Mingqing Xing 1 School of Economics and Management, Weifang University, Weifang ,

Transcription

1 [Tye text] [Tye text] [Tye text] ISSN : Vlume 1 Issue 1 BiTechnlgy 14 An Indian Jurnal FULL PAPER BTAIJ, 1(1, 14 [ ] The imact f en surce sftware n rrietary sftware firms rfit and scial welfare Minging Xing 1 Schl f Ecnmics and Management, Weifang University, Weifang 6161, (CHINA Neural Decisin Lab, Weifang University, Weifang 6161, (CHINA mxing1979@163.cm ABSTRACT en surce sftware has been achieved ntable success in recent years and becmes a werful rival t rrietary sftware in the sftware industry. Thrugh mdifying the Curnt mdel, this study analyzes hw en surce sftware affects the rfit f rrietary sftware firms and scial welfare. This aer suses that rrietary sftware firms aim at maximizing rfit and en surce sftware can be freely available. It mainly finds that the emergence f en surce sftware desn t always decrease (res. reduce the rrietary sftware firm s rfit r utut (res. rice and increase the scial welfare. This cnclusin cntradicts the traditinal recgnitin f ele t en surce sftware. KEYWORDS Oen surce sftware; Prrietary sftware; Scial welfare; Netwrk externality. Trade Science Inc.

2 BTAIJ, 1(1 14 Minging Xing 6349 INTRODUCTION Oen surce sftware (OSS is tyically develed by vlunteers frm arund the glbal and becmes a werful rival t rrietary sftware (PS in many sftware markets in recent years. In server erating system market, the en surce Linux erating system cmmands abut 3 ercent share, where Micrsft s Windws, a rrietary sftware, hlds arximately 5 ercent share (Netcraft, 1 [1] ; Mre than 6 ercent f websites use the en surce web server sftware Aache in web server market, while nly less than 3 ercent surts Micrsft s Internet Infrmatin Services (a rrietary sftware (Netcraft, 6 [] ; Sendmail, as an en surce sftware, hlds abut 8 ercent share in traffic market (Weber, 4 [3]. Accrding t O Reilly (1999 [4], en surce sftware is sftware whse surce cde allws sftware develers t share, identify and crrect errrs, and redistribute, which is usually available at n charge, and which is ften develed by vluntary effrts. The academic literature ays mre and mre attentin t the en surce rblem, in which cmetitin between en surce and rrietary sftware is a very ht area. Dalle and Jullien (1 [5] investigate the technlgical cmetitin between en surce and rrietary sftware; Meng and Lee (5 [6] and Xing (1 [7] cnsider the cmatibility f rrietary sftware t en surce sftware; Mustnen (5 [8] analyzes cmetitin between rrietary and en surce sftware when rrietary sftware firms surt the develment f substitute en surce sftware; Lin (8 [9] examines the influence f user skill and netwrk effect n the sftware market where rrietary sftware cmetes with en surce sftware; Xing (1 [1] studies hw en surce sftware affects the uality f rrietary sftware. Frm the views f technlgy cmetitin, sftware cmatibility, user skill and sftware uality, the abve literature analyzes cmetitin between en surce and rrietary sftware. Hwever mst f them have nt cnsidered hw en surce sftware influences the rfit f rrietary sftware firms and scial welfare. Thugh extending the Curnt mdel, this aer studies the imact f en surce sftware n rrietary sftware firms and scial welfare in a sftware market with netwrk externalities. We knw that the sftware market generally resents netwrk externalities, which is that the benefit that users enjy frm buying ne r several f its rducts deends n the number f ther users that use the same r cmatible rducts (Katz and Shair, 1985 [11]. The rest f this study is rganized as fllws. In sectin, tw mdels are resented. In sectin 3, the timal results are cmared. In final art, the aer is cncluded. THE MODELS T analyze the imact f en surce sftware n the rfit f rrietary sftware firm and scial welfare, this aer sets u tw mdels. One mdel suses that the rrietary sftware firm is a mnly in the market. The ther ne suses that the rrietary sftware firm faces cmetitin frm en surce sftware. The mdel f rrietary sftware mnlizing This art cnsiders nly rrietary sftware in a sftware market, which is nted by subscrit. The rrietary sftware is rduced by a rrietary sftware firm. Extending the Curnt mdel as in [1], the inverse demand functin fr rrietary sftware is given by a + u (, (1

