Digital Music Set Free: The Flip Side of DRM

Transcription

1 Digital Music Set Free: The Flip Side of DRM Dinah A. Vernik The Fuqua School of Business, Duke University, Working paper October 27, 2008 Digital rights management (DRM) refers to technologies designed to control how end users may access, copy, or convert digital media. In the context of music downloads, DRM makes illegal copying of digital music more difficult to prevent download piracy. Although DRM certainly makes illegal copying harder, is there also a downside to limiting customers ability to use the products they have purchased? Or, without DRM, might download piracy volume be higher, and the profits of the music industry decline, as the industry seems to believe? This article addresses these and related questions by developing a model of a music distribution channel that allows a record label to sell through both traditional CD retailers and download services at different wholesale prices. Consumers have heterogeneous preferences for downloaded versus CD music and differ in their propensity to engage in piracy. Comparing two cases - one in which the music download service sells DRM-protected music and another in which it sells DRM-free songs - suggests the effects of eliminating DRM protection. Among the interesting results, the analysis indicates that the level of download piracy may decline when DRM protection is removed while sales of music in digital format increase and that the traditional retailer prefers to compete with digital music pirates rather than with legal music download services. 1. Introduction Digital rights management (DRM) refers to technologies designed to control how end users can access, copy, or convert information goods, such as software, music, movies, or books. For years, DRM was the primary means to protect digital products from unauthorized copying and distribution. Similar to most other information good industries, the music industry believes that DRM technologies decrease download piracy and that without DRM protection, piracy volumes would grow, just because it would become easier to copy digital music illegally. Furthermore, the music industry believes that download piracy adversely affects its profits in the music distribution channel. Existing research addresses the second part of this belief chain, namely, the connection between piracy and profits. For example, some researchers support the music industry s belief about the negative impact of piracy on industry profits, though others question this

2 2 Dinah A. Vernik: Dissertation Essay 1 conjecture and demonstrate that piracy can positively affect the profits of the copyright owners in certain conditions. The model presented herein instead addresses the first part of the belief system: By focusing on the relationship between DRM and piracy, it challenges the music industry s assumption that a higher degree of DRM protection results in lower piracy volumes. From the moment music became available for sale in a digital format, it was protected by DRM technologies. Yet the music industry, worth more than $35 billion worldwide (see IFPI 2004), has been suffering the effects of download piracy all along. For example, in 2005 alone, approximately 13.2 billion songs were downloaded illegally in the United States, according to the International Federation of the Phonographic Industry (IFPI, 2006). The music industry also posits that without DRM, piracy volumes would be even higher (RIAA, 2008). But is the industry correct? Certainly, DRM makes illegal copying harder, which should decrease piracy volumes. But there also may be a downside to using DRM technologies, because they restrict the ways consumers can access or listen to music that they have purchased. Will the introduction of DRM-free music lead to increases in download piracy, as expected by opponents of DRM-free music? Will the music industry suffer decreased profits or actually enjoy profit increases? What will the effects be for CD retailers? To address these and related questions, this research models a music distribution channel that allows for both traditional CD retailers and download services like itunes. Although the proposed model applies to various types of information goods, for simplicity of exposition, the paper focuses on the music industry, with a music album as a product for sale. The model assumes that a music album is available to consumers in either digital (e.g., downloadable files) or traditional (e.g., CDs) format. Furthermore, music in digital format can be either DRM-protected or DRM-free. Consumers are assumed to have heterogeneous preferences for downloaded music versus CDs, and they derive higher utility from DRM-free than from DRM-protected digital music. A record label can distribute music via itunes-like download services and traditional retailers selling CDs. Consumers can obtain the music in digital or traditional format legally from an official retailer, or they can steal music in digital format from music pirates. Finally, consumers differ in terms of their

3 Dinah A. Vernik: Dissertation Essay 1 3 propensity to engage in piracy, which might increase if unprotected, DRM-free, digital music were to become available from digital retailers. In the benchmark hypothetical case, the music is distributed only via a traditional retailer that competes with music pirates. The second and third cases introduce a legal music download service with either DRM-protected or DRM-free music. An interesting result of this analysis is that the traditional retailer prefers to compete with music pirates rather than with both an official digital music retailer and music pirates. Even though the volume of piracy is higher and demand for the legal music is lower when there is no official digital music retailer, the traditional retailer can charge a higher price for CDs and earn higher profits. However, from the record label s perspective, profits are higher when digital music is available via a legal download service. In this case, the total volume of piracy is lower because consumers with higher preference for digital music and lower propensity to steal music prefer to buy digital music from the legal retailer. The analysis clearly shows that download piracy decreases once the record label allows legal downloads via the digital music retailer. Counterintuitively, download piracy might decrease even more when the firm sells DRM-free music. This finding is a result of the competition between digital and traditional retailers. Compared with DRM-protected music, DRM-free music is a stronger competitor for the music in traditional format as well as for the pirated music. Therefore, with the introduction of DRM-free music, the retail price for music in traditional format decreases, and more consumers prefer buying legal music to stealing it. The rest of this article is organized as follows: The next section provides background on the music industry and highlights the importance of research questions studied in this paper. Section 3 provides a review of relevant literature and defines the positioning of this article among current research. Section 4 features the model and related assumptions. Section 5 presents the results and some conclusions with direct bearing on the music industry. Finally, the conclusion and some future research directions appear in Section Background on the Music Industry Before recording technologies, music could be experienced only in person - in a church, at social gatherings, or during live concerts. People could not take music home, buy or sell

