Deartment f Ecnmics Wrking Paer Series Des Reliable Pirated Prduct Lead t Mre Piracy? Yuanzhu Lu and Sugata Pddar 01/05
Des Reliable Pirated Prduct Lead t Mre Piracy? Yuanzhu Lu and Sugata Pddar China Ecnmics and Management Academy, Central University f Finance and Ecnmics, Beijing, China. Deartment f Ecnmics, Auckland University f Technlgy, Auckland, New Zealand. Abstract Cnventinal wisdm wuld suggest if a irated rduct, which is cheaer than the riginal rduct, becmes mre reliable then the relative demand f the irated rduct r the rate f iracy will increase when cnsumers have different willingness t ay. Hwever, is this always true? We address this questin in a framewrk where the riginal rduct develer makes cstly investment t deter irate(s) in a given regime f IPR rtectin. We shw that the relatinshi between the rate f iracy and the reliability f the irated rduct deends n the nature f the irate as well as n the nature f the market cmetitin if the irate is cmmercial. Under cmmercial iracy, when the riginal firm and the irate cmete in quantities, the cnventinal wisdm hlds i.e. the mre reliable the irated rduct, the higher is the rate f iracy. Hwever, the relatinshi is nn-mntnic, hence the wisdm des nt hld when they cmete in rices r the irates are the end-users. Keywrds: IPR rtectins, rice cmetitin, quantity cmetitin, rduct quality JEL Classificatins: D3, D43, L13, L86 Address fr crresndence: Sugata Pddar, Deartment f Ecnmics, Auckland University f Technlgy, Auckland, New Zealand. Email: sddar@aut.ac.nz 1
1. Intrductin When the cnsumers are hetergeneus in their willingness t ay fr a rduct then a irated rduct is likely t sell in the market when iracy is accmmdated and it is cheaer than the riginal rduct. Nw suse the quality r the reliability f the irated rduct (which is usually f lwer quality than the riginal rduct) gets better; des that mean that the relative demand f the irated rduct r the rate f iracy will increase? We ask this questin in tw different framewrks, namely, in the envirnment f cmmercial iracy and the end-users iracy. Under cmmercial iracy, there are ne riginal rduct develer, a cmmercial irate and a gru f hetergeneus cnsumers; and under end-users iracy there are ne riginal rduct develer and a gru f hetergeneus cnsumers wh are als the irates. 1 The issue f iracy r cyright vilatins and intellectual rerty rights (IPR) rtectin is resently receiving a great deal f attentin in varius ecnmic analyses. Cyright vilatins take lace when there is illegal cying r cunterfeiting f the riginal rduct. These rducts can be digital rducts (like sftware, music CDs, mvie DVDs, vide games etc.) r nn-digital rducts i.e. regular items (like clth, shes, bks, bags, medicines etc.). In recent years, there is a renewed interest t study the imlicatins f iracy, and mstly thse f digital gds iracy because f the raid advancement f digital cying technlgy. Cnventinal cying r cunterfeiting f nn-digital rducts (e.g. the fake brands f riginal gds), was always there in several markets and wuld cntinue t be there in future as well. But the grwth f digital iracy is nw sing an additinal threat. Since digital iracy is a relatively new henmenn cmared t the cnventinal cunterfeiting, a lt f recent studies have fcused their attentin n digital iracy. T study the imlicatins f digital iracy, mst f these studies cnsidered a scenari where the irates are mainly the end-users (see Cnner and 1 S far studies n iracy r illegal cying are bradly divided in tw categries in the literature, cmmercial iracy and end-users iracy. Under cmmercial iracy, a irate sells the irated rduct fr rfit, whereas under end-users iracy, individual user irates the rduct fr his/her wn use. Glbally cunterfeiting activities have risen t 5-7% f wrld trade, r abut $00 billin t $300 billin in lst revenue, accrding t sme estimates fr the Eurean Unin sme years back (see Time Magazine 001). We believe that the figure has increased in recent years due t the significant increase in digital iracy.
