On Software Piracy when Piracy is Costly

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1 Deartment of Economics Working aer No htt://nt.fas.nus.edu.sg/ecs/ub/w/w0309.df n Software iracy when iracy is Costly Sougata oddar August 003 Abstract: The ervasiveness of the illegal coying of software is a worldwide henomenon. However, the level of iracy across various markets as well as across various countries varies a great deal. In some markets (countries), we observe ramant iracy while in some other markets (countries) iracy is rare. In this aer, we develo a simle economic model to exlain both these features when there is one original firm/retailer and one irate in the market. We find out under what condition iracy will take lace. We show that the irate survives in the market, when cost of iracy is not too high, which in turn deends on the legal environment (e.g. the enforcement olicy against the irate) under which the irate oerates; and the irate roduces a coy that is moderately reliable and moderately differentiated from the original roduct available in the market. JEL classifications: D3, D43, L13, L86 Keywords: Software iracy, Raising rival s cost, roduct reliability, roduct differentiation, Cometition 003 Sougata oddar, Deartment of Economics, National University of Singaore, 1 Arts Link, AS Level 6, Singaore , Reublic of Singaore. Tel: (65) ; Fax: (65) ; I would like to thank the seminar articiants at the Deartment of Economics at NUS, and at the University of Tokyo; the conference articiants at Australian Economic Society Meeting (00), Adelaide, Indian Statistical Institute, Kolkata (003) and EARIE (003), Helsinki for the most helful comments and suggestions. This aer is a art of the research roject titled "Economics of Software iracy" (00). Financial suort from NUS in the form of research grant (R ) is gratefully acknowledged. Views exressed herein are those of the author and do not necessarily reflect the views of the Deartment of Economics, National University of Singaore.

2 1. Introduction The ervasiveness of the illegal coying of software is a worldwide henomenon. It is not only having a rofound effect on the users of the software, but also on the software industry as a whole. It is also having a tremendous effect on the develoment of digital intellectual roerties and technologies. However, the level of iracy across various markets varies a great deal. In some markets, we observe ramant iracy while in some other markets iracy is rare. 1 In this aer, we develo a simle economic model to exlain both these features when there is one original firm/retailer and one irate in the market. We find out under what condition iracy will take lace and when it can be stoed. The basic assumtion we use here is stoing iracy is a costly activity, but if such costly activity is undertaken, it raises the cost of iracy to the irate, which consequently limits/stos iracy. In this aer, we assume the original develoer of the software or the original retailer takes the costly effort to sto/limit iracy. It invests ariori in something that raises the cost of iracy. For examle, before the irate arrives, the original firm may set u an oeration in order to monitor the market so that when the irate comes, it can catch the irate and sto iracy. In other words, setting u an arrangement of monitoring by the original firm raises the cost of iracy to the irate. We cature this notion by assuming that the irate s marginal cost of roducing a coy increases with the monitoring effort of the original develoer. So higher the monitoring level, higher the marginal cost of roducing irated coies. Hence, overall iracy becomes costly with the degree of monitoring arrangement made by the original firm. Secondly, instead of monitoring or in addition to monitoring, the original firm can invest in R&D before, so that it can develo a technology (like utting a rotective device into the software), which increases the cost of coying its software. Now to develo such technology usually costly R&D must be undertaken before. So the idea is, the original firm can increase the cost of irate s activity by investing in something (in terms of setting u the monitoring arrangement and/or doing R&D) before the irate could start its oeration. Since this investment is costly, the question that naturally arises, whether it will be rofitable to the original firm to actually undertake such oeration. And if at all it 1 iracy rates defined as the ratio of the number of irated coies to total installed coies, vary from 5 ercent in US to 94 ercent in Vietnam in the year 001. (Source: IR reort for BSA 00) 1

