Innovation or Imitation: Some Economic Performance and Social Welfare Policy Perspectives

Transcription

1 48 Internatonal Journal of Informaton Systems and Socal Change, (3), 48-66, July-September Innovaton or Imtaton: Some Economc Performance and Socal Welfare Polcy Perspectves Sohel Ghl, Sharf Unversty of Technology, Iran Hengameh Shams, Sharf Unversty of Technology, Iran Madjd Tavana, La Salle Unversty, USA ABSTRACT Ths paper develops a mathematcal model of nnovaton n technology wth two man characterstcs. Frst, t dscusses the endogenously made decson on not only how much to nnovate, but also, how much to mtate. Second, t demonstrates that the decson to nnovate or mtate are not mutually exclusve and a frm can nnovate and mtate smultaneously. A mathematcal model s presented, and the authors explan the barrers to nnovaton development and dffuson. The model s further used to nvestgate the effectveness of two technology nnovaton and mtaton polces. It s shown that an ntellectual property rght (IPR) polcy wll better functon f the prce of nnovaton s set to a level lower than the cost of nnovaton. The concept superfluous nnovaton (nnovatons whose costs are hgher than ther benefts) s also proposed and developed through nvestgatng the polcy of levyng subsdes on nnovaton. Keywords: Approprablty, Game Theory, Imtaton, Innovaton, Intellectual Property Rghts, Publc Goods, Socal Welfare INTRODUCTION The tradeoff between nnovaton development and nnovaton dffuson has been wdely studed n the technology change and ndustry performance lterature. Ths tradeoff arses from the fact that what we do to prevent free avalablty of exstng nnovatve dscoveres to all producers, although benefcal from an expost effcency standpont, wll fal to provde the ex-ante ncentves for further nnovaton (Arrow, 96; Cohen & Levn, 989; Cohen DOI:.48/jssc.74 & Levnthal, 99). Such a dlemma s called the approprablty problem. In spte of ts long hstory, the problem of how frms decde on nnovaton-related ssues s stll of much nterest and mportance. In ts smplest form, the approprablty problem s concerned about a frm decdng on whether or not to nnovate - or how much to nnovate - based on the extent to whch the nnovaton s approprable (Arrow, 96; Qurmbach, 986; Ireland & Stoneman, 986; Levn, 988; Saracho, 996; Sakakbara, ). A newly emergng theme, mostly seen n Boldrn and Levn s (9a, 9b, 9c, Copyrght, IGI Global. Copyng or dstrbutng n prnt or electronc forms wthout wrtten permsson of IGI Global s prohbted.

2 Internatonal Journal of Informaton Systems and Socal Change, (3), 48-66, July-September 49 9d) recent works s dvsblty accordng to whch, the knowledge emboded n goods or people s not costlessly avalable. Therefore, f one frm s to mtate another, t should devote some tme, money and energy nto buyng some copes of the goods n whch the knowledge s emboded (Boldrn & Levne, 8, 9a). In other words, there s no free and unprced spllover. Therefore, the matter of nterest, here, s not only the nnovator decdng how much to nnovate due to the degree of approprablty, but also, how the mtator decdes on how much to mtate due to the degree of dvsblty (whch we wll refer to as mtablty). Boldrn and Levn (9b, 9c, 9d) have studed the approprablty and dvsblty decsons and ther effect on market sze and structure. In ths paper, we study the nterdependency between nnovaton and mtaton and show that a frm can be an nnovator and an mtator at the same tme. Whle the two-fold role of a frm has been addressed sporadcally n the feld lterature (such as Spence, 984), none of these studes have consdered the nterdependency between nnovaton and mtaton. Not all ndustres can be parttoned nto nnovators (.e. north) and adopters (.e. south) as argued by Helpman (993) and Akyama and Furukawa (9). Ths gap n the current lterature mght have led to some msdefntons of the problem. For nstance, t s always postulated that a frm has less ncentve for nvestng on easly mtable nnovatons only because t may then be mtated by others (Arrow, 96; Qurmbach, 986; Ireland & Stoneman, 986; Levn, 988; Saracho, 996; Sakakbara, ; Spence, 984). In ths paper we construct a model to address the queston of how much to mtate n the context of the two-fold role of a frm (.e. nnovator and mtator) n a strctly compettve game settng. We wll nvestgate how frms decde on how much to nnovate and mtate and how ther decsons affect socal welfare under dfferent condtons of mtablty. We wll also nvestgate the effects of two wdelynoted polces: frst, the ntellectual property rght (IPR) and second, the polcy of treatng nnovaton as a publc good. We argue that under dfferent condtons of mtablty, these polces may have dfferent effects on the outcome of the complex decson structure and hence on socal welfare. The remander of the paper s organzed as follows. In the next secton, we provde the man assumptons of the model and then we present the mathematcal model. In the followng secton, we provde the results obtaned from solvng the mathematcal model. We also explan the nsghts ganed from the soluton results and compare them to the current approprablty lterature. We then nvestgate the subsdy and IPR polces and examne ther effect on the proposed model. The last secton s devoted to conclusons and future research drectons. ASSUMPTIONS OF THE MODEL For the sake of smplcty, we assume that there are two frms producng the same product at the same prce n the market. We also assume equal market share but dfferent producton costs for the two frms. Snce prce and market share are assumed to be equal, the frm wth lower producton cost wll make more profts. The market s also assumed compettve, thus, one frm s cost reducton wll lessen the prce and consequently the proft of the other frm. As we wll see n the followng sectons, approprablty s captured n the model by lnkng producton cost of each frm to the proft of the other frm. Each frm can develop nnovaton by tself or mtate the nnovaton developed by the other frm. Developng or mtatng one unt of nnovaton results n reducton n the frm s producton cost but t has some costs assocated wth t. The effects of nnovatons have been consdered solely on producton cost, not on the qualty of goods. Such an assumpton s commonplace n the lterature (Cole, ). One unt of nnovaton developed by a frm and one unt of nnovaton mtated from the other frm wll equally reduce producton cost although the cost of developng one unt of nnovaton may dffer from that of mtatng t. Copyrght, IGI Global. Copyng or dstrbutng n prnt or electronc forms wthout wrtten permsson of IGI Global s prohbted.

