The Alternative Compensation System: A Theoretical Approach

1. Introduction

4

2. Music industry

6

2.1 Background music industry 6

2.2 Alternatives for the music industry 7

2.3 The Alternative Compensation System (ACS) 10

3. Literature

12

3.1 Traditional copying literature 13

3.2 Sharing literature 27

3.3 Literature with strategic interaction 35

3.4 Literature with information good as experience good 39

3.5 Other literature 48

3.6 Empirical literature music industry 54

3.7 Policy implications 55

4. Standard bundling model

58

4.1 Pure unbundling 59

4.2 Pure bundling 60

4.3 Mixed bundling 62

4.4 Comparison bundling models 64

5. The Alternative Compensation System (ACS)

66

5.1 Model without piracy 67

5.2 Model with piracy 73

5.2.1 Framework model with piracy 73

5.2.2 Numerical example 76

5.2.3 Analysis of equilibria 78

5.4.1 Numerical example 83

5.4.2 Analysis of equilibria 86

5.5 Comparison of all models 90

5.6 Policy implications 93

6. Conclusion

96

References

98

Appendices

101

Appendices Chapter 4 101

Appendix A: Derivation pure bundling equilibrium (

p

bu

≤

1

) 102 Appendix B: Derivation mixed bundling equilibrium

Appendices Chapter 5

Appendix C: Derivation of Consumer Surplus in model with P2P 106 Appendix D: Remaining possibilities in model with P2P 108 Appendix E: Derivation demand case 1 in model with P2P 110 Appendix F: Derivation demand case 2 in model with P2P 112 Appendix G: Derivation demand case 3 in model with P2P 114 Appendix H: Derivation demand case 4 in model with P2P 116 Appendix I: Derivation demand case 5 in model with P2P 118 Appendix J: Derivation demand case 6 in model with P2P 120 Appendix K: Derivation consumer surplus in model with P2P 122 Appendix L: Derivation consumer surplus in ACS model 130

Appendix M: Numerical outcomes all models 131

With the rise of the Internet, piracy has rapidly increased. New technologies, like peer-to-peer networks, enable people to exchange large files with other users from all over the world. Examples of files traded are software and music files. Last year, the recorded music industry claimed that 35 percent of all music discs sold worldwide were illegal copies (International Federation of the Phonographic Industry (IFPI), 2004)1. Furthermore, 37 percent of the software used in 2000 was pirated according to the Business Software Alliance (BSA)2.

Intuitively, one expects that piracy places an enormous burden on the music and software industry. For that reason, piracy has been the subject of economic research repeatedly, either in a theoretical way or empirical way. Economic literature is, however, ambiguous with respect to the harm that piracy causes. On the one hand, some articles argue that piracy decreases profits. On the other hand, some articles disagree and argue that piracy may even increase profits. Opponents of piracy are convinced of the harm that piracy causes as the following quote by Paul Solleveld3 illustrates: "People have to understand the work, passion and tenacity involved in making and selling music and other entertainment products. They need to realize that many dedicated artists but also sound engineers, talent scouts, designers and so many more individuals involved in the making of one song, actually try to make a living out of it. By stealing and distributing tracks on the Internet, both the industry and the music suffer greatly. That is why legal action is

necessary."4

By comparing a model without piracy and a model with piracy, this thesis first answers the theoretical question whether music piracy at the Internet hurts profits or not. Next, it focuses on an alternative for the music industry: the Alternative Compensation System (ACS), which has been advocated by William Fisher5. The ACS is a proposed system in which broadband Internet users pay a fixed fee per period and these proceeds are then redistributed to the copyright holders. This thesis takes a theoretical approach in order to analyze Fisher’s proposal from society’s perspective. By modeling an ACS model, I study the effects on consumer surplus (CS) and producer profits. Besides looking at the effects of a switch to an ACS model on profits and CS, it is also interesting to verify Fisher’s claim that the introduction of the ACS model may crowd out slow Internet providers. To my knowledge, this is the first attempt to model the ACS as an alternative for the music industry.

1 _{http://www.ifpi.org/site-content/press/20040722.html} 2 _www.bsa.org

3 _{Paul Solleveld is Managing Director at Nederlandse Vereniging voor Producenten en Importeurs van beeld- en geluidsdragers}

(NVPI) in the Netherlands. The NVPI is an organization which represents the interests of the entertainment industry (audio, video and computer games) in the Netherlands.

4 _{http://www.ifpi.org/site-content/press/20040722.html}

5 _{William Fisher is professor of intellectual property law at Harvard University. Besides that he is also director at Berkman center for}

The agenda of this thesis is as follows. The first part of this thesis sets out some background issues of the music market and the relevant literature of copying. That is, Chapter 2 illustrates some background issues for the music industry. Chapter 3 sets out the relevant literature concerning the unauthorized production of information goods. By doing so, Chapter 3 also focuses on the modeling aspects of this literature since modeling the ACS model is a crucial element in this thesis. The second part of this thesis deals with the development of the ACS model. Chapter 4 presents the standard bundling model which is the starting point of the three models that are constructed and analyzed in Chapter 5: a model without piracy, a model with piracy, and the ACS model as an alternative for the music industry. Finally, this thesis ends with a conclusion in Chapter 6.

The music industry is the subject of this thesis and therefore this Chapter describes the most important issues with respect to the music industry. In particular, it explains the market structure of the music industry and it explains some of the characteristics of music (section 2.1). Section 2.2 evaluates some of the recently proposed alternatives for the music industry in order to fight piracy. This Chapter ends with a short description of the ACS, as proposed by Fisher, in section 2.3. The ACS model may serve as a proper alternative for the music industry.

2.1 Background music industry

The music industry is dominated by four major record labels which engage in manufacturing, distributing and promoting music. These major record labels are Warner Music, EMI Group, Universal Music Group (UMG), and Sony BMG music entertainment, and together they are called the Big Four. These record labels account for approximately 70% of the industry’s market share6. Hence, the music market is an oligopolistic market7. Besides these record labels, there are some other important players on this market: artists, retailers, and consumers. However, record companies account for most of the marketing and promotion efforts. In addition, they are also involved in scouting, recording, and production.

