Copying, Superstars, and Artistic Creation Francisco Alcalá∗and Miguel González-Maestre† May 2010

Abstract We provide a new perspective on the impact of unauthorized copying and copy levies on artistic creation. Our analysis emphasizes three aspects of artistic markets: the predominance of superstars, the important role of promotion expenditures, and the difficulties of talent sorting. In the short run, piracy reduces superstars’ earnings and market share and increases the number of niche and young artists. In the long run, copying can also have a positive effect on high-quality artistic creation by helping more young artists start their careers, which increases the number of highly talented artists in subsequent periods. The long-term impact of levies on copy equipment on artistic creation depends on whether their yields primarily accrue to superstars who already receive rents or are allocated to help young artists. Keywords: artistic creation, superstars, private copy, piracy, levies. JEL Classification: L10, L82, Z1.

∗

Corresponding author. Affiliation: Universidad de Murcia and IVIE. Address: Departamento de Funda-

mentos del Análisis Económico, Universidad de Murcia, Campus de Espinardo, 30100 Murcia, Spain. E-mail: [email protected]. Phone: 34-868883767. Fax: 34-868883758. † Affiliation: Universidad de Murcia. Address: Departamento de Fundamentos del Análisis Económico, Universidad de Murcia, Campus de Espinardo, 30100 Murcia, Spain. E-mail: [email protected].

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1

Introduction

The music industry and other artistic markets are experiencing profound changes as a result of digital recording, Internet file-sharing, and new electronic devices. This has launched a far-reaching debate on the consequences of new technologies for artistic creation and the possible need to redefine intellectual property rights. According to some individuals and companies in the artistic industry, file sharing and unauthorized copying are bound to have a very negative impact on artistic creation. These individuals have asked for controls and restrictions on the use of the Internet for copying and for levies on copy equipment that would restore incentives for artistic creation. Their arguments have led many countries in Europe and other parts of the world to implement new taxes and levies on copy equipment and electronic devices.1 Revenues from levies tend to be allocated to copyright holders, performers, and publishers according to their sales in the market. In contrast, it has also been argued that current copyrights are excessive in most Western countries and that their yields mostly accrue to a relatively small number of superstars and artistic firms that obtain economic rents. New communication technologies and filesharing may help the careers of young and niche artists and reduce the concentration of sales in artistic markets. Restrictions on file-sharing and the implementation of levies on copy equipment may revert this process and harm the general public. 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 creation? Even more, might it be possible that file sharing and copying enhance high-quality creation in the long run? This paper analyzes the short- and long-term consequences of unauthorized copying for artistic creation and the effects of implementing different types of copy levies. It does so within a theoretical framework that emphasizes three key aspects of artistic markets that have largely been neglected in the conventional analyses: the predominance of superstars, the important role of promotion expenditures, and the dynamics of talent-sorting. These three aspects of artistic markets can be briefly explained as follows. First, artistic creation is intensive in an innate input: talent. Rosen (1981) shows that this 1

The average copy tax implemented in Western European countries is 0.17 euros for blank data-CDs and

0.45 euros for blank DVDs. Copy taxes on devices such as Mp3 players, memory cards, and hard-disk DVD recorders depend on their GB memory and range from 4 to 50 euros (see De Thuiskopie, 2009).

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factor, combined with the scale economies associated with the joint consumption of artistic goods, leads to the superstar phenomenon: the concentration of output and extremely large rewards for the most talented artists.2 Second, promotion costs are a crucial ingredient in explaining the demand for artistic products and greatly affect the division of market shares between superstars and niche as well as young artists.3 Third, there is a dynamic positive link between the current number of young artists and the future number of highly talented superstars. As pointed out by MacDonald (1988), talent and charisma are not easily detected. As a result, to have a large number of highly talented artists in the future, one needs to have many young artists starting an artistic career today (even though most of them will not succeed).4 Consistent with these circumstances, our analysis makes an explicit distinction between superstars (or high-type artists) and niche and young artists (or low-type artists). First, we consider the short-run equilibrium in artistic markets. In the short run, the number of superstars is exogenously given whereas there is free entry into the sub-market of niche and young artists. Piracy reduces superstars’ earnings and the incentives to invest in their promotion. This tends to increase the number and market share of niche and young artists. Second, one must analyze the dynamics of the market and its long run equilibrium. We build a simple overlapping-generations model of artists in which only a fraction of young artists starting an artistic career show talent and become superstars later in their careers. This endogenizes the number of superstars. Piracy may help more young artists to start 2

Several papers provide evidence of the strong concentration of sales in the market for popular music. See

Rothenbuhler and Dimmick (1982), Crain and Tollison (2002), and Krueger (2005), among others. Krueger (2005), for example, reports that in 2003, the top 1% of artists obtained 56% of concert revenues, with the top 5% taking in 84%. Similarly, there is evidence of the extremely skewed distribution of copyright yields across artists, even if data about these earnings are not easily accessible (they are privately held by collecting societies). For example, Kretschmer and Hardwick (2007) report data on the distribution of payments in 1994 by the UK Performing Right Society. This society distributed £20,350,000 among 15,500 writers for the public performance and broadcasting of their works. The top 9.3% of writers earned 81.07% of the total. Ten composers earned more than £100,000, whereas 53.1% of the composers earned less than £100. These authors’ estimations for the period 2004-2005 show similar results. For evidence on superstars’ rents in the motion picture industry, see Chisholm (2004). 3 For example, Peitz and Waelbroeck (2005) cite several sources showing that marketing and promotion are the main costs of making and selling a recorded CD. 4 See Terviö (2009) for a general analysis of the market’s failure to discover talent and how this leads to inefficiently low output and higher earnings for known talents.

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their careers, which in turn may increase the number of highly talented artists in the long run. Third, policy issues are important to consider. We compare the consequences of different levies on copy equipment and analyze alternative schemes for allocating their yields. We find that taxes on copying may hinder the promotion of niche and young artists and hamper artistic creation in the long run. Moreover, the most common policy in Western countries of distributing levy yields in proportion to market sales strongly favors superstars. This increases the incentives to promote superstars, thereby fueling market concentration, which in turn reduces artistic diversity in the short run and high-quality artistic creation in the long run.5 We find that artistic creation can be stimulated more effectively in both the short and long term by allocating levy yields using non-linear (concave in sales) schemes that favor young artists. A growing body of economic literature is gradually addressing the effects of the new information and copying technologies on artistic markets and other industries (see Peitz and Waelbroeck, 2006, for a survey). Alcalá and González-Maestre (2009) and Zhang (2002) are the closest papers to this one. Alcalá and González-Maestre (2009) build a model with the three aspects of artistic markets emphasized here and analyze the optimal length of the copyright term. Nonetheless, they do not consider the possibility of unauthorized copying and do not explore its consequences. Zhang (2002) considers the role of promotion costs and copying in artistic markets using a duopoly model in which digital copies help to reduce the distortionary effects of the large-audience artist’s persuasive advertising. However, in Zhang’s (2002) model there is no entry into the low-type sub-market, or to the high-type artistic sub-market. In contrast, analyzing entry into each of these markets is crucial to our investigation of how unauthorized copying and copy levies may affect artistic creation in the short and in the long run.6 Two final notes on the scope and the limitations of this paper are the following. First, the paper mostly concerns the music and recording market. However, similar mechanisms 5

Moreover, as long as not all of the equipment subject to copy levies is used for copying artistic material

(as happens with many data CDs, hard disks and pen drives), this scheme for allocating copy levies may involve a transfer 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 of these levies on artistic creation.

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are present in most activities to which creative work is important and in which it can be easily copied, as in the movies. Second, a key assumption throughout the paper is that superstars’ earnings are above their opportunity cost, i.e., that they obtain rents. This seems a reasonable hypothesis and is motivated by the empirical evidence regarding the concentration of market share and of revenues to superstars. Moreover, the dynamic model in Section 3, in which the number of superstars is endogenized, shows that superstars can indeed obtain rents in equilibrium (even if there is free entry into the artistic market as young artists and all talented young artists become superstars later in their careers). The rest of the paper is organized as follows. Section 2 lays out the static version of the model and analyzes the short-run equilibrium of artistic markets with and without piracy. Section 3 introduces the dynamic version of the model and investigates the long-run impact of copying on artistic creation. Section 4 considers different types of levies on copy equipment and analyzes their impact on artistic creation. Section 5 concludes.