3 5 Internatonal Journal of Informaton Systems and Socal Change, (3), 48-66, July-September Therefore, the problem faced by each frm s to optmze the extent of ts nnovaton development and mtaton (.e. to maxmze ts proft). In other words, the decson-makng varables for each frm are the extent of nnovaton development and mtaton and the objectve s to maxmze proft. We further assume perfect nformaton n the model whch s also a common assumpton n nnovaton dffuson models (Hylton, 3; Goodwn et al., 5). Ths assumpton s realstce snce each frm can predct how the other frm wll decde. If one frm dd not know that the other frm wll mtate t, approprablty would not have evolved as a major concern n the lterature on nnovaton dffuson and poltcal economy. In ths model, there s no varable named welfare but the prce of the product n the market s consdered as an ndex of socal welfare. Such an assumpton s made on one hand for the sake of the smplcty; on the other hand, t accords wth the common assumpton of welfare economcs whch perceves more consumpton as an ndex of welfare (.e., ISEW or the ndex of sustanable economc welfare) (Nordhaus & Tobn, 97; Daly & Cobb, 989). In our model, a lower prce s an ndcator of a hgher consumpton rate snce the lower prce, although not leadng to an ncrease n consumpton, leaves more dsposable ncome for people. MATHEMATICAL MODEL The mathematcal notatons and defntons presented n Appendx A are used to derve the models presented n ths secton. The prce of the product s obtaned from Eq. (): Cu + Cu Prce = P + () where Prce s the market prce of the product and Cu and Cu are the total costs of producng one unt of the product for frm and frm, respectvely. The relatonshp between the prce and Cu s based upon the assumpton of a compettve market and therefore a reducton n the total cost results n a reducton n the market prce. P s a constant ndcatng the average proft per unt. Although the prce could have been formulated as n a Cournot duopoly, we dd not do so for two reasons: smplcty and the assumpton of strct competton. Frst, our man objectve n ths study s to nvestgate how frms decsons on nnovaton and mtaton nterplay n a compettve envronment. Focusng on the form of the competton wll only add to the complexty of the model and dvert us from the man objectve of ths study. Second, the competton represented by Eq. () s strct because the sum of the frms profts s equal to the constant P. Cournot setup could not be used here because of the assumpton of strct competton. Although we are not gong to use the theorems related to strctly compettve games, we do use ts logc when provdng explanatons for the results. We fnd each frm s proft by multplyng ts proft per unt tmes the number of unts sold (Q): Cu Proft = Cu Q P ( Prce ) = + Cu Q () where Q s equal for both frms and Eq. can be used smlarly to fnd the proft for frm. In addton, the approprablty s captured by these equatons snce Cu s not the sole determnant of Proft. Cu also plays a role n determnng the proft for frm - the less Cu, the less Proft. Ths s the reason why frm decdes on less nnovaton when ts nnovaton s mtated. The total costs for each frm conssts of two components: drect or varable costs and ndrect or fxed costs. The drect costs of producng a product can be represented by: Cu = m C Drect (3) + d Copyrght, IGI Global. Copyng or dstrbutng n prnt or electronc forms wthout wrtten permsson of IGI Global s prohbted.

