;
Xi ¼ðn� 1Þ 1þ ðn� 1Þ ui
u0 � 1� �� �
1þ ðn� 1Þ uiu0
� �2
aSc
;
phi ðAi;u0Þ ¼ aS 1� 1
1n�1þ
uiðAiÞu0
!2
� Ai:
Substituting for a and ui with (2) and (B.2), maximizingwith respect to Ai, and taking ui = u
0yields the SPE value
of a:
20 Details of all the derivations in this appendix are available uponrequest.
a� ¼ 1� nc
1
2ðn� 1Þ2kþ 1: ðB:3Þ
In turn, low-type artist j’s revenues are pljðYj;Yi�1Þ ¼
ð1�aÞSY � c
h iYj. The Cournot equilibrium in the low-type
sub-market yields pl ¼ mm�1 c and Yj ¼ m�1
m2ð1�aÞS
c . The equilib-rium number of active low-type artists m* is determined by
the free entry condition plj ¼ Fl, which yields the following:
m� ¼ 1
2ðn� 1Þ2kþ 1
nS
cFl
!12
: ðB:4Þ
B.2. Piracy
As in the main text, we consider piracy in an economywith a continuum of consumers that have different (con-stant) marginal rates of substitution t for copies and orig-inals. The consumer’s problem is now as follows:
maxxi ;zi ;y;zy
a lnXn
i¼1
½uixi þ tzi� !"
þð1� aÞ lnXm
j¼1
yj þ tzj� � !#
; ðB:5Þ
s:t:Xn
i¼1
phi xi þþ
Xn
i¼1
pczi þXm
j¼1
plyj þXm
j¼1
pczj ¼ 1:
Assuming that t is uniformly distributed across individualsalong the interval [0,1], the fraction d of individuals thatbuy originals in the case of high-type goods is d ¼ uipc=ph
i
(provided that pc < phi ). Hence, expenditure on high-type
originals isPn
k¼1phkXk ¼ aSuipc=ph
i . Moreover, phk ¼ ukph
i =ui.Therefore, the inverse demand function for each superstaris ph
i ¼ ui pcaS=Pn
k¼1ukXk
� �� �1=2. Similarly, if pc < pl, thedemand for low-type artists’ originals is Y = pc(1 � a)S/(pl)2.21
We assume that pc is low enough that in equilibriumpc < pl
6 ph. As a result, all artists are pirated. Let us calcu-late a symmetric SPE for the game assuming that all thehigh-type artists except the deviant artist i choose thesame level of uk = u
0. At the last stage of the game, Cournot
competition among high-type artists yields
phi ¼
1þ ðn� 1Þ uiu0
n� 12
c;
Xi ¼ðn� 1Þ ui
u0 � 1� �
þ 12
� �n� 1
2
� �2
1þ ðn� 1Þ uiu0
� �3
2pc
caSc
;
phi ðAi;A�iÞ ¼
ð2n� 1Þ ðn� 1Þ uiu0 � 1� �
þ 12
� �2
1þ ðn� 1Þ uiu0
� �3
pcui
caS� Ai:
pay not only for the original version of the good, but also for the piratedversion. Obviously, this will reduce superstars incentives to pay advertisingcosts. This in turn will reinforce the idea that piracy enhances the entry oflow-type artists by reducing superstars’ market share.
F. Alcalá, M. González-Maestre / Information Economics and Policy 22 (2010) 365–378 377
Substituting for a and ui with (2) and (B.2), maximizingwith respect to Ai, and taking ui = u
0yields the value of a
when piracy is occurring:
ac ¼ 1� nc
1ak
cpc
4n2n� 1
1ð4n� 3Þðn� 1Þ þ n½ � 1n kþ 1
:
ðB:6Þ
In turn, low-type artists’ profit maximization conditionalon the demand when their work is pirated (i.e., when
pc < pl) yields pl ¼ 2m2m�1 c and Yj ¼ ð1� aÞ pc
c2 S ð2m�1Þ24m3 . Then,
using the free entry condition, we obtain the short-runequilibrium number of low-type artists in the case ofpiracy:
mc ¼ 1ak
2mc � 1mc
n2n� 1
1ð4n� 3Þðn� 1Þ þ n½ � 1n kþ 1
nS
cFl
!1=2
:
ðB:7Þ
Comparing (B.4) with (B.7) shows that mc > m* if mc > n. Tosee this, note that the result is ensured if 2ðn�1Þ2n
ð4n�3Þðn�1Þþn > 1.This is satisfied for all n P 3, which seems a reasonableassumption.
Appendix C. Relegated proofs
C.1. Proof of Proposition 2
As explained in the main text, there are five possiblecases depending on the exogenous level of pc:22
(i) pc > ph: copies are blockaded;(ii) ph P pc P ph: superstars deter copies;
(iii) ph > pc > pl: only superstars are copied;(iv) pl P pc P pl: low-type artists deter copies and
superstars are copied; and(v) pl > pc: both low-type artists and superstars are
copied.
