Kennesaw State University DigitalCommons@Kennesaw State University Faulty Publiations 00 Liensing and Patent Protetion Arijit Mukherjee University of Nottingham Aniruddha Baghi Kennesaw State University, abaghi@kennesaw.edu Follow this and additional works at: http://digitalommons.kennesaw.edu/fapubs Part of the ntelletual Property Law Commons Reommended Citation Mukherjee, A., & Baghi, A. (00). Liensing and Patent Protetion. Eonomis Bulletin, 30(3), 00-06. This Artile is brought to you for free and open aess by DigitalCommons@Kennesaw State University. t has been aepted for iusion in Faulty Publiations by an authorized administrator of DigitalCommons@Kennesaw State University. For more information, please ontat digitalommons@kennesaw.edu.
Volume 30, ssue 3 Liensing and Patent Protetion Aniruddha Baghi Kennesaw State University, USA Arijit Mukherjee University of Nottingham, UK Abstrat e show the impat of tehnology liensing on optimal patent poliy. Strong patent protetion that eliminates imitation may not be the equilibrium outome in the presene of liensing. Depending on the ost of innovation, liensing may either inrease or redue the strength of the patent protetion. e thank an anonymous referee for helpful omments and suggestions. The usual dislaimer applies. Citation: Aniruddha Baghi and Arijit Mukherjee, (00) ''Liensing and Patent Protetion'', Eonomis Bulletin, Vol. 30 no.3 pp. 00-06. Submitted: May 07 00. Published: July 30, 00.
. ntrodution ndustry ases show that there has been an inrease in the number of ollaborative ventures among firms in reent deades (Mowery 88). One suh ativity is liensing of tehnology. Grindley and Teee (7) point to the inreasing use of liensing by firms suh as BM, Hewlett-Pakard, Texas nstruments and AT&T. Arora et al. (00) provide a omprehensive list on the size and setoral omposition of liensing. However, liensing has not been adequately onsidered in the literature on patent design (see, e.g. Gilbert and Shapiro 0, Klemperer 0, and Gallini ). Hene, the patent poliies presribed in the existing literature may not be appropriate in industries where tehnology liensing is ommoy observed. The present paper is a step to fill this gap. e onsider two patent regimes: (i) weak patent protetion, where knowledge spillover reates ompetition in the produt market, and (ii) strong patent protetion, where knowledge spillover does not our, thus making the innovator a monopolist. e show that strong patent protetion may not be the equilibrium outome if liensing is an option. This result has an important impliation for ompetition poliy. t suggests that if firms have the option to inrease profits through liensing, the government should not design the patent poliy in a way that disourages liensing. Strong patent protetion may dampen the inentive for liensing by preventing imitation. This, in turn, has a negative impat on welfare. Thus, liensing (ompared with no liensing) indues weaker patent protetion. More interestingly, we also show that the presene of transation osts in liensing may enourage a government to inrease the strength of patent protetion ompared to a situation with no liensing. Beause of transation osts, firms may not engage in liensing under a weak patent regime, sine the gain from liensing may be outweighed by its ost. Hene, a weak patent regime prevents soiety from apturing the benefit of liensing. To get around the problem, the government needs to strengthen patent protetion.. Patent Regimes without Liensing Consider an eonomy with an innovator, alled firm and an imitator, alled firm. Firm spends to invent a tehnology orresponding to the marginal ost of prodution ĉ, whih is normalized to 0. e onsider two types of patent regimes: (i) strong patent regime, and (ii) weak patent regime. The main differene between the two regimes is that under a strong patent regime, imitation is not feasible and firm is a monopolist, while imitation ours under a weak patent regime and the firms ompete as Cournot duopolists. The marginal ost of the imitator under a weak patent protetion is > 0, and it dereases with a weakening of the degree of patent protetion. e onsider the following game. n stage, the government selets the degree of patent protetion, denoted by that maximizes welfare of the eonomy, whih is the sum of net industry profit and onsumer surplus. n stage, firm deides whether to innovate or not. n stage 3, firm deides whether to imitate or not. n stage 4, prodution takes plae and the profits are realized. e solve the game through bakward indution. The inverse market demand funtion is P = q () where P is prie and q is the total output. Gallini and inter (85), Katz and Shapiro (85), Kultti and Takalo (8) and Mukherjee (005) examine the effets of liensing on R&D but ignore the issue of patent protetion. Mukherjee and Pennings (004) onsider the impliations of imitation and liensing on patent protetion but fous on tehnology adoption. Mukherjee (006) shows whether patent protetion inreases innovation in the presene of liensing. However, it does not onsider optimal patent poliy.
