Strategic Pricing of Technology License under Product Differentiation

Transcription

1 Academc Forum Strategc Prcng of Technolog Lcense under Product Dfferentaton Abstract YoungJun Km, Ph.D. Assstant Professor of Economcs Ths paper studes factors that mght affect the prce (.e. a fed lcensng fee and the demand for technolog lcensng. The author fnds that the lcensor s lcensng fee s found to ncrease n the degree of product dfferentaton between technolog holders, the degree of knowledge napproprablt, and the level of transacton costs of technolog lcensng. Also, product dfferentaton between technolog holders rases the lcensees demand for technolog. 1. Introducton Technolog lcensng, where the appropraton and adaptaton of technologcal advances takes a central role, has become ncreasngl mportant for the compettve strateg of frms n hgh technolog ndustres. As Anand and Khanna (000 observe, t s one of onl a few sgnfcant methods of technolog transfer between frms, and one of the most commonl observed nter-frm contractual agreements these das. Reflectng an ncreasng mportance of lcensng actvt, t has been a popular subject of ndustral economcs. Snce Arrow has (196 acknowledged the profts a patent holder can obtan from lcensng, Kamen and Tauman (1986 and Kat and Shapro (1985, 1986 establsh a game theoretc framework for the analss of the technolog owner s optmal lcensng strateges. Issues related to technolog holders strategc ncentves to lcense are addressed b man other studes as well. In Galln (1984, lcensng can be used strategcall to lmt potental entr and reduce competton whle Shepard (1987 observes that lcensng can also be used to enhance demand b creatng a suppl. The relatonshp between sequental nnovatons and lcensng strateges are also eamned n Green and Scotchmer (1994. Volumnous pror studes focus on technolog holder s strategc lcensng behavor ncludng, for eample, the optmal number of lcenses to sell. The more realstc setup, however, would be that technolog holders compete wth prce rather than quantt of lcenses. In addton, lterature has mostl dealt wth the suppl sde of technolog lcensng (.e. lcensor, and the demand sde of technolog lcensng (.e. lcensee has been somewhat gnored n the model. Ths paper tres to fll ths vod and theoretcall eamnes factors that affect the lcensor s prce (.e. fed lcensng fee of lcense n the market where multple sellers and buers of technolog est. Technolog owners perform the prce competton based on a lcensee s demand for technolog assumng mperfect prce competton of duopol at the technolog market. We assume that multple technolog holders provde dfferentated products. Ths s a plausble assumpton snce companes ma tr hard to dfferentate themselves from each other to avod ferce competton at the product market. The net Secton develops the model and Secton 3 concludes. 11

2 Academc Forum The model Consder that there est two frms, frm and frm, that have ndependentl developed and patented propret technologes, and, for the producton of a good. Such a good can ether be perfectl homogeneous between the products produced wth the two technologes or dfferentated. Apart from two technolog holders, we assume that there are N ( = 1,, N heterogeneous frms that own b branches each who cannot nnovate, but can produce f the receve the rghts to use the technolog from one of ncumbent technolog holders. Assume that all potental entrant branches of frms are able to obtan technolog from ether one of technolog holders and technolog holders suppl ther technologes whenever there s a demand. It s assumed that ncumbent lcensor collects a fed lcensng fee, F, from each lcensee through the use of the lcensor s technolog. We also assume that technolog lcensng from the lcensor to the lcensee nvolves a fed transacton cost, T 0. These nclude costs of wrtng contracts, enforcng contracts, gatherng nformaton about lcensees and barganng wth them. The theoretcal framework of the model s a three-stage game. We use a backward nducton approach. Game Structure The Frst Stage: Technolog holders compete wth lcensng fee the charge to lcensees. The Second Stage: C.E.O.s of potental lcensee frms choose optmal technolog for ther branches of frms. The Thrd Stage: All frms (ncludng both lcensors and lcensees that have technolog produce products and compete at the product market. The Thrd Stage: Product Market Competton n output We assume Cournot competton n the product market. Inverse demand functons for product produced wth each technolog, and, are as follows: p = 1 ( + µ ( +, (1 where D D p = 1 ( + µ ( +, ( p, technolog, ( D and D p denote the prces, ( + D + D D s the quantt suppled b frms producng wth s the quantt suppled b frms endowed wth technolog, and D Z are total demand for technolog and respectvel. We assume that µ [ 0,1], wth products beng homogeneous for µ = 1 and completel dfferentated for µ = 0. Hgher values of µ represent more homogeneous products between ncumbent technolog holders. It s also assumed that, once the producton technologes have been acqured, the cost of producton s neglgble; these costs are set at ero. 1

