A Model of Piracy. Sang-Hoo Bae* and. Jay Pil Choi. Michigan State University. Abstract

Transcription

1 A Model of Piray By Sang-Hoo Bae* and Jay Pil Choi Mihigan State Uniersity Abstrat This paper deelops a simple model of software piray to analyze the short-run effets of piray on software usage and the long-run effets on deelopment inenties We onsider two types of osts assoiated with piray: the reprodution ost that is onstant aross users and the degradation ost that is proportional to onsumers aluation of the original produt We show that the effets of piray depend ruially on the nature of piray osts Poliy impliations onerning opyright protetion are also disussed JE Classifiation: D9, H, K4, Keywords: opyright protetion, piray, intelletual property, self-seletion *Sang-Hoo Bae Department of Eonomis, Mihigan State Uniersity East ansing, MI baesangh@msuedu Jay Pil Choi Department of Eonomis, Mihigan State Uniersity East ansing, MI hoijay@msuedu

2 Introdution As the urrent ontroersy surrounding the Napster ase testifies, unauthorized reprodution of intelletual property has been a serious but ontroersial issue for opyright holders, onsumers, and poliy makers alike, espeially with adent of digital tehnology Aording to a reent study by the Business Software Alliane 00, for instane, the piray rate in 000 is estimated to be 37%, whih an be translated into $75 billion dollar losses for software publishers The piray rates in the ar East, espeially China, Indonesia and Vietnam, represent in eah ase oer 90% The orresponding rates for Western Europe and North Ameria are 34% and 5%, respetiely Based on these figures, opyright holders laim that piray is a seere threat to inenties to deelop new produts, as well as reenue loss from the deeloped software As typial with other information goods that bear high fixed deelopment ost and low marginal ost, software is expensie to deelop but heap to reprodue In order to promote the progress of siene and useful arts, Intelletual Property Rights IPR are required to protet the software publishers interests and to gie them unique rights to prohibit piray 3 The folklore of IPR from the preious studies proposes that an inrease in Intelletual Property Rights IPR dereases ex post effiieny by reduing total usage of the already deeloped software; whereas, it promotes ex ante effiieny by inreasing deelopment inenties for potential software publishers Consequently, the optimal leel of IPR needs to strike a deliate balane between the long-term inenties to innoate and the short-term dissemination of work already reated 4 This paper reonsiders the folklore by deeloping a simple model of software piray to analyze the short-run effets of piray on software usage and the long-run effets on deelopment inenties The premise in this paper is to distinguish two types Sixth Annual BSA Global Software Piray Study May 00 onduted by International Planning and Researh Corporation IPR for the Business Software Alliane BSA and its member ompanies Varian 998 defines information goods as anything that an be digitalized, suh as text, images, date, audio and ideo 3 Artile I, Setion 8, of the US Constitution The US Constitution grants the Congress the power to promote the progress of siene and useful arts, by seuring for limited times to authors and inentors the exlusie right to their respetie writing and disoeries 4 See, for instane, Nordhaus 969

3 of osts assoiated with piray onstant and type-proportional and to show that the effets of piray depend ruially on the nature of piray osts At this stage it is useful to omment briefly on two types of osts The first type is reprodution ost, whih is onstant aross all onsumers The onstant reprodution ost an be thought of as the prie of an illegal opy made by piray retailers Een with the assumption that atual reprodution ost is zero, onsumers will need to exert efforts to obtain an authorized opy or may hae to spend time to find the software, and then to opy or to download it for installation purposes We assume that these osts are the same aross all users or at least independently distributed with the alue of onsumers attahed to the produt The seond type of ost is the degradation rate assoiated with unauthorized opying, whih is determined by eah onsumer s aluation of the software The examples of the proportional degradation rate are the following: or most ases, an authorized opy of the software is bundled with manuals, installation software, online series, as well as disount on upgrades Users who pirate the software, in ontrast, may not be able to aess the entire omplimentary bundle Some software publishers strategially inlude some web-based funtions, whih require personal identifiation numbers PIN, and the same PIN annot be used on the Web at the same time 5 With an illegal opy, a onsumer an use the software off line, but is not able to use online funtions, thus induing quality degradation 6 or the most extreme ase, software publishers use a web authentiation system that requires the owner of the software to hae the original media, and produt key 7 This web-based anti-piray system ensures that there will be only one running opy of the software per liense Een this tehnology, howeer, it is not perfet and an be irumented urthermore, there an 5 With deelopment of high-speed Internet, the new omponents of game software are online game series, in whih you an play the game with someone through the Internet With the database for the registration keys the software publisher is able to prohibit the pirated opies with the dupliated key from running on the web 6 or TurboTax software, eah authorized opy is designed to file tax returns eletronially for only one ustomer Hene, users with an unauthorized opy are only able to do tax returns exept eletroni filing 7 To redue software piray, Mirosoft uses software-based produt atiation tehnology for Windows XP and Offie XP This tehnology requires that authorized users atiate the software within 30 days This proess loks a produt identifiation number assigned to eah opy of the software to the PC When the atiation proess is omplete, the user registers the atiation ode with Mirosoft, whih stores it in a 3