Rumelt (1991), Takeyama (1994), Shy and Thisse (1999), Chen and Png (003), Bae and Chi (006), Belleflame and Picard (007) amng many thers). 3 Excet few studies (see Slive and Bernhardt (1998), Banerjee (003), Pddar (005), Kiema (008)) the issue f cmmercial iracy has nt been addressed adequately s far in the literature. Even if thse few studies addressed cmmercial iracy, the exlicit influence f exgenus IPR rtectin n iracy is never incrrated in the mdels. Recently, a study by Lu and Pddar (01) deals with this issue in a mdel where there is ne riginal rduct develer (the incumbent) and a cmmercial irate (the tential entrant). The riginal rduct develer makes cstly investment t deter the cmmercial irate in a given regime f IPR rtectin anticiating the entry f the irate. The IPR rtectin can be weak r strng and is exgenus t the mdel. Its imact n the existence (r nnexistence) f iracy and its relatinshi t the riginal rducer s timal deterrence effrt t limit iracy are discussed in detail in that framewrk. 4 Nw it is generally bserved that the irated rduct may als vary widely in terms f quality r reliability as the quality (and hence the rice as well) deends largely n the hetergeneity f the cnsumer demand and their willingness t ay fr it. Our main fcus f this aer is t first study whether a mre reliable irated rduct increases r decreases the rate f iracy (i.e. the relative demand fr the irated gd) in the market. Cnventinal wisdm wuld suggest that mre reliable irated rducts wuld mean higher relative demand f the irated gd r iracy rate when cnsumers are hetergeneus in their willingness t ay. Hwever, we find that the actual relatinshi between the rate f iracy and the reliability f the irated rduct is far mre cmlicated and it deends n the nature f the irate as well as n the nature f the rduct market cmetitin if the irate is cmmercial and cmetes with the riginal firm. Namely, under cmmercial iracy when the riginal firm and the irate cmete in quantities in the rduct market, the cnventinal wisdm hlds i.e. the mre reliable the irated rduct, the higher is the rate f iracy, thus the relatinshi is mntnic. Hwever, the same wisdm des nt hld when they cmete in rices. There we find 3 Fr a gd survey n infrmatin (digital) gds end-user iracy, see Peitz and Waelbreck (006). 4 It is fairly well dcumented that different cuntries have different levels f IPR rtectins. Usually develed natins have strnger IPR laws (and enfrcements) than mst develing natins. 3
that the relatinshi is nn-mntnic. When the irated gd is f relatively lwer quality, iracy rate increases with the quality f the irated gd, but it decreases with quality when the irated gd is f relatively higher quality. Mrever, in the intermediate range f quality f the irated gd, the relatinshi between the rate f iracy and the quality f the irated gd als deends n the effectiveness f the IPR rtectins. We then extend ur analysis t the case f end-user iracy as it is als quite revalent in varius markets, articularly in the markets fr digital rducts. Here instead f assuming any cmmercial irate, we assume there are numerus irates wh are basically the end-user cnsumers and the market structure is mnly with the riginal rducer as the nly firm. End-users irate the rduct fr their wn benefit nly and are nt invlved in any rfit making cmmercial activity. The IPR rtectin and the deterrence effrt f the riginal rducer nw target the end-users. There we find the relatinshi between the rate f iracy and the reliability f the irated rduct is again nn-mntnic and it als deends n the effectiveness f the IPR rtectins. 5 Finally, we make an verall cmarisn f different scenaris f iracy we cnsidered in the analysis. We find that a irate is mst likely t survive under cmmercial iracy and when it cmetes with the riginal firm in quantities and least likely t survive under end-user iracy. In terms f timal deterrence effrt f the cyright hlder we find that t deter iracy, the riginal rducer has t give maximum effrt under quantity cmetitin as sed t ther tw situatins, while when the irate is accmmdated, the riginal rducer gives least effrt fr deterrence under quantity cmetitin and the maximum effrt is given under end-user iracy. Frm ur analysis, we cnclude that it is the nature and the degree f cmetitin between the riginal rducer (i.e. the cyright hlder) and the irate(s) lay a majr rle fr all the utcmes in different scenaris. We used the basic framewrk f Lu and Pddar (01) t d the analysis. 5 An alternative scenari which is als cnsistent with end-user iracy wuld be when there is a cmetitive fringe f cmmercial irates (i.e. a large number f identical cmmercial irates instead f just ne) but each irate makes zer rfit due t erfect cmetitin amng them. This case is nn-strategic. Althugh the wrking fr this case wuld be little different frm the end-user iracy case, hwever, it can be easily verified that the final results with regard t rate f iracy and the quality f the irated gd largely remain unchanged (wrking is available un request). 4