4 4 Dinah A. Vernik: Dissertation Essay 1 it, or even hear it again. The introduction of recording technology in the late nineteenth century transformed music into more than just a service; it also became a product that could be bought and sold. The technology began with piano rolls, followed by phonograph cylinders, gramophone discs, tapes, and CDs. The most recent developments entail digital recording, enabled by the invention of purely electronic recording formats such as WAV digital music files and the MP3 compressed file type. Recent advances in digital technologies, including digital recorders, personal computers, and the Internet, have yet again changed the way music gets consumed and distributed. On the consumption side, the digitization of music has generated a new type of portable, computerized, digital audio player, the MP3 player. The first, the Eiger Labs MPMan F10/F20, was released in the United States in the summer of By 2001, the category of portable MP3 players had become popular among mainstream consumers primarily through the entry of the ipod. Currently, the ipod dominates the U.S. digital music player category, with more than 70% of the market (Marsal 2006). As of 2008, there are more than 140 million ipods (see Figure 1 for the dynamics of ipod sales). As is the case with almost every product, musical recording can be acquired either legally or illegally; that is, it can either be bought or stolen. Before MP3s, the most popular form of pirated music was available as cassettes and CDs, formats that unlike vinyl could be copied on home machines. Although counterfeit music cassettes and CDs became available shortly after the first legal cassettes and CDs were sold, copying was still a laborious process. Recently, the digitization of music has significantly simplified its reproduction, driving the costs of making a copy to virtually zero and ensuring copies of identical quality to that of the original. Moreover, with the rapid adoption of broadband technology, growing accessibility of the Internet, and better compression technologies, it has become even easier for consumers to share digital music using the Internet. The spread of download piracy was further accelerated by firms such as Napster, one of the first widely used peer-to-peer music sharing services, operated between June 1999 and July 2001 and allowed music fans to share MP3 format song files easily. The music industry accused Napster of massive copyright violations and prompted a court order to shut down the original service. Yet Napster also paved the way for decentralized peer-to-peer file-sharing programs, which

5 Dinah A. Vernik: Dissertation Essay 1 5 have been much harder to control. The content industry argues that piracy costs several billion dollars per year (see SIIA 2001; IFPI 2002). Since 1999, sales of music on physical media have began declining (see Figure 2). Although music industry executives have blamed an array of factors for this decline (e.g., increasing popularity of video games and DVDs, decreasing number of new music releases, etc.), the main culprit has been the increasing popularity of digital music. Recognizing the shift in consumer preferences toward digital music and observing the success of the Internet as a music distribution channel, record companies started launching their own online music stores. However, because of their piracy concerns, they introduced audio files protected with DRM technologies to ensure that online stores did not simply add to the piracy problem. Record companies were initially reluctant to license their music catalogs because of their concerns for piracy. As a result, the first online stores were fully owned and controlled by the record labels. In 2000, Sony Music Entertainment opened the first online store for digital music, but its service failed for several reasons, such as a price of $3.50 per song. Moreover, at that price, users still could only rent the music tracks, which eventually expired and could not be played again without repurchasing. In 2002, Universal Music Group and Sony teamed up to open Pressplay, and EMI, AOL/Time Warner and BMG together began selling music via their MusicNet service. Both services struggled, suffering from high prices and limitations on how consumers could use the downloaded files. Sales of downloadable music really accelerated only after Apple Inc. opened the itunes Store on April 28, 2003 (see Figure 2). For years, DRM provided protection for digital music against unauthorized copying and distribution. As the number of broadband Internet connections reached mass market size (i.e., approximately 80 million lines in 2007 (Plunkett Research Ltd. 2007)), better compression technologies, and the decreasing cost of digital media made it even easier for consumers to copy, share, and download digital music. At first glance, this development seems to suggest that firms should move toward more stringent DRM protection. Instead, in 2007, music retailers such as Apple Inc. convinced record companies such as EMI to allow them to sell DRM-free music. From the sellers perspective, the elimination of DRM

6 6 Dinah A. Vernik: Dissertation Essay 1 Figure 1 Total ipod sales, Figure 2 Retail value of music on physical media (e.g., CD, cassette, vinyl) and digital (downloaded) formats (RIAA 2007). entails great risks, because it might significantly increase piracy. The stakes are remarkably high: BMI, one of the largest music companies in the world, reported revenues of $779 million for the 2006 fiscal year, and Forrester Research Inc. indicates that only 10% of consumers who download music on the Internet pay for the content. Yet, today even more record labels and online stores sell DRM-free digital music. So why are record companies doing that if download piracy is already a big concern? What impact does DRM-free music legally available in stores have on traditional retailers? These are some of the the questions explored in this paper and the next section proceeds with a review of related academic literature.