2

Superstars and Niche Artists: the Short Run

In this section, we introduce the static version of the model and analyze the short-run equilibrium of artistic markets. Artists may be either high-type (superstars) or low-type (niche and young artists). In the short run, the number of high-type artists is exogenous, whereas there is free entry into the submarket for low-type artists. The exogeneity of the number of high-type artists captures the idea that the set of superstars changes with lower frequency than the set of niche and young artists. The number of high-type artists is endogenized in the dynamic model in Section 3 in which we analyze artistic markets in the long run. Each active artist creates a single artistic good (such as a song, novel, movie, etc.). Therefore, artistic creation is proportional to the number of artists, though we may distinguish between high-quality artistic creation (which results from high-type artists’ work) and low-quality artistic creation (low-type artists’ work). Being active as an artist involves opportunity costs F l for low-type artists and F h for high-type artists.7 As discussed in the Introduction, we assume throughout the paper that superstars’ earnings are above their 7

F l and F h can be interpreted as the fixed cost of creating a low- and a high-type artistic good, respec-

tively. In addition to including the artists’ time opportunity cost, these parameters can be interpreted as also including the costs of other inputs needed for creation (e.g., recording or filming equipment).

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opportunity cost F h , i.e., they obtain rents. Once an artistic good is created, it can be infinitely reproduced at some constant marginal cost. Consumers can consume artistic goods by buying original reproductions (originals for short), which pay copyrights, or unauthorized copies (copies for short), which do not. We first analyze artistic markets when piracy does not exist; i.e., when individuals can only buy originals. Then, we introduce piracy and consider the case in which all artists are copied. We end this section by addressing the possible intermediate cases in which superstars are affected by copying but low-type artists are not. Introducing and solving a model with different types of artists whose work has imperfect substitutes (unauthorized copies) that are valued differently across heterogeneous groups of consumers and in which advertising and dynamics play an important role, can be complicated and tedious. In the main text, we simplify a number of issues to make the main argument more transparent. We indicate our generalizations in Appendices A and B.

2.1

The Model Without Piracy

There is a measure-S continuum of consumers. They spend an amount of money on artistic goods that is normalized to 1. The representative consumer solves the following utility maximization problem: maxxi ,yj s.t.

h ´i ³P P m a ln ( ni=1 xi ) + (1 − a) ln , y j=1 j Pm Pn h l i=1 xi p + j=1 yj p = 1;

(1)

where xi (respectively, yj ) is consumption of superstar i’s originals (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) number of high-type (resp. low-type) artists.8 In Appendix A, we explicitly introduce horizontal differentiation (and monopolistic 8

Usually, consumers buy at most one unit of each artistic good. This is the case for the symmetric

equilibrium of this model if we assume that S is large enough so that the number of artists will be large with respect to the consumer’s expenditure. In such a case we have xi ≤ 1 and yj ≤ 1 ( i = 1, ...n; j = 1, ...m).

Then, xi (resp. yj ) should be interpreted as the probability that the representative consumer will buy the

work of artist i (resp. j). Because there is a measure−S continuum of identical consumers, these probabilities translate into certain aggregate sales Xi = xi · S and Yj = yj · S. Also note that this consumer problem

could be framed in a more general two-stage budgeting model with a general consumption good in addition to artistic goods (see Alcalá and González-Maestre, 2009).

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competition) within each group of artists. Superstars’ market share a is endogenous and positively depends on superstars’ expenditures on promotion and marketing. Only high-type artists enjoy promotion and marketing expenditures, which may be thought of as managed by competitive artistic promotion firms.9 A firm’s advertising tends to increase both the relative demand for that firm’s good and the overall demand for the type of good being advertised (Sutton, 1991). This second effect is the most important one in our argument. Hence, in order to simplify we consider only this second effect in the main text, which is captured by a positive effect of superstars’ total promotion expenditure on their market share a. In Appendix B we consider a more general set-up with vertical product differentiation where each superstar’s promotion expenditure also increases consumer preference for her specific work. Let Ai be artist i’s promotion expenditures (Ai ≥ 0) and A ≡

Pn

i=1

Ai . Superstars’

market share is increasing in n and in promotion expenditures per consumer A/S, bounded above zero if their total advertising is zero, and equal to 1 if their total advertising A is infinite: a = 1 − βe−γnA/S ;

(2)

where β and γ are exogenous parameters, 0 < β < 1, γ > 0. We consider the following timing of competition: Stage 1: Each high-type artist chooses simultaneously and independently her Ai . Stage 2: Each potential low-type artist decides whether to enter and be active in the low-type artistic sub-market. As noted, entry involves a fixed opportunity cost F l . Stage 3: All active artists decide how many original reproductions of their work to bring to the market (they compete a la Cournot).

P P We use the following notation: Xi = xi S , X = ni=1 Xi , X−i = nk6=i Xk , Yj = yj S, Y = Pm Pm j=1 Yj , Y−j = k6=j Yk . Let us consider the Cournot-Nash equilibrium at Stage 3. Standard

calculations yield inverse demand functions ph = aS/X and pl = (1 − a)S/Y . Hence, hightype artist i’s earnings as a function of her output Xi and other high-type artists’ output 9

The relationship between creators and artistic firms (such as labels and publishers) are regulated by

contracts that can make artistic firms the main beneficiaries of the market. The potential conflict of interest between creators and artistic firms has been analyzed in Gayer and Shy (2006). Here we simplify this issue by assuming that artistic promotion firms are perfectly competitive or, alternatively, by considering each superstar in the model to be a vertically integrated structure consisting of a high-type artist and a promotion firm.

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X−i , are

aSXi − cXi − Ai , i = 1, 2, ..., n. X n aS Cournot-equilibrium first order conditions yield ph = n−1 c; Xi = (n−1) . Hence superstar n2 c π hi (Xi , X−i ) =

i’s earnings as a function of her and other superstars’ advertising are as follows: π hi (Ai , A−i ) =

aS − Ai . n2

(3)

Substituting with (2) and maximizing π hi with respect to Ai yields the subgame perfect equilibrium (SPE) value of superstars’ total market share (which is denoted by a∗ ): n βe−γnA/S γ − 1 = 0 → a∗ = 1 − . n γ

(4)

Inequality γ > n/β must hold to insure Ai > 0. We assume that γ is always high enough to guarantee this condition. Moreover, π hi > F h requires n to be small enough or S large enough.10 In turn, each low-type artist j’s revenues as a function of her output and other high-type artists’ output, are π lj (Yj , Y−j ) = [(1 − a)S/Y − c] Yj . Cournot equilibrium in the low-type sub-market yields pl =

m c, m−1

Yj =

m−1 (1−a)S . m2 c

The equilibrium number of active low-type

artists m∗ is then determined by the free entry condition π lj = F l , which yields: ∗

m =

2.2

µ

nS γF l

¶ 12

.

(5)

The Impact of Piracy

We now introduce piracy. Consumers can obtain unauthorized copies of any artistic good at an exogenous cost pc . The characteristics of market equilibrium may change depending on the value of pc with respect to the equilibrium values of ph and pl . Different cases lead to different combinations of superstars’ and niche artists’ copies being blockaded, deterred, or accommodated. In this subsection we assume that pc is low enough such that in equilibrium pc < pl ≤ ph . As a result, all artists are pirated. This case may seem the most relevant one from the empirical point of view and is likely to make the strongest case against piracy. In the next subsection, we briefly characterize the other possible cases (copying is deterred, only superstars are copied, etc.). 10

As discussed in the Introduction, we assume throughout the paper that superstars’ earnings are above

their opportunity cost F h ; i.e., they obtain rents.

