Piracy and Network Externality An Analysis for the Monopolized Software Industry

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1 Piracy and Network Externality An Analysis for the Monoolized Software Industry Ming Chung Chang Deartment of Economics and Graduate Institute of Industrial Economics Chiu Fen Lin Graduate Institute of Industrial Economics Dachrahn Wu Deartment of Economics and Graduate Institute of Industrial Economics Abstract In this aer, we roose a model to analyze a monoolized software industry. In articular, the model considers the software with the roerty of ositive network externality and consumers income distribution. By analyzing the monooly s otimal rice decision, we find that the software users enjoy the maximal network externality in such a monoolistic market structure. We then roceed with comarative statics analysis and obtain the following results: (1) Increasing the size of enalty has no effects on the monooly rice, the demand of the authorized software and the demand of the irated software. () The demand of the authorized software decreases and the demand of the irated software increases as the robability of iracy arresting increases. (3) The demand of the authorized software increases and the demand of the irated software decreases as the iracy cost increases. Keyword: network externality, iracy, income distribution. 1. Introduction According to Eighth Annual BSA (Business Software Alliance) Global Software Piracy Study, the average iracy rate of software is 39% in. It is estimated that the legal software firms revenue was declined by U.S.$ 13.8 billions due to these global software iracies. Convention wisdom suggests that legal software firms and government need to take severe actions on software iracy. Early theoretical researches such as Novos & Waldman (1984), Johnson (1985), and Liebowitz (1985)) suort this oinion by showing that unauthorized coies are harmful to intellectual roerty right holders 89

2 whenever the demand for originals does not reflect the demand for coies. Later, a grou of economists (including Conner & Rumelt (1991), Takeyama (1994), Slive and Bernhardt (1998), and Shy & Thisse (1999)) argue that in some situation it is rofitable for the original software develoer to allow limit iracy. The key factor behind such an unconventional result is the effect of network externality, a very revalent feature in the software market. Nonetheless, Poddar () roosed another model to show that even in the resence of the intense effect of network externality, rotection as oosed to allowing iracy is always otimal for the original software develoer. Although the role of network effects has been discussed extensively, the analysis for government olicy to software iracy is almost neglected. Banerjee (3) thus offers a formal analysis on government s role in controlling iracy through its choice of olicy instruments (including monitoring and enalizing the irate s illegal oeration). He found that welfare maximization may or may not result in monitoring as the socially otimal outcome. The outcome deends on the monitoring technology reflected in the monitoring cost, which is a deadweight loss, and other arameters such as the size of the market and the reliability of the irated software. So the social-welfare maximizing objective determines the government s aggressiveness or assiveness toward iracy, which in turn determines the otimal market structure. This aer rooses a model to analyze a monoolized software industry. Following the main thread of revious researches, we incororate effects of network externality in the model. To delineate the risks of using irates, we further assume that consumers are differentiated in their incomes so that they have different attitudes (risks) to obtaining the irated software. From analyzing the monooly s otimal rice decision, we find that the software users enjoy the maximal network externality in such a monoolistic market structure. By comarative statics analysis, we further obtain the following results: (1) Increasing the size of enalty has no effects on the monooly rice, the demand of the authorized software and the demand of the irated software. () The demand of the authorized software decreases and the demand of the irated software increases as the robability of iracy arresting increases. (3) The demand of the authorized software increases and the demand of the irated software decreases as the iracy cost increases. Note that the ublic oinion tends to ush government to raise the size of enalty or the ossibility of iracy arresting to curb software iracy. Conversely, our analysis suggests that the first olicy is ineffective, and that the second olicy obtains a reverse outcome (i.e., the quantity of iracy is increased). These results that clarify 9

3 our knowledge to functions of these olicy instruments toward iracies should be noticed in future researches on the role of government in dealing with software iracies. The rest of the aer is organized as follows. In section, we introduce the model. Section 3 derives the market demands of the authorized software and irated software, and then analyzes the monooly s otimal ricing. The comarative statics analysis and conclusion are in Section 4 and 5 resectively.. The Model Consider a monoolized software market in which the monooly roduces the software without roduction costs. There is a continuum of consumers that are uniformly distributed on the interval [, M] with density 1. The locations of consumers reresent their incomes. Each consumer consumes at most one unit of the software, either from buying the authorized software at the rice, or irating the software at the cost c. Suose that each consumer has the same utility function, U = x + y where x and y denote the utilities obtained from using the software and other goods resectively. Let N denote the number of software users that includes the authorized software buyers and irates. To delineate the roerty of network externality of the software, we assume that x = f ( N ) and f ' ( N ) >. Let β ( β 1) and b ( c b M ) denote the robability of iracy arresting and the corresonding fine. A consumer located at m thus has the following exected utility function. m EU = + f ( N ), ( 1 β ) m + β max[, m b] c + f ( N ), m, We assume that consumers are risk aversive. if he buys the authorized software, if he irates, if he does not use the software. Hence, a consumer will buy the authorized software when his exected utility of buying the authorized software equals that of irating the software are equal. Note that consumers have no incentive to irate when β is (relatively) too large. To avoid such a trivial case, we need to restrict β to satisfy β < 1 c. b 3. The Software Demands and the Monooly Price 91