7 Dinah A. Vernik: Dissertation Essay Literature Review When digital music was introduced to the market, it was protected by DRM technologies. The music industry believes that DRM technologies decrease download piracy and that without DRM protection, piracy volume would grow, just because it would be easier to copy digital music illegally. Furthermore, the music industry believes that download piracy adversely affects profits in the music distribution channel. Current literature already has addressed several aspects of this belief system. First, research investigates the download piracy phenomenon, digital rights management systems, and how profits are made in music industry. Second, the vast majority of research addresses the connection between piracy and profit. Some articles support the music industry s belief about negative impacts of piracy on its profits, whereas others question this claim and demonstrate that piracy sometimes can affect the profits of the copyright owners positively. The following subsections provide overviews of these research streams. The work presented herein provides a missing piece, in that it addresses the relationship between DRM and piracy and challenges the music industry s assumption, which is also widely accepted in academic research, that a higher degree of DRM protection results in lower piracy volumes Piracy of digital products Internet piracy refers to the uploading of copyrighted music, movies, books, and other digitized goods to the Internet for anyone to copy or the downloading of such content from Web sites. Copying and distributing copyright-protected digital content from the Internet usually violates copyright law, which attempts to reward creators and encourage them to create more works. Therefore, the creator of an original work has the exclusive right to reproduce, sell, and distribute copies. For example, if a person writes a book or a song, others may not sell that book or song without the author s consent. Although violation of law is easily apparent when someone steals a book from Barnes & Noble or a CD from Circuit City, a significant majority of Internet users believe that downloading a book or song from the Internet without paying for it is not illegal. In their survey, Lenhart and Fox (2000) find that

8 8 Dinah A. Vernik: Dissertation Essay 1 78% of Internet users who download music do not think it is stealing to save music files to their computer hard drives. A majority of the general Internet population also hold this view; 53% say downloading music is not stealing and only with 31% believe it is. Whether they are Internet users or not, young, highly educated, and relatively affluent consumers support downloaders right to receive music online for free. 61% of music downloaders say they do not care if the music they capture is copyrighted. Clement (2003) offers a good background of the piracy of digital products, including an analysis of the piracy value chain. Piracy is not new to the media industry, but a new quality of illegal mass distribution has been reached (Clement, 2003, p. 325). Clement also illustrates his analysis with details about illegal copying methods and interesting examples of piracy in music and video industry. Early studies of economic, behavioral, and demographic factors that cause piracy focused on software piracy. For example, Solomon and O Brien (1991) study the effects of demographic factors on attitudes toward software piracy and report that women, older consumers, and people with an ethical predisposition toward legal justice tend to pirate less. Later Gopal et al. (2004) present a model of behavioral dynamics that indicates the general model of software piracy applies to audio piracy, with some key differences. They therefore provide recommendations for the recording industry about which steps may be more likely to decrease piracy. For example, they suggest that a greater awareness of the implications of piracy is likely to reduce actual piracy behavior DRM technologies From existing literature pertaining to DRM technologies, two streams of research emerge 1. Studies of methods for controlling or preventing piracy. 2. Studies of consumer acceptance of DRM. In the first stream, Gopal and Sanders (2006) develop an analytical model to test the implications of antipiracy measures on publisher profits, considering both preventive and deterrent controls. Preventive controls attempt to decrease piracy by preventing copying or making it costly, whereas deterrent controls use legal sanctions to check crime. Their results suggest that preventive controls decrease profits, whereas deterrent controls may increase them. Conner and Rumelt (1991) also provide an analytical model of the decision

9 Dinah A. Vernik: Dissertation Essay 1 9 Figure 3 Individual acceptance of usage constraints. to pirate and analyze preventive protection policies, noting that increased protection might have the opposite effect on profits, with and without the network externalities. From a technology perspective, an array of papers consider effective ways to increase protection, including Lin et al. s (2005) discussion of advances in digital video content protection, Liu s (2003) comprehensive review of DRM protection mechanisms for multimedia files, and van Oorschot s (2003) summary of software protection papers. The most popular strategy for fighting piracy involves encrypting digital content to prevent copying and illegal distribution. Studies of consumer acceptance od DRM show that with this strategy, legitimate users may experience constraints on their legitimate usage of the content (see Berry 2002; Pfeiffer Consulting 2001). According to the IDC s (2000) research regarding which constraints music consumers will accept, as summarized in Figure 3, most consumers reject all restrictions, and the most objectionable constraint is limiting a content to a particular device - exactly the restriction Apple previously applied to songs sold on itunes. Yoon (2002) also show that various restrictions on the usage of the content decrease the utility that legitimate users derive from that content. The model proposed herein therefore uses these findings to justify the claim that consumers may prefer a DRM-free version of a product to a DRM-protected version Impact of piracy on the business of content providers As Figure 2 reveals, music sales have been declining during the past decade; most of the industry blames illegal music downloads. Some authors provide empirical evidence in support of that claim, such as Liebowitz (2002), who integrates 30 years of data to determine the most important influences on record sales. He concludes that record sales