The rest f the aer is rganized as fllws. In the next sectin, we set u the mdel f cmmercial iracy. In sectin 3, we d ur main analysis f cmmercial iracy under bth quantity and rice cmetitin. In sectin 4, we d ur analysis f end-user iracy. Sectin 5 makes verall cmarisn f utcmes acrss different iracy scenaris. Sectin 6 cncludes.. The Mdel f Cmmercial Piracy.1 The Original Firm and the Pirate Cnsider an riginal firm and a cmmercial irate. The irate has the knw-hw r the technlgy t cy/cunterfeit the riginal rduct. We assume the irate rduces cies, which are f lwer quality than the riginal. The rduct quality f the irated gd (cmared t riginal) is catured by the arameter q, q 0,1. In the case f digital rduct, althugh the irated cies are almst like riginal, they d nt cme with any guarantee r surting services, thus making them inferir cmared t the riginal. We cnsider a tw-erid mdel, where in the first erid t 1, the riginal rduct develer undertakes cstly investment in rder t deter iracy. It adts the fllwing entry deterring strategy. It tries t deter the irate by increasing the cst f cying, in articular, raising the marginal cst f rducing a irated cy. The tential irate aears in the market f the riginal rduct in the secnd time erid t. We assume the higher the entry deterring investment made by the riginal rduct develer in the first erid (the higher the deterrence level), the higher wuld be the marginal cst f cying by the irate. The irate if survives, cmetes with the riginal develer in rices r quantities by ssibly rducing a lwer quality. We assume at t 1, the cst f investment f the riginal rduct develer t chse the level f deterrence, x, is given by c x x. Thus, if the rfit f the rduct develer at t is dented by then the net rfit f the develer at the end f the game is c x x. When the level f deterrence is x, the marginal cst f rductin fr the irate will be c x, where c is a arameter c 0 5
exgenusly given. We wuld like t interret c in the fllwing way: it is the degree r the strength f IPR rtectin in ur mdel. It essentially catures the strength f legal rtectin and enfrcement t st iracy and it is beynd the cntrl f the riginal firm (i.e. the cyright hlder). 6 It is generally understd that the gvernment r the regulatry authrity can influence c. 7 In ur mdel, we interret c as the ublic effrt frm the gvernment and x as the rivate effrt frm the rduct develer t st/limit iracy. In this study, we first fcus n what wuld be the best entry-deterring strategy x (hence, the timal entry deterring rivate investment in resnse t tential iracy) fr the riginal rduct develer given an enfrcement envirnment f IPR rtectin (i.e. given c). Secndly, we analyze the main fcus f ur study, namely, the relatinshi between the rate f iracy and the quality/reliability f the irated rduct and hw it deends n the nature f rduct market cmetitin which can be in rices r in quantities.. Cnsumers Preferences Cnsider a cntinuum f cnsumers indexed by X 0,. X measures the taste r the cnsumer s willingness t ay fr the riginal rduct. A high value f X means higher valuatin fr the rduct and lw value f X means lwer valuatin fr the rduct. Therefre, ne cnsumer differs frm anther n the basis f his/her valuatin r the taste fr the articular rduct. Valuatins are unifrmly with density 1 6 It needs t be nted here that withut rer enfrcements, legal rtectin may nt be effective. 7 Accrding t a recent study by Andres (006) (als see Park and Ginarte (1997)), the strength f IPR rtectin f a cuntry mainly cnsists f tw categries: membershi in the internatinal cyright treaties and enfrcement rvisins. We assumed an additive frm between c and the level f deterrence x that is chsen by the riginal firm. The reasn is as fllws. We view irate s cying cst has tw cmnents. One is due t riginal rducer s rivate effrt t deter iracy, which may include technlgical adtin t rtect cying; and/r it culd be rivate mnitring, identifying and suing the irate and all f these effrts can be reflected in x. The ther cmnent is due t the IPR regime i.e. the strength f IPR legislatins and enfrcements which is reflected in c. Bth the riginal firm s rivate effrt (investment) and the legal rtectin and enfrcement f cyright legislatins cntribute t the deterrence f iracy. 6
distributed ver the interval 0,. 8 Each cnsumer urchases at mst ne unit f the gd. A cnsumer s utility functin is given as: where and X if buys riginal rduct, U qx if buys irated rduct, 0 if buys nne, are the rices f the riginal and irated rducts resectively. 10 9 3. Analysis and Main Results: Cmmercial Piracy We lk fr subgame erfect equilibrium f the tw-erid game and slve the game using the usual methd f backward inductin. We start by deriving demands f the rduct develer and the irate. 3.1 Deriving Demands f the Prduct Develer and the Pirate The demand fr the riginal rduct and fr the irated rduct, D and derived frm the distributin f buyers as fllws. D, can be Recall that cnsumers are hetergeneus with resect t their values twards the rduct. Thus, the marginal cnsumer, X wh is indifferent between buying the riginal rduct and the irated versin, is given by X O qx, r X P O 1 q P. The marginal cnsumer, Y wh is indifferent between buying the irated rduct and nt buying any rduct, is given by P qy P 0; Y Thus, the demand fr riginal q 8 S the number f cnsumers is nrmalized t ne. 9 Nte that q 0 will eliminate the irated rduct, while q 1 will make the tw rducts identical. In ur mdel q 1 is never ssible as we have assumed that the irated gd is f lwer quality. Als technically, q 0,1 is needed s that demands, rices and rfits are nt indeterminate. 10 The utility reresentatin is brrwed frm the standard mdel f vertical rduct differentiatin in the literature (see Shaked and Suttn (198), Tirle (1988)). 7