3 Academc Forum An frm (ether technolog holder or lcensee branches of frms producng wth technolog,, mames the followng profts at the product market, choosng the quantt of,, respectvel, ma π = p, (3 ma π = p, (4 The frst order condton of (3 s gven b: 1 µ ( + = 0. (5 D D Imposng smmetr above across frms usng same technolog, we obtan: 1 D µ µ D = 0, (6 from whch 1 µ (1 + D =. (7 + D Smlarl, for the frm wth technolog s: 1 µ (1 + D =. (8 + D From (7 and (8, we obtan the Nash equlbrum output b the frm wth technolog and technolog, respectvel: ( + D µ (1 + D =, (9 ( + D ( + D µ (1 + D (1 + D = ( + D ( + D ( + D µ (1 + D µ (1 + D (1 + D. (10 Substtutng (9 nto (1 and (3, (10 nto ( and (4 respectvel, we can compute the equlbrum prce and thus equlbrum proft at the product market for each frm endowed wth technolog as follows: ( + D µ (1 + D π = ( + D ( + D µ (1 + D (1 + D Smlarl, for the frm wth technolog s: π = ( + D ( + D ( + D µ (1 + D µ (1 + D (1 + D, (11. (1 Proposton 1. Each frm s proft n the product market s decreasng n µ. π π Proof. < 0 and < 0. µ µ The above proposton mples that each frm s proft decreases due to an ncreased competton at the product market when goods produced b frms are more homogeneous (.e. 13

4 Academc Forum the hgher µ between technolog holders. The more smlar goods produced b frms are, the fercer the competton the face at the goods market. Ths competton effect lowers frms profts accordngl. The Second Stage: Lcensee s demand for technolog Assume that each N ( = 1,,,N lcensee frm conssts of the same number of branches b that can adopt new technolog and produce outputs. Also, each branch s assumed to have a unque branch characterstc (.e. amount of know-how or tact knowledge, number of hghsklled engneers, commercalaton and marketng ablt, organatonal structure, management sklls, R&D ntenst, se. Thus lcensee frms are heterogeneous n a sense that the heterogenet of branch characterstcs among lcensee frms ma lead to heterogeneous behavor. It s assumed that the branch characterstc s unforml dstrbuted between 0 and 1, [ 0,1]. For nstance, 0 % chemcal engneer (100 % botechncans for = 0, whle 100% chemcal engneers (0 % botechncans for = 1. The C.E.O. of each potental lcensee frm wth branch characterstc s assumed to purchase ether varet or varet for hs branches from two ncumbent technolog holders, and. We assume that he consders both eplct proft and mplct (tact proft n decdng whch varet to choose. That s, the former s the proft lcensee branches can obtan at the product market eplctl, and the latter s the nherent proft the can generate from the more effcent producton, learnng, nventon, and the bgger n-house tact knowledge necessar for the obtaned technolog. Thus, the two avalable technologes are not the same to lcensee frms n terms of ther total potental profts (eplct and mplct that lcensee branches of frms can generate through technolog lcensng. For nstance, suppose varet s bo-related technolog. Then technolog s assumed to be best suted to branches wth branch characterstc = 0 (.e. 100 % botechncans. In ths case, technolog has the nherent advantage of mplct proft over technolog. In Fgure 1, as we move awa from branch characterstc 0 toward 1, ths nherent proft of technolog over technolog s assumed to decrease, reducng the per-unt total proft of technolog. On the other hand, technolog,.e. chemcal-related technolog, s best suted to branches wth branch characterstc = 1 (.e. 100 % chemcal engneers, and thus has the nherent mplct proft over technolog. As we move awa from the branch characterstc 1 toward 0, ths proft of technolog over technolog decreases. -- In Fgure 1, horontal as represents branch characterstcs, and lne (1 has a negatve slope whle ( has a postve slope. Before the ncrease of the lcensng fee, a potental lcensee frm wth *0 *0 less than equlbrum would adopt technolog, whle greater than equlbrum would purchase technolog. In Fgure, the demand for technolog s derved. Suppose a lcensng fee of technolog 0 1 ncreases from F to F, then per-unt total proft of technolog decreases and ths causes lne (1 to shft to lne (3 n Fgure 1. Accordngl, we can derve the demand for technolog b connectng those two ponts n Fgure. Hence, holdng others constant, the market share of technolog out of 14