10 10 Dinah A. Vernik: Dissertation Essay 1 suffered four declines prior to 2001, and the modern decline does not appear different in character from previous ones; however, recent data about record sales support the claim that MP3 downloads harm the recording industry. Hui and Png (2002) develop and test hypotheses from theoretical models of end-user and reseller piracy using international panel data for music CDs and find empirically that demand for music CDs decreases with piracy, suggesting that theft outweighs any positive effects. However, they also note that the impact of piracy on CD sales is considerably smaller than industry estimates. Peitz and Waelbroeck (2004) support the claim of losses due to Internet piracy with cross-country evidence and detailed U.S. survey data. Also, Takeyama (1997) demonstrates that if dynamic effects are taken into account, losses in profits due to copying may be even greater. Yet Slive and Bernhardt (1998) present an opposing argument and suggest limited piracy should be permitted in the presence of strong network externalities because piracy represents a form of price discrimination. Connor and Rumelt s (1991) model further suggests that in some circumstances, even with significant piracy, the absence of DRM protection increases firms profits due to positive network externalities, such as the incentive to economize on postpurchase learning and customization costs. Shy and Thisse (1999) arrive at similar findings in a duopoly, and Takeyama (1994) finds that in the presence of positive network externalities, piracy can lead to a Pareto improvement in social welfare. Takeyama (2003) also demonstrates that the information value of copying can improve social welfare (for both producer and consumer), though only in cases marked by asymmetric information about product quality. Alvisi et al. (2004)argue that in the absence of piracy, the monopolist has no incentive to differentiate its products. With piracy though, the monopolist might produce more than one level of quality, in which case the introduction of lower quality products may enable the monopolist to capture some consumers who would otherwise prefer to pirate. King and Lampe (2002) prove that assumptions common to literature that supports piracy as a positive network externality are not simply convenient but also necessary for the firm to consider piracy a profit-maximizing tactic. Specifically, these assumptions are that customers have differential abilities to pirate, the seller does not have the ability to

11 Dinah A. Vernik: Dissertation Essay 1 11 price discriminate directly among different customers, the number of potential pirates is relatively small, and the ability to pirate is inversely correlated with customers willingness to pay. are customers have a differential ability to pirate; the seller does not have an ability to directly price discriminate between different customers; the number of potential pirates is relatively small; and the ability to pirate is inversely correlated with customer willingness-to-pay. Some of these assumptions might seem too restrictive, especially in the context of the music industry. For example, consider consumers who have fast Internet connections and are aware of existence of p2p networks such as BitTorrent, which enable them to download any song for free. However, these consumers might also be highly moral and not want to violate their ethical code, which prevents them from stealing. These consumers are willing to pay for legal music, but they are certainly able to pirate. Their willingness to pay depends on how much they like the music they consider obtaining, not on their ability to pirate, which remains constant regardless of how much they like a song. Furthermore, Lenhart and Fox (2000) find that 78% of downloaders do not consider it stealing to download music online without paying. Does 78% of potential pirates really represent a relatively small number? Thus, a critical look at these four assumptions suggests that at least some are unlikely to hold in the context of the music industry. In such conditions, existing literature suggests that piracy harms the content providers profits and that DRM protection should be enforced to decrease piracy volume. There is little question that piracy can be harmful for profits; however, this study questions the assumption that DRM enforcement necessarily results in lower piracy rates. This article augments a stream of analytical papers pertaining to piracy by analyzing, instead of the relationship between piracy and profits, the relationship between piracy and DRM. Counterintuitively, A lack of DRM protection actually might decrease piracy, which would conflict with the assumptions and findings from existing research (e.g., Conner and Rumelt s (1991) proposition 1; Heileman et al. s (2007) assumptions). If piracy decreases, profits in the music distribution chain increase. That is, the proposed model demonstrates that a lack of DRM protection actually might

12 12 Dinah A. Vernik: Dissertation Essay 1 increase profits, though unlike most current literature, this article does not use network externalities or indirect appropriability arguments to achieve this result. Rather, this conclusion results from competitive interactions between digital and traditional retailers in the presence of distributors of pirated goods. 4. Model This section lays out the assumptions about products, consumers, retailers, and the manufacturer. As it was mentioned above, although the proposed model applies to various types of media content, for simplicity of exposition, the following description focuses on the music industry, with a music album as the product for sale Products Music is distributed in two formats: digital (e.g., MP3 or acc files) and traditional (e.g., CDs 1 ). If the content does not have DRM (i.e. it is not copy protected), consumers can copy and translate it from one format to another without any restrictions. In traditional formats, the content is not DRM protected, whereas content in a digital format can be either DRM protected or DRM free Consumers Consumers valuations of digital and traditional formats follow a Hotelling (1929) model in which preference for the digital versus traditional format is represented by parameter x, which is uniformly distributed between 0 (digital format) and 1 (traditional format). There can be various factors underlying such preference: some consumers might like portability and compactness of the digital music, while others might like the booklet and artwork which come with a CD, or a possibility to display a CD as a part of music collection. Ultimately, each consumer makes a choice of format to buy music in, the choice which depends on consumer s preference for format and prices of each product. The traveling cost coefficient is denoted t, and represents a phycological cost a consumer experiences when settling for one format or another. The value of an ideal product is θ U for 1 Because the effects of bundling are outside of the scope of this paper, the product is assumed to be the same in terms of content in both digital and traditional formats: the unit of sale is a music album. 2 Although it is possible to apply DRM protection to music on Cds, and some copyright owners have tried to sell such products, this practice has not become widespread (Halderman and Felten 2006)