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Consumers behave heterogeneously with respect to their attitude towards originals or unauthorized copies (this may be due to differences on several dimensions: valuation based on quality, moral restraints on copying, opportunity cost of the time needed to search for and download files from the Internet, etc.). The theoretical literature has formalized consumer heterogeneity in different ways (see Peitz and Waelbroeck, 2006). In this paper, we consider a continuum of consumers with different (constant) marginal rates of substitution υ between copies and originals. The consumer problem is now recast as follows: h ³P ´i P m a ln ( ni=1 [xi + υzi ]) + (1 − a) ln [y + υz ] , j j j=1 P P P Pn n m m h c l c i=1 xi p + i=1 zi p + j=1 yj p + j=1 zj p = 1;

maxxi ,zi ,yj ,zj s.t.

(6)

where zi and zj are respectively consumption of copies of superstar i’s and low-type artist j’s work. Assuming that υ is uniformly distributed across individuals along the interval [0, 1], the fraction δ of individuals that buy originals in the case of high-type goods is δ = pc /ph (provided that pc < ph ; otherwise, δ = 1). The remaining fraction 1 − δ consume copies.

Hence, if pc < ph , the demand for high-type originals is now X = aSpc /(ph )2 . Similarly, if

pc < pl , the demand for low-type artists’ originals is Y = pc (1 − a)S/(pl )2 (otherwise, their

demand is Y = (1 − a)S/pl as in the previous subsection). Thus, demand is more elastic as a result of competition from copies.

As already indicated, in this subsection we assume that pc is low enough such that in equilibrium pc < pl ≤ phi . Hence, all artists’ work is pirated (although not all consumers buy copies). Using the corresponding new demand function at the last stage of the game, Cournot competition among high-type artists yields: 2n (2n − 1)2 pc aS ; p = c; Xi = 2n − 1 4n3 c2 2n − 1 pc aS πhi (Ai , A−i ) = − Ai . 4n3 c h

(7)

As before, substituting for a with (2) and maximizing π hi with respect to Ai yields the new level of a denoted as ac : βe−γnA/S =

1 c 4n2 1 c 4n2 c → a . = 1 − γ pc 2n − 1 γ pc 2n − 1

(8)

In turn, low-type artists’ profit maximization conditional on the demand when their work is pirated (i.e., pc < pl ), yields equilibrium price pl = 9

2m c 2m−1

and per artist output

c

2

Yj = (1 − a) pc2 S (2m−1) . Then, using the free entry condition, we obtain the short-run 4m3 equilibrium number of low-type artists in the case of piracy: c

m =

µ

2mc − 1 n nS mc 2n − 1 γF l

¶1/2

.

(9)

Comparing (5) with (9) shows that mc > m∗ if mc > n (which is taken for granted). Proposition 1 Consider the short-run equilibrium in which the number of superstars is given. If the parameters are such that all artists’ work is pirated, the number of niche and young artists in the market is larger with piracy than if piracy can be completely prevented. The intuition behind this result is that superstars’ promotion expenditures act as a barrier to entry against low-type artists. Copying reduces the profitability of superstars’ promotion, thereby leaving a larger market share for low-type artists (compare (8) with (4)).11 This positive effect is large enough to compensate for the fact that low-type artists are also copied. Copying also brings about a reduction in the prices of both high- and low-type artistic goods, which benefits consumers.12 In Appendix A we show that the same qualitative result is obtained in a Dixit-Stiglitz (1977) model of monopolistic competition with horizontal differentiation. In Appendix B we show that the same qualitative result is obtained in a model with vertical differentiation in which each superstar’s advertising has a specific effect on the demand for her work.

2.3

The General Case: From Blockaded Copying to Accommodation

In general, there are several possible scenarios for the value of pc with respect to the equilibrium levels of ph and pl . This leads to different characteristics of equilibrium. We briefly 11

Empirical evidence regarding the market for rock concerts seems to be consistent with the model’s

prediction regarding the decreasing market share 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 the ninth consecutive year with increasing revenues. However, the top 20 tours combined saw a 15% decline in ticket revenues from that of the top 20 tours from 2006. 12 The effect of copying on CD prices has been openly recognized by the Recording Industry Association of America. See RIAA (2007).

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describe the different cases here and refer to the Appendix C for a detailed analysis. Denote by ph the price of high-type originals as obtained in Subsection 2.1 for the case in which there is no piracy, ph ≡

n c, n−1

and by ph the price of high-type originals when high-type work

is copied, as computed in Subsection 2.2: ph ≡

2n c. 2n−1

Similarly, denote by pl the price of

low-type work when its market is not affected by piracy and by pl its price when low-type work is copied. The possible cases depending on the exogenous level of pc are as follows:13 (i)

pc > ph ;

(ii)

ph ≥ pc ≥ ph ;

(iii)

ph > pc > pl ;

(iv)

pl ≥ pc ≥ pl ;

(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-type work are blockaded) (iv) (copies of superstars’ work are accommodated whereas copies of low-type artists’ work are deterred), and (v) (copies of superstars’ work and that of low-type artists’ work are accommodated). This last case was the one analyzed in the previous subsection. Figure 1 depicts m as a function of pc based on the analysis in Appendix C. The key result is that m is larger in all cases in which the market is affected by piracy (cases (ii) to (v)) than when it is not (case (i)). The following proposition characterizes m as a function of pc in the five cases. Proposition 2 Consider the short run when the number of superstars is given. The number of niche and young artists m is a continuous function of the price of copies pc , which is characterized as follows. There is a critical value po < ph that maximizes m. This value po is the lowest value of pc such that superstars are pirated but low-type artists are not affected by piracy, which occurs for pc = pl . For pc > po , m is monotonically decreasing, whereas for pc < po , m is monotonically increasing. Moreover, m is constant for small values of pc such that all artists are copied, and for values such that none are copied. In all cases, the number of niche and young artists is larger when the market is affected by piracy than when it is not. 13

See the Appendix, where it is also shown that pl =

h

m m−1 c

and pl ≡

2m 2m−1 c.

It could also be the case that

p ≯ pl . In such a case, the analysis is somewhat simpler because case (iii) is replaced by a different case in which both high- and low-type artists fix the same price pc for their products thereby both deterring piracy.

11

Proof. See Appendix C. INSERT FIGURE 1 ABOUT HERE As noted, the key result is that m is larger in all cases in which the market is affected by piracy than when it is not. Still, there are quantitative differences between cases (ii) through (v) that will be of interest in discussing policy alternatives in Section 4. Thus, it is useful to briefly discuss which cases may be most relevant. Because casual observation indicates that the work of most artists is copied, it seems that the most relevant case is that analyzed in Subsection 2.2. Still, the case in which only superstars are copied may be of particular interest. Superstars’ work is more likely to be copied, not only because their originals tend to be more expensive but also because their larger market makes their work more easily available in P2P networks. However more importantly in the case of the music industry, revenues from records (as opposed to revenues from concerts) are relatively more significant for superstars than for young and niche artists. There is an important reason for this: the economies of scale of joint consumption that give rise to the superstar phenomenon entail a limitation on the number of live performances but no limitations on the number of records sold. In fact, the main goal of superstars’ concert tours, at least until the advent of the Internet, was to promote new records. This is not the case for niche and young artists, some of whom are willing to provide records on the Internet even for free as a way to become popular and increase demand for their live performances (see Peitz and Waelbroeck, 2004).14 The model can account for these circumstances by means of a reinterpretation. In the simplest reinterpretation, it can be assumed that the consumption of high-type artists’ work entails buying or copying records, as before, whereas consumption of low-type artists’ work entails attending live performances. (Now, in the case of low-type artists, Y represents concert ticket sales and c represents the marginal cost of using a venue with one more 14

At any rate, the importance of live performances is increasing for all types of artists. For example,

according to the Music Managers Forum (a trade group in London) musicians derived two-thirds of their income in 2000 from record labels, with the other one-third coming from concert tours and merchandise. In 2007, this proportion reversed. Still, consumers’ total expenditure on music seems to be roughly the same. According to some concert promoters, music lovers seem to have a mental budget to spend on music and have switched their spending from CDs to tickets and merchandising (see The Economist, July 5th 2007). This suggests that our assumption of a constant consumers’ budget in the artistic market may be reasonable even when the nature of the good being bought changes, with a shift from recorded music to concerts.