Piracy has been the subject of economic research several times (see Chapter 3 for more information). The introduction of the Xerox 914 in 19598, which was the first automatic office copier to use ordinary paper, already enabled people to copy books and articles. Nowadays, broadband Internet users use the Internet for copying (often called pirating) information goods on a large scale. The introduction of Internet has changed things dramatically and, regarding

information goods, we can state the following two effects: Internet has reduced the cost of copying while, at the same time, it has increased the quality of copies. These two effects are the result of the introduction of Peer-to-peer technologies (P2P), broadband Internet connections, and technologies such as MP3, or Divx9. For example, it is now possible to download a CD single in MP3 format, in only a few seconds. In addition, P2P enables people to download complete movies, games and software applications within a short period of time. However, downloading information goods from a P2P network does not come for free. There are several costs like search costs (time with respect to downloading, testing files), possibility of viruses, spy ware. Several authors take these search costs into account in their models, as we will see in the next Chapter.

6 _{http://www.oligopolywatch.com} 7

Economic literature often models a record label as a monopolist. In fact, each record label is a monopolist for each contracted artist. As a result, a record label can be seen as a multi-product monopolist.

8 _{www.xerox.com}

9 _{MP3 is a compression technique which enables people to compress an audio file with only a minor loss in quality. Divx is a similar}

Obviously, one of the greatest advantages for consumers is that they obtain music without paying for it (except for the costs mentioned earlier). In addition, P2P also provides consumers with the opportunity to sample music, which is important since music is often considered an experience good. This is an important characteristic of music: it is often assumed that the value of a CD to a consumer is only revealed after it has been consumed. Therefore, allowing these consumers to sample music raises their valuation for it (if they find a product they like). The next Chapter presents some models in which music is considered an experience good.

The previous paragraph already mentioned several types of information goods, such as music, books/articles, and software. As was noted earlier, these goods share some characteristics, however in some aspects, these goods also differ. In particular, these goods may differ with respect to whether network effects are present. Katz and Shapiro (1985) make a distinction between direct and indirect network effects. The former effect means that as more people buy a particular product, consumer valuations with respect to this product rises. Typical examples are: telephone and software. The latter effect states that the value of a particular good (say, a XBOX) rises whenever more complementary products become available for it (i.e. games for the XBOX). Bensaid and Lesne (1996) make a distinction between three types of network effects. First, methaphorical network effects, which mean that users of a good benefit from the same additional services and common expertise. Second, ‘word of mouth’ network effects occur whenever more users result in better information with respect to the product’s quality. It is often stated that ‘Word of mouth’ externalities are important for music products. In particular, ‘word of mouth’

externalities reduce search costs and increase the reservation prices of consumers. Third,

learning-by-doing externalities occur whenever more users lead to more and better updates which in turn increase the product’s quality. This type of externalities is important in the software market. In economic literature, there is consensus that network effects do exist in the software market. However, this is not the case for the music industry. Throughout the analysis that will follow in Chapter 5, I will assume that network effects are absent.

2.2 Alternatives for the music industry

Yu (2005) sets out potential solutions to counterattack the P2P industry. In particular, he suggests proposals like mass licensing, compulsory licensing, voluntary collective licensing, and

technological protection. These proposals are a way for the music industry to mitigate (or even completely recover) the claimed losses in profits due to P2P. These possible solutions are explained below.

1)Mass licensing

The number of legal downloads has tripled globally in the first half year of 2005 (compared to the same period in 2004)10. IFPI states that nowadays there are more than 300 online stores where consumers are able to download songs. Examples of some of the largest online music sites are iTunes, Napster, Buy.com, and Rhapsody. This rapid increase in the legitimate download market seems to come at a cost for the illegal downloading market. Popular P2P networks, like Kazaa, show a sharp decline in the number of users and music files available11.

The online music sites offer music products which are imperfect substitutes for consumers. Obviously, these products have a lower price than a CD single in a conventional store. For example, the largest music store in the Netherlands, the Free Record Shop, offers an original CD single called Even stil by the Dutch rapper Brainpower at a price of 2.50 euro. Furthermore, it is also possible to obtain a digital version of the CD single, by downloading it on the web site, which costs 0.99 eurocent12. The digital version is of slightly lower quality

compared to an original version (which also holds for an illegal music file). In addition, online music sites often use DRM which puts restrictions on the use and distribution of the digital music files. Examples of such restrictions are restriction on the number of times a file can be burned on a CD recordable, or the number of times a song can be played on a computer. Obviously, these restrictions result in a comparative disadvantage compared to illegal music files. The model by Jaisingh (2004), which falls into this category (see section 3.5), shows that online sales of music, next to traditional sales in music stores, may increase profits.

2)Compulsory licensing

The models proposed by Netanel (2003) and Fisher fall into this category. Netanel has proposed a similar system to that of Fisher’s ACS. Netanel only considers noncommercial uses, whereas Fisher suggests a role for the government in administering and redistributing the rewards for both commercial and noncommercial uses. Compulsory licensing already takes place on a small scale.

10 _{http://www.ifpi.org/site-content/press/20050721.html} 11 _{http://www.pro-music.org/musiconline/news050119c.htm}

In particular, in several European countries like the Netherlands and Germany, CD burners, blank CD recordables, and MP3 players are already taxed additionally to protect copyright holders. Gayer and Shy (2003) explore the effects of hardware taxation, as a means of copyright protection, on social welfare (see section 3.5). They show that it may be optimal for society to have a zero tax rate .

Yu acknowledges that there are some difficulties with such a system. Examples of these difficulties are how to redistribute the rewards to copyright holders, possibility of insufficient tax proceeds in order to compensate the music industry, and cross-subsidization of high-volume users by low-volume users. This latter effect means that people who rarely use P2P (low-volume users) subsidize people who use P2P on a large scale (high-volume users).

3)Voluntary collective licensing

Gervais’ proposal fits into this category. Gervais (2004) recommends a similar system in which file-sharing people pay a fixed fee per month as well but now on a voluntary basis13. Furthermore, participation of copyright holders is on a voluntary basis as well.

4) Technological protection

Technological protection can take several forms, take for instance encryption. Copyright holders are constantly using this form of copy protection, which makes it difficult for consumers to copy CDs and software. However, it is impossible for copyright holders to perfectly protect their work, especially after the introduction of the Internet14. The threat of breaking this copy protection (called decryption) creates an incentive for copyright holders to continuously update their protection technology. It is important to note that these protection measures impose an enormous financial burden on copyright holders. As Yu puts it: “Eventually, the repeated encryption and decryption will create a vicious cycle in which the entertainment industry and hacker community engage in an endless copy-protection arms race. Instead of devoting resources to develop artists and improve products, the industry will have to invest their resources in developing encryption technology and preventing consumers from accessing copyrighted works”, (Yu, 2005, pp. 53-54). Another disadvantage is that legal users are often annoyed by these protection measures15.