4 Internatonal Journal of Informaton Systems and Socal Change, (3), 48-66, July-September 5 where C and m are coeffcents for regulatng the dmenson of the equaton. The dmenson of C s the same as that of Cu Drect (the unt of money over the unt of product) and dmenson of m s the same as that of d and (the unts of nnovatons and mtatons, respectvely). d, represents the unts of nnovatons developed n frm and d, represents the unts of nnovatons developed n frm. Smlarly,, and, are the unts of nnovaton mtated by frm and frm, respectvely. Therefore, frm mtates from frm and vce versa. As we mentoned earler, the effect of one unt of nnovaton on the producton cost has nothng to do wth whether the product s developed wthn the frm or t s mtated. Ths fact s also captured by Eq. (3). The second component of the frm s total cost s ndrect producton expenses ncludng costs of developng and mtatng nnovatons: Cu Indrect = d C d + C d d x x (4) nq where C s the margnal cost of mtatng one unt of nnovaton and C d s the margnal cost of developng one unt of nnovaton. As we wll see later, the C s are formulated subject to the followng constrants: and d, because no frm s able to mtate more d than the amount of nnovaton developed by the other frm. n equals the number of years durng whch the nnovaton s usable; that s, the tme perod durng whch the nnovaton has an effect on the total costs before becomng obsolete due to substtuton. n s assumed exogenous and constant. The reason for ncludng n n the denomnator of the formula s that all of the terms n ths model represent a perod of one year (.e. ths s a statc one-year model). Consequently, only one out of the n years durng whch the nnovaton affects Cu Drect s consdered. Therefore, t s necessary to take nto consderaton / n th of ts assocated cost. In addton, we nclude Q n the denomnator because Cu Drect s an overhead cost. The margnal cost of mtatng nnovaton for frm s obtaned by Eq. (5) n whch the aforementoned constrant has been taken nto account: C, = I (5), d,, Accordng to ths equaton, where =, the cost of mtatng one more unt, d, wll approach nfnty. Therefore, the constrant s appled to Eq. (5). A smlar formula s used for the second frm s mtaton, d, cost. I s a coeffcent whch makes the dmensons of the two sdes consstent and s also an ndex for the mtablty of the nnovaton. That s, the less I, the less expensve s the mtatng nnovaton, makng t more mtable. If I s neglgble or zero, the nnovaton s easly mtable and f I s large, the nnovaton s non-mtable. I plays a sgnfcant role n ths study snce the man goal of ths paper s to analyze the stuaton n dfferent states of mtablty. I s consdered the ndependent varable n all the analyses and s the varable on the horzontal axs n all of the fgures. The margnal cost of developng nnovaton s assumed to be equal to the constant D : C = C = D (6) d, d, whch means that the per-unt expense of developng nnovaton s D. If we substtute Eq. (5) and (6) nto Eq. (4) and ntegrate the two sdes of the resultng equatons, C and C d can be elmnated and the equaton below wll be obtaned: Copyrght, IGI Global. Copyng or dstrbutng n prnt or electronc forms wthout wrtten permsson of IGI Global s prohbted.

5 5 Internatonal Journal of Informaton Systems and Socal Change, (3), 48-66, July-September D Cu = I nq nq d, d Indrect,,, + d ln,, d, (7) The total cost of each frm equals the sum of ts drect and ndrect costs. Cu = Cu + Cu (8) Drect Indrect We have thus far modeled the physcal structure of the problem. Next, we model the frms decsons whch nvolve four equatons; two of them are concerned wth how much nnovaton the frm should develop, and the other two correspond to how much nnovaton the frm should mtate. Frms determne the degree of ther nnovaton mtaton based on the amount of ther nnovaton development. As mentoned before, the effect that one unt of mtated nnovaton has on the drect cost of producton equals the effect of one unt of developed nnovaton. Therefore, f C > C, the frm can reduce ts d ndrect costs by developng one more unt of nnovaton n exchange for one less unt of mtaton, whle keepng ts drect costs unchanged. Smlar condtons exst for the stuaton where C < C. As a result, the optmum d decson concernng mtaton s made under the assumpton that C = C, and, hence: C C = C (9), d, = C (), d, and two other equatons maxmze the frms profts wth respect to developed nnovatons: Proft = () d, Proft = () d, d MODEL SIMULATION AND THE ANALYSIS OF THE RESULTS In order to solve ths model, we need to solve Eqs. (9-) for four unknown quanttes:,, and. It should be noted that the d, d,,, perfect nformaton assumpton s used here. For example, when substtutng Eq. () n Eq. (), we are mplctly assumng that frm s completely aware of the second frm s polcy on mtaton. In addton, the man objectve s to study how the mtablty of an nnovaton mpacts upon the smulaton results. Therefore, all the parameters are taken nto consderaton as constants except for I whch s used to sketch the fgures. We frst equalze the margnal cost of nnovaton development to that of the nnovaton mtaton (Eq. (9) for frm and Eq. () for frm ). As a result, the amount of mtaton s obtaned n terms of the amount of development. By solvng Eq. (9) for, the amount of mtaton for frm s: D = (3) d D + I,, and the amount of mtaton for the frm s: D = (4) d D + I,, As Eqs. (3) and (4) show, whle I s neglgble, a major fracton of the developed nnovatons s mtated. When I s large, the amount of mtaton s mnmal. Eq. (3) and (4) show how the nnovaton mtated ( ) by one frm s related to the nnovaton developed ( ) d by the other frm. When these equatons are substtuted n Eqs. () and (), the s are elmnated and Eq. () and Eq. () are turned nto a system of Copyrght, IGI Global. Copyng or dstrbutng n prnt or electronc forms wthout wrtten permsson of IGI Global s prohbted.