3 undertakes such oeration, under what circumstances it will be effective. We show that the answers to these questions deend on the overall rofitability of the original firm as well as the irate. Analyzing the model, we are able to exlain, why sometime irates oerate in the market, and why the original firm cannot do anything about it. We also show when the original firm will actually be able to sto iracy successfully. In other words, our analysis works out the condition (i.e. arametric configuration) when there will be a irate in the market and when there will be no irate oerating. The effects of installing rotection device into software as well as monitoring iracy have been analyzed in Chen and ng (1999) and Banerjee (00) among others. Chen and ng (1999) studies how original develoers of the software should set rice and determine enforcement olicy (monitor) in order to sto iracy. They show while monitoring reduces overall usage of the software and hence reduce social welfare, aroriate ricing olicy increases overall usage of the software and society s welfare. So they suggest society should favour dealing with iracy through rice rather than monitoring. n the other hand, Banerjee (00) examines the government s as well as the original firm s role in restricting iracy and shows that welfare maximization results in not monitoring as the socially otimal outcome. He also shows in order to eliminate iracy, rice discrimination and limit ricing are two ossible ricing strategies available to the original firm. In contrast in this aer, we aroach the roblem from a new angle and exlore the ossibility of stoing iracy by the original firm by raising the (rival) irate s cost of roduction. Raising rivals cost of roduction in order to induce its rivals to exit the industry has been studied for the first time by Salo and Scheffman (1983). They focused their study in an industry consisting of a dominant firm and a cometitive fringe, where the low cost dominant firm can cause injury to the rivals by strategically raising the cost of the fringe firms. Interestingly, further studies of this feature (of raising rival s cost) had not been done much in other tye of industries or market structures. The only excetion is vertically related markets. In this aer, we introduce the feature in a simle duooly framework where one cometitor (the original firm) endogenously raises the rival s See Salinger (1988), rdover et al. (1990), Sibley & Wiseman (1998), and Banerjee & Lin (003) for studies on this feature.

4 (irate) cost by undertaking some costly investment in the form of R&D (or arranging to monitor the market) before. We believe aart from the iracy asect of this aer, studying the strategic otion of raising rival s cost in this fashion in a simle duooly model is also a contribution to the literature of strategic entry deterrence. n software iracy, there is also a literature (see Conner and Rumelt (1991), Takeyama (1994), Slive and Bernhardt (1998), Shy and Thisse (1999) among others) which comes u with a fairly general exlanation of the existence of the iracy henomenon. There the argument basically stands on the feature of network externality 3 that is observed in the software user market. They show that when the network effect is strong (i.e. in the resence of high network externality), the original firm will allow (limited) iracy as it turns out to be the more rofitable otion than rotection. In contrast, in this aer, we come out with an alternative exlanation of the existence of software iracy without relying on the feature of network externality at all. 4 In this model, the existence (or non-existence) of iracy comes out as an endogenous outcome of the strategic game between the irate and the original firm under certain arametric configuration. The lan of the aer is as follows. In the next section, we describe the model in detail. In section 3, the main analysis is done, and the main result is derived. Section 4 concludes with some remarks.. The Model.1 The Software Firm and the irate Consider an original software firm and a irate. The irate has the technology to coy the original software. We assume the irate roduces software coies, which may not be as reliable as the original roduct. The robability that a irated software works is q, 3 The idea of network externality stems from the work of Katz and Shairo (1985), (see also Rohlfs 1974, Gandal 1994, and Shy 1996). Generally, the idea is that the utility that a given user derives from some roducts deends uon the number of other users who consume the same roducts. In other words, consumers references are said to exhibit network externality if the utility of each consumer increases with the cumulative number of other consumers urchasing the same brand. When this is the case, each additional urchase raises the value to existing users as well as the exected value to future adoters. A classic examle of a roduct that exhibits such a characteristic is found in the telehone network. 4 If we incororate network externality in our model, it can be shown that the results we obtain here will qualitatively remain unchanged, only the comutations will be little more involving. 3