13 _{Several surveys provide evidence that many file-sharing people are indeed willing to pay such a voluntary fee.}

14 _{By searching the Internet, a typical consumer is able to find a small decrypted file which is produced by people with the technical}

knowledge to ‘crack’ the encryption code. For example, the new popular soccer game Fifa 2005, produced by Electronic Arts, can easily be downloaded on a P2P network. However, this game cannot be played as such. The protection for this game comes in the form of the executive startup file (Fifa2005.exe). A non-protected version of this file can easily be found on a P2P network as well.

15 _{For instance, there are several real life examples in which consumers, possessing the legal version of a CD, are unable to play this}

Consequently, such protection measures result in disutility for legal users as well. The model by Jaigsing, which is explained in section 3.5, allows for disutility of protection for legal consumers.

Another technique often used by the entertainment industry is spoofing, which is the wide distribution of fake music files on P2P networks. Consequently, consumers often find music which does not function properly and the result is that consumers who download music files on P2P networks face substantially higher search costs.

2.3 The Alternative Compensation System (ACS)

William Fisher advocates the Alternative Compensation System (ACS) in one of his books16. According to Fisher, the ACS should be able to counteract the decrease in profits from the music industry. The ACS, in a nutshell, consists of three stages. First, all music producers have to register with some sort of government agency which sets the fixed fee and controls the

distribution of revenues. Second, these revenues are obtained by imposing a tax upon people who participate in file-sharing. Fisher notes that possible tax targets are: copying equipment (such as CD burners, computers, and blank CD recordables), P2P software, and Internet access. Fisher acknowledges that the best way is to tax Internet access since P2P participation fully depends on the use of the Internet. Moreover, U.S. citizens are only able to obtain Internet from domestic Internet Service Providers (ISP), not from foreign ISPs. The tax in the ACS takes the form of a fixed fee, which in turn gives consumers the right to unconditionally use P2P software and similar programs. In this case, it certainly makes sense to impose such a fee on broadband connections since these fast connections are necessary to participate in P2P in an proper way. Users of P2P networks need a fast Internet connection to be able to download multiple songs within a short period of time. As a result, Fisher also expects that slow Internet will disappear in the ACS model. Finally, the total amount of revenues is redistributed to the copyright holders on a popularity basis. For this purpose, Fisher proposes to take samples from households in order to determine popularity of the artists. The reason for this is that it is hard, if not impossible, to keep track of downloads.

This thesis takes a theoretical approach in order to verify Fisher’s proposal. Fisher proposed to levy a tax on broadband Internet. However, I will develop an ACS model in which a broadband Internet provider bundles the sale of broadband Internet and downloadable music. The reason for this is that we can regard a broadband ISP as a producer who offers two products: fast Internet and music downloads since each broadband Internet user has the possibility to share and

16

3. Literature

This thesis analyzes the effects of an introduction of the ACS model, from society’s perspective. Before constructing such a specific model, one should first study copying literature. This Chapter provides an overview of the most relevant articles concerning copying. Some articles (Takeyama, 1994, 1997) only assess what impact copying has on Consumer Surplus (CS), profits, and Social Welfare (SW), while other articles also focus on the role of copyright protection. For example, Conner and Rumelt (1991) examine the effect of increased copyright protection by a monopolist, whereas Shy and Thisse (1999) assess the effect of copyright protection in a strategic duopolistic setting. Alternatively, a small number of articles are concerned with sharing literature, such as Besen and Kirby (1985) or Varian (2000). Finally, several authors specifically focus on the music industry where they model music as an experience good (Zhang (2002) and Dûchene and

Waelbroeck (2004). In this way, I give a complete overview of the relevant literature concerned with copying.

Many of these articles show that profits may actually be higher with piracy present. As we will see later on, copying literature distinguishes between four different categories of mechanisms responsible for this increase in profit. First, network effects may increase profits since an increase in the user base (network) raises valuations of buyers, which in turn enables a producer to ask a higher price. As a result, profit may increase even though the number of buyers is lower. Second, indirect appropriability is a way for producers to earn higher profits with copying present. A good example is photocopying journals in libraries which increases profits. By asking a higher price from libraries for these journals, a monopolist can indirectly earn revenues from copying individuals. Consequently, profits may increase. Third, sampling

experience goods by consumers may also increase profits. With experience goods such as music, consumers have incomplete information with respect to the product’s characteristics. P2P sampling reveals the characteristics of music to consumers and increases a consumer’s willingness to pay for the product if he likes the product. As a result, profits may increase. Finally, there is a residual category that embraces some other possibilities like offering online music next to the traditional sale in stores, or taxing hardware and redistributing the proceeds of these taxes to music producers.

increase profits. I have tried to keep the algebra to a minimum, however in some cases tedious formulas are unavoidable.

In order to structure this Chapter, the following distinction is made between five

categories: traditional copying literature (section 3.1)17, sharing literature (section 3.2), literature with strategic interaction (section 3.3), literature with music as an experience good (section 3.4), and other literature (section 3.5). Next, section 3.6 briefly discusses empirical literature regarding the music industry18. Finally, section 3.7 sets out the policy implications.

3.1 Traditional copying literature

This section sets out the relevant literature concerning copying in which consumers have perfect information about the characteristics of the product. At first, the introduction of the possibility of copying in a basic monopolistic model is examined. Then, this basic model is extended to a dynamic ‘durable good’ model with two periods. Furthermore, this section also explains the role of copyright protection in a monopolist model. Economists often claim that protection results in changes in SW due to the underutilization and underproduction effect. This claim is verified in a single period model as well as in a two-period model. Finally, this section ends with a study of the effect of protection in a monopolistic model with network effects present.

A basic monopolistic model with copying

By comparing two models, one without copying and another one with copying present, Takeyama (1994) explores the effects of copying on profits and SW. In her model, copying may increase profits and SW due to network effects. Higher network effects result in higher consumer valuations. Consider a product, for example a telephone or software, for which network effects are present. The more people use such a product, the higher consumer valuations for this product. Consumers who copy, for example software, are still part of the total network and therefore, these copying consumers have a positive effect on valuations of buying consumers as well.

Takeyama starts with a model without copying as a benchmark. We have two types of consumers, high-valuation consumers and low-valuation consumers. The former type has valuation

v q

h

(

n

)

where

q

n is the total number of consumers. The latter type has valuation

(

).

l n

v q

Obviously, h

(

n

)

l

(

n

)

v q

>

v q

and the higher n

,

q

the higher the valuations (demand network externality). For the remainder of this section, I will simply denote these valuations as

17 _{The articles’ categorization is not always decisive. For instance, Liebowitz’s article (1985) is found in the section with sharing}

literature even though his work is considered as traditional.