4 be a ounter anti-piray program, whih an bypass the anti-piray proedure or reate a fake produt key Howeer, the web-based anti-piray system is apable of reduing quality of the software by bloking the users with a pirated opy from reeiing upgrades 8 As another example of poliy releane, onsider the Peer to Peer Piray Preention At whih was proposed by Rep Howard Berman, D-California, and is being onsidered in a House Judiiary subommittee as a way to protet intelletual property against file-sharing through peer-to-peer PP networks PP networks arose as a response to the shutdown of Napster Unlike Napster, PP networks do not host files on a entral serer; instead they list aailable files on indiidual PCs and diretly onnet those omputers, whih makes the enforement of opyrights more diffiult The proposed bill would allow the reord industry to hak into indiiduals PCs in searh of opyright iolations In our model, this type of opyright enforement would translate into an inrease in the osts of opying that are proportional to user types Another response by reord labels in fae of file-sharing, is to upload the so-alled spoof files ontaining little or no musi on PP networks to onfuse downloaders This pratie would inrease the expeted time of downloading for a partiular musi file and an be onsidered as an inrease in the uniform opy osts The purpose of this study is to onstrut a model of self-seletion with heterogeneous onsumers who hoose among three aailable options: the use of a legally purhased opy, the use of an illegal opy with unauthorized reprodution, or no onsumption We ondut a two-step analysis irst, we analyze how the threat of piray onstrains the priing behaior of the monopolist Depending on the relatie magnitudes of reprodution and degradation ost, the monopolist has to hoose the optimal hoie of regimes between limit priing and aommodation to opy We show that with the threat of piray the monopolist s prie is lowered, and usage for an authorized opy is inreased database Throughout this atiation tehnology, Mirosoft is able to identify onfliting atiation odes to identify software that has been installed on more than one mahine 8 Responding to piray of Windows XP operating system, Mirosoft announes that Windows XP Serie Pak and possibly all future updates will not install with pirated opies 4

5 in the both regimes 9 This result proides a sharp ontrast to the ommon laims of opyright holders, in whih the possibility of piray redues demand for a legal opy Seond, we examine the effets of an inrease in the two different margins of IPR When an inrease in IPR results from either the onstant reprodution ost or the typeariant degradation rate, it has two different effets: a demand swith and a total usage hange If an inrease in the opyright protetion enfores onsumers, who pirate the software, to purhase from the monopolist, it has a positie demand swith effet on soial welfare due to using more effiient tehnology In ontrast, inrease in IPR has a negatie effet if the opposite demand swith happens Sine an inrease in opyright protetion makes piray more ostly, fewer onsumers are able to pirate and, therefore, total usage hange always has a negatie effet on soial welfare It is obsered that with two different types of IPR, the opyright protetion has different impliations In the ase of an inrease in the onstant reprodution ost, we show that it has two opposite effets in the short run: positie demand swith and negatie total usage hange Therefore, it may enhane or redue ex ante soial welfare in the short run Howeer, we are able to pin down the effet on the soial welfare with an inrease in the degradation rate It onfirms the folklore of inrease in IPR in shortrun It redues ex post effiieny beause of the same negatie effets of demand swith and total usage hange Poliy impliations onerning opyright protetion are also disussed Earlier papers onerned with the effets of inreased opyright protetion on soial welfare inlude Noos and Waldman 984 and Johnson 985 among others Noos and Waldman 984 use the monopolist s quality hoie model with onsumers with the same aluation for produt, but heterogeneous opy ost They find that an inrease in IPR has a partial effet on ex ante effiieny and no ex post effet on total usage of partially nonexludable goods With aailability of a seondary soure that makes it possible for onsumers to make an unauthorized opy, inrease in opyright protetion may inrease or derease the monopolist s inentie to proide higher quality Based on the assumption of more effiient monopolist s tehnology, higher opyright 9 Choi and Thum 00 proide a similar framework, if we onsider purhasing an authorized opy of the software as entering the offiial eonomy, and making an illegal opy as operating in the shadow eonomy 5

6 protetion will bring inreased ex post effiieny by foring onsumers to purhase from the monopolist Johnson 985, in ontrast, makes a distintion between a household reprodution model with heterogeneous marginal ost and the fixed ost model of opying tehnology Both model onlude that the short run effet of opying on soial welfare depends on the extent of demand swithing ersus total demand inrease With adent of opy, some onsumers with low marginal ost hange to opying, thus induing welfare loss due to higher reprodution osts ompared to the monopolist s The long run effiieny is measured by number of work reated and the soial surplus per eah work Sine opying tehnology inoles marginal ost and no fixed ost in the first model all produers behae like a single-good monopolist In the long run, onsumers surplus an fall as reenue losses reduing the number of works Een with redution of the number of works, the long run effet in the seond model is determined by the alue of ariety and the elastiity of supply Our paper is also losely related to a reent paper by Yoon 00, who onsiders a similar model in whih he deries the optimal leel of opyright protetion With the onstant reprodution ost as the poliy parameter, in the short run, the effet of inrease in IPR is ambiguous; it an be positie or negatie depending on the magnitude of the reprodution ost Therefore, Yoon onludes that the optimal leel of opyright protetion is either no protetion or full protetion or the long-run inentie for deelopment, Yoon assumes that the deelopment ost is fixed The only measure for the ex ante effiieny with fixed deelopment ost is whether the monopolist deelops the new produt or not; the monopolist does not introdue a new produt if the deelopment ost an not be reoered due to weak protetion leel With this type of ex ante effiieny measure, the optimal protetion leel should be the step funtion beause the inentie of deelopment will be altered with the infinitesimal hange of IPR In our model, to hae a ontinuous effet of the inrease in IPR, we assume that the monopolist s long-run inentie is to hoose the quality of the software The remainder of the paper is organized in the following way: Setion sets up the basi model and shows how the monopolist s priing deision is affeted by the threat of piray We haraterize the pattern of self-seletion by onsumers and the optimal 6