5 ( 0,1) q and this robability is common knowledge. Therefore q serves as a roxy for the quality of the irated software. Usually irated coies does not come with the suorting services, so one can think even if the irated software is exactly same as the original one (because of digital coing), but the lack of suorting service does not allow the user to get the full value of the irated software, hence quality of the irated software q can also be interreted like this. There are two time eriods, where in the first eriod ( t = 1), the original develoer makes costly arrangement to monitor the market for any future otential irate s activity and/or undertakes some costly R&D in order to make iracy costly technologically. We assume all these costly actions of the original develoer essentially raise the marginal cost of roducing a coy by the irate. The otential irate aears in the market of the original roduct in the second time eriod (t = ). We assume the higher the investment effort by the original software develoer in the first eriod, the higher the marginal cost of coying of the irate. The irate if survives, cometes with the original develoer in rice by ossibly roducing less reliable yet cheaer roducts.. Costs and rofits of the Cometing Firms We assume at t = 1, the cost of investment by the original develoer to increase the marginal cost of the irate by an amount of x is given by ( x) level of deterrence. x c =. Let us call x as the Thus, if the rofit of the software develoer at t = is denoted by π = D is the rice charged by the develoer and rofit of develoer at = 1 t becomes π π c ( x), 5 where D is the demand it faces, then the net x = = π n the other hand, if the irate is in the market at t = then it s rofit function becomes π = ( cx) D, where demand and c is ositive constant ( > 0) is the rice charged by the irate and D is the irate s c exogenously given. c = 0 means iracy is costless or in other words, original firm s investment effort in the earlier eriod has no 5 Assuming the marginal cost of roduction of the software is zero for the original firm. 4

6 effect in deterring iracy. n the other hand, higher c increases the cost of iracy, which says, original firm s investment to sto iracy becomes more effective. We can interret the exogenous cost coefficient c as follows. It can be interreted as strictness of the enforcement olicy against iracy of a articular country. For examle, we can generally find a relatively high c in the develoed countries where iracy is taken as a serious crime; hence it raises the cost of iracy significantly. n the other hand, in most of the develoing countries, we will robably find c to be relatively low, because the enforcement olicies against iracy may not be as strict as the develoed nations, hence cost of iracy would remain relatively small. Thus, c can be interreted as the legal environment where the market oerates..3 Consumer Demand There is a continuum of consumers indexed by X, X [0,1]. A consumer s willingness to ay for the software deends on how much he/she values it measured by X. A high value of X means higher valuation for the software and low value of X means lower valuation for the software. Therefore, one consumer differs from another on the basis of his valuation for the articular software. We assume valuations are uniformly distributed over the interval [ 0,1] and the size of the market is normalized to 1. A consumer s utility function is given as: X if buy original software U = q X 6 if buy irated software 0 if buy none There is no way a consumer can get defected irated software relaced since there is no warranty for the irated software. 7 Hence, the consumer enjoys the benefit of the irated software only with robability q. In the event that the irated software urchased does 6 q X = q (X ) + ( 1 q )( ). If the irated software is not working, consumer does not derive any benefit from the software and instead only incurs a loss equivalent to the amount aid for the irated software. 7 In most markets irates oerate using some makeshift arrangement, if the arted software turns out to be defected, there is no chance of getting software relaced. 5

7 not work at all, the loss to the consumer is the rice aid for it. The original software is fully guaranteed to work and true that are the rices of the original and irated software resectively. It must be >. ( ) can be viewed as the remium a consumer ays for buying guaranteed-to-work software. 3. Analysis 3.1 Deriving Demand of the Software Develoer and the irate D and D can be derived from the distribution of buyers as follows. Figure 1: DISTRIBUTIN F BUYERS None irate riginal 0 Yˆ Xˆ 1 Recall that consumers are heterogeneous with resect to their values towards the software. Thus, the marginal consumer, Xˆ, who is indifferent between buying the original software and the irated version is given by: Xˆ Xˆ = = q Xˆ 1 q The marginal consumer,ŷ, who is indifferent between buying the irated software and not buying any software is: qyˆ Yˆ = = 0 q Thus the demand for original software is: D = ( 1 Xˆ ) = 1 1 q 6