.. Strong patents s, Under this regime, firm is a monopolist and its net profit is π = 4. n order to ensure that a monopolist has the inentive for innovation, we assume that < 4. f this assumption is violated, firm has no inentive to innovate irrespetive of the patent regime. Under strong patent, welfare of the eonomy is =. () 8 s, 3.. eak patents w, ( ) w, ( ) Under this regime, the profits of firms and are π = + and π =. Note that the patent system is alled weak if it reates effetive ompetition in the produt market, whih ours if < 0.5. elfare under a weak patent is w, ( + ) + ( ) + ( ) =. (3) 8 Now determine the optimal patent poliy. Let be the degree of weak patent protetion that makes firm indifferent between innovating and not innovating. Hene, ( + ) = and firm innovates if >. Sine < 4, exists and lies between 0 and 0.5 whenever >. n partiular, when < < 4, is given by = 3. w, t follows from (3) that is onvex in for [0,0.5]. Further, = at = 0.5, w, s, w, s, w, s, > at = 0, and the minimum value of is lower than. Hene, there s, w, exists a = suh that (i) = at s, w,, (ii) < for [0, ), and (iii) > for s, w, (,0.5]. This is depited in Figure below. elfare w, s, 0.5 Figure : elfare without Liensing
Proposition : (a) f <, welfare maximizes at = 0 (no protetion). ( + ) (b) f (, ), welfare maximizes at = (weak protetion). ( + ) 4 () f (, ), welfare maximizes at 0.5 (strong protetion). w, s, Proof: (a) f <, firm innovates even with no patent protetion. Sine > at = 0, the optimal value of is 0 in this situation. ( + ) s, w, (b) f (, ), then 0 < <. Hene, welfare maximizes at =, sine < for [0, ). () f ( + ) 4 (, ), then >. Hene, welfare maximizes at 0.5 3. Patent Regimes with Liensing Now extend the above analysis with liensing. Under liensing, firm makes a take-it-orleave-it offer to firm onsisting of a fixed-fee F and a royalty rate r. Firm s effetive marginal ost under liensing is r, sine liensing redues its prodution ost to 0. e assume that liensing involves a transation ost of K. As disussed in Teee (76) and Arora et al. (00), the soure of suh osts is the ost of writing ontrats, the ost of enforement, et. n this setion, the timeline is the same as in the previous setion for stages, and 3. However, in stage 4, firm deides whether to liense its tehnology. f firm offers a liensing ontrat, firm aepts the offer if liensing does not make firm worse off ompared with no liensing. Finally, in stage 5, prodution takes plae and the profits are realized. e solve the game through bakward indution. 3.. Strong patents Under strong patent, firm is a monopolist without liensing and has no inentive to liense its tehnology. Therefore, the profits and welfare are similar to that of subsetion.. 3.. eak patents Under weak patent, the profits of firms and are π w, ( + ) w, ( ) and π = = under no wl, ( + r) r( r) wl, ( r) liensing, while the respetive profits are π = + 3 + F and π = F under liensing. e assume for simpliity that the entire transation ost is inurred by firm. However, this assumption does not matter, sine firm an adjust the fixed fee that firm pays. t must also be noted that liensing ours if neither firm nor firm is worse off under liensing ompared to no liensing. t an be shown that the optimal royalty rate is r = and the optimal fixed fee is F = 0. The equilibrium net profits of the firms under liensing are wl, ( + ) + 3 ( ) wl, ( ) K and π π = =. The above disussion assumes that liensing is profitable, whih ours if it inreases the industry profit ompared with no liensing. Liensing is profitable if ( ) > K. (4) 3 The left hand side of (4) is onave in for [0,0.5] and is maximized at. Let 4 and be the values of that equate the two sides of (4). Hene, for K [0, 4], liensing is not profitable for [0, ) and (,0.5], while it is profitable for [, ]. f liensing is profitable, i.e., if ondition (4) holds, welfare is 3