13 Dinah A. Vernik: Dissertation Essay 1 13 the unrestricted (DRM-free) product and θ R for the restricted (DRM-protected) version. In addition, θ U > θ R, such that that consumers prefer the unrestricted product version to the restricted one. Consumers can obtain media content either legally by buying it or illegally by stealing it. When they steal it, consumers obtain the DRM-free version. In the spirit of Fetscherin (2003), when obtaining a product illegally, a consumer incurs a pirating effort, e, that represents a combination of the expected fine a consumer would pay if caught stealing the music and/or the costs of copying or searching for an illegal copy on the Internet. Generally, this effort varies from consumer to consumer due to variations in personal time costs, the subjective probability of being caught, risk aversion, and so forth. To simplify this variation in effort, this analysis assumes 1. The effort of stealing a product in a traditional format is prohibitively high for all consumers in the market, such that these products are only purchased. 2. Two consumer segments exist: consumers with high pirating effort e H (segment H) and consumers with low pirating effort e L (segment L). There are λ consumers in the high stealing effort segment, and 1 λ consumers in the low stealing effort segment, where λ [0, 1]. There does not have to be an underlying factor common to both piracy efforts e H and e L, so that each pirating effort might vary independently. The following example illustrates such a situation: Segment L consists of technically skilled consumers who not only have plenty of time to browse Internet for freely available, pirated, DRM-free digital products and download them but are also capable of cracking the DRM protection by themselves to obtain DRM-protected versions. Segment H, in contrast, includes consumers who engage in a different type of piracy by signing up for an online service, for a low monthly fee, that provides access to already cracked digital music. 3 In this situation, if the record label pursues the Web service, it increases pirating effort e H because these services become harder to find and may be more expensive for consumers. However, these actions have no impact on low stealing effort e L because consumers in segment L do not use the service. 3 For example, Napster provided this type of service before the company went out of business in 2001 after a series of lawsuits.

14 14 Dinah A. Vernik: Dissertation Essay 1 Alternatively, if the record label invests in improving its DRM protection, it makes it harder for consumers in segment L to obtain pirated products, because they must learn how to break new protection mechanisms. Therefore, stealing efforts can very independently and the next sections explores the effects of such changes. To address the concern of music industry that pirating music might become easier in the absence of DRM, it is assumed that when digital music becomes available for sale in DRM-free format, the pirating effort e i decreases to e U i is represented by parameter δ [0, 1] such that < e i. The decrease in stealing effort e U i < e i δ. (1) In this two-segment horizontal differentiation model, each consumer obtains at most one unit of the product, and there is no value from obtaining a second unit. Markets are completely covered, such that each consumer either buys or steals a product. Consumer i from segment j {L, H} maximizes his or her utility by selecting one of the available options: 1. Buying the product in traditional format at price p T and obtaining utility UT i (b); or 2. Buying the product in digital format at price p DR and obtaining the utility UDR i (b) if the product is DRM-protected or at price p DU and obtaining utility UDU i (b) if the product is DRM-free; or 3. Stealing the product in digital format and obtaining utility U i DU (s j). These utilities are equal to UDR i (b) = θ R tx i p DR, UDU i (b) = θ U tx i p DU, UT i (b) = θ U{ t(1 x i ) p T, and UDU i (s θu tx j) = i e U j, if digital unrestricted version is sold, θ U tx i e j, otherwise. (2) 4.3. Firms The model contains three players: the firm that owns the copyright to the media content and two competing retailers. In the case of the music industry, these players are, respectively, the record label (denoted ) and two music retailers: a digital retailer (denoted D), such as an Internet store that sells downloadable music files, and a traditional retailer

15 Dinah A. Vernik: Dissertation Essay 1 15 (denoted T ), such as a regular store that sells CDs. Although there are two segments of consumers, high and low pirating effort, again appear, neither retailers nor the record label can differentiate between low- and high-effort consumers, so the retail and wholesale prices for the same format of product do not differ for the two segments. When consumer i compares the utility of stealing an unrestricted, DRM-free digital product with the utility of buying a restricted, DRM-protected product, the result of the comparison does not depend on the consumer s location: U i DR(b) < U i D(s j ) if and only if θ R p DR < θ U e U j. Therefore, if one consumer in segment j prefers buying to stealing, each consumer prefers buying to stealing. To avoid singular cases in which all consumers buy or all consumers steal, low and high stealing efforts are assumed to be such that e L < θ U θ R + p DR, and (3) e H > θ U θ R + p DR. Thus consumers in the high pirating effort segment prefer to buy the DRM-protected digital product, and consumers in the low stealing effort segment prefer stealing the DRMfree version of it. This assumption receives support from the empirical findings by Smith and Telang (2006), which reveal that certain consumers always buy digital goods, regardless of whether they are available on the Internet for free. If there is a digital version of the product available for sale, the traditional retailer competes with the digital retailer for the high stealing effort segment, whereas it competes with distributors of the pirated digital product to attract the low stealing effort segment. By analogy, if the record label offers DRM-free digital and traditional products for sale, the low and high stealing efforts must be such that e U L < p DU, and (4) e U H > p DU.