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seat). Under this interpretation, which emphasizes the different origin of the main source of revenues for each group of artists, only superstars can be copied. The results of case (iii) are then the most interesting to consider.

3

Piracy and Artistic Creation in the Long Run

In this Section, we analyze the long-run consequences of piracy for high-quality artistic creation. To do so, we endogenize the number of high-type artists in a dynamic model. The number of highly talented artists in the market at a given point in time depends on the available opportunities for starting an artistic career as a young artist in the previous periods. Young potential artists may or may not be talented, but their talent and charisma can only be ascertained if they actually enter the artistic market and perform for the public. After some period in the market, only a small fraction of them show talent and become superstars.15 The rest of the young artists eventually drop out of the artistic market. In this context, the high earnings and market share associated with stardom have a conflicting impact on new artistic careers. Superstars’ large earnings attract young potential artists and push them to start an artistic career. However, the larger the market share absorbed by the current generation of superstars, the smaller the room for a new generation of talents to be tested and revealed. This reduces the future number of highly talented artists. Piracy weakens superstars’ position, which can then help young artists and, in the long run, increase high-quality artistic creation.

3.1

A Model of Overlapping Generations of Artists

We consider an overlapping-generations extension of MacDonald’s (1988) model of artistic markets. This extension is similar to the one in Alcalá and González-Maestre (2009). The key difference is that here we introduce piracy and consumer heterogeneity. Artists live for two periods. Every period, there is an infinite pool of potential young artists in the population. 15

Some economists have raised doubts about superstars necessarily having above average talent (see for

example Adler 1985). If superstars do not have more talent than the average artist, the arguments in this paper can be simplified and the results will be reinforced. In fact, our short-term static model would suffice to show that piracy increases overall artistic creation if there is no distinction between high- and low-quality creation.

13

The probability that young artists are talented is ρ, but neither they nor artistic promotion firms can observe their talent level until after they complete a period as active artists in the market. Individuals entering the artistic profession do so in their first period of existence as young artists. Only the fraction ρ of young artists that reveal themselves to be talented in this first period continue the artistic career in their second life period as high-type artists and receive advertising. Non-talented artists drop out of the artistic market at this point.16 Thus, during every period, the artistic market looks like it does in Section 2 except that low-type artists are now only interpreted as young artists, with the number of high-type artist at time t, nt , given by nt = ρ · mt−1 .

(10)

Every period, a new generation of potential young artists decide whether to enter the artistic market (in which case they create an artistic good) or to stay out of the market. We denote by F l the income that potential artists can earn outside the artistic market and assume a constant relative risk aversion utility function with coefficient σ. Then, the present ¡ l ¢1−σ 1 discounted value of not embarking on an artistic career is U = (1 + θ) 1−σ , where θ F

is the discount factor for second-period earnings. In turn, the present discounted expected utility of beginning an artistic career at time t as a young artist is Ut =

h ¡ ¡ ¢1−σ ii ¢1−σ 1 h¡ l ¢1−σ + θ ρ π ht+1 + (1 − ρ) F l πt . 1−σ

Because there is free entry to the market for young artists, the following expression will determine the number of young artists at time t: ¡ ¡ ¢1−σ i ¢1−σ 1 h¡ l ¢1−σ πt = 0. + θρ π ht+1 − (1 + θρ) F l 1−σ

(11)

In the following, we directly solve for the steady state equilibrium, which is obtained by taking n = ρ · m. 16

The details of the process of how artists with heterogeneous and unknown talent are sorted by the market

through information accumulation are analyzed in MacDonald (1988). Assuming that future performance is correlated with past performance, MacDonald shows that individuals enter 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 if they receive a good review of their performance in the first period. If this happens, their performances in the second life-period are attended by a larger number of consumers who pay higher prices (i.e., the artist becomes a superstar). Our setting is intended to indicate a reduced form of this process.

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3.2

The Long Run Impact of Piracy

As in the previous section, we first compare the case in which there is no piracy with the case in which all artists are pirated. Then, we briefly consider all of the intermediate cases of piracy. 3.2.1

The case in which all artists are copied

Consider first an economy in which unauthorized copying is not possible. In the short run, the SPE revenues for high and low-type artists are, respectively, ∙ ¸ S γ 1 γβ h π = − 1 − ln( ) ; γn n n n 2 Sρ . πl = γn

(12a) (12b)

Substituting these expressions into (11) yields à # "µ ¶ ∙ ¸1−σ ! 1−σ ¡ ¢ γ S 1 γβ 1 1−σ V ∗ (n) ≡ − (1 + θρ) F l − 1 − ln( ) ρ2(1−σ) 1 + θρ2σ−1 1−σ γn n n n

(13)

= 0.

The value of n solving this expression determines the steady state number of high-type artists n∗ss when there is no piracy. Similarly, from the previous analysis of the short-run equilibrium in the case where all artists are copied, we have the following: ∙ µ ¶¸ 1 γβ pc 2n − 1 S γ 2n − 1 pc h − 1 − ln ; π = γn n 4n c n n c 4n Sρ2 2n − ρ πl = . γn 2n − 1 Hence, substituting into (11) yields: µ ¶1−σ ∙ µ ¶¸1−σ S 1 γβ pc 2n − 1 1 γ 2n − 1 pc c − 1 − ln θρ V (n) ≡ 1 − σ γn n 4n c n n c 4n # "µ ¶ µ ¶ 1−σ 1−σ ¡ ¢ 2n − ρ 1 S 1−σ + ρ2(1−σ) − (1 + θρ) F l 1−σ γn 2n − 1 = 0

(14a) (14b)

(15)

The value of n solving this expression determines the steady state number of high-type artists ncss under piracy. 15

Now, we have: V c (n) − V ∗ (n) > 0 ⇐⇒

# ¶1−σ 2n − ρ −1 2n − 1 ∙ µ ¶¸1−σ 1 1 γβ pc 2n − 1 γ 2n − 1 pc 2σ−1 − 1 − ln +θρ 1 − σ n 4n c n n c 4n ∙ ¸1−σ 1 1 γβ γ − 1 − ln( ) −θρ2σ−1 > 0. 1−σ n n n 1 1−σ

"µ

Thus, Vic (n) − Vi∗ (n) > 0 can be ensured if θρ2σ−1 is small enough, which in turn is the case if θ is small enough or if σ > 1/2 and ρ is small enough. Under these conditions, this inequality is satisfied for any n, and, in particular, for n = n∗ss . Because both Vic (n) and Vi∗ (n) are strictly decreasing in n, it follows that θ or ρ being small enough (if σ > 1/2) is a ∗ C ∗ sufficient condition for nC ss > nss . Furthermore, n = ρm also implies that mss > mss . Hence,

we have the following. Proposition 3 Consider the case in which all artists are pirated. In the long run, if hightype artists obtain rents and θρ2σ−1 is small enough (that is, if the time discount factor or the probability of becoming a star is sufficiently low, with σ > 1/2), piracy increases the number of low- and high-type artists. Thus, the reduction in the superstars’ earnings that results from piracy does not necessarily reduce the number of young artists starting an artistic career. In fact, the opposite is true if the time discount factor or the probability of becoming a superstar is sufficiently low. Piracy shifts revenues from superstars to young artists (piracy reduces the profitability of superstar promotion, which therefore decreases thereby raising young artists’ market share). This, from a young artist’s perspective, implies the transformation of future potential earnings into actual current ones. Hence, the present discounted value of starting an artistic career increases. Furthermore, because the number of talented high-type artists in the long run depends on the abundance of young artists trying to develop an artistic career, piracy increases the long-run number of high-type artists. 3.2.2

Considering all cases

If pc < pl and pc < ph all artists are pirated, which is the case considered so far. We now briefly consider all possible cases of pc with respect to pl and ph (see Appendix C for details). 16

The results of Proposition 3 are conditional on the discount factor or the probability of becoming a superstar being low. The same is true for the remaining results. Bearing this in mind, in what follows we concentrate on the case θ = 0, which greatly simplifies the exposition. For θ = 0, (13) and (15) simplify to n∗ss = ρ2 ncss =