1 rduct is D dx 1q 1q X and the demand fr irated X 1 D dx q q q. rduct is 1 Y Nte that we have imlicitly assumed that q when we derive the demand functins as abve. When this assumtin des nt hld true, the demand fr irated rduct becmes zer while the demand fr riginal rducer is D we write the demand functins as the fllwing: and D D. Thus, 1q 1 q if q, (1) therwise q q 1 q if q 0 therwise. () In the secnd erid, the rduct market cmetitin can be in rices r in quantities. We will analyze bth cases in turn. 3. Quantity Cmetitin 11 Using backward inductin, ne can first btain equilibrium quantities in the quantity cmetitin stage and then wrk ut the chice f timal level f deterrence by the riginal firm in the first erid. Nte that the riginal rducer can decide t accmmdate r deter entry f the irate cmletely. 3..1 The Entry Accmmdatin Equilibrium and Entry Deterrence Equilibrium Assume bth riginal develer and the irate have sitive demand. Then frm (1) and (), ne can btain the fllwing inverse demand functins: 11 Cunterfeit htel r restaurant chains in turist laces culd be an examle f this kind f iracy where the cmetitin between the riginal and the cunterfeits are mainly ver the number f turists/visitrs, resembling a quantity cmetitin. 8
1D qd, (3) q 1D D. (4) In the quantity cmetitin stage, the riginal develer chses maximize, 1 D D D qd D, while the irate chses D t maximize, 1 D D q D D c x D maximizatin, we can btain bth firms reactin functins: D The equilibrium quantities are then Nte that nly when c x q that such that c x q D D. Frm the first-rder cnditins fr rfit 1 1 qd, 1 c x 1 D. q 1 D c x q 4 q, 1 D q c x q 4 q, D 0. S if the riginal rducer chses x such, i.e., x q c, then D 0. It is als clear that ifc q, there is n need t deter iracy. When cx q, ne can then btain the fllwing equilibrium rices and rfits fr bth firms: 1 cx q, 4 q q cx q, 4 q 1 cx q 4 q 1 q 4 q q c x.,. t 9
Nte that 4 when xq c, which is the same as when the firm chses a deterrence level higher than q c. 1 Thus, when the deterrence cst is taken int accunt, xq c is strictly dminated by xq c. In stage 1, the riginal develer chses the deterrence level x t maximize x 1 x cx q 4 q 4 q c q 4 q. T find the timal deterrence level x, d cx q d we first find x and 1. Nte that when dx dx 4 q d evaluated at x=0, 0. We then distinguish tw cases deending dx n whether d dx is sitive r negative. d d 4, 0. Since we als have 0, the rfit functin is dx dx When q strictly increasing in x. The riginal rducer will chse a deterrence level x as big as ssible subject t the cnstraint cx q. Thus, the timal deterrence level is x q c. d 4q, 0. The rfit functin is cncave in x. When evaluated dx When q d at x c, q 4 q q 4q c, which is sitive when c and dx 4 q 4 q q4q q4q negative when c. Therefre, when c, the timal 4 q 4 q deterrence level is x q c q 4q, while when c, the timal deterrence 4 q 1 When xq c, the riginal rducer, as a mnlist, will chse and btain rfits f 4. 10
d level is determined by dx x q c q. 4 4 q cx q x 0 and therefre, We thus have the fllwing rsitin characterizing the entry accmmdatin equilibrium and entry deterrence equilibrium. Define q, q 4q. 4 q Prsitin 1 (i) When q 4 and c q /, the riginal rducer s timal level f deterrence is n demand. x q c. In this case, it deters the irate and the irate has (ii) When 4q and c q /, (a) when c q,, the riginal rducer s timal level f deterrence is x c q 4 q. In this case, it accmmdates the irate and shares the market with the irate. (b) When deterrence is q, c q, the riginal rducer s timal level f x q c. In this case, it deters the irate and the irate has n demand. (iii) When c q /, there is n need t deter the irate strategically. Piracy is blckaded anyway due t exgenus high level f IPR rtectin. The cnditin 4q in Prsitin 1(i) can be interreted as when the cnsumers tastes are nt sufficiently diverse, i.e., fr any given q, is nt sufficiently big ( 4 q ). In such a case, the riginal rducer necessarily deters the irate as lng as the degree f intellectual rerty right is nt sufficiently high (i.e. c q /). 11
On the cntrary, when the cnsumer taste is sufficiently diverse (i.e. 4 q ) the riginal rducer deters the irate nly if the degree f intellectual rerty right is relatively high (i.e. q, c q ). On the ther hand, deterrence is t cstly if the degree f intellectual rerty right is lw (i.e. c q, there the riginal rducer accmmdates. Nte that the numeratr f q, sitive, i.e. q q 4 q ), has t be 4q 0, fr entry accmmdatin t arise in equilibrium. Since is maximized n the interval [0,1] at q=1 and the maximum is 3, a necessary cnditin fr entry accmmdatin t be timal is 3. One can als nte that as, the cnditin 4q is satisfied fr all 0,1 lng as 3 q. 3.. Rate f Piracy and Quality f the Pirated Prduct We define the rati f D D D t measure the rate f iracy. Thus the higher the rati, the higher will be the rate f iracy. When 4q and c q,, i.e. when the riginal firm accmmdates the irate, it is straightfrward t get 4 D q q c. In all the ther cases, entry is either D D 4q q 3q q c deterred r blckaded; thus, the rate f iracy is zer. When 4q and c q,, simle cmutatin yields D 4q c 4 4q 1q qc q 4q 81q3q. qd D 4q q 3q q c Since 4q and thus 4 8 1 3 8 1 3 81 q q q q q q q q q, the last term in D the numeratr is sitive. Therefre, 0. This result is summarized in the qdd fllwing lemma. (5) 1