4 In this section, we will derive the market demands of the authorized software and the irated software by analyzing consumers urchase decisions. Basing on the market demands, we then study the monoolistic firm s ricing behavior. 3.1 The market demand of the authorized software Note that the strength of network externality affects consumers urchase decisions (also the market demands). We thus analyze firstly the case of relatively small network externality (i.e, β b + c ) and then the case of relatively large network externality (i.e. > β b + c ). Case I: β b + c : The market demand of the authorized software is 1 c M, if D( ) = β, if > f ( N ), f ( N ). The demand curve is lotted in the following diagram. Diagram 1 β M + c β b + c f (N) q c M β Note that the demand function has a jum at = f (N). This imlies that the monooly rice cannot exceed the exected cost of irating the software, i.e., 1 See Aendix 1 and for the derivation of the demand function in Case I. 9

5 β b + c. Case II: > β b + c, The market demand of the authorized software is D ( ) M =, c, β if if β b + c, > β b + c. The demand curve is lotted in the following diagram. Diagram β M + c f (N) β b + c M b M + c β q As the demand function has a jum at = β b + c, the monooly rice cannot exceed the exected cost of irating the software in this case. Also note that in both cases, given an authorized software rice, the market demand of the authorized software increases as the iracy cost increases and also increases as the robability of iracy arresting increases. 3. The market demand of the irated software Since the irated software does not have its own rice, we thus define the market demand of the irated software D ( ) is a function of the rice of the authorized See Aendix 1 and for the derivation of the demand function in Case II. 93

6 software. Similar to the above subsection, we analyze firstly the case of relatively small network externality and then the case of relatively large network externality. Case I: β b + c The market demand of the irated software is D ( ) ( 1 + β ) β = f ( N ) β c, if ( 1 + β ) c, if The demand curve is lotted in the following diagram. > f ( N ), f ( N ). Diagram 3 β b + c f (N) ( 1 + β )c ( 1 ) β + β c q By the market demands of the authorized software and the irated software, we find that, given the network externality is relatively small (Case I), if the rice of the authorized software is too high (i.e., > f(n) ), there are no demand for the authorized 1+ β c software and a constant demand for the irated software (i.e., ). ( ) β Case II: > β b + c The market demand of the irated software is 94

7 D ( ) = β M c, ( 1+ β ) c, if if β b + c, > β b + c. The demand curve is lotted in the following diagram. Diagram 4 f (N) β b + c ( 1 + β )c M c q Note that, given the network externality is relatively large (Case II), if the rice of the authorized software is too high (i.e. > β b + c ), there is no demand for the authorized software. Moreover, the consumers that can afford the irate cost (i.e., M c consumers) irate the software. By contrast, in Case I some of the consumers who can afford the irate cost choose not to irate when the rice of the authorized software is too high (such that there is no demand for the authorized software). 3.3 The rofit function and the monooly rice Given the demand functions of the authorized software and the irated software, the monooly sets a rice to maximize its rofit, π = D( ). The rofit functions in both cases are lotted in the following diagrams. 95

8 Diagram 5: (Case I: β b + c ) π ( β M + c) 4β c β β M + c f (N ) β b + c Diagram 6: (Case II: > β b + c ) 96

9 π ( β M + c) 4β ( β b + c) ( M b) β M + c β b + c f (N ) Proosition 1: In both cases, the monooly rice M + = β ; the otimal * c * M c market demand of the authorized software D = + ; the otimal demand of the β irated software * D M 1 = 1 + c ; the firm s otimal rofit β ( β M + ) * * * β M + c M c c π = D = + =. β 4β Proof: See Aendix 3. Note that, under the monooly rice, the number of software users is * * N = D + D = M c. This means that excet those consumers who are too oor to afford the iracy cost, the other consumers use the software. The software users thus enjoy the maximal network externality in such a monoolistic market structure. 4. Comarative Statics Analysis In this section, we will analyze the effects of changes of the enalty b, iracy 97