18 _{I only discuss the empirical literature briefly since this thesis only looks at the music industry from a theoretical perspective.}

h

v and vl although they do depend on the number of users. Moreover,

q

h is the number of

high-valuation consumers, while

q

l is the number of low-valuation consumers and together they are the total number of consumers.

Takeyama considers two types of equilibria. First, an equilibrium in which only high-valuation consumers buy the product (regime 1). In that case, the monopolist gets price p₁=vh,

resulting in profit

π

₁h =[vh−c q] h. Second, an equilibrium in which both types of consumers buy (regime 2), with price

p

₂equal to vl resulting in profit

π

₂l =[vl−c q]( h +ql). The monopolist prefers the first equilibrium if

π

h >

π

l which leads to the following conclusion: the likelihood that the monopolist opts for

π

h is positively influenced by the proportion of the total number of high-valuation consumers to the total number of low-valuation consumers (

q

h

/

q

l). In

addition, the size of low-valuation (vl) has a negative effect on this likelihood whereas the size of high-valuation (vh) has a positive effect on this likelihood. This is intuitive since a monopolist opts more quickly for an equilibrium wherein he only sells to high-valuation consumers

(compared to the case in which he sells to both types of consumers) whenever there are relatively more of this type of consumers present, and/or the level of valuation for these consumers (vh) is higher. Obviously, the opposite holds for the size of valuation of low-valuation consumers (vl). The next step is to introduce the possibility of copying. For both types of consumers, the cost of copying is

p

c

.

Furthermore, copies are imperfect substitutes for originals, where

α

is the parameter measuring the quality of a copy, with 0≤

α

≤1.That is, valuation for a copy is

α

vi

for i=h l, .19 For the model with copying, Takeyama again considers two cases. First, only high-valuation consumers buy while low-high-valuation consumers copy (regime 3), whereas for the second case both types of consumers buy (regime 4).

For regime 3 (wherein high-valuation consumers buy, low-valuation consumers copy), we have the following conditions:

1a)vh −p₃ ≥

α

vh −pc (high type does not copy)20

1b)

α

vl−pc >vl −p₃ (low type does not buy)21

1c)

α

vl ≥0 (low type does copy)22

19 _{Takayama refers to the degree of substitutability. I will use the term quality: the higher , the higher quality.} 20 _{This incentive compatibility constraint ensures that high-type consumers prefer buying over copying.} 21 _{This incentive compatibility constraint ensures that low-type consumers prefer copying over buying.}

22

Price is derived from the binding condition (1a), resulting in the following profit function:

3 [(1 ) ].

h h h c

q v p c

π

= −

α

+ −

The second case with copying present is the case in which both types of consumers buy the product (regime 4). In that case, we have the following conditions:

2a)vl− p₄≥

α

vl−pc (low type does not copy)

2b) l ₄ 0

v − p ≥ (low type does buy)

In this case, price is derived from condition (2a), resulting in profit:

4 ( )[(1 ) ].

l h l l c

q q v p c

π

= + −

α

+ − The monopolist prefers the first case if

π

₃h >

π

l₄. Again, the likelihood that the monopolist opts for the high price equilibrium is positively influenced by the proportion of total number of high-valuation consumers to the total number of low-valuation consumers (

q

h

/

q

l) . The intuition is the same as before. In addition, the cost of copying has a negative impact. The reason for this latter result is that in both regimes the following holds: the higher the cost of copying, the higher the price that the monopolist can ask. However, in regime 3 this price is paid only by the high-valuation consumers whereas in regime 4 the price is paid by both types of consumers. As a result, the cost of copying has a stronger effect on profit in regime 4. That is, a change in price has a stronger effect on profits since this price is paid by more consumers.

The next step is to verify whether the presence of copying may be beneficial to the monopolist, by comparing the model with copying and the model without copying. As stated earlier, the monopolist is more likely to prefer only selling to high-valuation consumers (in regime 1 or 3) whenever ( h

/

l

q

q

) and vh are higher (or vlis lower). This holds whether copying is present (regime 3) or not (regime 1). If these conditions are satisfied and the monopolist prefers regime 1 over 2 (and regime 3 over 4 for the case in which copying is present), the following interesting question remains: does the monopolist prefer the case with or without copying? Or stated differently, does the monopolist prefer regime 3 over regime 1? In regime 3, the presence of low-valuation consumers (who copy) increases the network effect. Hence, high-type consumer valuations increase as well. By contrast, these copiers are not present in regime 1 and therefore high-type valuations are higher. Furthermore, the monopolist is more likely to prefer copying if the quality of copies is lower and/or the price of copying is higher since in that case, the

monopolist can ask a higher price in regime 3. By comparing regime 4 with regime 223, it can

easily be seen that the monopolist always prefers regime 2. Both regimes have the same quantity sold since the market is fully covered in both regimes. However, the price in regime 4 (with copying) is lower than the price in regime 2 (without copying), which is intuitive. Hence, profit is higher in regime 224.

What happens to SW when copying is introduced? SW is the same, with or without copying, if the monopolist sells to both types of consumers (compare regime 2 with regime 4). Profits decrease since price is lower whereas quantity remains the same. Consequently, this loss in profits is compensated by an increase in CS (due to the lower price). Finally, by moving from regime 1 to regime 3 both types of consumers again gain. In particular, low-type individuals earn a positive surplus now by copying while earning positive surplus is impossible in regime 1 for these individuals. The presence of these copying individuals increase the size of the network which in turn increases the valuation of buyers, where these buyers are the high-valuation

consumers in this case. Furthermore, the monopolist may also earn a higher profit (see discussion above). Therefore, the overall conclusion is that allowing copying may result in a Pareto

improvement in which producers and consumers are both better off. This happens if the monopolist only sells to high-valuation consumers while at the same time low-valuation consumers copy (regime 3).

A ‘durable good model’ with copying

In a successive article, Takeyama (1997) drops the assumption of network effects and adds another period. This model shows similarities with the durable good model by Bulow (1982). Hence, Takeyama takes a two period approach in order to assess the effects of copying on consumers and producers. Using two different periods, she is able to study the intertemporal effects of copying. Again, Takeyama compares a model without copying and a model with copying and she shows that high marginal costs (in relation to the degree of substitutability of copies and originals) may remove the time consistency constraint. In this way, the monopolist can credibly commit not to lower its price in period 2 in order to attract low-valuation consumers. That is, high-valuation consumers know that the monopolist is not able to (profitably) lower its price in period 2 and therefore they are willing to pay the (high) price in period 1.