8 Demand for irated software is: D = Xˆ Yˆ q = q( 1 We look for subgame erfect equilibrium of the two eriod game and solve using the usual method of backward induction. Let s first focus on the second eriod of the game. 3. rice Cometition in the roduct Market In the second eriod, if the irate oerates, the two firms engage in a Bertrand rice cometition and choose the rofit maximizing rices of the resective roducts. The rofit function of the irate is: π = ( cx) D = ( cx) q q ( 1 The rofit function of the original firm is: π = D = 1 1 q The reaction functions of the original firm and the irate are as follows. 1 q q cx R ( ) = + ; R ( ) = + Notice that as the original firms uts more investment effort in the first eriod, higher will be x in the second eriod, which means higher will be the marginal cost of coying to the irate. Thus a increase in x (or an increase in the exogenous arameter c ) will shift the reaction function of the irate uward. This will result higher equilibrium rices for both the original firm and the irate. It is easy to see that the original firm will gain from this change in the roduct market cometition stage as it is now charging higher rice while its costs in that eriod remains the same. However, for the irate since the total cost of iracy goes u for this change, the net effect in the change in total rofit remains ambiguous. The ossibility that there could be no real change in rofit or even a decline in rofit of the irate cannot be ruled out. The Nash equilibrium in rices are given by ( + cx q( cx =, = 4 q 4 q Equilibrium demands are given by D = q + cx ( 4 ( 1 ; D 1 cx = 1 4 q q 1 ( ( ) q 7

9 The equilibrium rofits are given by ( (1 + cx) ( 4 ( 1 π = and π = ( q( 1 cx( ) ( 4 q( irate s Decision The irate will be in business as long as it can make ositive rofit, which consequently uts an uer bound restriction on x. Equating π = 0, we get ( 1 ( q xˆ =. c Thus for all x xˆ, the rofit of the irate becomes non-ositive hence, the irate will not oerate, and iracy will be deterred. 3.4 Choice of timal Level of Deterrence by the Software Develoer Now we move on to the first eriod of the game. In this eriod, original firm decides on its otimal choice on the level of x to deter iracy. 1 π = π c x = π x with resect to x. Thus it maximizes its net rofit ( ) Solving, we get the otimal level of deterrence Now given the fact that when deterrence is given by min ( x, xˆ ) x = 4c( 1 ( 4 ( 1 c x = xˆ, the irate stays out; the actual otimal level of. Note that if c = 0 i.e. when the original firm s investment effort has no effect in deterring iracy, the original firm will not choose any investment in the first lace, hence x = 0. x = 0 is also true when the irate roduces exactly the same roduct (i.e. q = 1) as the original firm. When the roduct is same, the original firm s costly investment has no deterring effect at all. So it will not invest in the first lace. 8

10 Aart from the above restriction, to ensure > 0 1 q when c < ( 4 ( x we must have ( 4 q )( 1 > c i.e. = ϕ (say). Hence, the effective range of c for which the above analysis is valid is given by the following. 8 Lemma 1 The otimal level of deterrence x is strictly ositive if and only if < c < ϕ( 0. A necessary condition for the existence of > 0 1 q roof: Note that ( 4 when q = 0 ; which is x is: 0 < < max ( = c ϕ = is decreasing in q. Hence the maximum value is reached. Recall that ( 0,1) q. 3.5 Towards the Main Result Now we would like to see under what condition the otimal level of deterrence x where xˆ is the actual level of deterrence of the irate. This imlies when ( 1 ( 4 q c = c ( q ), (say) xˆ, In other words, when c is more than or equal to c (, the iracy will be stoed. Thus we have the following result. Lemma The original firm will be able to successfully sto iracy if c roof: The maximum value that ( c can attain is (For details see aendix). Hence, for any c , the irate will be out of business and the iracy will be stoed; otherwise we will always observe iracy. 8 Note that this effective restriction is coming on the range of c because our concerned q is less than one. 9

11 Recall, reviously we found that x > 0 for 0 < c < Now we found that the irate may oerate in the market and comete with the original firm as long as c < Thus, the final effective range of c where the analysis of rice cometition between the original develoer and the irate is valid is 0 < c < Thus, we have our main result. Theorem When iracy is costly the original firm will be able to sto iracy when (i).6631 c < ϕ( 0 and (ii) when 0 < < c, the condition for stoing iracy is c c (. 3.6 Economic Interretation Case (i) is obvious in the sense that one, when c is too high (thus the marginal cost becomes too high) for the irate to oerate rofitably. Case (ii) is interesting, as it says whether iracy will be stoed or not deends on the two arameters of the model, the cost coefficient of iracy, that is c (which is in the lefthand side), and the reliability of the irate s roduct that is q, which is combined in the exression c ( ) q (in the right-hand side). Result in (ii) imlies, when cost of iracy is relatively low, then unless the roduct is very unreliable (i.e. q is close to 0) or almost similar to the original roduct (i.e. q is close to 1), there will be iracy (see the exression of c ( ). In this case, the irate can oerate rofitably because first of all, cost of iracy is low and secondly, irate s roduct is moderately reliable (i.e. q is away from zero) and at the same time moderately differentiated (i.e. q is away from one) from the original roduct. This gives enough demand to the irate to oerate rofitably and thus the irate survives. n the other hand, in case (ii) when c is relatively high and the irate s roduct is very unreliable (i.e. q is close to 0) or almost similar to the original roduct (i.e. q is close to 1), the irate cannot oerate rofitably. The reasons are as follows. First of all, in this case, iracy becomes costly, so to cover that cost the irate has to earn enough rofit. cx 10