6 Internatonal Journal of Informaton Systems and Socal Change, (3), 48-66, July-September 53 two equatons wth two unknowns. By solvng ths system, we obtan d, and d, as follows: and (4), ntroducng the spllover fracton as a decreasng functon of I (Fgure )., d,, D = = D + I d, (6) (5) As expected, the amount of developed nnovaton for both frms s equal due to the symmetry assumpton n the problem defnton. As I approaches nfnty, d approaches mc nq. Ths fact s proved n Appendx B. D The result of the model (Eq. (5)) s presented schematcally n Fgure. ( D =, m = 5, C =, nq = ) A further analyss of the soluton reveals some sgnfcant results. Frst and foremost, the amount of developed nnovatons s an ncreasng functon of I. In other words, f mtaton costs ncrease, frms wll tend to develop more nnovatons. Second, nterestngly, those wllng to antcpate the effect of mtaton costs on the amount of nnovaton mtaton and development wthout consderng the model may conclude that rsng mtaton costs have a postve effect on the nnovaton development (resultng n more nnovaton) and have a negatve effect on the nnovaton mtaton (resultng n less mtaton). However, as the results show, ths s not the case wth every level of I. Increasng the mtaton costs may also ncrease mtaton. It s not dffcult to justfy ths seemngly surprsng result based upon the model relatonshps. When mtaton costs rse, a smaller part of the developed nnovatons s mtated (.e. the spllover fracton falls). Eq. (6) can be derved from Eqs. (3) On the other hand, snce the total amount of the developed nnovaton has ncreased, the amount of mtaton mght also rse n spte of the reducton n the spllover fracton. We consder prce as an ndex of welfare due to our nterest n studyng the effect of mtaton costs on socal welfare. Fgure 3, shows the prce varatons for dfferent I s. As shown n ths fgure, the prce s hghest when I has ts lowest value. The reason s that no nnovaton wll be developed because of the approprablty problem. Thus, there wll be no mtaton ether (Fgure ). Fnally, t s noted that our supposton of the exstence of only two frms, weakens the mportance of mtaton. In a market wth, for example, fve frms, each frm can mtate from four other frms. When the total amount of the developed nnovaton s calculated, mtated nnovatons wll gan a coeffcent of 4 and developed nnovatons wll gan a coeffcent of. Fgure 4 demonstrates the wdely mentoned nverted U-shaped relatonshp between the amount of mtablty of an nnovaton and socal welfare (O Donoghue & Zwemuller, 4; Furukawa, 7). Although the mportance of mtaton n realty mght be more than what our model shows, analyzng a stuaton n whch there are numerous frms s beyond the scope of ths paper. EXAMINING THE POLICIES ON THE MODEL In ths secton, we study two polces that a government can consder towards nnovaton mtaton between frms. We also show the effects of these polces on socal welfare. We do not compare the performance of these polces Copyrght, IGI Global. Copyng or dstrbutng n prnt or electronc forms wthout wrtten permsson of IGI Global s prohbted.

7 54 Internatonal Journal of Informaton Systems and Socal Change, (3), 48-66, July-September Fgure. The number of unts of developed, mtated and total nnovaton n accordance wth I and dentfy prortes. We ntend to show how dfferent polces functon and provde some nsghts nto ths nherently complex problem rather than defnng outputs for decson makng as suggested by Lynes (999). Whle analyzng each polcy, two ponts should be consdered: Frst, how the polcy s modeled and entered nto the model equatons. That s, how manpulatng that polcy changes the model parameters and equatons. Second, how these changes n the equatons affect the soluton results. Establshng an IPR for Innovaton Polcy One of the prevalent polces for preventng nnovaton from free mtaton s an IPR for nnovaton polcy (Galln & Scotchmer, ). The IPR for nnovaton polcy can resolve the approprablty problem by makng the nnovaton avalable to other frms n the market n exchange for a pre-determned amount of money to the nnovaton developer frm. Ths polcy changes two parts of the model. Frst, mtaton cost wll ncrease as much as the prce of buyng the nnovaton: C, = I + P (7), d,, where P s the prce of buyng one unt of nnovaton. By substtutng Eq. (7) n Eq. (9) and solvng for,, the amount of mtated nnovaton wll be obtaned: ( D P ) = d ( D P ) + I,, (8) Second, by mplementng ths polcy, the frst frm s ndrect costs wll go down accordng to the equaton below (there s a smlar change for the second frm): d,,, D d + C d Pd x x x Cu =, Indrect, Q (9) The amount for developed nnovaton can be obtaned by solvng ths set of equatons wth the method descrbed earler: Copyrght, IGI Global. Copyng or dstrbutng n prnt or electronc forms wthout wrtten permsson of IGI Global s prohbted.

8 Internatonal Journal of Informaton Systems and Socal Change, (3), 48-66, July-September 55 Fgure. The rato of the mtated to developed nnovaton n accordance wth I () Fgures 5, 6 and 7 show the changes n the amount of developed nnovaton, nnovated mtaton and product prce n terms of I for both the pre-mplementaton and post-mplementaton cases. As shown n Fgure 5, the mplementaton of the IPR polcy stmulates more nnovatons. Two man reasons can be suggested to understand ths phenomenon. Frst, ths polcy causes frms to develop more nnovatons when they know for sure that ther nnovatons wll not be mtated easly. Second, the nnovator frm knows that f another frm wants to mtate ts nnovaton, t must pay for t. In other words, the producton cost of the nnovator frm wll decrease and the producton cost of the mtator frm wll ncrease (whch s good for the nnovator frm due to the strctly compettve nature of the game). Therefore, the nnovator frm can generate some revenues n exchange for ther nnovaton. Meanwhle, Fgure 6 bears another nterestng result. The IPR polcy, an ant-mtaton polcy, leads to more mtatons. Ths polcy not only lessens the spllover percentage, but t also causes more nnovatons to be developed. As a result, more absolute value of the nnovatons wll be mtated. Takng Fgures 5 and 6 nto consderaton, we can see that an IPR polcy s not effectve for large I s. In other words, for large I s, nnovaton development, nnovaton mtaton and product prces are the same whether or not ths polcy s mplemented. The reason s because ths polcy ncreases mtaton costs and t does not work for cases where the mtaton costs are already hgh. Another ssue of concern s how to set P to better handle the IPR polcy. Note that f Copyrght, IGI Global. Copyng or dstrbutng n prnt or electronc forms wthout wrtten permsson of IGI Global s prohbted.