7 prie for the monopolist We then ondut a omparatie statis exerise that analyzes the effets of inreased opyright protetion It is shown that the effets ould hinge on how it affets the two margins of the piray osts disussed aboe In Setion 3, we extend the model to allow for an endogenous hoie of the software quality by produer The existene of piray reates ineffiiently low quality of the produt urthermore, we onlude that inreased opyright protetion an potentially mitigate this ineffiieny, whereas, the ex ante effet of inrease in IPR also depends on two type of the opyright protetion parameters Setion 4 ontains onluding remarks The Model of Piray: A Short-Run Analysis Before analyzing the more omplex effet of IPR protetion on software usage in the short run and deelopment inentie in the long run, we first deelop the simplest feasible model of a market with speifi software, whih is produed by a monopolisti software publisher with IPR There is a population of onsumers whose total number is normalized to unity Consumers are heterogeneous in their alue of using the software et denote a onsumer s gross utility of using the software The distribution of types is gien by the inerse umulatie distribution funtion with ontinuous density ' 0, that is, denotes the proportion of onsumers whose alue of the software is more than To analyze the ex post effiieny effets of piray, we assume that the software is already deeloped and the marginal ost of prodution is zero The inenties to deelop new software are onsidered later The opyright holder thus sets the prie of the software p to maximize his reenues As the onsumer s utility is priate information, the opyright holder annot prie disriminate and harges a uniform prie p 0 Optimal Priing without Piray As a benhmark ase, we first onsider a situation where the option to pirate opyrighted work is not aailable, that is, the onsumers only hoie is whether to purhase or not The utility of buying an authorized opy is gien by U B ; p p We normalize the onsumers payoffs from not using the software to zero Then, onsumers whose alue 0 In a dynami model, howeer, the monopolist an prie disriminate onsumers based on purhase history See udenberg and Tirole 998 for suh an analysis 7

8 of software is more than p will purhase the software We assume that the marginal ost of produing software is zero without any loss of generality The purhase behaior of the onsumers implies that the opyright holder maximizes his reenue: p max R p p p Sine the monopolist s prie p is uniquely determined by, we will find it more onenient to treat as the ontrol ariable: max R The marginal onsumer * that maximizes the opyright holder s reenue is impliitly gien by the first order ondition: * * ' * 0 We make the standard assumption that the distribution of types satisfies the monotone hazard rate ondition, that is, - / is inreasing: " ' 0 This assumption ensures that the opyright holder s objetie funtion is quasi-onae and the seond order ondition for the maximization problem is satisfied: ' k " 0 3 Then, the number of software users is gien by * The optimal prie of the software for the opyright holder is p* * Note that the optimal prie and the marginal onsumer without piray depends only on the distribution of onsumer types Needless to say, the soially optimal prie for the software, one it is deeloped, is its marginal ost, whih is assumed to be zero Due to monopolisti priing, onsumers whose types are below * do not use the software and the deadweight loss is gien by * 0 xd x Using the first order ondition, we an rewrite the seond order ondition as ' " / ' 0 The seond order ondition holds if the distribution satisfies the monotone hazard rate ondition This ondition is a standard assumption in the inentie literature and is satisfied by most widely used distributions; see udenberg and Tirole [99, p 67] 8

9 Optimal Priing with Piray Now we introdue the possibility of using the software through piray without purhasing a legal opy Piray saes the prie of the software for onsumers Howeer, it entails potentially two types of osts irst, the unauthorized opy may not be a perfet substitute for the legal opy and typially entail some degree of quality degradation In the ase of opying with analog tehnology before the adent of digital tehnology, for instane, more iteration of additional opying meant lower quality Een with digital opying, the unauthorized opy may lak tehnial supports or aess to other resoures offered by the manufaturer We assume that this ost is proportional to the aluation of the onsumer for the original, that is, the aluation of the type onsumer for the unauthorized opy is gien by -, where is the parameter for quality degradation Another interpretation is that an also represent the enforement efforts by the authority If illegal opiers are aught with the probability of, in whih ase the software is onfisated as punishment, the aluation of using an illegal opy would be gien by - In addition, we assume that illegal opying entails reprodution ost of, whih is assumed to be the same aross users Thus, the utility of using an unauthorized opy is gien by U UC In order to hae a meaningful analysis of unauthorized opying, we restrit our attention to the parameter regions in whih the piray onstraint is binding, that is, p* * 4, where * is defined by 3 This ondition is satisfied if the degree of quality degradation and/or the ost of opying are not too high When the piray ondition 4 is binding, the monopolist s problem is ompliated by the fat that some onsumers are better off opying the software gien the monopolist s prie of the software In response to piray, the monopolist has two If we let w, then U UC w Hene, we an denote w as the gross opy ost 3 If the possibility to opy the software does not onstrain the monopolist s maximization problem, the marginal type of onsumer is gien by * as defined by The marginal type * earns zero surplus when he makes a purhase from the monopolist If he makes an illegal opy instead, his payoff is U UC * * If / p* *, the surplus from making an illegal opy exeeds the 9