Lemma 1 When firms cmete in quantities, the relatinshi between the rate f iracy and the quality f the irated rduct is mntnic i.e. the mre reliable the irated rduct, the higher is the rate f iracy. The intuitin fr abve result is as fllws. When a cnsumer chses between a irated cy and riginal cy, she cares abut bth the reliability/quality and the rice difference. Since the rice difference effect when firms cmete in quantities is small cmared t the reliability effect, and mre cnsumers chse t buy a rduct as the irated rduct becmes mre reliable, a mntnic relatinshi between the rate f iracy and the quality f the irated rduct btains. 3.3 Price Cmetitin As in sectin 3., we first btain equilibrium rices in the rice cmetitin stage and then wrk ut the chice f timal level f deterrence by the riginal firm in the first erid. Since this rblem has been analyzed in detail by Lu and Pddar (01), here we just summarize the main findings frm that aer. 3.3.1 The Entry Accmmdatin Equilibrium and Entry Deterrence Equilibrium The entry accmmdatin equilibrium and entry deterrence equilibrium in the whle arameter sace f cq, and is characterized by Prsitin 1 in Lu and Pddar (011) which we relicate belw. Define q, q88q q q 1q 161qq 6q8q 1q q 4q 1q. 13
Prsitin q 4q 1q and c q /, the riginal rducer s timal (i) When level f deterrence is x q c q irate and the irate has n demand. q 4q 1q and c q /, (ii) When (a) When c q,. In this case, it deters the, the riginal rducer s timal level f deterrence is x c 1 q 4 q 1 q. In this case, it accmmdates the irate and shares the market with the irate. (b) When q, c q /, the riginal rducer s timal level f deterrence is x q c q. In this case, it deters the irate and the irate has n demand. (iii) When c q /, there is n need t deter the irate strategically. Piracy is blckaded anyway due t exgenus high level f IPR rtectin. Similar t the case f quantity cmetitin, in Prsitin (i), the cnditin q 4q 1q can be interreted as when the cnsumers tastes are nt sufficiently diverse, i.e., fr any given q, is nt sufficiently big ( q4 q1 q ). In such a case, the riginal rducer necessarily deters the irate as lng as the degree f intellectual rerty right is nt sufficiently high (i.e. c q /). On the cntrary, when the cnsumer taste is sufficiently diverse (i.e. q4 q1 q ), the riginal rducer deters the irate nly if the degree f intellectual rerty right is relatively high (i.e. q, c q / ). On the ther hand, deterrence is t cstly if the degree f intellectual rerty right is lw (i.e. c q, there the riginal rducer accmmdates. Nte that q4 q1 q ), is minimized at q=0.465 and the minimum is.74 and thus, a necessary cnditin fr entry accmmdatin t be timal is.74. 14
Furthermre, if the degree f intellectual rerty right is sufficiently high ( c q /), deterrence is blckaded. 3.3. Rate f Piracy and Quality f the Pirated Prduct As befre, we define the rati f D D D When c q, and the irate, it is straightfrward t get t measure the rate f iracy. q 4q 1q, i.e. when the riginal firm accmmdates D q 1q 4q q 4q c D D 3q 1q 4q 1q 4q c. In all the ther cases, entry is either deterred r blckaded; thus, the rate f iracy is zer. When c q, and q 4q 1q, simle cmutatin yields D 4q c 4q 48qq 84q c4 410q3q qd D 3q1q 4q 1q4q c. (6) As illustrated by numerical examles in Lu and Pddar (011) (see aendix 1), the attern f the change f the rate f iracy as the quality f irated rducts increases is as fllws: When q 0.465 (i.e. when q is small), the rate f iracy is increasing in q ; when q is sufficiently large, it is decreasing in q ; when q is intermediate, it is decreasing in q when c is small and increasing in q when c is large. Thus, we have the fllwing. Lemma (same as Prsitin 4 in Lu and Pddar (01)) When firms cmete in rices, the relatinshi between the rate f iracy and the quality f the irated rduct is nn-mntnic. The intuitin fr abve result is as fllws. When a cnsumer chses between a irated cy and riginal cy, she cares abut bth the reliability/quality and the rice difference. When the reliability f the irated rduct is far frm the riginal rduct, rice cmetitin is less intense and the rice difference is large. Hwever, as the irated rduct becmes mre reliable, the rice cmetitin between the irate and the riginal rducer becmes mre intense; as a result, the rice difference becmes smaller. This eventually leads t a nn-mntnic relatinshi. When q is small, the rice difference 15