9 56 Internatonal Journal of Informaton Systems and Socal Change, (3), 48-66, July-September Fgure 3. The product prce for each frm n accordance wth I ( P =. ) the amount of P s chosen to be more than D, there wll be no reason for the frms to mtate from each other because the margnal cost of nnovaton development wll always be less than that of nnovaton mtaton ( C < C ). In other words, when P d s large, developng an nnovaton s always more economcal than mtatng the nnovaton and no mtaton wll occur. Ths mportant result gves us an nterestng nsght nto adoptng sutable polces for nnovaton prces. As shown n Fgure 7 (product prce versus I for P = D / ), the product prces for low I s s less than those for nfnte I s. In other words, lower prces are reached when P s set to quanttes smaller than D. Therefore, our model proposes settng nnovaton sellng prces smaller than nnovaton development costs so that ths polcy functons more effectvely. Ths analyss suggests the mportance of makng a dstncton between the two purposes of the IPR polcy mentoned above. The frst purpose s to motvate the frms by guaranteeng a protecton aganst mtaton; and, the second purpose s to motvate them wth the proft from sellng ther nnovatons. If P s very large, t wll certanly protect frms aganst spllover. But, ths very protecton can also dscourage mtaton and therefore may result n a loss of earnngs for the frm snce ts nnovaton s not mtated by others. Hence, a large P may reduce the ncentves to develop nnovatons. Establshng an Imtable Innovaton as Publc Goods (Tax-Subsdy Polcy) There are two elements n the defnton of publc goods. Frst, usng publc goods by someone s not an mpedment for others to use t. Second, t s very costly to prevent someone from usng publc goods (Varan, 99). It s obvous that publc goods can t be produced by the market because of the free rdng problem (Waldman, 987). Innovaton entals the frst characterstc of publc goods. When an nnovaton s used by one frm, t does not prevent other frms from dong so. Meanwhle, f the nnovaton s mtable, t wll also have the second characterstc. It can be Copyrght, IGI Global. Copyng or dstrbutng n prnt or electronc forms wthout wrtten permsson of IGI Global s prohbted.

10 Internatonal Journal of Informaton Systems and Socal Change, (3), 48-66, July-September 57 Fgure 4. The total unts of nnovaton n a market of 5 frms ( ) stated that the approprablty problem s nothng but the free rdng problem n a specfc case that the nnovaton of the product s mtable. Consequently, t seems that ntroducng a tax system for compensatng frms nnovaton costs could be an approprate polcy for encouragng frms to develop more nnovatons that are easer to mtate. Governments can collect a fracton of the total nnovaton costs from both frms n the form of taxes. That s, f the nnovaton development costs for frms and are C D, and C D,, respectvely, the government wll levy a tax equal to a C + C D, D, on each frm. Then, the government can use these collected taxes to pay ac D, to frm and ac D, to frm ( < a < ). Accordngly, the government makes frms partcpate n each other s nnovaton development costs. Ths polcy changes the equatons as follows (smlar modfcatons should be appled to the equatons concernng Frm ): D ( a) = d D ( a) + I,, () a s a coeffcent whch shows what fracton of frms nnovaton costs s subject to the tax-subsdy polcy. In fact, a s an ndex of how strctly the government enforces the taxsubsdy polcy. If a equals zero, t means that the government collects no taxes at all. In other words, Eqs. () and () are the same as Eqs. (4) and (3), representng the no tax condton n the model. The amount of developed nnovaton can be obtaned by solvng ths set of equatons wth the method descrbed earler: ( d d ),,, a D d + a C d C d Cu =,, Indrect, nq x d x x () (3) Copyrght, IGI Global. Copyng or dstrbutng n prnt or electronc forms wthout wrtten permsson of IGI Global s prohbted.

11 58 Internatonal Journal of Informaton Systems and Socal Change, (3), 48-66, July-September Fgure 5. The total unts of developed nnovaton (wth and wthout IPR polcy ( P D =. 5 )) Fgures 8 and 9 show the amount of developed and mtated nnovatons versus I (Fgure 8 schematcally represents Eq. (3)). Product prces are also shown versus I n Fgure (n order to study welfare). As shown n Fgure 8, mplementng a tax-subsdy polcy stmulates frms to develop more nnovatons for all quanttes of I because frm knows that frm wll bear a part of frm s nnovaton costs (a smlar story for frm ). The benefts to the frm are twofold. Frst, ths could result n a reducton of the frm s nnovaton development costs and ultmately a reducton n the total costs. Second, t wll lead to an ncrease n the rval frm s costs whch s benefcal for the nnovatng frm due to the strctly compettve nature of the game. As shown n from Fgure, the taxsubsdy polcy decreases the total producton cost for relatvely low I s. Ths mght be due to the fact that nnovaton development occurs less when I s low and ths polcy nduces frms to develop more nnovatons. Fgure also shows that when I s large, the tax-subsdy polcy not only does not reduce the total producton cost, but rather ncreases t. When analyzng ths apparently strange result, t should be taken nto consderaton that more nnovatons do not necessarly lead to a hgher level of welfare. More nnovatons lead to more welfare only when the benefts of nnovaton changes exceed ts assocated costs. As we already mentoned, whle ths polcy s mplemented, a percentage of each frm s nnovaton development costs wll be mposed on the other frm. Therefore, frm starts to develop nnovatons n a large scale because t pays less for ts nnovaton development n comparson wth the stuaton n whch there s a no taxsubsdy polcy. That s, wth a tax- subsdy polcy, frm mposes a part of ts nnovaton development costs on frm by means of the tax collected from both of them. Frm acts exactly n the same way and a porton of frm s nnovaton development costs wll be mposed on frm. In other words, although both frms pay less for developng the nnovatons, they nadvertently suffer from each other s costs, so they wll develop superfluous nnovatons (nnovatons whose costs are hgher than ther benefts) whch can lead to hgher total costs and hence hgher prces. Copyrght, IGI Global. Copyng or dstrbutng n prnt or electronc forms wthout wrtten permsson of IGI Global s prohbted.