10 hoies One option is to limit prie the software so that opying is not an attratie option The other option is to prie the software to sell only to the highest types and allow opying for intermediate types of ustomers imit Priing Regime without Piray With the piray onstraint binding p* *, the limit prie should satisfy the following inentie onstraint to eliminate the inenties to opy: U B ; p = p = U UC for any We obsere that U B ; p is inreasing in, whih implies that if the onstraint U UC aboe holds for, then it also holds for any suh that > Thus, all we need is that the inequality aboe be satisfied for = 5 This in turn implies that the limit prie and the marginal type are gien by p Notie that the no piray inentie onstraint 5 is always binding under the assumption p* * emma When the piray onstraint is binding, the optimal limit prie that preents the inentie to opy is gien by p In this ase, the monopolist s reenue is gien by R p p Copying Regime p > p If p > p, the no piray onstraint is iolated for some s that are higher than but lose to Eah onsumer has two different hoies for using the software, whih inur two different types of ost irst, when a onsumer buys a legal opy from the monopolist, he has to pay the prie p and enjoys the full quality of the software Howeer, with hoie of making an illegal opy, his ost will be the sum of degradation of quality, whih is proportional to his own aluation of the software, and one from other options Thus, possibility to opy the software seres as a binding onstraint for the monopolist s reenue maximization problem 0

11 onstant reprodution ost We assume at this time that the parameters of IPR for the degradation rate and for the reprodution ost are fixed When onsumers make their usage deision, they hoose the one, whih yields the highest net utility or a gien prie of a legal opy p > p and the leel of IPR, onsumers optimal hoies an be shown as follows: p p purhase a legal opy make an illegal opy no use Now the monopolist should take into aount that potential onsumers hae another option to obtain the software The monopolist, therefore, maximizes p Max p One again, we treat the marginal onsumer type Max p as the ontrol ariable: The first order ondition 0 6 determines the marginal type of onsumer ~, who is indifferent from purhasing an authorized opy from the monopolist and making an unauthorized opy 4 Therefore, with the option of making an illegal opy, onsumers with low alue do not use the software Those with intermediate alue ~ make illegal opies Only onsumers with high alue ~ purhase legal opies from the monopolist [see igure ] No use Copy Buy igure ~ *

12 We now an ompare the monopolist s priing behaior with and without piray Proposition With the possibility of piray, the prie of the software is lowered, thereby induing more demand for legal opies Inrease in usage of both legal and illegal opies under the opying regime brings higher ex post usage for the software Proof Ealuate 5 at * whih is the marginal onsumer when no opying is feasible: [ * * *] * * 0 Hene, * ~ Under the opying regime, there exist onsumers, whose alue lies between and ~, making opies Therefore, total ex post usage for the software is unambiguously inreased with piray Being just a threat limit priing regime or an atual fat opying regime, piray has the same effet on the monopolist s priing behaior: the prie is lower than the one in the benhmark ase A more surprising result is that the usage of legal opies inreases een in the presene of opying Thus, the extent to whih legal opies are used is omplementary with the extent of the usage of unauthorized opies The intuition for this result an be found in the monopolist s priing behaior in response to the threat of unauthorized opying If there were no prie hange, that is, at p = p*=* defined in, some of the preious purhasers of the legal opy will swith to the option of opying with the result of a lower number of legal opies being sold Proposition, howeer, shows that the prie redution by the monopolist from p* to ~ p ~ not only eliminates the inenties to swith for the preious buyers but also expands the base of buyers Under the opying regime onsumers willingness to pay for the software is not equal to their aluations Sine they hae another option, whih is piray, onsumers hoose to make an illegal opy if the prie exeeds the gross opy ost w Therefore, the monopolist s demand is now determined by the gross opy ost, whih onsists of the onstant reprodution ost and the proportional degradation rate Due to the existene of piray the monopolist now has less market power, whih results in lower prie for legal opies Proposition gies an extreme but intuitie fat about the ex post soial welfare 4 Variables under the opying regime are denoted by a tilde ~

13 Proposition If the ost of piray is only of degradation, the number of legal users is the same regardless of the possibility of piray There is no swith The prie of the software is lower with the threat of piray and depends on the degradation fator p p * Ex post soial welfare is inreased with the possibility of piray sine there are illegal users who are pure addition to the number of total users Comparatie Statis We now analyze the effets of marginal inrease in the intelletual property rights As with the preious studies in the literature Noos and Waldman [984], Yoon 00, et, we model the inrease in the intelletual property rights as an inrease in the ost of piray It is shown that the effets an hae different impliations depending on whih regime the monopolist is operating under and the type of osts assoiated with piray Proposition 3 Under the limit priing regime, both types of an inrease in IPR indues higher software prie and less authorized usage Proof Under the limit priing regime, we hae p, and q p If we take partial deriaties of p and p with respet to and respetiely, we hae the following results: p p p p 0, 0, p p 0 p p p, and 0 p The intuition underlying Proposition 3 is straightforward Due to the possibility of piray, the monopolist is not able to harge the monopoly prie Howeer, the monopolist modifies his priing behaior aording to the relatie magnitude of IPR, in whih he an eliminate piray The maximum prie he an harge under limit priing is p, whih depends on the leels of the degradation rate and the reprodution ost The marginal inrease in IPR from either the degradation rate or the reprodution ost proides the monopolist more market power, allows him to harge a higher prie Proposition 4 Under the opying regime, as expeted, the monopoly prie inreases with the strengthening of IPR The effets of inrease in IPR on the usage of software is 3