effect dminates (as the rice f the irated rduct is lw) and a larger fractin f cnsumers chse t buy irated rduct as q increases; whereas when q is sufficiently large, the reliability/quality effect dminates (as bth the irated gd and the riginal rduct are clse in quality) and thus a smaller factin f cnsumers chse t buy irated rduct as q increases further. When q is intermediate, which effect dminates deends n the degree f IPR rtectin since the rice difference effect is larger when c is big than when c is small. In ther wrds, the rice cmetitin is sfter (i.e. rices are far aart) when c is big than when c is small. Mrever, we can als shw the timal level f deterrence als increases in c, which makes the rice cmetitin even sfter fr a big c. As a result, the rate f iracy increases in q when c is big while decreases in q when c is small. 3.4 Cmarisn between Price and Quantity Cmetitin It is useful t int ut hw the cmetitin in rices r in quantities in the rduct market affects the strategic resnses f the riginal rduct develer and the irate. T d that we first exlre hw the accmmdatin/deterrence ssibilities f the irate are affected due t the nature f market cmetitin. Cmaring the cnditin in Prsitin 1(iia) and the ne in Prsitin (iia), we have the fllwing finding. Prsitin 3 Entry accmmdatin f the irate is mre likely t be bserved under quantity cmetitin than under rice cmetitin. Prf: Observing the fact that 4q q4q1 q and q, q,. The abve result reflects the fact that quantity cmetitin is less stiff than rice cmetitin. When firms cmete in quantities, the riginal develer has less incentive t cmletely deter the irate. As fr the relatinshi between the reliability f irated rducts and the rate f iracy, cmbining Lemmas 1 and, we have ur main result. 16
Prsitin 4 In an envirnment f cmmercial iracy, when the riginal rducer and the irate cmete in quantities, the relatinshi between the rate f iracy and the quality f the irated rduct is mntnic (i.e. the mre reliable the irated rduct, the higher is the rate f iracy); whereas when they cmete in rices, the relatinshi is nn-mntnic. Prf: Fllws directly frm Lemma 1 and Lemma. In a brader sense, the difference in the results n the rate f iracy is als due t the very nature f rice and quantity cmetitin. Fr any given level f quality q f the irated rduct, quantity cmetitin is always less stiff (i.e. sfter) than rice cmetitin. Thus a cmeting firm is less sensitive and hence less reactive in its strategic resnse due t change in q in the case f quantity cmetitin cmared t rice cmetitin. Mrever, the degree f sensitivity and reactin under rice cmetitin gets mre rnunced cmared t quantity cmetitin as q becmes significantly high (i.e. the rducts becme clse). This is reflected in the fllwing way. When irated gd is significantly lw in quality, rate f iracy is increasing in quality fr bth quantity and rice cmetitin i.e. the qualitative behavir in the change f the iracy rate acrss the tw tyes f cmetitin matches. Hwever, when the irated gd is significantly high in quality, the intensity f cmetitin under rice gets much higher than under quantity; hence we get a divergence in the behavir n the iracy rate. In ther wrds, the difference in the intensity r the degree f cmetitin ver rice and quantity des nt seem t matter much when the irated gd is relatively lw in quality, but it matters when the irated gd is relatively high in quality. 4. End-User Piracy Nw we extend ur analysis t the case f end-user iracy. End-user iracy is quite revalent, in articular, in the market fr digital gds as it is relatively easy t cy a digital rduct. 13 Here, we assume there is n cmmercial irate in the ecnmy, and the cnsumers (i.e. all tential rduct users) are the tential irates. As befre, there is ne riginal rduct develer and cnsumers valuatins are unifrmly distributed ver 13 Mst cmmn digital rducts are cmuter sftware, music, mvies and games. 17
the interval 0, with density 1. Cnsumers have the chice t buy the riginal rduct frm the rduct develer r they can irate themselves. The activity f the riginal rduct firm remains exactly the same as befre, excet that nw it targets the end user irates t st r limit iracy as sed t cmmercial irate that we have analyzed befre. Hwever, unlike befre, here the riginal firm des nt face any direct cmetitin frm anybdy in the market; instead, it stands t lse its tential market because f end user irates. Under this circumstance t limit/st iracy, it invests t raise the cst f iracy t the end users. 14 Thus a cnsumer s utility functin is given as: X if buys riginal rduct U qx c x if irates riginal rduct 0 therwise, where x is the level f deterrence fr iracy frm the riginal rducer and c 0 is the exgenus cst arameter as befre measuring the degree f IPR rtectin and this time it is targeted t st/limit end-user iracy. 4.1 Deriving Demand f the Original and Pirated Prduct The demand fr the riginal rduct and fr the irated rduct, derived frm the distributin f buyers as fllws. D and D, can be The marginal cnsumer, Xˆ, wh is indifferent between buying the riginal rduct and irating is given by Xˆ c x. The marginal cnsumer,yˆ, wh is indifferent 1 q c x between irating the rduct and nt buying any rduct is given by Yˆ. Thus, q the demand fr the riginal firm is fr the irated rduct is D 1 Xˆ Yˆ D 1 Xˆ dx 1q cx 1 q and the demand q cx dx. Here we have imlicitly assumed q 1 q 14 Here, we d nt need the tw erid time structure as befre, everything can be frmulated within a single erid withut lss f generality. There is n strategic game here; it s a mnly analysis. 18
q c x s that the demand fr the irate rduct is nnnegative. When instead q c x, the develer s demand is D. 4. Chice f Otimal Price and Level f Deterrence by the Prduct Develer When the develer chses and x such that q c x, the firm s rfit maximizatin rblem is q cx q 1 1 max D c x x 0, x0 1, st.. q cx which is labeled Prblem I. When the develer chses and x such that q c x, the firm s rfit maximizatin rblem is 1 max D c x x 0, x0, st.. q cx which is labeled Prblem II. 4..1 The Otimum We summarize the timum in the fllwing rsitin after slving Prblems I and II (see aendix fr all the details). Define q, q 1q 1. q 19