In her model, we again have two types of consumers, namely consumers with high valuations (vh) and consumers with low valuations (vl) for a durable good, with vh ≥vl.

Furthermore,

p

_i refers to price in period i (i=1,2) and is the discount factor. Finally,

q

i

24 _{Takeyama also compares regime 2 and 3 and shows that under certain conditions, the monopolist prefers regime 3 with copying}

represents the number of consumers with valuations i (i=1,2). Consumers can buy the product in period 1, resulting in utility 1 1.

b i i

U = +v

β

v − p Consequently, these consumers will not buy in the second period. On the other hand, if consumers do not buy in the first period, but do buy in period 2, utility is Ub2 =

β

(vi−p₂). The last possibility is the outside option, resulting in a utility of zero.

Takeyama starts with a model without copying, in which she makes a distinction between two cases. First, a price discriminating case wherein high-valuation consumers buy first and low-valuation consumers buy in the next period. These low-low-valuation consumers buy in the second period at p₂ =vl. In order to avoid high-valuation consumers to postpone their purchase

p

₁ should not be too high. That is, high-valuation consumers buy in period 1 as long as

1 2

0

b b

U ≥U ≥ which boils down top₁≤vh+

β

vl. In equilibrium, this constraint is binding:

2 .

h l

p =v +

β

v

The second case is the case in which all consumers buy in the first period. This will be the case if p₁≤vl +

β

vl,which is again binding in equilibrium. This leads to the conclusion that the ratio of high-valuation consumers to low-valuation consumers (

q

h

/

q

l), the level of

high-valuation (vh), and marginal costs all have a positive influence on the likelihood that the monopolist opts for case 1. Only the discount factor and the level of low-valuation (vl) have a negative effect on this likelihood. This result is similar to the result of Takeyama’s first model (see previous section) and the intuition is similar as well.

The next step is to incorporate the possibility of copying into the model. Now, consumers have six possibilities. First, they can buy in period 1 and do nothing in period 2, resulting in utility Ub1 = +vi

β

vi−p₁. Second, they can copy in period 1 and decide to buy the product in period 2, resulting in utility Ucb =v_ci −p_c+

β

(vi− p₂). In this case,

p

_c can be seen as the production cost of a copy for consumers. Furthermore, valuation for a copy (v_ci) lies in the

interval [0,vi]. Third, consumers may copy in the first period and do nothing afterwards, resulting in Uc1 =v_ci +

β

vi_c− p_c. Fourth, they can also do nothing in period 1 and buy in period 2, resulting in 2 ( 2).

b i

of zero. Finally, Takeyama assumes that high-valuation consumers do not copy, which need not be the case in reality.

With respect to intertemporal price discrimination (with copying present), Takeyama investigates two separate cases again and compares these cases (with copying present) with the corresponding cases without copying present. In the first case, high-valuation consumers buy in period 1 whereas valuation consumers buy in period 2. The highest price at which low-valuation consumers buy in the second period is: p₂ =vl−v_cl. Again, high-valuation consumers buy in the first period (they do not copy at all). However, in order to prevent these consumers to postpone their purchases, the price in period 1 should not be too high. It can be shown that profit is lower in this case than for the corresponding model without copying. With copying present,

p

₂

is (vl −v_cl)as opposed to vl in the case without copying. Moreover,

p

₁ equals vh +

β

(vl −v_cl)

with copying instead of

(

v

h

+

β

v

l

)

without copying. Hence, prices are lower in both periods due to the introduction of copying, which is intuitive.

Takeyama also considers a second intertemporal price discriminating case which prevails if (vl −v_cl)<c. If this condition holds, low-valuation consumers will not buy in the second period, only copy. High-valuation consumers now buy at a price, p₁=vh+

β

vh−c, and therefore copying increases profits for this price discriminating case. Marginal costs are high enough such that the monopolist is unable to set such a low price that low-valuation consumers buy as well in period 2. Rather, these consumers now copy. The high level of marginal costs (or stated differently, the high level of substitutability of copies and originals) enables the monopolist to precommit himself to a single price. High-type consumers know that the monopolist will not drop its price in period 2 in order to attract low-valuation consumers since the monopolist will not be able to attract these consumers due to the high marginal costs. As a result, the monopolist charges a high (single) price in period 1. Takeyama’s model shows similarities with the traditional durable good model by Bulow (1982) in which consumers buy at most 1 unit of a durable good. In a two-period setting, consumers rationally expect that the monopolist drops its price in period 2 in order to attract additional consumers, and therefore consumers are not willing to pay the full monopoly price in period 1. However, in Takeyama’s model this time consistency constraint is removed by the high level of marginal costs in relation to the degree of

Copyright protection and the underproduction and underutilization effect

The model by Novos and Waldman (1984) differs from the previous ones in that they allow for copyright protection. Takeyama compared a situation without copying with a situation with copying present. By contrast, Novos and Waldman explore the effect of increased copyright protection on SW. More explicitly, they make a distinction between SW loss due to

underproduction and SW loss due to underutilization. An increase in protection is said to have two opposing effects. First, an increase in protection increases SW (decreases SW loss) since it allows producers to reap the benefits from their production of intellectual property and therefore they increase their production. That is, the SW loss due underproduction effect is reduced. Without protection, some people get access to the product without paying for it. This is a free riding problem. Second, an increase in protection decreases SW (increases SW loss) since less people have access to these protected products. This is called the underutilization effect. The producer has market power due to protection, which results in some people, willing to pay a price equal to marginal cost or slightly higher, who will not obtain the product. In the end, both authors provide support for the underproduction effect. However, they reject the presence of the

underutilization effect.

The model is defined as follows. There is a monopolist who produces a good M for which he has the following cost function: TC q( , )

α

=F( )

α

+cq, where F( ) is the fixed cost, c is the constant marginal cost, q is the number of units, and represents the quality of the good.