wl, ( + ) + ( ) + 6 ( ) + ( ) = K. (5) 8 wl, Now we analyze the hange in the welfare funtion due to liensing. Note that is wl, w, s, negatively sloped and onave in for [0,0.5], + K = = at = 0.5 and wl, w, s, + K = > at = 0. First, onsider the ase of K = 0. n this ase, note from (4) that if liensing is an wl, w, option, firm lienses its tehnology for (0,0.5). Further, if K = 0, > for (0,0.5). Hene, if K = 0 and liensing is an option, a strong patent regime is never optimal. n ontrast, it follows from Proposition () that without the option to liense, a ( + ) strong regime is optimal for (, 4). Next, onsider the ase of K > 0. For a given K > 0, Figure shows the profits of firm and welfare for different values of. Gross Profit of firm π + K wl, D B P π + w, A elfare C / 0.5 E S G H wl, L s, F / w, M 0.5 Figure : Profit of firm and welfare with and without liensing The upper panel of Figure shows the gross profit of firm (whih iudes the ost of innovation) and the lower panel of Figure shows welfare for different values of. The urve AB is the profit of firm without liensing and the urve ACPDB is the profit of firm with liensing. Notie that liensing ours for [, ]. 4
s, n the lower panel of Figure, the urves SF, EHMF and EHGLMF depit, w, wl, and respetively. Sine liensing does not our under the weak patent regime for w, wl, [0, ) and (,0.5], we obtain = in these situations. Now onsider as the ost of innovation in Figure. Under no liensing, the optimal regime must be strong ( = 0.5). However, under liensing, the equilibrium patent protetion is, whih implies that liensing redues the strength of patent protetion in this situation. Next, onsider the ase where the ost of innovation is. n this situation, the equilibrium patent protetion under no liensing orresponds to. However, in the presene of liensing, sine liensing ours for [, ], the optimal patent protetion is =, sine suh a poliy maximizes welfare (given by point G) subjet to the onstraint that firm innovates and lienses its tehnology. Therefore, liensing inreases the strength of patent protetion if the ost of innovation is. This result is presented in the proposition below. Proposition : (a) f liensing is ostless, strong patent protetion is not the equilibrium outome in the presene of liensing. (b) f there is a positive ost of liensing, liensing may inrease or redue the strength of patent protetion, depending on the ost of innovation. For a given positive ost of liensing, liensing inreases the strength of patent protetion if the ost of innovation is suh that the optimal level of patent protetion under no liensing is less than and liensing does not our at the optimal level of patent protetion under no liensing. However, if the ost of innovation is suh that liensing ours at the level of patent protetion that is optimal under no liensing, liensing redues the strength of patent protetion. Referenes Arora, A., A. Fosfuri and A. Gambardella (00) Markets for tehnology: the eonomis of innovation and orporate strategy, The MT Press, Massahusetts nstitute of Tehnology, USA. Gallini, N. T. () Patent poliy and ostly imitation Rand Journal of Eonomis 3, 5-63. Gallini, N.T. and R.A. inter (85) Liensing in the theory of innovation Rand Journal of Eonomis 6, 37-5. Gilbert, R. and C. Shapiro (0) Optimal patent length and breadth Rand Journal of Eonomis 6, 37-5. Grindley, P.C. and D.J. Teee (7) Liensing and ross-liensing in semiondutors and eletronis California Management Review 3, 8-4. Katz, M. L. and C. Shapiro (85) On the liensing of innovations Rand Journal of Eonomis 6, 504-0. Klemperer, P. (0) How broad should the sope of patent protetion be? Rand Journal of Eonomis, 3-30. 5
Kultti, K. and T. Takalo (8) R&D spillovers and information exhange Eonomis Letters 6, -3. Mowery, D. (Ed.), 88, nternational ollaborative ventures in U.S. manufaturing, Ballinger Press, Cambridge, Massahusetts. Mukherjee, A. (005) nnovation, liensing and welfare The Manhester Shool 73, -3. Mukherjee, A. (006) Patents and R&D with imitation and liensing Eonomis Letters 3, 6-0. Mukherjee, A. and E. Pennings (004) mitation, patent protetion and welfare Oxford Eonomi Papers 56, 75-33. Teee, D. (76) The multinational orporation and resoure ost of international tehnology transfer, Ballinger Press, Cambridge, Massahusetts. 6