Prsitin 5 (i) When c q, (this imlicitly requires q accmmdates iracy, the timal rice is timal level f deterrence is (ii) When q, x 1 q c 1q 1. 1 q 1), the riginal develer q 1q 1q c 1 1 and the q c, the riginal develer deters iracy, the timal rice is 1 qc q q c and the timal level f deterrence is x. q q (iii) When c, the iracy is blckaded and the riginal develer s timal rice is the mnly rice. 4.3 Rate f Piracy and Quality f the Pirated Prduct As befre, we define the rati f D D D When q1q 1 and c q, it is straightfrward t get t measure the rate f iracy., i.e. when the riginal firm accmmdates the irate, D q 1q q c1. In all the ther cases, D D q 1q 1q c 1 entry is either deterred r blckaded; thus, the rate f iracy is zer. When q1q 1 and c q, Clearly, when, simle cmutatin yields c 1 c 1 q 1 1 1 D qd D q q qc. (7) 1 q, the sign f the artial derivative is sitive; when sitive if c is relatively large, i.e. q 1 c q, small, i.e. 0 1 1 q, it is while negative if c is relatively c q. Thus, we have a similar cnclusin as in Lemma. 0
Prsitin 6 The relatinshi between the rate f iracy and the quality f the irated rduct under end user iracy is nn-mntnic. T illustrate this result, we resent sme numerical examles. Fix 5. Then the cnditin q 1q 1 is satisfied when 0.764 q 0.736. q, q=0.5168 and the maximum is 0.1676. Thus, a necessary cnditin fr iracy accmmdatin t be timal is c 0.1676. When c=0.05, then d D 11 10100q dq D D 11101q100q negative when 0.505 q 0.736. When c=0.1, then is maximized at, which is sitive when 0.764 q 0.505 and d D 351100q dq D D q q 6 51 50 which is sitive when 0.764 q 0.51 and negative when 0.51 q 0.736. When c=0.15, then d D 13 10300q dq D D 13103q100q 0.764 q 0.515 and negative when 0.515 q 0.736., which is sitive when The intuitin fr this result is similar t the ne fr Lemma., 4.4 Cmarisn between End-user iracy and Cmmercial Piracy under Price Cmetitin Cmaring the cnditin in Prsitin (iia) and the ne in Prsitin 5(i), we have the fllwing result. Lemma 3 Entry accmmdatin f irates is less likely t be bserved under end-user iracy than under cmmercial iracy under rice cmetitin. Prf: Fllws frm the fact that q4q1q q1 q and q, q,. 1
Under accmmdatin, the riginal firm faces mre severe cmetitin frm the end-user irates cmared t the cmmercial irate under rice cmetitin. Nte that the cst f iracy t the end-user irates is ( c x) ; whereas the rice f the cmmercial irate satisfies P c x and mre ften it is mre than ( c x). Thus keeing ther things cnstant, the riginal firm will have a greater incentive t avid the situatin f accmmdatin with end-user irates cmared t the cmmercial irate under rice cmetitin. 5. Cmarisn Acrss all Three Scenaris 5.1 Accmmdatin/Deterrence Pssibilities f the Pirate Nw we cnsider all the three alternative scenaris (i.e. (i) cmmercial iracy under quantity cmetitin, (ii) cmmercial iracy under rice cmetitin, (iii) end-user iracy under mnly) we discussed s far t make an verall cmarisn f accmmdatin and deterrence ssibilities f the irate(s). Given q, q, q, and 4 q q4 q1 q q1 q, we have a clear rdering n the accmmdatin/deterrence ssibilities f the irate(s) which we summarize belw in the fllwing rsitin. Prsitin 7 A irate is mst likely t survive under cmmercial iracy and when it cmetes with the riginal firm in quantities and least likely t survive under end-user iracy. This result is als a cnsequence f the fact that the riginal firm faces the sftest cmetitin frm the irate under quantity cmetitin and the tughest cmetitin frm the end-user irates. 5. Piracy Deterrence Effrt by the Cyright hlder acrss three Scenaris The cmarisn f the timal deterrence effrts x f the riginal rducer t st/limit iracy acrss the three scenaris can be summarized as fllws. Since x 0 in the blckaded entry case, we exclude it in the fllwing discussin.
Prsitin 8 Under deterrence: x ( quantity ) x ( rice) x ( end user ) Under accmmdatin: x ( end user ) x ( rice ) x ( quantity ) Prf: Fllws directly frm cmaring the relevant exressins we derived befre. T deter under quantity cmetitin, the riginal firm has t incur higher effrt level as the irate is mst easily accmmdated in this case cmared t ther tw. On the ther hand, fr accmmdatin, since the cmetitin is mst relaxed under quantity, deterrence effrt is the least fr the riginal firm. T relax the cmetitin under the tughest cmetitin which haens under end-user iracy, the riginal rducer has t incur maximum level f effrt. The intensity f the rice cmetitin is between these tw cases, s is the level f timal effrt f deterrence f the riginal firm. 6. Cnclusin In this aer, we study whether reliable irated rducts lead t higher rate f iracy. We address this questin in a framewrk where the riginal rduct develer i.e. the cyright hlder makes cstly investment t deter the irate(s) in a given regime f IPR rtectin. The irate can be cmmercial r end-users. The IPR rtectin can be weak r strng and is exgenus t the mdel. The irated rduct may vary widely in terms f quality r reliability. In this set-u, we shw that the relatinshi between