5 Academc Forum *0 *1 total technolog market decreases from to (note that snce s unforml dstrbuted between 0 and 1, we can nterpret as the market share. Smlarl, we can derve the demand for technolog. -- <Fgure.1> The per-unt total proft as a functon of $ (1 ( (1: per-unt total proft of technolog (before (3 the change of a lcensng fee; 0 [ π + ( 1 µ π (1 ] F (: per-unt total proft of technolog 0 [ π + ( 1 µ π ] F (3: per-unt total proft of technolog (after the ncrease of a lcensng fee; *1 * [ π + ( 1 µ π (1 ] F <Fgure.> Demand for technolog $ (4: Demand for technolog ; D = N b = F 1 0 Nb[ π π + (1 µ π F + F ] F (4 * (1 µ ( π + π *1 *0 Nb Therefore, the C.E.O of each potental lcensee frm mames the followng total profts (both eplct and mplct from lcensng b selectng the proporton ( φ of ts branches endowed wth technolog, subject to nequalt constrant, 0 φ 1: ma v = [ π + 1 µ π (1 ] bφ F bφ φ ( +[ π 1 µ π ] b(1 φ F b(1 φ Lagrangan s as follows: π + 1 µ π (1 bφ F +, (13 ( L = [ ( ] bφ + [ π ( 1 µ π ] b(1 φ F b(1 φ +, + λ 1 φ + λ ( φ, (14 ( where φ = the proporton of branches endowed wth technolog b lcensee frm. ( 1 φ = the proporton of branches endowed wth technolog b lcensee frm. b = the number of branches of each lcensee frm. F, F = fed lcensng fee pad to lcensor frm, and frm, respectvel. 15

6 Academc Forum π, π = eplct proft assocated wth technolog and technolog n the product market, respectvel. ( 1 µπ = dfference of mplct proft between technologes. Note that µ stands for the degree of product dfferentaton across varetes. ( 1 µ π (1 =mplct proft of varet for the branch wth branch characterstc. ( 1 µπ = mplct proft of varet for the branch wth branch characterstc. L φ The frst order condton of the Lagrangan wth respect to φ s gven b: = [ π + ( 1 µ π (1 ] b F b [ π + (1 µ π ] b + F b The Kuhn Tucker condtons are: λ 0, λ 0, ( 1 φ 0, φ 0, λ + λ = 0. (15 λ ( 1 φ = 0, λ φ = 0, Frst, n case where φ = 1, and λ 0, λ = 0, then: [ π + ( 1 µ π (1 ] b F b [ π + ( 1 µ π ] b + F b = λ. (16 That s, total value of technolog mnus total value of technolog s greater than or equal to ero snce λ 0. Ths means that technolog s more valuable than, and thus lcensees would prefer to lcense technolog. Second, n the case where φ = 0, and π + 1 µ π b F + 1 λ = 0, λ 0, then: [ ( ] b [ ( µ π (1 ] b + F b π = λ. (17 Ths means that technolog s more valuable than, and thus lcensees would prefer to lcense technolog. Fnall, n the case of nteror soluton where 0 < φ < 1, and λ = 0, λ = 0, then: [ π + ( 1 µ π (1 ] b F b [ π + 1 µ π ] b + F b ( = 0. (18 Ths means that technolog and are equall valuable and lcensee s ndfferent between the two technologes. From (18 * π π + (1 µ π F + F =, (19 (1 µ ( π + π * where denotes the branch characterstc for the potental lcensee that s ndfferent between * technolog and. Thus all branches wth the branch characterstc less than obtan * technolog, whle all branches of the branch characterstc greater than purchase technolog. Snce we assume that the branch characterstc s unforml dstrbuted between ero and one, s equal to the market share of technolog and ( 1 s the market share of technolog out of total technolog market. Therefore, as Fgure llustrates, the total demand 16

7 Academc Forum for technolog ( D s equal to the product of the number of potental lcensee frms (N, the number of branches each lcensee has (b, and the market share of technolog ( : Nb[ π π + (1 µ π F + F ] = D = N b *. (0 (1 µ ( π + π Smlarl, we can derve the total demand for technolog : * Nb[ π π + (1 µ π F + F ] D = N b (1 =. (1 (1 µ ( π + π Proposton. The total demand for each technolog s decreasng n µ. D D Proof. < 0; < 0. µ µ The above proposton mples that the total demand for each technolog decrease wth the homogenet of products between technolog holders. Consderng that each frm s proft decreases due to an ncreased competton at the product market when goods are more homogeneous (.e. the hgher µ between technologes (Proposton 1, product homogenet gves potental lcensees less ncentve to adopt technolog. Proposton 3. The total demand for each technolog s ncreasng n terms of the lcensng fee of the other technolog, and decreasng n terms of ts own lcensng fee. D D D D Proof. < 0 and > 0, < 0 and > 0. The proposton 3 s ver ntutve. Frms tend to demand the cheaper technolog. The Frst Stage: Market for Technolog Competton n a fed lcensng fee Gven the proft at the product market and total demand for each technolog, each ncumbent technolog owner sets ts prce of technolog, a fed lcensng fee, to mame proft at the technolog market (.e. assumng mperfect prce competton of duopol, no frm can acheve the hgher proft b changng the lcensng fee charged for ts technolog. The technolog holder solves the followng: ma V = π + θf D TD, ( F where θ denotes the degree of knowledge approprablt (.e. the level of patent protecton enforcement. We assume that θ [ 0,1], wth perfect knowledge approprablt for θ = 1 and no knowledge approprablt for θ = 0. For nstance, lower value of θ represents the weaker patent protecton enforcement. The low degree of knowledge approprablt (.e. strong patent protecton enforcement ncreases the danger of lcensors patents beng nfrnged and lcensee frms can freel cop the lcensor s patented technolog and use t for generatng etra proft wthout pang for t. Further, lcensees ma have an ncentve to shrk a contract fee under the weak patent protecton regme. * 17