12 Internatonal Journal of Informaton Systems and Socal Change, (3), 48-66, July-September 59 Fgure 6. The total unts of mtated nnovaton (wth and wthout IPR polcy ( P D =. 5 )) In summary, the tax-subsdy polcy s only approprate for the condtons n whch the nnovaton s mtable, that s, t has low mtaton cost (.e. low I ). In other condtons, ths polcy leads to superfluous nnovatons and ncreases producton costs. Ths result further valdates our model snce we have already stated that any nnovaton can be consdered as publc goods where I s low. Therefore, when I s hgh, nnovaton cannot be consdered as publc goods, mplyng that the free rdng problem wll not occur. Each frm tends to develop as many nnovatons as t needs whle tax-subsdy polcy results n more developng nnovatons than are needed. Note that one of the model s assumptons was that market demand s nelastc, that s, the sales quantty ( Q ) s fxed and s not affected by the prce. Such an assumpton s not necessarly true for all knd of markets snce demand s generally elastc n realstc crcumstances. When demand s elastc, the tax-subsdy polcy wll not create as much negatve effect as our model shows. If an ncrease n nnovaton development leads to hgher prces (havng superfluous nnovaton), hgher prces wll lead to less demand and less Q, and less Q leads to less proft for the frms. In the real world, frms make decsons on the bass of ther profts, so a decrease n profts wll gude them to gve up developng nnovatons n a way that s unproftable. The superfluous nnovaton effect, however, s not the only damagng effect of the tax-subsdy polcy on the performance of the system. Another effect s that the tax-subsdy polcy decreases the margnal cost of nnovaton development, wth the margnal cost of mtaton remanng unchanged. Therefore, as shown n Fgure 9, we should expect the spllover fracton, and maybe even the absolute value of mtaton to decrease 3 (see Eqs. 6 and ). We should also note that ths effect could not be captured wth a model not endogenzng the mtaton decsons (e.g.spence, 984). CONCLUSIONS AND FUTURE RESEARCH DIRECTIONS The model ntroduced n ths paper explaned how the approprablty problem mght arse from the nteractons between frms. The above-mentoned model dffers from the present Copyrght, IGI Global. Copyng or dstrbutng n prnt or electronc forms wthout wrtten permsson of IGI Global s prohbted.

13 6 Internatonal Journal of Informaton Systems and Socal Change, (3), 48-66, July-September Fgure 7. The product prce (wth and wthout IPR polcy ( P P =., =. 5 )) D models n the lterature n that t consders two frms whch both can smultaneously develop and mtate nnovaton; therefore, two key ponts about the frms decsons are consdered smultaneously n ths model. Frst, a frm s decson on how much nnovaton to develop nfluences ts decson on how much to mtate and vceversa. Second, a frm s decson about how much to nnovate and mtate s dependent on rval frms decson. We have already examned the effect of mtablty of nnovaton on socal welfare through a smple framework whch s also close to the real world. In ths analyss t was ndcated that the mtablty of an nnovaton mght not only reduce the extent of creatng nnovaton (known as approprablty) but also reduces the degree of mtatng nnovatons. We used the model to analyze two polces usng a descrptve rather than a prescrptve approach. That s, our purpose was manly to gve nsghts nto the problem, and not to prescrbe a soluton. We llustrated that IPR polcy leads to more nnovaton development n two ways. Frst, t guarantees that the frm s nnovatons wll not be easly mtated (t approprates nnovaton). Secondly, t guarantees that f the frm s nnovatons are mtated, t wll earn a proft from sellng that nnovaton and also an equal cost wll be ncurred to the mtatng compettor. It was also shown that the latter functon s not fulflled when the ntellectual property s prced hgh. The results have also shown that mtable nnovaton (havng low I ) can be consdered as publc goods. By smulatng the model, we observed that n ths case, tax-subsdy polcy mght result n more nnovaton development and more socal welfare. Meanwhle, t was noted that ths polcy does not functon properly n the case of non-mtable nnovatons (havng hgh I ). Meanwhle, we showed that as I ncreases, the effect of the tax-subsdy polcy gradually becomes less effectve and even harmful to welfare snce t causes a large amount of superfluous nnovaton to be developed. Whle the aforementoned nsght s qute nterestng, the man contrbuton of nvestgatng the effects of a tax-subsdy polcy s the proposton of superfluous nnovaton. The output of ths work ncludes not only the nsghts drven from the model, but also the model tself. Ths model can be used as an nstrument for analyzng how dfferent factors affect the approprablty problem and ts rec- Copyrght, IGI Global. Copyng or dstrbutng n prnt or electronc forms wthout wrtten permsson of IGI Global s prohbted.