S ; γF l

2ncss − ρ 2 S ρ . 2ncss − 1 γF l

(16) (17)

Clearly, because ρ < 1, we have n∗ss < ncss . Furthermore, ncss is a continuous function of pc , which we denote as nss (pc ). Figure 2 illustrates this function. The results are summarized in the following: Proposition 4 In the long run, if high-type artists obtain rents, piracy increases the number of low- and high-type artists. Moreover, the number of both types of artists is constant as a function of pc for both small and large pc , increasing for intermediate-low values of pc and decreasing for intermediate-large values of pc . The maximum level for both types of artists is reached when pc equals the critical level pl below which low-type artists are not affected by piracy. Proof. See Appendix C. INSERT FIGURE 2 ABOUT HERE Thus, nss follows the same pattern, as a function of pc , as does m(pc ) in Figure 1. Again, as in Section 2, the differences between cases (ii) to (v) do not affect our key result that piracy always leads to a larger number of artists. Notwithstanding, these differences will be of some interest when we discuss policy alternatives in the next section. 3.2.3

Superstars’ rents

As with the short-run analysis, the results in this section are conditional on superstars obtaining rents: πh > F h . It is thus important to show that superstars can indeed obtain rents in the long run, even if there is free entry to an artistic career for young artists. The intuition is that artists must go through a young-artist period in which they show their talent as a prerequisite to becoming a superstar. However, the market for young artists may 17

be small. In fact, the more resources that superstars spend on their promotion, the smaller the market is. As a result, superstars’ promotion expenditures may create a bottleneck and limit access to superstar status. Formally, consider the case in which all artists are copied. For every pc (and every set of parameters), there is a maximum number of superstars such that they obtain non-negative profits. Using (14a), the set of pairs (pc , n) satisfying π h (pc , n) = F h is given by the following: ½ µ ¶ µ ¶ ¾ pc 2n − 1 1 1 c 4n2 γF h c (p , n) : γ + ln − 1+n =0 . (18) c 4n2 n βγ pc 2n − 1 S This schedule is also illustrated in Figure 2. A higher pc involves less piracy, so that the market can support a larger number of superstars. The pairs (pc , n) such that superstars obtain rents are those below the schedule. Depending on the value of parameters such as S and F h , this schedule will cross the m(pc ) schedule at different points (e.g., a larger market or lower opportunity costs shift the πh (pc , n) = F h schedule upwards). Superstars obtain rents in equilibrium whenever this crossing occurs to the left of the relevant value of pc (which is never smaller than c).

4

Levies on Copying Equipment: Facilitating Artistic Creation?

As noted in the Introduction, the policy response to file-sharing and copying in most European countries has been to implement levies on recording equipment and electronic devices such as CDs, DVDs, hard discs, and MP3s. Most revenues from these levies are then allocated among writers, performers, and copyright holders in proportion to their legal sales. In this section, we discuss the implications for artistic creation of these and other alternative policies. To analyze the impact of different policy alternatives, it is useful to think about copy levies as involving two separate policies: a tax on copy equipment and a subsidy for artists. We first discuss the impact of different copy taxes and then consider the impact of different schemes for allocating tax revenues across artists. When the different cases outlined in the previous sections lead to different results here, we focus on the case in which all artists are copied and on the case in which only superstars are copied because these are the two most relevant cases as indicated by the discussion at the end of Section 2.

18

4.1

Taxes on Copy Equipment

Note first that taxes on copy equipment may or may not be proportional to the amount of the material being copied. For example, levies on CDs and DVDs may be roughly proportional to the amount of copying. In contrast, levies on electronic devices such as MP3 players and last-generation cell phones, are not. Levies on electronic devices instead represent a fixed cost on copying. We must therefore distinguish between proportional copy taxes (e.g., taxes on CDs and DVDs) and fixed copy taxes with respect to the amount of copying (e.g., taxes on MP3 players, cell phones, and the like). These two policy alternatives can easily be mapped in terms of the model in this paper. A proportional copy tax is equivalent to a rise in pc . In turn, a fixed tax is equivalent to a reduction in the amount S to be spent on artistic goods. According to expressions (9) and (17), which are valid for the case in which all artists are copied, larger number of consumers S increases m and nss . The same occurs for cases (ii)−(vi) (see expressions (C.1), (C.3) and (C.4), and (C.5)-(C.7) in Appendix C). Therefore, given the equivalence between the policies and the parameters in the model, fixed taxes on electronic devices reduce m and nss . On the other hand, Figures 1 and 2 show that a small increase in pc (which, as we have noted, is equivalent to implementing a proportional copy tax) has no effect on m and nss if all artists are copied (i.e., for pc < pl ). The reason is that these taxes have two opposing effects on low-type artists’ revenues: a positive effect on low-type artists’ earnings given their market share and a negative effect due to their market share loss in favor of superstars. However, when only superstars are affected by copying (i.e., if pl < pc < ph ), a proportional copy tax (which is equivalent to increasing pc ) has a negative effect on m and nss . The following proposition summarizes these results. Proposition 5 Fixed taxes on electronic devices reduce the short-run number of niche and young artists, and the long-run number of high-type artists. If only superstars are affected by copying, proportional copy taxes also have a negative impact on the short-run number of niche and young artists and the long-run number of all artists.

4.2

Allocating the Revenues from Copy Levies

The allocation of levy revenues across artists may or may not be in proportion to their legal sales (e.g., niche and young artists could receive a share of levy revenues larger than their share of sales). We will distinguish between a proportional-to-sales allocation of levy 19

revenues (in which revenues are allocated across artists in proportion to their legal sales) and a lump-sum allocation (in which artists receive a fixed amount that is independent of their sales). Clearly, there may also be many intermediate policies involving revenue allocations that are non-linear in sales, which would be roughly equivalent to a combination of these two policies. Again, these two policy alternatives can easily be mapped in terms of the model in this paper. A lump-sum allocation of levy revenues across artists is equivalent to a reduction in artists’ opportunity costs F h and F l . In the case where all artists are copied, expressions (9) and (17) show that lower F l increases m and nss . Therefore, lump-sum payments to artists increase m and nss . The same occurs for cases (ii) − (vi) (see expressions (C.1), (C.3) and (C.4), and (C.5)-(C.7) in Appendix C). On the other hand, a proportional allocation of levy revenues across artists is equivalent to a subsidy that reduces the cost c of each original reproduction. To ascertain the impact of this policy, note that whenever c or pc enters any expression determining the number of artists, the ratio at play is c/pc . Hence, a proportional-to-sales payment to artists has the same effect as a proportional copy tax. Therefore, the same analysis carried out for proportional copy taxes (summarized in the second part of Proposition 5) holds for proportional-to-sales allocations of levy returns. In summary, we have the following Proposition 6 Allocating the revenues from levies as lump-sum payments to artists increases the short-run number of niche and young artists and the long-run number of hightype artists. However, allocating the revenues from levies across artists in proportion to their legal sales may reduce the short- and the long-run number of artists. This will in fact be the case if only superstars are affected by copying. Propositions 5 and 6 warn about the risks for artistic creation of a policy based on levies that are allocated according to legal sales. These policies may only favor superstars. If levy revenues are allocated in proportion to official sales, they raise the incentives to invest in the promotion of superstars, which offsets the effect of piracy in loosening market concentration.17 17

Also note that in principle, levies are such that the total revenues being collected equal the total payments

to the beneficiaries of the levy. Hence, the total amount of resources allocated to the artistic industry remains constant. However, it has been argued that not all the equipment subject to copy levies is used for copying

20

Proposition 6 suggests that the most effective policy from the point of view of artistic creation would be to use the yields from levies to help young artists. Of course, any lumpsum-like scheme for allocating levy revenues should ensure that artists are indeed active. This may require conditioning payments on a minimum threshold of output in terms of sales or live performances. Non-linear strongly concave schemes linking levy payments received by artists to their sales may constitute an effective compromise between strictly proportional schemes and lump-sum schemes. Moreover, resources allocated to young artists need not to be implemented as direct payments but can also take the form of subsidies for young artists’ production costs and live performances or can otherwise be used to reduce general taxes on these activities.18