16 16 Dinah A. Vernik: Dissertation Essay Sequence of events The timeline consists of four stages. During the first stage, the record label chooses the formats of music albums for sale: traditional only, traditional and digital with DRM protection, traditional and digital without DRM protection, or traditional and digital both with and without DRM protection. In the second stage, the record label chooses wholesale prices for the traditional and digital products, in accordance with the formats of the albums for sale, denoted w T, w DU, and w DR. In the next stage, the retailers set their retail prices simultaneously, denoted p T, p DU, and p DR. Finally, consumers maximize utility by choosing the optimal product available in the market. Let D kj (p D, p T, w D, w T ) where denote the demand for retailer k {D, T } by segment j {L, H} and D k (p D, p T, w D, w T ) = λ D kh + (1 λ) D kl denote the total demand for retailer k. The profit functions for both retailers and record label then are as given in Equations (5)-(7) Record label : Π = w D D D (p D, p T, w D, w T ) + w T D T (p D, p T, w D, w T ). (5) Traditional retailer : Π T = (p T w T )D T (p D, p T, w D, w T ). (6) Digital retailer : Π D = (p D w D )D D (p D, p T, w D, w T ). (7) 5. Analysis This section derives the optimal strategies for each stage, including the optimal pricing and product choice decisions. Section 5.1 analyzes the case in which the record label sells music albums only in the traditional format. Section 5.2 pertains to the case in which the record label sells both traditional and DRM-protected digital versions of the product. In Section 5.3, the DRM-free digital version also appears in the market. Finally, Section 5.4 considers the case in which the record label sells traditional and DRM-free digital versions of the product. Each section analyzes the game in backward fashion, by deriving the choice of consumers first, then determining the optimal retail prices, and finally obtaining the optimal wholesale prices set by the record label. After analyzing each strategy separately, the analysis proceeds with a comparison of these strategies in Section 5.5, along with a discussion of the optimal strategy choice for the record label in Stage 1. Throughout

17 Dinah A. Vernik: Dissertation Essay 1 17 Sections it is assumed that the pirating effort does not change when DRM-free music becomes available for sale, i.e. that e U i = e i. In Section 5.6 this assumption is relaxed, and the record label s equilibrium strategy is derived in a more general setting Selling music in traditional format only The record label may decide to offer music albums for sale in traditional formats only through a single retailer. Because no digital version is legally available, the traditional retailer competes with pirated digital products in both the high and low pirating effort segments. The assumed parameters of the model are such that piracy in each segment is non-zero. As specified by Equation (2), a consumer with pirating effort e j located at point x derives a total utility of U DU (s j ) = θ U tx e j when stealing an album in digital format and U T (b) = θ U t(1 x) p T when buying it in a traditional format. The location of the consumer who is indifferent between buying and stealing is derived by solving UDU i (s j) = UT i (b) for x. The solution to this equation is xj = p T e j + t. Thus, the total volume of 2t piracy is equal to and the total demand of retailer T is D P = λx H + (1 λ)x L = p T + t λe H (1 λ)e L, 2t D T = λ(1 x H ) + (1 λ)(1 x L ) = t + λe H + (1 λ)e L p T 2t Substituting this demand function into the profit function Π T given in Equation (6) yields ( ) t + λeh + (1 λ)e L p T Π T (p T, w T ) = (p T w T ). 2t Maximizing this profit function with respect to p T by solving first-order conditions (FOC), provides the optimal retail price for the traditional product as a function of the wholesale price w T : p T (w T ) = e L(1 λ) + λe H + t + w T 2.. (8) Substituting this expression into the record label s profit function Π, as given in Equation (5) yields: Π (w T ) = w T (t + e H λ e L (1 λ) w T ). 4t

18 18 Dinah A. Vernik: Dissertation Essay 1 Table 1 Optimal pricing decisions, consumer demand, piracy volume, and profits: Only traditional products available for sale. Prices Retail Wholesale Profits p T = 3 (λeh + t + (1 λ)el) 4 wt λeh + t + (1 λ)el = 2 Retailer T s Π (λeh + t + (1 λ)el)2 T = 32t Record label s Π (λeh + t + (1 λ)el)2 = 16t Demand Total DT t + λeh + (1 λ)el = 8t segment H DT t 3eL(1 λ) + eh(4 3λ) H = 8t segment L DT t 3λeH + el(1 + 3λ) L = 8t Piracy Total DP 7t λeh (1 λ)el = 8t segment H DP 7t + 3eL(1 λ) eh(4 3λ) H = 8t segment L DP 7t + 3λeH el(1 + 3λ) L = 8t The record label maximized profit by choosing the optimal wt. Substitute the derived optimal wholesale price for the traditional product into Equation (8) to obtain the optimal retail price p T. The optimal pricing decisions, consumer demand, piracy volume, and profits of the channel members (marked with ) are summarized in Table 1. Consider the effect of pirating effort e j when each pirating effort might vary independently. With an increase of pirating effort e j, piracy in segment j goes down. Because consumers who do not steal buy the legal product, the demand for the legal product increases in this segment as pirating effort increases: (4 3λ) = e H 8t DP L (1 + 3λ) = 8t D P H < 0 = D DH e H < 0 = D DL > 0. > 0, and However, in the other segment, piracy increases, which implies that demand for the legal product decreases as pirating effort increases: D P H = DP L e H 3(1 λ) 8t > 0 = D DH = 3λ 8t > 0 = D DL e H < 0. < 0, and