14 ambiguous, depending on the types of osts assoiated with piray Higher degradation rate indues a higher software prie and less authorized usage With higher reprodution ost, the prie of the software will inrease and more authorized usage [see table ] Proof Total differentiation of the first-order ondition with respet to : [ ~ ~ ~ ] d ~ d d~ ~ 0 d H where H ~ ~ ~ 0 by the seond-order ondition Total differentiation of the first-order ondition with respet to : [ ~ ~ ~ ] d ~ ˆ ~ d d~ ~ ~ ~ ~ 0 d H H Sine the monopolist s demand is determined by the gross opy ost under the opying regime, the effets of inrease in IPR depend on the types of osts assoiated with piray With higher reprodution ost, all onsumers fae the same inrease in the gross opy ost, whih is equialent to an outward parallel shift in demand for legal opies With an inreased demand, the monopolist responds with a prie hike The prie inrease, howeer, does not ompletely offset the initial demand inrease with the result of inreased sales In ontrast, if an inrease in IPR is deried from higher degradation rate, we obsere a piot hange in demand that affets the slope of the demand ure for legal opies Due to proportional inrease in the gross opy ost, higher aluation onsumers are more affeted by an inrease in the degradation ost A steeper demand ure means that elastiity of onsumers is lower with more market power Thus, the monopolist is more interested in sering only the high aluation onsumers Compared to the targeted opyright enforement model by Harbaugh and Khemka 00, an inrease in IPR from higher degradation rate illustrates similar effets, but different results In their model, with prie disrimination, the opyright enforement only affets the high alue onsumers opy osts, whih indues inrease in both the monopolist s reenue and the onsumer surplus of the low type In our model, higher degradation rate imposes higher opy ost for the high type, whih has the similar effets, 4

15 The monopolist s optimal hoie An inrease in the reprodution ost An inrease in the degradation rate Benhmark imit Priing Copying Regime * * ~ * ~ p * p p p* p~ ~ p p* N/C 0 and ~ 0 0 ~ p and 0 N/C p ~ ~ p 0 and 0 0 and 0 Table but also affets the lower alue onsumers without prie disrimination Therefore, it inreases monopolist s reenues, but less piray Welfare Effets of Inrease in IPR in the Short Run We are now in position to examine the effets of inrease in IPR on the soial welfare In the benhmark ase, the piray onstraint is not binding p* *, therefore, piray is not feasible Sine the software publisher behaes as an unonstrained monopolist, both types of inrease in IPR do not hae welfare effets When the monopolist s optimal hoie is limit priing, it is straightforward to show the effet of inrease in IPR on soial welfare As either the degradation or the reprodution ost inreases, making an illegal opy beomes less attratie or more expensie To response to this, the monopolist is able to harge a higher prie and fewer onsumers use a legal opy Sine the inreased profit margin is only a monetary transfer from the onsumers to the monopolist, deline in soial welfare is resulted from less authorized usage Proposition 5 Under the limit priing regime, both types of inrease in IPR indues lower soial welfare Proof With limit priing, the soial welfare is idential to the gross onsumers surplus from authorized usage: SW p d d We examine the effet of inrease of IPR on soial welfare as 5

16 SW 0, and SW 3 0 If the monopolist s optimal hoie is aommodating piray, the welfare effets of inrease in IPR depend on the types of osts assoiated with piray As expeted, both types of inreases in IPR make piray more ostly In addition to this effet, these osts hae two different hannels to affet the soial welfare: demand swith and total usage hange or the inrease in the type-independent reprodution ost, it is equialent for the monopolist an outward parallel shift in demand To response to this, his optimal reation will be harging higher prie to the extent where it still indues more sales Additional inrease to the monopolist s demand will inrease the welfare, beause of hange to more effiient way of prodution [positie demand swith] Seond, it dereases the soial welfare beause with higher gross opy ost, the number of onsumers who are making opy shrinks [total usage hange] Therefore, the welfare effets of inrease in IPR by higher reprodution ost depend on the size of those two ounterailing effets An inrease in IPR with higher degradation rate shows two different hannels but the same negatie effets on the soial welfare irst, sine higher degradation rate enhanes the monopolist s market power, he harges a higher prie with redution in sales Some onsumers who preiously were legitimate users now are fored to hoose piray Additional dedution from the monopolist s demand will derease the welfare beause of the hange to a less effiient way of prodution [negatie demand swith] Seond, it will also derease the soial welfare beause, with higher gross opy ost, the number of onsumers who are making opy ontrats [total usage hange] Proposition 6 Under the opying regime, the effets on soial welfare of inrease in IPR depend on the types of osts assoiated with piray Proof The soial welfare an be deried from the sum of the monopolist s reenue and the onsumer s surplus: SW ~ p R ~ p CS ~ p 6

17 ~ ~ ~ ~ ~ ~ d ~ d ~ ~ [ ] d We examine the effet of inrease of IPR on soial welfare as SW ~ p ~ [ ~ ~ ] ~ SW ~ p ~ [ ~ ~ ] ~ [ ] d ~ ~ 0 d, and 0 d 0 rom the aboe equations, we an separate two different hannels The first part of the equations represent demand swith, whih indues welfare gain or loss from the hange of the prodution methods The seond part identifies an inrease in onsumers gross opy ost aused by an inrease in either type of ost It dereases soial welfare beause onsumers who pirate an offiial opy hae to endure a higher ost On the other hand, sine the effet on the marginal onsumer, who is indifferent from no use and piray, is the seond-order, the aboe equations do not illustrate the effet of total usage hange on soial welfare [see figure ] total usage hange the opy ost inrease demand swith total usage hange opy ost inrease demand swith No use Copy Buy ~ a welfare effet of higher reprodution ost No use Copy Buy ~ b welfare effet of higher degradation rate igure Uniform Distribution Example We now illustrate our results using a simple uniform distribution that generates a linear demand ure for the monopolist This example also allows a losed-form solution for 7