5

Concluding Comments

New communication and copy technologies are affecting artistic industries in many different ways. This paper focuses on the effects in a setting that emphasizes three central aspects of artistic markets: the difficulties of talent sorting, the importance of promotion expenditures, and the predominance of superstars. Under reasonable conditions, we find that piracy may lower superstars’ market share, which may make entry and survival by niche and young artists easier. As a result, the number of artists and therefore artistic diversity may increase. Furthermore, the chances of discovering a new talent depends on how much room there is in the market for young artists. Hence the number of highly talented superstars at a given point of time depends on how many young artists were able to start an artistic career in previous periods. By providing more market opportunities for young and niche artists, piracy may enhance high quality creation in the long run. Superstars’ market concentration and profits have a conflicting impact on new artistic careers. The large profits of superstars push young potential artists to start artistic careers. However, if superstars concentrate too much of the revenues in the market, there will be little room for new generations of talent artistic material. If this is so, copy levies will involve a transfer of resources from the rest of the economy to the artistic industry. More specifically, levies with proportional-to-sales allocation of revenues that are raised from taxing equipment not used for copying artistic material entail a subsidy to superstars from the rest of the economy. 18 For related literature discussing alternative mechanisms to finance creation that may be more efficient than granting monopoly rights see Shavell and van Ypersele (2001) and Romer (2002).

21

to be tested and revealed. These conflicting effects of stardom may lead to a conflicting long-run impact of piracy on artistic creation. It follows from the analysis that it cannot be taken for granted that copy levies recently implemented in many Western countries, whose revenues are mostly allocated in proportion to sales, will favor artistic creation. These levies on copy equipment and other possible restrictive policies may reinforce the already-strong market position of top artists and hinder the promotion of new talent. As noted throughout the paper, these results are conditional on the premise that superstars obtain rents. Is this hypothesis reasonable? Many people may consider it obvious that this is the case. However, economists are rightly skeptical of anything taken for granted. Our model shows that superstars can indeed permanently obtain rents. Moreover, we cite empirical evidence that is consistent with this hypothesis. Still, more detailed data on the distribution of artists earnings would be useful. Collecting societies do not readily share data on the distribution of copyright earnings. Because collecting societies now benefit from the legislative and administrative capacities of governments to implement levies, it would seem reasonable that the statistics on the distribution of levy yields across artists and copyright holders be made public. This information would help us to assess how skewed the distribution of payments is in favor of a small number of superstars and how reasonable the hypothesis is that superstars obtain rents. During the last century, technological progress in the design of communication and recording devices (such as radio, TV, records, tapes, etc.) greatly skewed some artistic markets in favor of a small number of top artists who obtained increasingly larger revenues. This process is not over, with recent changes in the economic and political environment continuing to facilitate the globalization of culture, thereby increasing cultural uniformity and favoring the further concentration of revenues in artistic markets. However, communication and copy technologies can now also have a counterbalancing effect. To borrow from Tom Friedman’s (2005) metaphor, new communication and copy technologies are flattening the artistic market by leveling it in favor of the long tail of young and niche artists. Governments should make sure that policies intended to favor artistic creation do not hinder this recent development.

22

6

Appendix A: Horizontal Differentiation

In this appendix we show that the same central qualitative results can be obtained in an explicit model of monopolistic competition with horizontal differentiation. To make the model easy to manage, we consider a Dixit-Stiglitz (1977) model in which the amount of each artist’s work that consumers want to consume may be any real number and in which the number of artists is large enough so that their individual price decisions do not affect the average product price in the market. Consumers now solve the following maximization problem: maxxi ,yj s.t.

∙ ´1/η2 ¸ ³P Pn m η 1 1/η1 η2 a ln ( i=1 (xi ) ) , + (1 − a) ln j=1 (yj ) Pm Pn h l i=1 (xi pi ) + j=1 (yj pj ) = 1.

(A.1)

It is assumed that 0 < η 1 < η 2 < 1; that is, the elasticity of substitution within the set of superstar artistic goods, 1/(1 − η 1 ), is lower than within the group of low-type artists (as a result of higher differentiation). All other components in the model are the same as in the main text. Also, the timing is similar to in the main text except that now in Stage 3, artists do not play a Cournot game but instead simultaneously choose the price that they will charge for original reproductions of their work. Let us consider the equilibrium at Stage 2. The demand function for artist i’s output is P Xi = Sa · (phi )1/(η1 −1) / ni=1 (phi )η1 /(η1 −1) .19 The same is true for low-type artists. Then, stan-

dard calculations under the usual Dixit-Stiglitz assumptions yield phi = c/η 1 , plj = c/η 2 , Xi =

a Sn ηc1 , Yj = (1 − a) Sn ηc2 . Hence, high-type artist i’s revenues as a function of her and other

superstars’ advertising are π hi (Ai , A−i ) = a Sn (1 − η 1 ) − Ai . Maximizing π hi with respect to Ai after plugging in expression (2) yields the superstars’ total market share: a∗ = 1 −

1 . γ (1 − η 1 )

(A.2)

S (1 − η 2 ). Hence, because In turn, low-type artist j’s revenues are π lj (Yj , Y−j ) = (1 − a) m

there is free entry in this market at cost F l , the equilibrium number of low-type artists is as 19

Note that the first-order conditions of (A.1) yield a (xk )η1 −1 / η −1

Pn

η1 = phk , k = 1, .., n. Hence, i=1 (xi ) ¡ ¢η /(η −1) η η phi /phk ⇒ (xi ) 1 = phi /phk 1 1 (xk ) 1 ⇒

for any two high-type artists i and k, we have (xi /xk ) 1 = Pn η1 η Pn ¡ ¢η /(η −1) ¡ h ¢η 1 /(η 1 −1) = (xk ) 1 i=1 phi 1 1 / pk . Substituting this into the previous expression yields i=1 (xi ) ¡ h ¢1/(η1 −1) Pn ¡ h ¢η1 /(η1 −1) / i=1 pi . xk = a pk

23

follows: m∗ =

S 1 − η2 . γF l 1 − η 1

(A.3)

With piracy, the consumer’s problem is the following: ∙ ³P ´1/η2 ¸ Pn η1 1/η 1 m η2 maxxi ,zi ,yj ,zj a ln ( i=1 [xi + υzi ] ) ,(A.4) + (1 − a) ln j=1 [yj + υzj ] Pn Pn Pm Pm h c l c s.t. x p + z p + y p + i i j i j i=1 i=1 j=1 j=1 zj p = 1.

Assuming as in the main text that υ is uniformly distributed across individuals along the

interval [0, 1], the fraction of individuals that buys superstar i’s originals and low-type artist j’s originals is, respectively, δ h = pc /phi and δ h = pc /plj (provided that pc < phi and pc < plj ). As a result, demand becomes more elastic and mark-ups will be lower. The number of consumers buying superstar i’s originals is now Spc /pi . Hence, the demand P function for i’s originals is Xi = (pc /phi )Sa · (phi )1/(η1 −1) / ni=1 (phi )η1 /(η1 −1) . The same is true

for low-type artists. Then, standard calculations yield phi = c (2 − η 1 ) , plj = c(2 − η 2 ), Xi = c

c

1

2

a Sn (2−ηp )2 c2 , Yj = (1−a) Sn (2−ηp )2 c2 . Hence, high-type artist i’s revenues as a function of her and c

1−η 1 p other superstars’ advertising are π hi (Ai , A−i ) = a Sn (2−η − Ai . As before, maximizing πhi )2 c 1

with respect to Ai after plugging in expression (2) yields the new equilibrium total superstar market share: ac = 1 −

(2 − η 1 )2 c . γ (1 − η 1 ) pc

(A.5) c

S 1−η2 p . Using the free entry In turn, low-type artist j’s revenues are πlj (Yj , Y−j ) = (1 − a) m (2−η )2 c 2

condition yields the equilibrium number of low-type artists in the case of piracy: mc =