19 Dinah A. Vernik: Dissertation Essay 1 19 However, total demand increases with pirating effort and thus total piracy volume declines: D P = DP e H (1 λ) 8t < 0 = D D = λ 8t > 0 = D D e H > 0. > 0, and Both retail and wholesale prices increase with greater pirating effort. Because total sales also increase with pirating effort, both the record label and the retailer benefit. The record label earns the greatest part of the profit margin, because the wholesale price w T constitutes two-thirds of the retail price p T (see Table 1). Thus, the record label benefits more from increased stealing efforts than does the retailer, as demonstrated by the following lemma: Lemma 1. Increasing the pirating effort has a positive impact on profits, which is greater for the record label than for the retailer, Π e j > Π T e j > 0. Proof See Appendix. Profits also increase with λ, the size of segment H: Π T λ = (e H e L )(e L (1 λ) + λe H + t) > 0, and 16t Π λ = (e H e L )(e L (1 λ) + λe H + t) > 0. 8t Competition is greater for the low stealing effort segment, so when the size of this segment declines (i.e., λ increases), both the retailer and the record label can set higher prices and earn higher profits. That is, when it sells only the traditional format, the record label faces piracy by both high and low stealing effort segments. Consumers with a strong preference for the digital format cannot be served by the official retailer and obtain illegal digital versions. A desire to address at least part of the demand for digital music therefore provides a strong motivation for the record label to launch official sales of digital formats Selling music in traditional and DRM-protected digital formats This section details the responses of consumers and retailers to the record label s decision to sell music albums in both traditional and digital formats. In this case, the record label

20 20 Dinah A. Vernik: Dissertation Essay 1 sells music through two retailers: retailer D (which sells the digital version) and retailer T (traditional version). Record label offers only the DRM-protected version of the digital product for sale. As mentioned previously (see Inequality (3)), high pirating effort e H is such that consumers in segment H prefer buying the digital version to stealing it. Therefore, retailers T and D compete for this segment, whereas retailer T competes with distributors of pirated products for the low stealing effort segment. The location of an indifferent consumer for segments H and L is defined by the following equations: { UDR(b) = U T (b), and U DU (s L ) = U T (b). where these utilities are as defined in Equation (2). These locations are: x H = p T p D + t θ, and 2t x L = p T e L + t. 2t The perceived difference between the value of the unrestricted (DRM-free) product, θ U, and the value of the restricted (DRM-protected) product, θ R, is denoted θ, such that θ = θ U θ R. The total demand realized by retailer D is D D = λx H, whereas that for the traditional product is D T = λ(1 x H ) + (1 λ)(1 x L ). Retailers maximize their profits by choosing optimal prices p T D T and p D. Similar to the previous section, substituting D D and into the retailers profit functions, as defined in Equations (6)-(7), taking the FOC, and solving for the optimal retail prices yields: p T (w T, w D ) = 2e L(1 λ) + θλ + t(2 + λ) + 2w T + λw D, and 4 λ p D (w T, w D ) = e L(1 λ) θ(2 λ) + 3t + w T + 2w (9) D. 4 λ Next, given consumer demand and the retail prices set by retailers D and T, the record label maximizes its profit by choosing the optimal wholesale prices. Again, these demands and retail prices may be substituted into the record label s profit, as defined in Equation (5), to obtain FOC and solve for the optimal wholesale prices. Table 2 summarizes these optimal pricing decisions, profits, sales, and piracy volume (marked with ). As pirating effort e L increases, so do retail prices. However, the retail prices for traditional product increase faster. Indeed, p T 3(2 λ) (5 2λ) = > 2(4 λ) 2(4 λ) = p D.