18 welfare analysis or example, we now assume that onsumers ealuations for the software are uniformly distributed oer the unit interal, suh as i U[0, ] Howeer, other assumptions, suh as uniersal reprodution ost and proportional degradation ost, remain the same Then, gien the monopolist s prie and two different types of IPR protetion, we derie two types of marginal onsumers The first marginal type, who is indifferent between making an illegal opy and no use, is denoted by ˆ opy, no use The seond marginal type, who is indifferent between buying a legal opy and making an illegal opy, is denoted by ˆ opy, buy p If ˆ no use, opy ˆ opy, buy, we hae the benhmark ase in whih piray is not possible In the ase of ˆ no use, opy ˆ opy, buy the monopolist lowers the prie enough to deter piray The last ase is ˆ no use, opy ˆ opy, buy, in whih the monopolist aommodates piray Hene, the optimal hoies of onsumers an be summarized as follows: Benhmark ase No piray: with p, only onsumers whose alues satisfy p buy legal opies, and no piray is possible imit priing regime: with p, onsumers who belong to buy offiial opies, and the monopolist s prie is low enough to blokade piray Copying regime: with p, onsumers who belong to p purhase authorized opies, and those who belong to p use the software by making illegal opies or the benhmark ase, where the option to opy the software is not feasible, onsumer s hoie is whether to purhase or not With the uniformly distributed onsumers aluation, the monopolist s demand is * where the marginal onsumer s aluation is * p The monopolist s problem is to hoose the prie p of the legitimate opy is as to maximize his reenue: max R p p p The first order ondition 0 8

19 determines the marginal onsumer * p* Therefore, when, the monopolist s optimal hoie is to harge the monopoly prie without piray 5 We now turn to the monopolist s optimal priing problem with piray The first option for the monopolist is to aommodate piray in whih the monopolist sets a higher prie and tolerates opying In this ase, the monopolist s objetie beomes: p Max p p One again, we treat the marginal onsumer type as the ontrol ariable: Max The first order ondition 0 yields ~ and ~ p Comparing * and ~ in the uniform distribution example we an easily erify Proposition As a result, when 0, the monopolist s optimal hoie is to allow piray and harge a higher prie 6 The seond option is for the monopolist to eliminate piray by setting the prie suffiiently low Sine the monopolist should redue the prie until the piray onstraint is binding, p, the optimal prie and reenues are p, and p p Therefore, when, the monopolist s optimal hoie is to lower the prie until onsumers do not hae any inentie to make an illegal opy or the last remark we an illustrate the monopolist s optimal regime hange depending on the relatie magnitude of IPR parameters [see figure 3] 5 If we substitute * p* into the onsumers optimal behaior ondition under the benhmark ase p, we hae If, the gross opy ost exeeds the aluation for the software, whih is not a meaningful ase to onsider 9

20 NO PIRACY IMIT PRICING COPYING REGIME igure 3 With liner demand and losed form solutions the effet of inreased opyright protetion an be shown more learly in the uniform distribution example Under the limit priing regime, we an erify that both types of inrease in IPR indues higher software prie and less usage With the optimal hoie of prie p and quantity q p under the limit priing, we an alulate as follows: p q 0, 0 p 0 q, and 0 Under the opying regime, it is obsered that the effets of inrease in IPR depend on the types of osts assoiated with piray [see figure 4] As we expet, an inrease in both types of osts trigger a higher prie but ambiguous effet on demand swith These effets are learly shown as p q p q 0, 0, 0, and If we substitute p* into the onsumers optimal behaior ondition under the opying regime p, we hae 0 0

21 p p q q a the effet of reprodution ost inrease igure 4 b the effet of the degradation rate inrease or the last part of the short-run analysis, we examine welfare effets of inrease in IPR If, we identify that the monopolist prefer to eliminate piray by lowering the prie; in other words, the possibility of piray enfore the monopolist set a lower prie as p It is straightforward to show the effet of inrease of IPR on soial welfare Consumer surplus and the monopolist s reenue under the limit priing are omputed as follows: CS x dx, and p p Defining soial welfare as SW CS we obsere that SW 0 SW, and 0 3 If 0, the welfare effets of inrease in IPR depend on the types of osts assoiated with piray The onsumer surplus and the monopolist s reenue in the opying regime are gien by p ~ ~ CS p x dx x p dx, and ~ ~ p p p

22 3 We then alulate soial welfare as ~ ~ ~ SW p CS p With positie demand swith and negatie total usage hange, the effet of an inrease in IPR with higher reprodution is unertain Howeer, with negatie demand swith and negatie total usage hange we are able to pin down the effet of an inrease in IPR with higher degradation rate These results an be illustrated by the following two partial deriaties [see figure 5] SW is fixed , and SW 3 4 is fixed 4 7 SW SW To determine the sign of, let ĉ be the ritial alue, whih satisfies 0 and SW we hae ĉ Hene, if ˆ, we hae 0 Otherwise, we obsere 3 SW 0 SW SW SW Rp SW Rp Copying regime imit priing No piray imit priing Copying regime imit priing No piray a the effet of inrease in the reprodution ost b the effet of inrease in the degradation rate igure 5 7 Sine we hae parameter region for the opy regime suh as SW, we an erify that 0