14 Internatonal Journal of Informaton Systems and Socal Change, (3), 48-66, July-September 6 Fgure 8. The total unts of developed nnovatons (wth and wthout tax-subsdy polcy) Fgure 9. The total unts of mtated nnovatons (wth and wthout tax-subsdy polcy) Copyrght, IGI Global. Copyng or dstrbutng n prnt or electronc forms wthout wrtten permsson of IGI Global s prohbted.

15 6 Internatonal Journal of Informaton Systems and Socal Change, (3), 48-66, July-September Fgure. The product prce (wth and wthout tax-subsdy polcy ( P =. )) ommended polces. Some of these mportant factors are: asymmetry n producton costs or mtaton costs between two frms, asymmetry of frms szes (whch heghtens the mportance of economes of scale), and nnovaton obsolescence tme, etc. For example, some factors such as cost structure or market share of the two frms can be consdered as asymmetrc and the results could be solved and nterpreted for an asymmetrc case. Furthermore, the boundary of ths model can be extended n some aspects. For example, one way mght be addng uncertanty effect to the model and then studyng nteractons between approprablty and uncertanty by omttng the perfect nformaton assumpton. Such an omsson could lead to the transformaton of our statc model to a dynamc structure because when frms do not know, they should learn and learnng s a dynamc phenomenon. Ths mght be the reason why Arrow (96) has used some dynamc terms such as pre-nventon and post-nventon. Another nterestng extenson of the model s to consder nnovaton s obsolescence tme as endogenous rather than external and exogenous snce some nnovatons are substtuted for others. The rate of the nnovaton development mght affect ts lfe tme (.e., I d may affect n) and ultmately mpact the results and polces extracted from the model. In addton, t would be nterestng to nvestgate the effects of possble cooperaton between frms on the amount of nnovaton development and mtaton. In order to do ths, one should replace the smple strctly compettve market structure of our model wth a Cournot structure - or some other standard structure whch allows for the possblty of cooperaton and examne the effects of collusons on nnovaton related ssues. Fnally, t would be nterestng to study our model n the context of the theory of nternatonal poltcal economy and the rapdly changng polces and economc condtons of the nternatonal communty. More precsely, the nterlnk between economcs and poltcs and the strategy that the state develops to ensure economc stablty (Evaghorou, ). The systems thnkng approach suggested by Kamppnen et al. (8) could also be useful n understandng and managng the multtudes of Copyrght, IGI Global. Copyng or dstrbutng n prnt or electronc forms wthout wrtten permsson of IGI Global s prohbted.

16 Internatonal Journal of Informaton Systems and Socal Change, (3), 48-66, July-September 63 condtons and effects that consttute economc stablty. ACKNOWLEDGMENT The authors would lke to thank the anonymous revewers and the edtor for ther nsghtful comments and suggestons. REFERENCES Akyama, T., & Furukawa, Y. (9). Intellectual property rghts and approprablty of nnovaton. Economcs Letters, 3(3), do:.6/j. econlet Arrow, K. J. (96). Economc welfare and the allocaton of resources for nventon. In Nelson, R. R. (Ed.), The rate and drecton of nventve actvty: Economc and socal factors (pp ). Prnceton, NJ: Prnceton Unversty Press. Boldrn, M., & Levne, D. K. (8). Perfectly compettve nnovaton. Journal of Monetary Economcs, 55(3), do:.6/j.jmoneco.8..8 Boldrn, M., & Levne, D. K. (9a). A model of dscovery. The Amercan Economc Revew, 99(), do:.57/aer Boldrn, M., & Levne, D. K. (9b). Does ntellectual monopoly help nnovaton? Revew of Law & Economcs. Berkeley Electronc Press, 5(3), 9. Boldrn, M., & Levne, D. K. (9c). Market structure and property rghts n open source ndustres. Washngton Unversty Journal of Law and Polcy, 3, Boldrn, M., & Levne, D. K. (9d). Market sze and ntellectual property protecton. Internatonal Economc Revew, 5(3), do:./ j x Cohen, W. M., & Levn, R. C. (989). Emprcal studes of nnovaton and market structure. In Schmalensee, R., & Wllg, R. D. (Eds.), Handbook of ndustral organzaton (Vol., pp. 59 7). Amsterdam, The Netherlands: Elsever. Cohen, W. M., & Levnthal, D. A. (99). Absorptve capacty: A new perspectve on learnng and nnovaton. Admnstratve Scence Quarterly, 35(), 8 5. do:.37/ Cole, J. H. (). Patents and copyrghts: Do the benefts exceed the costs? The Journal of Lbertaran Studes, 5(4), Daly, H. E., & Cobb, J. B. (989). For the common good. Boston, MA: Beacon Press. Evaghorou, E. L. (). The state strategy n today s global economy: A reset poston n the theory of nternatonal poltcal economy. Internatonal Journal of Socety Systems Scence, (3), do:.54/ijsss Furukawa, Y. (7). The protecton of ntellectual property rghts and endogenous growth: Is stronger always better? Journal of Economc Dynamcs & Control, 3(), do:.6/j. jedc.7.. Galln, N., & Scotchmer, S. (). Intellectual property: When s t the best ncentve system? In Jaffe, A., Lerner, J., & Stern, S. (Eds.), Innovaton polcy and the economy (Vol. ). Cambrdge, MA: MIT Press. Goodwn, N., Nelson, J. A., Ackerman, F., & Wesskopf, T. (5). Mcroeconomcs n context. Boston, MA: Houghton Mffln. Helpman, E. (993). Innovaton, mtaton, and ntellectual property rghts. Econometrca, 6(6), do:.37/9564 Hylton, K. N. (3). Anttrust law: Economc theory and common law evoluton. Cambrdge, UK: Cambrdge Unversty Press. do:.7/ CBO Ireland, N., & Stoneman, P. (986). Technologcal dffuson, expectatons and welfare. Oxford Economc Papers, 38(), Kamppnen, M., Vhervaara, P., & Aarras, N. (8). Corporate responsblty and systems thnkng - tools for balanced rsk management. Internatonal Journal of Sustanable Socety, (), do:.54/ IJSSOC.8.57 Levn, R. C. (988). Approprablty, R&D spendng, and technologcal performance. The Amercan Economc Revew, 78(), Lynes, J. M. (999). System dynamcs for busness strategy: A phased approach. System Dynamcs Revew, 5(), do:./(sici)99-77(999)5:<37::aid-sdr58>3..co;-z Nordhaus, W., & Tobn, J. (97). Is growth obsolete?new York, NY: Columba Unversty Press. Copyrght, IGI Global. Copyng or dstrbutng n prnt or electronc forms wthout wrtten permsson of IGI Global s prohbted.