10 cost c, and the robability of iracy arresting β on the monooly rice, the otimal demand of authorized software and the otimal demand of irated software. 4.1 Effects of the size of enalty Proosition : Increasing the size of enalty has no effects on the monooly rice, the demand of the authorized software and the demand of the irated software. * Proof: = b and D * * * D D = = =. b b b 4. Effects of the robability of iracy arresting Proosition 3: The demand of the authorized software decreases and the demand of the irated software increases as the robability of iracy arresting increases. D Proof: = c β β < D, = c β β >. Proosition 3 indicates that raising the robability of iracy arresting obtains a reverse effect on iracy reduction. Such a eculiar result is caused by a higher monooly rice due to the increase of the robability of iracy arresting * M ( = > ). As the effect of a higher monooly rice dominates the effect of β the exected iracy cost increasing, we then have the outcome. Proosition 4: If β M > c, the monooly rofit increases as the robability of iracy arresting increases. If β M < c, the monooly rofit decreases as the robability of iracy arresting increases. Proof: * π = β ( β M + c)( β M c) 4β. 4.3 Effects of iracy cost Proosition 5: The demand of the authorized software increases and the demand of the irated software decreases as the iracy cost increases. 98

11 D 1 D Proof: = >, o ( ) 1 = 1 + <. c β c β 5. Conclusion In this aer, we roose a model to analyze a monoolized software industry. In articular, the model considers the software with the roerty of ositive network externality and consumers income distribution. Through the derivations of the market demands of the authorized software and the irated software, we then analyze the monooly s otimal rice decision and find that the software users enjoy the maximal network externality in such a monoolistic market structure. Finally, by comarative statics analysis, we obtain the following results: (1) Increasing the size of enalty has no effects on the monooly rice, the demand of the authorized software and the demand of the irated software. () The demand of the authorized software decreases and the demand of the irated software increases as the robability of iracy arresting increases. (3) The demand of the authorized software increases and the demand of the irated software decreases as the iracy cost increases. Note that the ublic oinion tends to ush government to raise the size of enalty or the ossibility of iracy arresting to curb software iracy. Conversely, our analysis suggests that the first olicy is ineffective, and that the second olicy obtains a reverse outcome (i.e., the quantity of iracy is increased). References: Banerjee, D.S. (3), Software Piracy: A Strategic Analysis and Policy Instruments, International Journal of Industrial Organization, 1, Besen, S.M. (1986), Private Coying, Reroduction Costs, and The Suly of Intellectual Proerty, Information Economics and Policy, 5(), 5-. Besen, S.M. and S.N. Kirby (1989), Private Coying, Aroriability and Otimal Coying Royalties, Journal of Law & Economics, 3, Business Software Alliance (BSA).(3), Eighth Annual BSA Global Software Piracy Study. Washington, DC: US. Chou, C.H. & D. Wu (), the rotecting decision on intellectual roerty right for monooly software firm, SCU economics worksho (in Chinese.) Chou, C. and O. Shy (1993), Partial Comatibility and Suorting Services, Economics Letters, 41, Conner, K. and R. Rumelt (1991), Software iracy: an analysis of rotection strategies, Management Science, 37,

12 Givon, M., V. Mahajan and E. Muller (1995), Software iracy: estimation of lost sales and the imact on software diffusion, Journal of Marketing, 59, Johnson, W.R.(1985), The Economics of Coying, Journal of Political Economy, 93(1), Liebowitz, S.J. (1985), Coying and indirect aroriability: hotocoying of journals, Journal of Political Economy, 93(5), Lin, Y.J. (1991), Price, rofits & iracy in the PC software industry, Taiwan Economic Review, 19(3), Novos, I.E. and M. Waldman (1984), The effects of increased coyright rotection: an analytic aroach, Journal of Political Economy, 9(), Poddar, S. (), Network Externality and Software Piracy, working aer, Deartment of Economics, National University of Singaore. Slive, J. and D. Bernhardt (1998), Pirated for Profit, Canadian Journal of Economics, 31(4), Shy, O. and J. Thisse (1999), A Strategic Aroach to Software Protection, Journal of Economics & Management Strategy, 8, Shy, O. (1), The Economics of Network Industries, Cambridge University Press. Smith, E., and Wright, R. Why Is Automobile Insurance in Philadelhia So Damn Exensive? The American Economic Review, 8(4), (199), Takayama, L. (1994), The Welfare Imlications of unauthorized Reroduction of Intellectual Proerty in the Present of Demand Network Externalities, Journal of Industrial Economics, 4(),

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