Individuals have two options in obtaining the good. First, individuals can buy one unit of good M with quality i, where the quality differs over consumers. The authors assume that the valuation for quality is the same for all consumers (v). A consumer who buys good M with quality i, incurs a cost of ei. Therefore his net utility is: i i i_.

v e

π

=

α

− Second, individuals can reproduce, or copy, good M. For that purpose, the individual incurs reproduction costs

c

+

z

i

(1

+

h

),

where h represents the level of copyright protection. Note that copying costs differ across consumers. The authors assume that zi is distributed across individuals, according to a density function g(.). Obviously, a consumer will copy if

[

c

+

z

_i

(1

+

h

)]

<

p

,

where p is the monopoly price. In this case, all consumers with i

(

) /(1

)

z

>

p

−

c

+

h

will buy the good from the monopolist. Therefore, the monopolist’s profit function equals:

( ) /(1 )( ) ( ) ( ), Z _{i i} p c h p c g z dz F

π

α

− + = − − where Z is the

upper value of the distribution, whereas (p−c) /(1+h) is the lower value25. The monopolist

maximizes this function with respect to p and , subject to the condition that

α

v

≥

p

,

which is a binding condition in equilibrium. Then, the authors derive, after some straightforward

calculations, the monopolist’s optimal quality

α

m

( ).

h

The authors compare this result with the optimal solution, *. For that purpose, they construct a SW function, which is the sum of all individuals’ utilities. This function looks like

0

( ) ( ) ( )

Z

i i

v c g z dz F

α

− −

α

, which is maximized with respect to , resulting in *. Note that the product is sold to consumers at marginal cost if social welfare is maximized. Finally, it can be shown that

α

m

( )

h

<

α

*for all h. That is, the SW loss due to underproduction does exist. What happens to this loss if we increase protection from h1 to h2? The authors show that

1 2

( )

(

),

m m

h

h

α

>

α

provided that the following condition holds:

g z

'( )

i

≥

0.

If that is the case, quality produced by the monopolist increases. Hence, SW loss decreases. The intuition is that due to an increase in protection, more consumers buy the original product (since copying costs have increased). The conclusion is that the higher the level of copyright protection, the higher the quality of the product since the marginal revenue from an increase in quality is higher. As a result, an increase in copyright protection decreases the SW loss due to underproduction..

Copyright protection: the underproduction and underutilization effect reconsidered in a two-period model

Yoon (2002) also studies the effect of protection, but in a different manner26. As Novos and Waldman, Yoon concentrates on the effect of copyright protection on SW by again looking at the underproduction and underutilization effect. However, Yoon uses a two-period model to study the effects of increased protection, where the first stage is the production stage whereas the second stage is the consumption stage. Finally, he investigates the effects of protection for consumers, producers, and society as a whole.

There are two different ways for a consumer to obtain the product, say software. First, consumers can buy software, resulting in utility

U

b

= −

v

i

p

.

Second, they can make a copy which results in utility

U

c

= −

(1

α

)

v

i

−

z

i

.

In these equations, vi represents gross utility for consumer i, p is the price of the software package, and zi denotes the production cost of the copy. Production costs increase with the level of protection, that is ∂zi/∂ >h 0. An important point here is that the copied version is an imperfect substitute, hence gross utility is lower for a copied version. In particular, gross utility is

(1

−

α

) ,

v

i where lies in the interval (0,1). We can also rewrite utility for a copied version as Uc= −vi wi. In that case, wi (the gross reproduction cost) is

α

vi+zi.

The model is solved by backward induction, meaning that we take the second stage (utilization or consumption stage) as a starting point. The authors assume that the reproduction costs are the same for each consumer i. Hence,

z h

i

( )

=

z h

( )

where the level of protection h is exogeneous27. Furthermore, consumers’ valuations are uniformly distributed on the interval [0,1]. In stage 2, consumers decide whether to buy or copy the product or even do nothing at all. Yoon

arrives at a case in which non-users, copiers, and buyers are all present28. For

,

(1

)

z

p

α

≥

−

the number of nonusers equals

(1

)

z

α

−

while the number of copiers equals

(

)

.

(1

)

p

z

z

α

α

−

₋

−

26 _{Actually, Yoon’s article does not belong to the traditional copying literature. However, Yoon’ article is placed in this section}

because of the similarities with Novos and Waldman’s article.

27

This is not crucial for the qualitative results, as Yoon shows in the appendix by relaxing this assumption. That is, the model is robust for different production costs for consumers.

28 _{Actually, there exists a low-price case as well. In particular, the price in this case is too low (or copying costs z are too high) for}

Consequently, the number of buyers and therefore the monopolist’s demand equals ( ) ( ) 1 p z . D p

α

− = −

The producer incurs a fixed development cost R in the production or development stage (i.e. stage 1). In the next stage, the consumption or utilization stage, he incurs a constant marginal cost c. Hence, total cost is C q( )= +R cq. In the second stage, the monopolist maximizes profit with respect to p. Straightforward calculations then result in equations for profit ( ), CS, and SW. Yoon shows that two opposing forces come into play as a result of an increase in protection. First, reproduction costs rise and, as a result, copying consumers have to incur higher costs. This effect lowers SW and the following holds: whenever reproductions (or copying) costs are lower, this negative effect on SW is smaller. Second, some consumers switch from copying to buying, which increases SW. The reason for this is the following. The indifferent consumer derives utility

c i i

U = −v w from a copied version, and

U

b

= −

v

i

p

from an original version. Marginal consumers who have w close to p, choose to buy whenever protection rises since reproduction costs (w) rise. Since p is larger than c, we know that this consumer’s switch is actually a switch to a more efficient method (by the monopolist). Therefore, SW rises. This intuition is similar to the intuition given by Novos and Waldman.

Yoon shows that as the level of copyright protection (h) increases, profit increases. However, CS decreases with an increase in protection. Interestingly, SW may actually increase. Yoon shows that an increase in copyright protection may actually increase or decrease SW loss due to underutilization. SW decreases if increased protection results in less consumers who have access to the software package (hence the negative effect of the increase in copying costs dominates). More precisely, this happens for high marginal costs (relative to quality). On the other hand, for low marginal costs relative to quality, SW increases. That is, SW loss due to underutilization is decreased and this occurs whenever the second effect dominates. The intuition of this latter effect is that increased protection results in some consumers switching from copying to buying and this is a switch to a more efficient method and therefore SW rises. In my opinion one should give greater weight to this last result when considering software or music products since for these products marginal costs are nearly zero. In this case, the line of reasoning is the same as in the model by Novos and Waldman: an increase in protection decreases SW loss due to underutilization since consumers switch to a more efficient method.

produces. As we know that profit increases with z, there exists a threshold value for z, say z*. If *

z

<

z

the monopolist does not produce and a SW loss due to underproduction exists. For higher levels of z the SW loss due to underproduction equals zero. Hence, the SW loss due to

underproduction is either zero (if the monopolist produces) or maximal (if the monopolist does not produce at all).