Case (i): This case was analyzed in Section 2.1, yieldingexpression (5) for m. Note that in this case, mdoes not depend on pc.
Case (ii): In this case, we have ph = pc. Hence, the profitsfor each high-type artist at Stage 1 of the gameare ph
i ¼pc�cnpc aS� Ai � Fh. The first-order condi-
tions of the SPE of the game yield the following:
22 As alreadysimpler becauhigh- and lowartists deter c
be�cnA=Sðpc � cÞpc
� 1=c ¼ 0! a ¼ 1� pc
cðpc � cÞ :
Then, the number of low-type artists is given bythe free entry condition, which combined withthe expression for a above implies thefollowing:
noted in the main text, the analysis for ph � pl is somewhatse case (iii) is replaced with a different case in which both-type artists fix the same price pc and thereby, both groups ofopies.
" #
mðpcÞ ¼ 11� c=pc
S
cFl
1=2
: ðC:1Þ
Note that this is decreasing in pc. Also note thatfor pc ¼ n
n�1 c, expressions (5) and (C.1) yield thesame value for m, so that m is continuous as afunction of pc at the frontier between cases (i)and (ii).
Case (iii): In this case, we have ph ¼ 2n2n�1 c. Hence, output
per artist is Xi ¼ ð2n�1Þ24n3
pcaSc2 , and each high-type
artist’s earnings at Stage 1 are phi ¼ 2n�1
4n3pcaS
c �Ai. We can rewrite this profit function for eachhigh-type artist as
phi ðAi;AÞ ¼
2n� 14n3
pcScð1� be�cnA=SÞ � Ai;
i ¼ 1;2; . . . ;n:
The first-order conditions for the SPE of thegame yield the new SPE level for a, which isindicated with superscript c:
ð2n�1Þ4n2
pcSc
be�cnA=S�S=c¼0!ac¼1�n2
c4c
pcð2n�1Þ :
ðC:2Þ
Using this expression and the free-entry condi-tion in the low-type market yields the numberof low-type artists:
" # mðpcÞ ¼ cpc
4n2
2n� 1S
cFl
1=2
: ðC:3Þ
Note that m is decreasing in pc. Also note thatEqs. (C.1) and (C.3) yield the same number oflow-type artists for pc ¼ 2n
2n�1 c, so that m is con-tinuous as a function of pc at the frontier be-tween cases (ii) and (iii).
Case (iv): In this case the equilibrium price in the low-type market is pl = pc. Hence the earnings of eachlow-type artist at Stage 3 of the game are givenby the free entry condition:
pljðmÞ ¼
ðpc � cÞð1� aÞSmpc
¼ Fl:
Thus, substituting with expression (C.2) for ac,we find:
mðpcÞ ¼ ð1� c=pcÞ cpc
4n2
2n� 1S
cFl: ðC:4Þ
Because c/pc > c/ph = (2n � 1)/2n > 1/2, it is eas-ily seen that m is increasing in pc. Moreover,m takes the same value for pc ¼ m
m�1 c whenusing expressions (C.3) and (C.4), so that m iscontinuous at the frontier between cases (iii)and (iv).
Case (v): This case was already considered in the maintext, yielding expression (9) for m. Moreover,m takes the same value for pc ¼ 2m
2m�1 c whenusing expressions (C.4) and (9), so that m is con-tinuous at the frontier between cases (iv) and(v). The overall relationship between pc and m
378 F. Alcalá, M. González-Maestre / Information Economics and Policy 22 (2010) 365–378
is illustrated in Fig. 1, where the curve m(pc)represents the equilibrium level of m as a func-tion of the copying price. Note that m(pc)reaches a maximum at point p0 ¼ pl, at the fron-tier between region (iii) and (iv).
C.2. Proof of Proposition 4
In the long run, and using the simplifying assumptionh = 0, the steady state value of n as a function of pc canbe obtained by substituting n = q�m into expressions (4),(C.2), (C.3), (C.4), and (9), which correspond respectivelyto cases (i)-(v), in the previous short-run analysis. Cases(i) and (v) were already analyzed in the main text, yieldingexpressions (16) and (17). For the other three cases, wehave the following:
Case ðiiÞ : nss ¼1
1� c=pc
q2S
cFl
" #1=2
: ðC:5Þ
Case ðiiiÞ : nss ¼12þ 2
cpc
q2S
cFl: ðC:6Þ
Case ðivÞ : nss ¼1
2� 4ð1� c=pcÞ cpc
qScFl
: ðC:7Þ
Recall from the main text that n is independent of pc incases (i) and (v). Now, it is easy to see that n is decreasingin pc in cases (ii) and (iii), whereas it is increasing in case(iv). Hence, nss as a function of pc follows the same patternas m(pc) (see Figs. 1 and 2), with a maximum at the frontierbetween regions (iii) and (iv).
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