12 Now when the roduct is very unreliable (i.e. q is close to 0), the demand of the irate becomes very low, as a result irate cannot survive in the market when iracy comes with significant cost. n the other extreme, when its roduct becomes very similar to the original firm s roduct (i.e. q is close to 1), then very tough cometition in rice lowers the irate s rofit significantly. Also note that in the situation when c is relatively high, in the roduct market cometition, the irate cometes with the original firm with a significant cost disadvantage. Thus, in this situation, the irate finds very hard to survive rofitably. 3.7 ther ossible Deterrence When x < xˆ (i.e. otimal level of deterrence is less than the actual deterrence level of the irate), the whether iracy will be actually deterred or not by the original roducer deends on whether entry-deterring monooly rofit of the original roducer is more or less than its accommodating duooly rofit. In this case, the entry deterring monooly rofit of the original roducer is given by ( 1 ( M ( ) ( ˆ) ( ˆ) 1 1 q π xˆ = c x = x = (1) c n the other hand, the accommodating duooly rofit the original roducer is given by 4c( 1 c ( 4 ( 1 ( 4 ( 1 ( 1 ) q ( ) ( 1 ) A c c q π x = ( 4 ) ( 1 ) () q q c roosition When otimal level of deterrence is less than the actual deterrence level of the irate (i.e. x < xˆ ), iracy will be stoed if and only if M ( ) A ( π xˆ > π x ). If the above fails to hold, the original roducer will fail to deter the irate and as a result iracy will take lace anyway. 11

13 4. Discussion on Welfare Here we will try to make a comarison on social welfare in two cases, namely (i) when the irate is out of the market due to successful entry deterrence by the original firm, and (ii) when the original firm is unable to deter the irate. Case (i) corresonds to a monooly situation and it is true when min ( x, xˆ ) Welfare is defined as sum of consumer surlus (CS), industry rofit () minus the cost of deterrence (DC). In this monooly situation, let s say welfare ( 1 ( 1 ( 1 ( 1 = xˆ M W is given by, q 3 1 q W M = CS + DC = + = (3) 8 4 c 8 c Case (ii) corresonds to the duooly situation when the irate is resent and it is true when min ( x, xˆ ) = A M x and ( x ) π ( xˆ ) π >. In this case, total welfare W is given by, 1 W = π + π + CS + CS The following is true. 4c( 1 ( 4 ( 1 c (4) Lemma 3 In the case of successful deterrence, the monooly rice of the original firm roof: See aendix. in the in the duooly case. 1 M = is greater than the rice Thus we have the following: > > which imlies the total consumer surlus M (CS) is higher in the resence of the irate (duooly case) comared to the monooly situation. n the other hand, the total industry rofit in the duooly case is lower than the industry rofit in the monooly case. Finally, ( x) c ˆ in case (i) is greater than ( x ) So comaring (3) and (4) we get, W M W = CS + + DC c in case (ii) as x < xˆ 1