Copyright protection with network effects present

Conner and Rumelt (1991) also examine the effect of an increase in protection by a monopolist. Just as in Novos and Waldman’s model, consumer’s copying costs increase with the level of protection and copies are perfect substitutes. However, Conner and Rumelt also allow for network effects. In fact, the presence of network effects is crucial in their analysis. Furthermore, Conner and Rumelt allow for marginal copying costs for consumers which increase with the level of protection. They show that not protecting is optimal for the monopolist if network effects are strong.

Consumers who buy the original product derive a net utility i

,

v

−

p

where vi represents gross utility and p is the price. On the other hand, consumers who copy the product derive a net utility i i

,

v

−

c

where ci is the cost of a copy with ∂ci/∂ >h 0. That is, the cost of pirating a product increases with the level of protection h. Therefore, a consumer wants to buy if

min( , ),

i i

p

≤

v c

he prefers to pirate if i

min( ,

i i

),

c

≤

v p

and he prefers to do nothing if

min( , ).

i i

v

≤

c p

This results in the following demand function

( , )

{ :

min( , ( ))}.

i i

q p h

=

i p

≤

v c h

Conner and Rumelt first consider the case for which the network effect is absent. In this case, price and profit increase as the level of protection increases. The intuition is that protection increases the cost of copying, which results in a decrease in the number of people who copy and an increase in the people who do not use the product. An increase in protection gives the monopolist more market power and therefore the monopolist is able to raise its price.

users (U)29. Stated differently, this cost of pirating is

C

i

= −

c

i

g U

i

( ),

where ci is the intrinsic cost of piracy, whereas gi(U) captures the network effect’s influence on the cost of pirating. As we can see, this cost is reduced with gi(U), where gi increases with the number of users U. Individuals’ choices now follow the following rules:

min(

i i

( ),

i i

( ))

p

≤

c

−

g U v

+

f U

(Buy)

( )

min( ,

( ))

i i i i

c

−

g U

≤

p v

+

f U

(Pirate)

( )

min(

( ), )

i i i i

v

+

f U

≤

c

−

g U

p

(Do nothing)

An increase in the number of users (U) has several effects. On the one hand, it decreases the cost of piracy and therefore, ceteris paribus, increases the number of pirating individuals (S). On the other hand, it increases individuals’ valuations of the product. However, this does not

automatically result in more people buying the product. If we take a look at the buying constraint, we see that

[

c

i

−

g U

i

( )]

has decreased but

[

v

i

+

f U

i

( )]

has increased. Conner and Rumelt define an additional variable N that represents the number of users (buying or pirating) whenever the number of effective users (U) is considered fixed. Then, the number of users increases if the number of effective users increases.

The next step is to explore the effects of an increase in protection. Conner and Rumelt assume the following relationship between the number of users (u) and price (p):

,

u= −z

ω

p with

ω

>0 (3.1)

where z is the intercept and is the reduction in the number of users for each unit of increase in price. Furthermore, they assume the following positive relationship between U and N:

[ ][1 ],

N = z−

ω

p +

γ

U (3.2)

where ( 0) measures the impact of increases in U on the total number of users. From above, we already know that the number of pirating individuals (S) increase with U, hence:

( )(1 ) ,

S =

α ω

− +

γ

U p where

α ω

> >0 (3.3)

Finally, the number of buyers (Q) then has the following relationship (equal to N-S):

( )[1 ]

Q= z−

α

p +

γ

U (3.4)

As was noted earlier, N is the total number of users whenever the number of effective users (U) is fixed. Obviously, in a rational expectations equilibrium the following has to hold:U =N.

Solving the model above works as follows. The rational expectations equilibrium solution for U is obtained by solving equation (3.2) above while inserting condition U =N. Next, the optimal solutions for S and Q can easily be obtained by inserting the expression for U into equations (3.3)

and (3.4), respectively. Profits are maximized by setting MR equal to MC (which is zero here), resulting in an optimal price p*.

Obviously, the main question here is what the effect of an increase in protection is on prices and profits. An increase in protection has two opposing effects on the monopolist’s price. First, protection increases the reservation price of (potential) buyers since the cost of copying is higher and therefore the monopolist can ask a higher price. Second, the higher cost of copying affects the behavior of the copiers. In particular, some copiers choose to buy, others prefer not using the product at all. The copiers (who are also part of the network) who choose not to use the product (as a result of higher protection) cause the total number of users to decrease which has a decreasing effect on the consumers’ valuations for the product. This second effect exerts a negative influence on the monopolist’s price. Hence, the effect of protection on prices and profit depends on the extent of the network effect. The main conclusion of this article is that, if network effects are strong, protection results in lower prices and lower profits. Whenever network effects are strong, protection leads to a ‘loss’ of copiers, who would otherwise be part of the network as well, which places a relatively heavy burden on the monopolist’s profit. By contrast, this burden on profit is less heavy as long as network effects are weak. Consequently, protection leads to higher prices and higher profits if network effects are weak.

Overview traditional copying literature

Table 3.1 provides an overview of the most relevant characteristics of the literature described above. In my opinion, Takeyama’s models, either with a network effect or with two periods, is a good starting point for analyzing literature concerning unauthorized production of intellectual property since these models (with only two types of consumers) are a simple framework to study the effect of copying on a monopolist’s profit. In both models, copying may actually increase profits. In the first model network effects are responsible for this result: low-type consumers who copy increase the user base which in turn increases high-type consumers’ valuations. However, Takeyama does not allow for copying costs while in reality these costs do exist. In particular, if these costs are considerable (and/or the level of low-type consumers’ valuations is low) these consumers do not copy at all. Economists agree upon the presence of network effects for software products, but whether these network effects exist for music products is questionable. According to this model, copying is harmful for the music industry as long as network effects are absent in the music industry.

good problem’: the monopolist can credibly commit to not lowering its price in period 2. In my opinion, this outcome is not likely to occur for software and music products since marginal costs are nearly zero for these products. Taking this into account, my conclusion is that copying is indeed harmful for the software and music industry (according to Takeyama’s second model). Finally, Takeyama’s model assumes that there are two types of consumers: either all consumers, within a particular type, buy or not. As a result, one only compares the prices with and without piracy in order to check in which situation profit is higher. Take for instance the equilibrium in which type 2 consumers only buy in period 2. As long as price is lower, profit is lower as well since Takeyama only considers a price effect but not a volume effect (within this group of consumers). In reality, some of these consumers choose not to use the product at all which means that volume effects are important as well.