21 Dinah A. Vernik: Dissertation Essay 1 21 Table 2 Prices Retail Wholesale Profits Retailer T s Retailer D s Record label s Demand Optimal pricing decisions, consumer demand, piracy volume, and profits: Both traditional and DRM-protected digital products available for sale. Traditional version, total Trad., segment H Trad., segment L Digital version, total Piracy Total p T = 6t+(1 λ)(3e L(2 λ)+2λt+λ θ ) 2(4 λ)(1 λ) p DR = 6t+(1 λ)(e L(5 2λ)+5t 2 θ(3 λ )) 2(4 λ)(1 λ) wt = t(1+λ)+e L(1 λ) 2(1 λ) w DR = 2t+(e L θ)(1 λ) 2(1 λ) Π T = (t(2+λ)+2e L(1 λ)+λ θ) 2 8t(4 λ) 2 Π D = λ(3t+e L(1 λ) θ(2 λ)) 2 8t(4 λ) 2 Π = (e L(1 λ)+t(1+λ))(t(λ+2)+λ θ+2e L (1 λ)) 8t(4 λ)(1 λ) + + λ(e L(1 λ)+2t θ(1 λ))(3t+e L (1 λ) θ(2 λ)) 8t(4 λ)(1 λ) DT = 2e L(1 λ)+t(2+λ)+ θλ 4t(4 λ) D T H = 1 3t+e L(1 λ) θ(2 λ) 4t(4 λ) D T L = 1 t(14 8λ) (1 λ)(e L(2+λ) λ θ) 4t(4 λ) D D = D DH = 3t+e L(1 λ) θ(2 λ) 4t(4 λ) DP = 2t(7 4λ) (1 λ)(e L(2+λ) λ θ) 4t(4 λ) Traditional products compete directly with pirated digital products in the low stealing effort segment, in which e L effectively acts as a competitor s price. The DRM-protected digital product does not compete directly with the pirated product, so its pricing is affected by the pirating effort e L only through the retail price set by retailer T. Thus, the pirating effort e L has a smaller effect on the retail price p D. Consider next the demand for the legal product by both segments and volume of piracy. Because p T increases with e L faster than does p D, the demand for the traditional product among the high stealing effort segment D T H actually drops as e L increases, whereas demand for the digital version increases. However, total demand for the traditional product D T increases with e L, and consequently, piracy volume declines. The following lemma demonstrates this point. Lemma 2. An increase in e L increases total demand for the traditional product D T well as the total demand for the digital product DD. Moreover, pirating effort has a greater impact on demand for the traditional product than on demand for the digital product: as

22 22 Dinah A. Vernik: Dissertation Essay 1 D T > D D > 0. Proof See Appendix. Next consider the impact on profits. With increase of pirating effort e L, demand for the digital version increases, as does the retail price. Wholesale price also increases but at a slower pace than the retail price: wd = 1 (5 2λ) < 2 2(4 λ) = p D. Therefore, with an increase in e L the overall profit of retailer D increases, as does that for the traditional retailer. The record label also benefits from higher pirating effort e L ; the increased pirating effort has the greatest impact on the record label s profit, because the record label gains through both retailers. However, the traditional retailer s profit suffers more because of piracy than does the profit of the digital retailer, as the following lemma notes: 4 Lemma 3. The record label s, traditional retailer s, and digital retailer s profits increase with greater pirating effort; changes in pirating effort have the greatest impact on the record label s profits. They also have a greater impact on the profits of the traditional retailer than on the profits of the digital retailer: Π > Π T > Π D > 0. Proof See Appendix. Thus, the increase of the pirating effort e L mostly benefits the record label, which may explain why EMI insisted that Apple renew DRM-protection mechanisms, not Apple that stepped up with this initiative. But is copyright law enforcement the only way for copyright owners to increase their profits? Consider the impact of the perceived difference in value between DRM-protected and DRM-free products, θ. Intuitively, the bigger this difference, the greater is consumers 4 Piracy effort might have a stronger effect on the record label s profits when only traditional versions of the product are available for sale or when both traditional and DRM-protected digital are sold. A comparative analysis indicates that the results may show both findings: With certain parameter values, the impact of e L is greater in the first case, whereas with others, it is greater in the latter.

23 Dinah A. Vernik: Dissertation Essay 1 23 incentive to steal the DRM-free version. With an increase of θ, the price for the traditional product increases: p T θ = λ 2(4 λ) > 0, which means demand for the traditional product in the low stealing effort segment declines and piracy volume increases. That is, when the difference competition between digital and traditional versions increases, retailer D must decrease its retail price: p D θ = 2(3 λ ) < 0. 2(4 λ) Yet demand for the digital product still decreases among the high stealing effort segment: D DH θ = ( 2 + λ ) 4t(4 λ) < 0. Consequently, demand for the traditional product among this segment increases, and overall demand for the traditional product increases as well: DT θ = λ 4t(4 λ) > 0. Although the wholesale price for the digital version of the product depends on θ, the wholesale price for the traditional version, w T, does not (see Table 2). If the traditional retailer increases its retail price, p T, with an increase of θ, the record label might increase the wholesale price as well. However, regardless of an increase or decrease in the perceived difference in value, the record label charges the traditional retailer the same price per unit. If the record label were to increase the wholesale price w T, it would further increase the retail price (see Equation (9), which demonstrates that the optimal p T depends on w T ), and would cause a further decline of sales in segment L. Alternatively, if the record label retains the wholesale price w T, no further decline in sales would occur in segment L. In segment H, all the consumers would buy the legal product, so the total volume of sales remains the same, and the record label can vary its revenues by changing either w D or w T, such that it internalizes competition. For the record label, it does not matter which to vary; for each change in revenue from segment H, there exist multiple pairs of wholesale prices that will result in this revenue change. Thus, it is optimal for the record label to