14 From above we get CS < 0, > 0, and DC < 0, so the overall difference is ambiguous. Thus, the overall effect on social welfare due to the resence of the irate is ambiguous. This can be contrasted with a situation when stoing iracy is costless as well as the case when the irate does not face any cost for iracy. In that situation, it is always true that the resence of the irate is social welfare imroving (See oddar 00). But here we find the overall effect on social welfare due to the resence of the irate may not be necessary welfare imroving always. This is mainly because the irate faces a significant deterring cost of iracy while oerating and at the same time resence of monitoring/r&d cost of the original firm may result in lower industry rofit. 5. Conclusion We believe if the main result of this model is interreted likewise (above), it does rovide us a satisfactory exlanation on the economics of software iracy in this framework. We show that the great degree of variance in the incidence of iracy across markets and countries can well be understood through the two exogenous arameters of the model. The first one is c, the cost coefficient, which we interret as the strictness of the enforcement olicy against iracy in a articular country or region i.e. it is the legal environment under which the firms oerate; and the second one is q, the reliability of the irated software roduct that is available in the market. If we have a reasonably good information on these two arameters (or if we can estimate reasonably well about the values) in a articular market, then we can have a reasonably accurate rediction regarding the existence (or non-existence) of software iracy in that market. f course, this is robably a much simlified situation than the real life case; nevertheless, the analysis does give some insights about the henomenon of varying degree of software iracy. We also believe that this exlanation verifies our natural intuition regarding the henomenon when a irate could rofitably survive in the market alongside the original roducer, and when it would fail to do so. 13

15 Reference Banerjee, Dyuti S. (003), Software iracy: A Strategic Analysis and olicy Instruments, International Journal of industrial rganization, Vol 1, Banerjee, S., and Lin,. (003), Downstream R&D, Raising Rivals Cost, and Inut rice Contracts, International Journal of industrial rganization, Vol 1, Chen, Y, and ng, I. (1999), Software ricing and Coyright: Enforcement Against End-Users, SSRN Working aer Series. Conner, K.R., and Rumelt, R.. (1991) Software iracy: An Analysis of rotection Strategies, Management Science, Vol. 37, No, Gandal, N. (1994), Hedonic rice Indexes for Sreadsheets and an Emirical Test of Network Externalities Hyothesis, Rand Journal of Economics, 5, Katz, M. and Shairo, C. (1985), Network Externalities, Cometition and Comatibility, American Economic Review, Vol. 75, No, June. rdover, J., Saloner, G., and Salo, S. C., (1990), Equilibrium Vertical Foreclosure, American Economic Review, 80, ricewaterhousecooers for Business Software Alliance (1998), Contributions of the ackaged Software Industry to the Global Economy, Washington D.C. oddar, S. (00) Software iracy and Welfare in Economics of Software iracy Research Reort, NUS Research Grant R Rohlfs, J. (1974) A Theory of Interdeendent Demand for a Communication Service, Bell Journal of Economics, Vol 8, Salinger, M., (1988), Vertical Mergers and Market Foreclosure, Quarterly Journal of Economics, 77, Shy, z. (1995) Industrial rganization: Theory and Alications, Cambridge: MIT ress. Shy,. and Thisse, J. F. (1999) A Strategic Aroach to Software rotection. Journal of Economics and Management Science, Vol. 8, No., Sibley, D. S. and Weisman, D. L. (1998) Raising Rivals Costs: The Entry of an Ustream Monoolist into Downstream Markets. Information Economics and olicy, Vol. 10, Slive, J. and Bernhardt, D. (1998) irated for rofit. Canadian Journal of Economics, Vol. 31, No. 4,

16 Salo, S. and Scheffman, D. (1983) Raising Rivals Costs, American Economic Review, Vol. 73, Takeyama, L. N. (1994) The Welfare Imlications of Unauthorized Reroduction of Intellectual roerty in the resence of Demand Network Externalities. Journal of Industrial Economics, No., Internet Source 1998, 000, 00 Global Software iracy Reort htt:// Aendix roof of Lemma : Let s denote q( 1 ( 4 as f (. It can be easily shown that for q ( 0,1), f ( attains maximum when q = Hence, the maximum value of f ( is ( ) Now from section 3.5, note that f ( = c ( ( ) Thus maximum value of ( c = This imlies maximum value of c ( = Result follows. roof of Lemma 3: To show M = 1 > = ( 1 + cx 4 q when x = x Above imlies3q > cx After simlification this imlies c 3c ( <. Now since we are under the subcase (i.e. the case of iracy) c c ( Hence, the result follows. <, the above is true. 15

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