3 635 The imact f en surce sftware n rrietary sftware firms rfit and scial welfare BTAIJ, 1(1 14 where a > and u(. In (1, a dentes the reservatin rice f rrietary sftware; u( measures the netwrk externalities n the demand functin (Regibeau and Rckett, 1996 [13], in which is the initial netwrk size fr rrietary sftware firm. Accrding t (1, the rfit functin fr rrietary sftware firm is given by π ( a + u. ( Nte that the marginal cst f rrietary sftware is assumed t eual zer. Taking the derivative f ( with resect t, and then setting it eual t zer, the first rder cnditin is given by is btained π + a u. Therefre, the timal uantity fr rrietary sftware firm a + u. (3 Obviusly, satisfies the secnd rder cnditin ( π <, therefre it is the uniue timal slutin. Substituting (3 int (1 and (, the timal rice and rfit fr rrietary sftware firm are resectively given by a + u, (4 ( a + u 4 π. (5 The scial welfare in this mdel euals cnsumers surlus lus sellers rfit. Given the inverse demand functin in (1, the scial welfare at the timal slutin meeting the first rder cnditin can be calculated SW ( a + u x dx ( 3 ( a u π (6 The mdel f rrietary sftware cmeting with en surce sftware Cnsider tw sftware rducers in the market in this art. One rduces rrietary sftware and the ther ne rduces en surce sftware. Oen surce sftware is dented by subscrit. The inverse demand functins fr rrietary and en surce sftware are resectively given by a + u (, d, (7 a + u (, +β d c, (8 where a >, a >,,, < β< 1, < d < 1 and < c< a. In (7 and (8, a and a dente the reservatin rices fr rrietary and en surce sftware resectively; d measures the

4 BTAIJ, 1(1 14 Minging Xing 6351 degree f substitutin between rrietary and en surce sftware; u(, and u (, refer t the netwrk externalities n the demand functin fr rrietary and en surce sftware resectively, in which i ( i, is the initial netwrk scale fr firm i ( i, ; c dentes the learning (maintenance r develment csts when cnsumers use en surce sftware; β indicates the cntributin degree f each user t the reservatin rice when he/she uses en surce sftware (r call it user s sftware develment skill arameter. In reality, en surce sftware is usually free and can be dwnladed in en surce cmmunity. Therefre, is assumed t eual in this study. Slving (8, we btain a + u d c. (9 1 β Substituting (9 int (7, we btain the rice fr rrietary sftware ( 1 β ( a + u d( a + u c ( 1 β d 1 β. (1 Accrding t (9 and (1, the rfit functins fr rrietary and en surce sftware rducer are resectively given by β + + c ( 1 β d π 1 β ( 1 ( a u d( a u, (11 π. (1 Nte that the marginal csts fr rrietary and en surce sftware are assumed t eual zer. As the rfit fr en surce sftware firm always euals zer, we nly need t slve the timal uantity fr rrietary sftware firm. Taking the derivative f (11 with resect t, and then setting it eual t zer, we derive ( 1 β ( a + u d( a + u π c ( 1 β d 1 β. (13 Slving (13, the timal uantity fr rrietary sftware firm is given by β + + ( 1 ( a ( u d a u c 1 ( β d. (14 This aer suses the arameters meet the ineuality >. T make sure the uniue timal slutin, must satisfy the secnd rder cnditin, which reuires π 1 ( β d <. (15 1 β

5 635 The imact f en surce sftware n rrietary sftware firms rfit and scial welfare BTAIJ, 1(1 14 Since 1 β>, the (15 hlds if 1 β d >. (16 The arameters are assumed t meet the abve ineuality, therefre is the uniue timal uantity fr rrietary sftware firm. Substituting (14 int (9, (1 and (11, the timal rice and rfit fr rrietary sftware firm and the timal uantity fr en surce sftware firm are resectively given by a + u ( a + u c d, (17 ( 1 β [( 1 β ( a ( ] + u d a + u c π 41 ( β( 1 β d, (18 [ 1 ( β d ]( a + u c ( 1 β d( a + u 1 ( β( 1 β d. (19 The scial welfare is given by ( + SW a u x d dx ( a u x d c dx. ( + + +β da+ u c + 1 β d a + u c ( 1 β d( a + u} 81 ( β ( 1 β d ( 1 β[ 3( 1 β d ][( 1 β ( a + u ( ] {[ ( ]( COPARISON The timal rice, uantity and rfit fr rrietary sftware firm and the scial welfare in afrementined mdels are cmared in this sectin. Fr urses f analysis, this sectin nly cnsiders the netwrk externalities n demand are linear (Katz and Shair, 1985 [11] and the intensity f netwrk externalities, the reservatin rice and initial netwrk scale fr rrietary sftware firm eual in tw mdels in sectin. The netwrk externality functins mentined in sectin are resectively given by u ( α, (1 u (, α ( + k, ( 1 u (, α ( + k, (3