the rate f iracy and the reliability f the irated rduct deends very much n the nature f the irate as well as n the nature f the market cmetitin if the irate is cmmercial and cmetes with the riginal rducer. Under cmmercial iracy, when the riginal firm and the irate cmete in quantities, the cnventinal wisdm hlds i.e. the mre reliable the irated rduct, the higher is the rate f iracy. Hwever, the relatinshi is nn-mntnic, hence the wisdm des nt hld when they cmete in rices r the irates are the end-users. We als find that a irate is mst likely t survive under cmmercial iracy and when it cmetes with the riginal firm in quantities and least likely t survive under end-user iracy. This result is a cnsequence f the fact that the riginal firm faces the sftest cmetitin frm the irate under quantity cmetitin and the tughest 3
cmetitin frm the end-user irates. The timal level f deterrence f the riginal firm als reflects that fact. References Andres, A. R. (006), The Relatinshi between Cyright Sftware Prtectin and Piracy: Evidence frm Eure, Eure Jurnal f Law and Ecnmics, Vl. 1, 9-51. Bae, S. H. and Chi, J. P. (006), A Mdel f Piracy, Infrmatin Ecnmics and Plicy, Vl. 18, 303-30. Banerjee, D. S. (003), Sftware Piracy: A Strategic Analysis and Plicy Instruments, Internatinal Jurnal f Industrial Organizatin, Vl 1, 97-17. Banerjee, D. S. (006), Lbbying and Cmmercial Sftware iracy, Eurean Jurnal f Plitical Ecnmy, Vl., 139-155. Belleflamme, P. and Picard, P.M. (007), Piracy and Cmetitin, Jurnal f Ecnmics and Management Strategy, Vl. 16, 351-383. Chen, Y. and Png, I. (003), Infrmatin Gds Pricing and Cyright Enfrcement: Welfare Analysis, Infrmatin Systems Research, Vl 14, N. 1, 107-13. Cnner, K.R. and Rumelt, R.P. (1991), Sftware iracy An Analysis f Prtectin Strategies, Management Science, Vl. 37,15 139. Kiema, I. (008), Cmmercial Piracy and Intellectual Prerty Plicy, Jurnal f Ecnmic Behavir and Organizatin, Vl. 68, 304-318. Lu, Y. and Pddar, S., (01) Accmmdatin r Deterrence in the Face f Cmmercial Piracy: the Imact f Intellectual Prerty Rights (IPR) Prtectin, Frthcming in Oxfrd Ecnmic Paers. Park, W. G. and Ginarte, J. C., (1997), Intellectual Prerty Rights and Ecnmic Grwth, Cntemrary Ecnmic Plicy, Vl. XV, July, 51-61. Peitz, M. and Waelbreck, P., (006) Piracy f Digital Prducts: A Critical Review f the Theretical Literature, Infrmatin Ecnmics and Plicy, Vl. 18, 449-476. Pddar, S. (005), Netwrk Externality and Cmmercial Sftware Piracy, Wrking aer N. 05-16, Natinal University f Singare. 4
Shaked, A. and Suttn, J., (198), Relaxing Price Cmetitin thrugh Prduct Differentiatin, Review f Ecnmic Studies, Vl. 49, 3-13. Shy, O., Thisse, J., (1999), A Strategic Arach t Sftware Prtectin, Jurnal f Ecnmics and Management Strategy, Vl. 8, 163 190. Slive, J., Bernhardt, D., 1998. Pirated fr Prfit, Canadian Jurnal f Ecnmics, Vl. 31, 886 899. Takeyama, L.N., (1994), The Welfare Imlicatins f Unauthrized Rerductin f Intellectual Prerty in the Presence f Netwrk Externalities, Jurnal f Industrial Ecnmics, Vl. 4, 155 166. Tirle, J. (1988) The Thery f Industrial Organizatin, Cambridge, MA, MIT Press. Internet Surce: Time Magazine (001), Chasing Shadws, June 11. htt://www.time.cm/time/magazine/article/0,9171,1900,00.html Aendix 1 Numerical examles: q q, 0.5 5 0.345 sign D D D q 0 when c 0.19 0 when 0.19 c 0.345 0.47 5 0.340 0 when c 0.01 0 when 0.01c 0.340 0.6 5 0.30 0 when c 0.30 0.9 10 0.089 0 when c 0.089 Nte: When q=0.9, q q q 4 1 7.169. 5
Aendix Prblem I Nw we slve Prblem I first. Define Lagrangian q cx q 1 1 1 L1, x, x qc x necessary cnditins fr the timum are the fllwing: 1q. The sufficient and L1, x, 1q c x q 0, (A1) L1, x, x 0, (A) x 1q 0, 0, q cx q c x. (A3) If 0, then we can slve fr and x frm (A1) and (A) after lugging 0 int these equatins and get 1 1 q q q c 1 1 and 1 q c x. We als 1q 1 need t check whether q c x is satisfied and we find that this cnditin is satisfied when q 1q 1 c. In this case, the develer s rfit is q where the suerscrit A indicates this is an accmmdatin case. A 1q c, 1q 1 If instead q c x, then we can slve fr and x frm (A1), (A) and q c x, 1 qc q c and get, and x. Nte that x 0 when q q q c. We als need t check whether 0 is satisfied and we find that this cnditin is satisfied when q 1q 1 c. In this case, the develer s rfit is q suerscrit D indicates this is a deterrence case. D c q c q, where the 6
Prblem II Next we turn t Prblem II. Define Lagrangian 1 L x x q c x,, fr the timum are the fllwing:. The sufficient and necessary cnditins L, x, q 0, (A4) L, x, x 0, 0, x 0, (A5) q cx q c x. (A6) If 0, then we can slve fr and x frm (A4) and (A5) after lugging 0 int these equatins and get and x 0. We als need t check whether q cx q is satisfied and we find that this cnditin is satisfied when c. This is clearly the blckade case since the cnditin q c x is satisfied when the riginal develer chses the mnly rice,, and zer deterrence level, x=0. In this case, the B develer s rfit is, where the suerscrit B indicates this is a blckade case. 4 If instead q c x, then we can slve fr and x frm (A4), (A5) and q c x, 1 qc q c and get, and x. We als need t check whether 0 is q q q satisfied and we find that this cnditin is satisfied when c. This is clearly the deterrence case and the develer s rfit is D c q c. q 7