As stated earlier, the articles by Novos and Waldman and Yoon have some similarities. However, there are some important differences as well. First, Novos and Waldman define underproduction whenever the quality set by the monopolist is less than the optimal quality (from a SW perspective). By contrast, Yoon defines SW loss due to underproduction as the loss in SW due to the fact that the product is not developed. Here, the SW loss either exists (completely) or equals zero. Second, Novos and Waldman define SW loss due to underutilization as the extra costs consumers have to make by copying instead of buying from the monopolist (following the increase in protection). In their model, all consumers use the product, either legally or illegally. Novos and Waldman do not allow for the possibility of not using the product which follows from the fact that consumer valuations are the same across consumers. By contrast, in Yoon’s model it is also possible that consumers do not use the product at all. As a result, some consumers choose not to use the product if copyright protection increases. In other words, by increasing protection, some consumers switch from using the product to not using the product at all. Obviously, this causes SW to decrease. In my opinion, the fact that consumers now have the option of not using the product adds more realism to Yoon’s model.

Novos and Waldman show that an increase in copyright protection lowers SW loss due to underutilization. The intuition is that some copying individuals become buyers which is

Therefore, one should attach greater weight to the first effect in my opinion. That is, the switch to a more efficient method lowers the SW loss due to underutilization in Yoon’s model.

Finally, Conner and Rumelt provide us with a framework which is the most complete of all models in my opinion. In their model, consumers differ with respect to their valuations as well as copying costs. Furthermore, the size of the network does not only affect consumers’ valuations but also consumers copying costs. I believe this is an important issue in real life since the more people possess a particular software application the lower copying costs are. The reason for this is that it is easier to obtain originals which can be copied. Conner and Rumelt show that it is optimal to have zero protection if network effects are strong. However, the model by Conner and Rumelt can be perfectly applied to the software market due to the presence of network effects. With respect to the music industry, I believe this is more difficult due the questionability of the presence of network effects for music products.

Table 3.1: Characteristics traditional copying literature

Takeyama (1994) Takeyama (1997) Novos & Waldman (1984)

Yoon (2002) Conner &

Rumelt (1991) Market structure Monopolist Monopolistic durable good model

Monopolist Monopolist Monopolist

Network effect Yes No No No Yes

Differentiation consumers Consumers differ w.r.t. valuations (2 types of consumers) Consumers differ w.r.t. valuations (2 types of consumers) Consumers differ w.r.t. copying costs (continuously) Consumers differ w.r.t. valuations (continuously) Consumers differ w.r.t. copying costs (continuously) and w.r.t. valuations (continuously) Quality of copies Imperfect substitutes Imperfect substitutes Perfect substitutes Imperfect substitutes Perfect substitutes Number of periods 1 2 1 2 1

Role protection No No Yes Yes Yes

Role government

No No No No No

3.2 Sharing literature

music by means of a P2P network (see section 3.4) is illegal and music producers are not able to indirectly appropriate revenues from these illegal users30. This section starts with the empirics of sharing scientific journals in libraries followed by an overview of two articles considered with a theoretical analysis of sharing.

The empirics of sharing and photocopying journals

Liebowitz (1985) addresses the empirical question whether unauthorized copying of intellectual property hurts producers or not31. Liebowitz identifies a mechanism through which these producers can generate revenues, that is, indirectly appropriate revenues from users who copy intellectual property. Finally, he shows that this can actually be beneficial for producers.

The concept of indirect appropriability works as follows. Take, for example, a library which offers several journals to all people who are subscribers of this library. The journals’ producers sell their products to this library but also to individual buyers. Journals in libraries are more often photocopied than journals in possession of individuals. This raises libraries’ demand compared to individual demand, which means that producers can ask a higher price from libraries. That is, producers can price discriminate between libraries and individual buyers. It should be the case that the more copies from a certain journal are made, the higher the price for this journal (for the library). A crucial element in sharing literature is that copies can only be made from originals, not from other copies. This is a distinction with earlier models in the

previous section, where copies can be made from other copies. In reality, copies can also be made from other copies.

Liebowitz constructed a sample of 80 journals and performed a regression, in which the dependent variable is the ratio of the price charged to libraries and the price charged to

individuals. Obviously, it is very difficult, if not impossible, to monitor the amount of copies from all journals in libraries. Therefore, he uses the number of citations of each journal as a proxy for its popularity. The larger the number of citations, the more heavily such a journal is

photocopied; hence this variable is expected to have a positive effect on price ratio. Furthermore, he makes a distinction between journals, which have been sold by commercial publishers and by noncommercial publishers, since the former are supposed to charge higher prices. Therefore, he includes a dummy for journals provided by commercial publishers, which is expected to be positive. Based on the regression results (which are all as expected and highly significant),

30 _{For the remainder of this thesis, sharing stands for indirect appropriability whereas P2P sharing refers to the (illegal) exchange of}

digitial music files on a P2P network.

31 _{Liebowitz’s article is an empirical article and it should therefore be situated in the empirical literature part of this thesis. However,}

Liebowitz concludes that, by looking at the positive coefficient for citations, indirect

appropriability does exist. Liebowitz concludes that price the monopolist charges the libraries is higher whenever a journal is used more intensively in the library. He also concludes that commercial publishers charge higher prices than noncommercial publishers.

As noted earlier, these publishers are able to indirectly appropriate some of the revenues. In addition, there may be a sampling effect, which occurs if individuals try or sample a (copied) product from and, if they enjoy it, buy it afterwards (see also section 3.4). Therefore, it is possible that photocopying of journals makes producers actually better off.

Sharing information goods: a theoretical approach

Varian (2000) examines the issue of sharing information goods from a theoretical perspective. In this case, a distinction is made between individual buyers and institutional buyers, such as libraries or video stores. The latter have a higher willingness to pay and therefore, under certain conditions, indirect appropriability of revenues increases profits. Varian sets out a simple model and shows that profits can actually increase with sharing present. Varian compares two cases: one wherein consumers have homogeneous preferences and one wherein consumers have

heterogeneous preferences. Both cases are explained below.

Consumers with homogeneous preferences

In this case, consumers’ preferences are homogeneous and Varian compares two cases: one in which a monopolist sells a product, and one wherein he rents this product. Varian’s model is defined as follows. A monopolistic publisher of a book has the following profit function:

( )

,

b

r q

cq

F

π

=

−

−

which he maximizes with respect to q. Here, F represents fixed costs, whereas c represents constant marginal cost. Furthermore, q is output. Finally, r(q) denotes the willingness to pay (of qth consumer). This results in the optimal solution qb, where everyone’s only option is to buy.