6 BTAIJ, 1(1 14 Minging Xing 6353 where,, α, k1 1 and k 1. The arameter α is the intensity f netwrk externalities, k 1 is the cmatibility degree f rrietary sftware t en surce sftware and k is the cmatibility degree f en surce sftware t rrietary sftware. Cmarisn f rices, uantities and rfits Setting c a +α ( + k αk ( 1 β d, c a +α ( + k + d( a +α αk ( 1 β and 1 1 [ a+α ( + k 1 ] c3 a+α ( + k ( 1 β ( a+α d ( 1 β( 1 β d c< c,, the fllwing rsitin is btained. 1 Prsitin 1: (i when 1 > ; when c> c1, < ; (ii when c< c, > ; when c> c, < ; (iii when c< c3, π ; when c> c3, π. [ a ( ] ( Prf. (i Accrding t (4 and (17, +α + k d αk1 1 β cd. Therefre, > 1 ( β [ a +α ( + k] d + ( a + α ( when c< c1 and < when c> c1 ; (ii Accrding t (3 and (14, d αk1 1 β cd. 1 ( β Therefre, > when c< c and < when c> c ; (iii Accrding t (5 and (18, a ( +α ( 1 β( 1 β d [ a +α ( + k1]( 1 β + [ a +α ( + k d dc] π π ( 1 β( 1 β d c c. Therefre, π > π when c< c3 and π < π when c> c3. We btain π when < 3 and π when c> c3. Prsitin 1 shws that, if the learning (maintenance r develment csts f en surce sftware are sufficiently high, the timal uantity and rfit (res. rice fr rrietary sftware firm are mre (res. higher when rrietary sftware mnlizes the market than when it cmetes with en surce sftware, and the site situatins may aear if the learning (maintenance r develment csts f en surce sftware are sufficiently lw. That is, the aearance f en surce sftware in a sftware market des nt necessarily decrease (res. lwer the uantity and rfit (res. rice f rrietary sftware firm. This cnclusin deends n the level f the learning (maintenance r develment csts fr en surce sftware. Prsitin : when k1, >, > and π. Prf. When k1, c1 a +α ( + k > c and c a +α ( + k + d( a +α > c. Accrding t art (i and (ii f rsitin 1, > and >. Mrever, π when k 1 because π and π. Prsitin demnstrates that, if the cmatibility degree f rrietary sftware t en surce sftware euals zer (i.e. rrietary sftware isn t cmatible t en surce sftware, rrietary sftware firm will rice higher, utut mre and btain greater rfit when rrietary sftware mnlizes the market than when it cmetes with en surce sftware. Ntice that the results f rsitin dn t deend n the learning (maintenance r develment csts f en surce sftware. Making rb{ A } indicate the rbability f event A haening, the fllwing rsitin can be btained.

7 6354 The imact f en surce sftware n rrietary sftware firms rfit and scial welfare BTAIJ, 1(1 14 Prsitin 3: (i rb{ > }, rb{ > } and rb{ π } (res. rb{ < }, rb{ < } and rb{ π } will nt increase (res. decrease with c r k 1 ; (ii rb{ > } and rb{ > } (res. rb{ < } and rb{ < } will nt decrease (res. increase with β, d, a, k r ; (iii when k1, rb{ π } (res. rb{ π } will nt decrease (res. increase with β r d ; (iv when k1 k, rb{ π } (res. rb{ π } will nt decrease (res. increase with. Prf. (i rb{ c < c 1 } will nt increase with c. Cmbining with rsitin 1, rb{ > }, rb{ > } and rb{ π } (res. rb{ < }, rb{ < } and rb{ π } will nt increase c ( (res. decrease with c. Since 1 α 1 β, c 1 will nt increase with k 1. Therefre, rb{ c < c 1 } k1 d will nt increase with k 1. Accrding t rsitin 1, rb{ > }, rb{ > } and rb{ π } (res. rb{ < }, rb{ < } and rb{ π } will nt increase (res. decrease with k 1 ; similarly t art (i, art (ii and (iii als can be rven. Prsitin 3 shws that, the learning (maintenance r develment csts f en surce sftware, user s develment skill, initial netwrk scale fr rrietary sftware firm, sftware cmatibility and sftware differentiatin may influence the rbability f >, >, π, <, > r π. Cmarisn f scial welfare This art cmares the scial welfare levels. Accrding t (6 and (, the scial welfare difference in tw cases is 31 ( β ( 1 β d ( a + u ( 1 β[ 3( 1 β d ][( 1 β ( a + u da ( + u c] {[ 1 ( β d ]( a + u c ( 1 β d( a + u} SW SW 81 ( β ( 1 β d. (4 As the exressin fr scial welfare difference is very cmlex, this aer analyzes thrugh a numerical examle. Setting a a 1, 5, 5, α β 15., k1 k and d 5., the tw slutins f ( SW SW ( c are given by c and c Figure 1 resents the scial welfare difference as a functin f the learning (maintenance r develment csts f en surce sftware. Accrding t Figure 1, SW > SW when c1 < c< c and SW < SW when c< c 1 r c> c. That is, there exists an interval f the learning (maintenance r develment csts f en surce sftware, in which the scial welfare is higher when rrietary sftware mnlizes the market than when it cmetes with en surce sftware. Mrever, if the learning (maintenance r develment csts f en surce sftware are lw enugh (r high enugh, the scial welfare is lwer when rrietary sftware mnlizes the market than when it cmetes with en surce sftware. Therefre, the emergence f en surce sftware in a sftware market mnlized by rrietary sftware firm desn t necessarily increase the scial welfare, what haens in reality deends n the learning (maintenance r develment csts f en surce sftware.