S 1 − η 2 (2 − η 1 )2 . γF l 1 − η 1 (2 − η 2 )2

(A.6)

Because η 1 < η 2 , we have mc > m∗ . Therefore, the number of niche and young artists in the market is larger with piracy than if piracy could be completely prevented. Similar qualitative results hold for the long-run equilibrium of the dynamic model. Under the simplifying assumption θ = 0 and using n = ρm, the long run number of high-type 2 artists assuming that there is no piracy is n∗ss = ρ γFS l 1−η . With piracy, the number is 1−η 1

2

2 (2−η 1 ) ncss = ρ γFS l 1−η . Hence, again, η 1 < η 2 implies ncss > n∗ss . 1−η (2−η )2 1

2

24

7

Appendix B: Vertical Differentiation and Individual Effects of Advertising

In this appendix we introduce vertical differentiation and a more general role for advertising. We show that the same central qualitative results hold as in the main text. No Piracy Consider the following utility maximization problem where ui is the relative valuation of superstar i’s artistic work within superstars’ work: h ´i ³P P m a ln ( ni=1 ui xi ) + (1 − a) ln , y maxx1 ,..,xn ,y j j=1 P Pn h m l l s.t. i=1 pi xi + p j=1 p yj = 1.

(B.1)

There is a continuum of consumers of measure S. Superstars’ total market share a and individual valuations ui are endogenous and depend on expenditures on promotion. As before, superstars’ total market share a depends on the sum of superstars’ promotion expenditures according to expression (2). Moreover, the individual valuation of superstar i’s work ui depends on i’s individual promotion expenditure Ai . To simplify the computations, we assume a functional form for ui similar to (2). The additional parameter λ ≥ 0 in the next expression calibrates promotion expenditures’ impact on individual valuations ui (the case analyzed in the main text corresponds to λ = 0): ´λ 1³ 2 (B.2) 1 − βe−γn Ai /S , i = 1, 2, .., n . ui = n Competition takes place according to the same three-stage game as in the main text. Consider first the Cournot-Nash equilibrium in Stage 3. Note that optimal consumer choices imply phk = uk phi /ui . Then, standard calculations yield inverse demand functions phi = P ui aS/ ( nk=1 uk Xk ) , i = 1, ..., n, and pl = (1−a)S/Y . Hence, each high-type artist’s earnings P are πhi (Xi , X−i ) = (ui aS/ [ nk=1 uk Xk ] − c) Xi − Ai . To compute firm i’s optimal Xi in a

symmetric SPE, we consider a common uk = u0 for all k 6= i. From the Cournot-equilibrium

first order condition we have the following:20 ¢¤ £ ¡ ui ¶ µ − 1 (n − 1) 1 + (n − 1) u 1 aS 0 i u + 0 c; Xi = ; phi = £ ¤ 2 u n−1 u c 1 + (n − 1) ui0 !2 à 1 π hi (Ai , u0 ) = aS 1 − 1 − Ai . ui (Ai ) + 0 n−1 u 20

Details of all the derivations in this Appendix are available upon request.

25

Substituting for a and ui with (2) and (B.2), maximizing with respect to Ai , and taking ui = u0 yields the SPE value of a: 1 n . (B.3) γ 2(n − 1)2 λ + 1 h i − c Yj . The Cournot equiIn turn, low-type artist j’s revenues are π lj (Yj , Yi−1 ) = (1−a)S Y a∗ = 1 −

librium in the low-type sub-market yields pl =

m c m−1

and Yj =

m−1 (1−a)S . m2 c

The equilibrium

number of active low-type artists m∗ is determined by the free entry condition π lj = F l , which yields the following: ∗

m =

µ

nS 1 2(n − 1)2 λ + 1 γF l

¶ 12

.

(B.4)

Piracy As in the main text, we consider piracy in an economy with a continuum of consumers that have different (constant) marginal rates of substitution υ for copies and originals. The consumer’s problem is now as follows: maxxi ,zi ,y,zy s.t.

³P ´i h Pn m , a ln ( i=1 [ui xi + υzi ]) + (1 − a) ln j=1 [yj + υzj ] Pn c Pm l Pm c Pn h i=1 pi xi + + i=1 p zi + j=1 p yj + j=1 p zj = 1.

(B.5)

Assuming that υ is uniformly distributed across individuals along the interval [0, 1], the fraction δ of individuals that buy originals in the case of high-type goods is δ = ui pc /phi (proP vided that pc < phi ). Hence, expenditure on high-type originals is nk=1 phk Xk = aSui pc /phi .

Moreover, phk = uk phi /ui . Therefore, the inverse demand function for each superstar is P 1/2 phi = ui [pc aS/( nk=1 uk Xk )] . Similarly, if pc < pl , the demand for low-type artists’ originals is Y = pc (1 − a)S/(pl )2 .21

We assume that pc is low enough that in equilibrium pc < pl ≤ ph . As a result, all artists

are pirated. Let us calculate a symmetric SPE for the game assuming that all the high-type artists except the deviant artist i choose the same level of uk = u0 . At the last stage of the 21

Note that we ignore the (reasonable) possibility that the vs are also increasing in Ai . In such a case,

advertising will increase the willingness to pay not only for the original version of the good, but also for the pirated version. Obviously, this will reduce superstars incentives to pay advertising costs. This in turn will reinforce the idea that piracy enhances the entry of low-type artists by reducing superstars’ market share.

26

game, Cournot competition among high-type artists yields ¢ 1¤ £ ¡ ui ui − 1 + 2 (n − 12 )2 2pc aS (n − 1) 1 + (n − 1) 0 0 h u u c; Xi = ; pi = £ ¤3 c c n − 12 1 + (n − 1) uui0 ¢ 1 ¤2 £ ¡ ui − 1 + 2 pc ui (2n − 1) (n − 1) 0 u π hi (Ai , A−i ) = aS − Ai . £ ¤ 3 c 1 + (n − 1) ui0 u

Substituting for a and ui with (2) and (B.2), maximizing with respect to Ai , and taking

ui = u0 yields the value of a when piracy is occurring: ac = 1 −

n 1 c 4n 1 . λ c γ a p 2n − 1 [(4n − 3)(n − 1) + n] n1 λ + 1

(B.6)

In turn, low-type artists’ profit maximization conditional on the demand when their work is pirated (i.e., when pc < pl ) yields pl =

2m c 2m−1

2

c

and Yj = (1 − a) pc2 S (2m−1) . Then, using the 4m3

free entry condition, we obtain the short-run equilibrium number of low-type artists in the case of piracy: c

m =

µ

nS 1 1 2mc − 1 n 1 λ c a m 2n − 1 [(4n − 3) (n − 1) + n] n λ + 1 γF l

¶1/2

.

(B.7)

Comparing (B.4) with (B.7) shows that mc > m∗ if mc > n. To see this, note that the result is ensured if

2(n−1)2 n (4n−3)(n−1)+n

> 1. This is satisfied for all n ≥ 3, which seems a reasonable

assumption.

8

Appendix C: Relegated Proofs

Proof of Proposition 2 As explained in the main text, there are five possible cases depending on the exogenous level of pc :22 (i) (ii)

ph ≥ pc ≥ ph : superstars deter copies;

(iii)

ph > pc > pl : only superstars are copied;

(iv)

pl ≥ pc ≥ pl : low-type artists deter copies and superstars are copied;

(v) 22

pc > ph : copies are blockaded;

pl > pc : both low-type artists and superstars are copied.

As already noted in the main text, the analysis for ph ≯ pl is somewhat simpler because case (iii) is

replaced with a different case in which both high- and low-type artists fix the same price pc and thereby, both groups of artists deter copies.