23 3 Copyright Protetion and Inenties to Create Up to now, we hae analyzed the effets of opyright protetion on priing and the inenties to pirate one the software has been produed In this setion, we analyze the long-term effets of intelletual property rights on the inentie to reate To analyze this issue, we introdue the ost of reating the software and endogenize the quality of the software et measure the quality of software that is reated at ost C [with C ' 0, C" 0 ] The quality of the good enters positiely into the utility of onsumers; the utility of onsumer of type is We onsider now the long-term effets of piray in whih the monopolist deides not only on the priing of the software but also on the quality of the software In this ase, the presene of piray may lead to dereased reenue, whih in turn may adersely affet the quality and quantity of the software We ontinue to assume that the marginal ost of software is fixed at zero regardless of the quality of the software one it has been deeloped Software Quality without Piray Before analyzing the monopolist s quality proision with the possibility of piray, we start with the benhmark ase, in whih onsumers fae a monopolisti software publisher but do not hae the opportunity to make an illegal opy Hene, the onsumers only deision is whether to purhase or not Sine the onsumers payoff from not using the software is zero, onsumers with non-negatie net utilities purhase an offiial opy: p 0 Gien the purhase deision of onsumers, the opyright holder uses the prie and the leel of quality to maximize his profit: 8 max, The first order onditions C ' 0 C' 0 8 determines the marginal onsumer * and the monopolist s optimal leel of quality * 7 8 Again, we use as a ontrol instead of p 3

24 Proposition 7 Gien the number of software users *, the quality of the software is sub-optimally low Proof Gien the number of software user *, ie all onsumers of type * buying the software, the soially optimal quality of the software an be found by soling The first order ondition max * ' d C ' d C' determines the soially optimal leel of quality * opt 0 opt Integration by parts of the first term on the left hand side shows ' d * * As we hae * * C' * * from 7, marginal benefits and marginal osts of the quality of the software when proided by the monopolist are below the soially optimal leel: C' opt C' * Therefore, the leel of the software quality is sub-optimally low: opt * The intuition for this result is the following The hoie of * by the monopolist is determined by the marginal type * An inrease in the benefit of the marginal onsumer is aptured ia higher prie of the software by the opyright holder The effet on the inframarginal onsumers is irreleant for the monopolist as he annot prie disriminate between onsumers In ontrast, the seond-best leel opt is determined by the aggregate or aerage benefits for all onsumers with alues [ *, As the aerage onsumer s aluation for the software is higher than the one of the marginal onsumer, the seond-best leel of quality of the software exeeds the one proided by the monopolist 9 Software Quality with Piray Now we turn to the monopolist s hoie of the software quality, when he faes piray: how does the potential threat or atual piray affet the monopolist s hoie of the software quality? To answer this question, we use the preious optimal priing framework with the monopolist s hoie of the software quality We still assume there 4

25 are two different types of ost assoiated with piray: the onstant reprodution ost and the proportional degradation rate The degradation rate now affets the aluation of the type onsumer for the unauthorized opy as Thus, the utility of using an unauthorized opy is gien by U UC In order to hae a meaningful analysis of unauthorized opying, we hae the same restrition to the parameter regions, in whih the piray onstraint is binding, that is, p* * * 9, where * and * are defined by 6 and 7 This ondition is satisfied if the degree of quality degradation and/or the ost of opying are not too high Therefore, with the binding onstraint 8, the monopolist praties ether limit priing or aommodation to piray Software Quality under imit Priing Regime With the piray onstraint 8 binding, the monopolist faes the onstrained profit maximization problem as following: Max Subjet to p p C p Sine the onstraint is always binding under the assumption p* * *, the optimal prie p, and reenue is R C The monopolist now determines the optimal hoie of the software quality with the optimal limit prie as following: The first order ondition Max C 9 This point is losely related to a monopolist s hoie on produt quality; see Spene 975 and Tirole 988, pp

26 6 0 C 0 determines the monopolist s optimal hoie of software quality Proposition 8 Under the limit priing regime, the monopolist hooses a lower leel of quality than the one without piray Proof et us ealuate the first order ondition 9 at * whih is the leel of quality without piray * * * * C We know that * * * * * * The inequalities aboe follow from the fat that is a onae funtion whih is maximized at * and our assumption that * * * p Thus, we hae 0 * * * * C, whih implies that * Software Quality under the Copying Regime Under the opying regime onsumers ompare the payoffs from buying an authorized opy [ p ] or making an unauthorized opy [ ] Gien the purhase behaior of onsumers, the monopolist maximizes his profit: ~ max, C The first order onditions 0 ~ 0 ~ C again determine the marginal onsumer ~ and the software quality ~ How does the existene of piray as another option for onsumers affet the outome? There is a learut answer to this question:

27 Proposition 9 Under the opying regime the existene of piray leads to a further underproision of the software quality but more authorized usage Proof Ealuating at * yields * * * * 0 Hene we hae ~ * Also, ealuating at * yields * * 0 and ~ therefore * The intuition underlying this result is the following The hoie of ~ by the monopolist is determined by the marginal type ~ At the deelopment stage of the software the monopolist expets that the marginal onsumer is not * but ~ when there is piray Gien this antiipation, the optimal hoie of the software quality should be lower than the one from the benhmark ase As we already identify from Proposition 9, the deision on the software quality by the monopolist already leads to an underproision opt * The existene of piray aggraates the ineffiient proision of the software quality Our result thus lends theoretial support for the laim that piray redues the inenties to deelop new software Comparatie Statis rom the preious opying regime we obsere that the monopolist has less inentie to proide higher quality of the software due to piray We now turn to analysis of the effets of marginal inrease in IPR on the monopolist s deelopment inentie Proposition 0 Under the limit prie regime, both types of inreases in IPR indue higher software quality and less authorized usage Proof We an rewrite 9 as C 0 By totally differentiating the first-order ondition, we hae d C d C d 0 d d [ C C ] By totally differentiating the first-order ondition, we hae Also we an easily erify that C d C d C d 0 d C 0 d [ C C ] 0 7