8 BTAIJ, 1(1 14 Minging Xing sw-sw c Figure 1 The imact f the learning (maintenance r develment csts f en surce sftware n the scial welfare difference. CONCLUSIONS T analyze hw en surce sftware imacts rrietary sftware firms rfit and scial welfare, tw mdels have been set u in this study, ne f which is rrietary sftware mnlizing the sftware market and the ther ne f which is rrietary sftware cmeting with en surce sftware. This aer assumes that rrietary sftware firm ursues rfit maximizatin, en surce sftware is free fr users and the sftware market resents netwrk externalities. Cmaring the timal results fr tw mdels, it mainly finds that: (i the aearance f en surce sftware in a sftware market des nt necessarily decrease (res. lwer the uantity and rfit (res. rice f rrietary sftware firm; (ii if rrietary sftware isn t cmatible t en surce sftware, rrietary sftware firm rices higher, ututs mre and btains greater rfit when rrietary sftware mnlizes the market than it cmetes with en surce sftware; (iii the aearance f en surce sftware desn t necessarily increase the scial welfare. ACKNOWLEDGEMENTS We gratefully acknwledge the financial surt frm the Natural Science Fundatin f Shandng Prvince (N. ZR13GL5, the Scial Science Planning Research Prject f Shandng Prvince (N. 1CJRJ17 and the Shandng Higher Schl f Humanities and Scial Science Research Prjects (N. J13WF11. REFERENCES [1] Netcraft; Setember 1 web server survey. Available: htt://survey.netcraft.cm/survey/index- 19.html, (1. [] Netcraft; Nvember 6 web server survey. Available: htt://news.netcraft.cm/archives/web_server_survey.html, (6. [3] S.Weber; The Success f Oen Surce. Harvard University Press, (4. [4] T.O Reilly; Lessns frm Oen-surce Sftware Develment. Cmmunicatins f the ACM, 4(, (1999. [5] J.Dalle, N.Jullien; Oen-surce vs. Prrietary Sftware. Available: htt://ensurce.mit.edu/nline_aers.h. [6] Z.Meng, S.Y.Lee; Oen Surce vs. Prrietary Sftware: Cmetitin and Cmatibility. SSRN elibrary. Available: htt://ssrn.cm/aer7884, (5. [7] M.Q.Xing; Game Analysis f Cmatible Decisins between Oen Surce and Prrietary Sftware. Prceedings f the nd Internatinal Cnference n Infrmatin Science and Engineering, (1.

9 6356 The imact f en surce sftware n rrietary sftware firms rfit and scial welfare BTAIJ, 1(1 14 [8] M.Mustnen; When Des a Firm Surt Substitute Oen Surce Prgramming. Jurnal f Ecnmics and Management Strategy, 14(1, (5. [9] L.H.Lin; Imact f User Skills and Netwrk Effects n the Cmetitin between Oen Surce and Prrietary Sftware. Electrnic Cmmerce Research and Alicatins, 7(1, (8. [1] M.Q.Xing; Imact f Oen Surce Sftware n the Quality f Prrietary Sftware and Sftware Differentiatin. Jurnal f Cnvergence Infrmatin Technlgy, 7(, 4-49 (1. [11] M.Katz, C.Shair; Netwrk Externalities, Cmetitin, and Cmatibility. American Ecnmic Review, 75(3, (1985. [1] A.L.Bwley; The Mathematical Grundwrk f Ecnmics, Oxfrd: Oxfrd University Press, (194. [13] P.Regibeau, K.E.Rckett; The Timing f Prduct Intrductin and the Credibility f Cmatibility Decisins. Internatinal Jurnal f Industrial Organizatin, 14(6, (1996.