27

Case (i): This case was analyzed in Section 2.1, yielding expression (5) for m. Note that in this case, m does not depend on pc . Case (ii): In this case, we have ph = pc . Hence, the profits for each high-type artist at Stage 1 of the game are πhi =

pc −c aS npc

− Ai − F h . The first order conditions of the SPE of the game

yield the following: pc βe−γnA/S (pc − c) . − 1/γ = 0 → a = 1 − pc γ(pc − c) Then, the number of low-type artists is given by the free entry condition, which combined with the expression for a above implies the following: ¸1/2 ∙ S 1 c m(p ) = . 1 − c/pc γF l

(C.1) n c, n−1

Note that this is decreasing in pc . Also note that for pc =

expressions (5) and (C.1)

yield the same value for m, so that m is continuous as a function of pc at the frontier between cases (i) and (ii). Case (iii) In this case, we have ph =

2n c. 2n−1

Hence, output per artist is Xi =

high-type artist’s earnings at Stage 1 are π hi =

2n−1 4n3

pc aS c

(2n−1)2 pc aS , 4n3 c2

and each

− Ai . We can rewrite this profit

function for each high-type artist as π hi (Ai , A)

2n − 1 pc S (1 − βe−γnA/S ) − Ai , i = 1, 2, ..., n. = 3 4n c

The first order conditions for the SPE of the game yield the new SPE level for a, which is indicated with superscript c: (2n − 1) pc S −γnA/S n2 4c c − S/γ = 0 → a = 1 − βe . 4n2 c γ pc (2n − 1)

(C.2)

Using this expression and the free-entry condition in the low-type market yields the number of low-type artists:

∙

c 4n2 S m(p ) = c p 2n − 1 γF l c

¸1/2

.

(C.3)

Note that m is decreasing in pc . Also note that equations (C.1) and (C.3) yield the same number of low-type artists for pc =

2n c 2n−1

, so that m is continuous as a function of pc at the

frontier between cases (ii) and (iii). 28

Case (iv) In this case the equilibrium price in the low-type market is pl = pc . Hence the earnings of each low-type artist at Stage 3 of the game are given by the free entry condition: πlj (m) =

(pc − c)(1 − a)S = F l. mpc

Thus, substituting with expression (C.2) for ac , we find: m(pc ) = (1 − c/pc )

c 4n2 S . pc 2n − 1 γF l

(C.4)

Because c/pc > c/ph = (2n − 1) /2n > 1/2, it is easily seen that m is increasing in pc . Moreover, m takes the same value for pc =

m c m−1

when using expressions (C.3) and (C.4), so

that m is continuous at the frontier between cases (iii) and (iv). Case (v) This case was already considered in the main text, yielding expression (9) for m. Moreover, m takes the same value for pc =

2m c 2m−1

when using expressions (C.4) and (9), so that

m is continuous at the frontier between cases (iv) and (v). The overall relationship between pc and m is illustrated in Figure 1, where the curve m(pc ) represents the equilibrium level of m as a function of the copying price. Note that m(pc ) reaches a maximum at point p0 = pl , at the frontier between region (iii) and (iv). Proof of Proposition 4 In the long run, and using the simplifying assumption θ = 0, the steady state value of n as a function of pc can be obtained by substituting n = ρ · m into expressions (4), (C.1), (C.3), (C.4), and (9), which correspond respectively to cases (i)-(v), respectively, in the previous short-run analysis. Cases (i) and (v) were already analyzed in the main text, yielding expressions (16) and (17). For the other three cases, we have the following: ¸1/2 ρ2 S 1 Case (ii) : nss = . 1 − c/pc γF l 1 c ρ2 S Case (iii) : nss = + 2 c . 2 p γF l 1 Case (iv) : nss = . ρS 2 − 4(1 − c/pc ) pcc γF l ∙

(C.5) (C.6) (C.7)

Recall from the main text that n is independent of pc in cases (i) and (v). Now, it is easy to see that n is decreasing in pc in cases (ii) and (iii), whereas it is increasing in case (iv). 29

Hence, nss as a function of pc follows the same pattern as m(pc ) (see Figures 1 and 2), with a maximum at the frontier between regions (iii) and (iv).

9

Acknowledgements

We thank Luis Corchón, the editor Martin Peitz, and an anonymous referee for very helpful comments, and seminar participants at U. Carlos III de Madrid, Bellaterra seminar, U. de Málaga, and U. de Valencia. Francisco Alcalá also thanks the Economics Department at NYU, which he visited while conducting part of this project, for the generous hospitality. We acknowledge financial support from the Spanish Ministry of Education and Science under projects ECO2008-02654/ECON and ECO2009-07616/ECON, and from the Fundación Séneca de la Región de Murcia under project 11885/PHCS/09.

References [1] Adler, M., 1985. Stardom and Talent. American Economic Review 75, 208-212. [2] Alcalá, F., González-Maestre, M., 2009. Artistic Creation and Intellectual Property. Economics Working Papers 3/2009, Murcia University, DIGITUM. Available at http://digitum.um.es/xmlui/bitstream/10201/4614/1/WPUMUFAE.2009.03.pdf?sequence=1 [3] Chisholm, D.C., 2004. Two-Part Share Contracts, Risk and Life Cycle of Stars: Some Empirical Results from Motion Picture Contracts. Journal of Cultural Economics 28, 37-56. [4] Crain, W.M., Tollison, R. D., 2002. Consumer Choice and the Popular Music Industry: A Test of the Superstar Theory. Empirica 29, 1-9. [5] De &

Thuiskopie, Practice.

20th

2009.

International

edition.

Dutch

Survey

Private

on

Copying

Private Society.

Copying Available

Law at

http://145.222.172.84/assets/File/Survey%202009%20Webversie%20Final.pdf [6] Dixit, A.K., Stiglitz, J.E., 1977. Monopolistic Competition and Optimum Product Diversity. American Economic Review 67, 297-308.

30

[7] Friedman, T.L., 2005. The World Is Flat. A Brief History of the Twenty-First Century. Picador/Farrar, Straus and Giroux, New York. [8] Gayer, A., Shy, O., 2003. Copyright Protection and Hardware Taxation. Information Economics and Policy 15, 467-483. [9] Kinokuni, H., 2005. Compensation for Copying and Bargaining. Information Economics and Policy 17, 349-364. [10] Kretschmer, right

and

German

M.,

Hardwick,

Non-Copyright writers.

P.,

2007.

Sources:

A

Authors’ survey

London/Bournemouth:

Earnings of

25,000

ALCS/CIPPM.

from

Copy-

British Available

and at

http://www.cippm.org.uk/downloads/ACLS%20Full%20report.pdf [11] Krueger, A.B., 2005. The Economics of Real Superstars: The Market for Rock Concerts in the Material World. Journal of Labor Economics 23, 1-30. [12] MacDonald, G.M., 1988. The Economics of Rising Stars. American Economic Review 78, 155-167. [13] Peitz, M., Waelbroeck, P., 2005. An Economist’s Guide to Digital Music. CESifo Economic Studies 51, 359-428. [14] Peitz, M., Waelbroeck, P. 2006. Piracy of Digital Products: A Critical Review of the Theoretical Literature. Information Economics and Policy 18, 449-476. [15] RIIA 2007. The CD: A Better Value Than Ever. Report Prepared By the Communications and Strategic Analysis Department of the Recording Industry Association of America. Available at http://76.74.24.142/F3A24BF9-9711-7F8A-F1D3-1100C49D8418.pdf [16] Romer, P., 2002. When Should We Use Intellectual Property Rights?. American Economic Review, Papers and Proceedings 92, 213-216. [17] Rosen, S., 1981. The Economics of Superstars. American Economic Review 71, 845-858. [18] Rothenbuhler, E.W., Dimmick, J.W., 1982. Popular Music: Concentration and Diversity in the Industry, 1974-1980. Journal of Communication 32, 143-149.

31

[19] Shavell, S., van Ypersele, T., 2001. Rewards versus Intellectual Property Rights. Journal of Law and Economics 44, 525—47. [20] Sutton, J., 1991. Sunk Costs and Market Structure: Price Competition, Advertising, and the Evolution of Concentration. MIT Press, Cambridge, MA. [21] Terviö, M., 2009. Superstars and Mediocrities: Market Failure in The Discovery of Talent. Review of Economic Studies 76, 829-850. [22] Zhang, M.X., 2002. Stardom, Peer-to-Peer and the Socially Optimal Distribution of Music. Mimeo, Sloan School of Management, MIT.

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