28 8 0 d d d d, and 0 d d d d The intuition underlying Proposition 0 is straightforward Due to the potential threat of piray, the only option, in whih monopolist an eliminate piray, is to lower his prie until p is binding The maximum prie he an harge under limit priing is p, whih depends on the relatie leel of the degradation rate and the reprodution ost Inreases in IPR from either the degradation rate or the reprodution ost indue less authorize usage, whih is equialent to higher aluation from the marginal onsumer ~ This dries monopolist has more inentie to proide higher quality Proposition Under the opying regime the effets of inrease in IPR depend on the types of osts assoiated with piray Higher degradation rate indues higher quality and less offiial usage In ontrast, higher reprodution ost results in lower quality and more authorized usage Proof By totally differentiating and, we hae d d d d By using Cramer s rule, we hae H d d, and H d d

29 9 where H is the determinant of the Hessian matrix with 0 H by the seond-order ondition for maximization 0 C H d d 0 0 H d d By totally differentiating the first-order onditions, we hae d d d d By using Cramer s rule, we hae H d d, and H d d 0 ] [ C H d d 0 It an be easily erified that 0, 0 C, 0, and 0 It an also easily erified that, 0, 0, 0, and 0 We hae 0, 0 C 0, and 0

30 The monopolist s optimal hoie An inrease in the reprodution ost An inrease in the degradation rate Benhmark imit Priing Copying Regime * * ~ * ~ p * p p p* p~ ~ p p* * * ~ ~ * N/C d ~ d ~ 0 and 0 0 and 0 d d N/C 0 and ~ 0 d 0 d ~ and 0 d Table d d [ H { } ] 0 3 Sine the monopolist s quality proision is determined by the marginal onsumer s aluation for the software, the effets of inrease in IPR depend on the hange of the marginal onsumer, whih is different aording to types of osts assoiated with piray With higher reprodution ost, all onsumers fae the same inrease in the gross opy ost, whih is equialent to oerall demand inrease for the monopolist Hene, The monopolist benefits from higher demand by harging the higher prie, yet inreasing sales at the same time aing the marginal onsumer s lower aluation, the monopolist has less inentie to proide higher quality In ontrast, if an inrease in IPR is deried from higher degradation rate, we obsere proportional inrease in the gross opy ost and omparatiely more market power for the monopolist With inrease in market power, the monopolist harges a higher prie by reduing quantity Responding to the marginal onsumer s higher aluation, the monopolist has more inentie to supply higher quality Uniform Distribution Example of the Software Quality We now assume onsumers aluation for the software is uniformly distributed suh as i U[0, ] To make our analysis more tratable, we also suppose that the monopolist s 3 We hae 0, 0, 0, and 0 30

31 ost of deeloping the software, whih deides the leel of quality, is gien by k C With uniform distribution we an easily erify Proposition 7, in whih gien the monopolist s optimal hoie of quantity, the quality proision under the benhmark ase is suboptimally low Sine the onsumers only deision is whether to purhase or not, the monopolist has the marginal onsumer whose aluation * p Gien this arrangement, the monopolist maximizes his profit: Max The first order onditions, k 0 3 k 0 4 determine * and * 4k Soially optimal leel of quality an be deried by maximizing the aggregate aluation of onsumers between [, ], whih is k Max d opt * We hae opt 3 8k, whih is Now we turn to the monopolist s optimal hoie of software quality with piray The monopolist s hoie depends on how he responds to the threat of piray With two margins of IPR [degradation rate and opy ost ] the monopolist has two different strategies to hoose 4 irst, we obsere that the monopolist maximizes the onstrained profit under the limit priing regime as following: Max p p k Subjet to p 4 The onsumers optimal behaiors are the same as the short run ase 3

32 The optimal prie p, and profit is k The monopolist then hooses his optimal hoie of quality by The first order ondition k Max k 0 5 determines the optimal leel of software quality for the monopolist If we aluate the first-order ondition at * 4k, we an erify that under the limit priing regime, the monopolist hooses lower leel of quality as the one without piray 5 or the last ase where the monopolist hooses to allow piray, the marginal onsumer who is indifferent between buying and opying is gien by p faing demand of, the monopolist s profit maximization problem is k Max The first order onditions determine 0 p With 6 k 0 7 ~, whih is ~ ~ * Also, if we ealuate k at ~ *, we an erify * 4 k 5 With our assumption p* * * we an erify the sign of 5 at * suh as 4k 6k 0 6k 4 8k 8k 3

33 The effet of inreased opyright protetion on deelopment inenties an be shown more learly in the uniform distribution example By totally differentiating 5 we an show both types of inrease in IPR indues higher software quality and less authorized usage as the following: d k d 6 d d 0, 0, d d d d 3 d d 0, and 0 d d Moreoer, we an easily erify the effets of inrease in IPR under the opying regime: higher quality and less offiial usage with inreased degradation rate, and lower quality and more authorized usage with inreased reprodution ost By totally differentiating 6, 7 and using Cramer s Rule we an present a simplified ersion of proposition as follows: d d [ H ] k d 0, [ ] 0, d H d d H [ k ] 0, and d d [ ] 0 H 4 Conluding Remarks In this paper, we deelop a simple model of piray to analyze impliations of inreased intelletual property rights on the short-run and long-run resoure alloations In a model of self-seletion with heterogeneous users, we show that the onsumers option to use illegal opies onstrains the opyright holder s ability to harge a monopoly prie Consequently, the unauthorized opy ould lead to more usage of the legal opies In this sense, the presene of the unauthorized opies an at as a omplement to use of the legal opies rather than a substitute 33