17 64 Internatonal Journal of Informaton Systems and Socal Change, (3), 48-66, July-September O Donoghue, T., & Zwemuller, L. (4). Patents n a model of endogenous growth. Journal of Economc Growth, 9(), 8 3. do:.3/ B:JOEG c Qurmbach, H. C. (986). The dffuson of new technology and the market for an nnovaton. The Rand Journal of Economcs, 7(), do:.37/55566 Sakakbara, M. (). Formaton of R&D consorta: Industry and company effects. Strategc Management Journal, 3(), do:./smj.7 Saracho, A. I. (996). The dffuson of a durable emboded captal nnovaton. Economcs Letters, 54(), do:.6/s65-765(97)3-7 Spence, M. (984). Cost reducton, competton, and ndustry performance. Econometrca, 5(),. do:.37/9463 Varan, H. R. (99). Mcroeconomc analyss (3rd ed.). New York, NY: W.W. Norton and Company. Waldman, M. (987). Noncooperatve entrance, uncertanty, and the free rder problem. The Revew of Economc Studes, 54(), 3 3. do:.37/9759 ENDNOTES Such a formulaton captures the fact that a low rate of mtaton can occur not only when the mtaton process s costly, but also when the nnovaton development s not dffcult to mplement. Now, we can queston the recommendaton that all polces should be desgned n such a way to encourage more nnovaton. 3 Ths effect could be greater even when the number of frms s greater than. Copyrght, IGI Global. Copyng or dstrbutng n prnt or electronc forms wthout wrtten permsson of IGI Global s prohbted.

18 Internatonal Journal of Informaton Systems and Socal Change, (3), 48-66, July-September 65 APPENDIX A. Table A. Mathematcal notatons and defntons C d, Margnal cost of developng unt of nnovaton n frm C d, Margnal cost of developng unt of nnovaton n frm C D, Total cost of developng nnovaton n frm C D, Total cost of developng nnovaton n frm C, Margnal cost of mtatng unt of nnovaton n frm C, Margnal cost of mtatng unt of nnovaton n frm Cu Drect, Drect producton costs for frm Cu Drect, Drect producton costs for frm Cu Indrect, Indrect producton costs for frm Cu Indrect, Indrect producton costs for frm Cu Total costs for frm Cu Total costs for frm D Cost of developng unt of nnovaton d, Total unts of nnovaton developed by frm d, Total unts of nnovaton developed by frm, Total unts of nnovaton mtated by frm, Total unts of nnovaton mtated by frm I n Prce A parameter representng nnovaton mtablty Lfe tme of nnovaton (years) Prce per unt Proft Proft of frm Proft Proft of frm P P Q a Cost of buyng unt of nnovaton under IPR Average proft per unt of the good Sales volume for each frm A fracton of the frms nnovaton costs whch s subject to tax- subsdy polcy Copyrght, IGI Global. Copyng or dstrbutng n prnt or electronc forms wthout wrtten permsson of IGI Global s prohbted.

19 66 Internatonal Journal of Informaton Systems and Socal Change, (3), 48-66, July-September APPENDIX B. mc nq We stated that as I approaches nfnty, d approaches. Ths fact s proved here. D The amount of developed nnovatons can be obtaned through the equaton below: D + I mc I nq = = d D + I D I ( D + I D I ln ) + D + I + D + I d,, Usng the followng equaton for the natural logarthm: x ln ( + x) ~ x +... x We see that as I (mtaton cost) approaches nfnty, the amount of developed nnovatons approaches: lm I I d = mc I nq D I D I D + I = mc nq D Copyrght, IGI Global. Copyng or dstrbutng n prnt or electronc forms wthout wrtten permsson of IGI Global s prohbted.