8 Academc Forum Thus, ncumbent technolog holder s total proft s the sum of the profts from ts own producton (= π and total fed fee paments from D lcensees (= θ F D mnus transacton costs of lcensng (=T D. Smlarl, the problem for technolog holder s: ma V = π + θf D TD, (3 F From the sstem of the two frst order condtons obtaned from ( and (3, we can obtan, b mposng smmetr, the equlbrum lcensng fee: θ (1 µ π + T F =. (4 θ Proposton 4. The Equlbrum lcensng fee F s decreasng n µ. Proof. = ( 1 µ π µ π < 0 snce π µ < 0. µ The proposton 4 mples that the ncumbent technolog holder frm can charge a hgher lcensng fee for ts technolog when goods between technolog holders are more dfferentated (.e. the lower µ. The ntuton s that when the good s hghl dfferentated, each ncumbent technolog holder has ts own market nche. Hence product and technolog dfferentaton gve each technolog holder frm more market power. Consderng that market power s postvel related wth the lcensng fee technolog holders can charge, a product dfferentaton between technolog holders leads to the hgher lcensng fee. Proposton 5. The Equlbrum lcensng fee F s ncreasng n T and decreasng n θ Proof. > 0, < 0. T θ The above proposton shows that equlbrum lcensng fee ncreases wth transacton costs of lcensng whle the hgh degree of knowledge approprablt (.e. strong patent protecton enforcement nduces frms to charge less for ther technolog. In the presence of low transacton costs of lcensng, weaker pressure ma be brought to bear on technolog holders to charge the hgher prce for ther technolog due to an effcent transacton of technolog at the market. In addton, gven that strength of patent protecton s negatvel correlated to transacton costs of technolog lcensng (Arrow, 196; Merges, 1998, a strong patent protecton leads to fewer ncentves for technolog holders to set the hgh prce for ther lcenses due to the smlar arguments. 3. Concluson Ths paper studes lcensors strategc prcng of lcense and lcensees optmal demand for technolog when a product s dfferentated. The man aspect of the model s the endogenet of the degree of product dfferentaton n the olgopol market, endogenet that s a functon of the relatve proportons of frms adoptng each technolog. Snce olgopol profts are a functon of the degree of product dfferentaton, technolog holders wll nternale ths effect when the set ther lcense prce. 18

9 Academc Forum We fnd that the lcensor s lcensng fee s found to ncrease n the degree of product dfferentaton between technolog holders, the degree of knowledge napproprablt, and the level of transacton costs of technolog lcensng. Also, product dfferentaton between technolog holders rases the lcensee s demand for technolog. References Anand, B.N., and T. Khanna, The structure of lcensng contracts, Journal of ndustral Economcs 48(1, 000, Arrow, K.J., Economc welfare and the allocaton of resources for nventon, In The Rate and Drecton of Inventve Actvt: Economc and Socal Factors, ed. R.R. Nelson. Prnceton Unverst Press Galln, N.T., Deterrence through Market Sharng: A Strategc Incentve for Lcensng, Amercan Economc Revew 74, 1984, Galln, N.T., and B.D. Wrght, Technolog Transfer under asmmetrc nformaton, Rand Journal of Economcs 1, 1984, Green, J. and Scotchmer, S., On the dvson of proft n sequental nnovaton, Rand Journal of Economcs, 6, 1995, Kamen M.I., Y. Tauman, Fees versus roaltes and the prvate value of a patent, Quarterl Journal of Economcs 101, 1986, Kat M.L. and C. Shapro, On the lcensng of nnovaton, Rand Journal of Economcs 16, 1985, Kat M.L. and C. Shapro, How to lcense ntangble propert, Quarterl Journal of Economcs 101, 1986, Merges, R., Propert rghts, transactons, and the value of ntangble assets. Mmeo, Boalt School of Law, Unverst of Calforna, Berkele,CA, Shepard, A., Lcensng to Enhance Demand for New Technolog, Rand Journal of Economcs 18, 1987,

10 Academc Forum Bograph Dr. YoungJun Km has been an assstant professor of economcs at Henderson State Unverst snce August 005. Before jonng to Henderson State, he taught at The George Washngton Unverst n Washngton D.C. as an adjunct professor ( Dr. Km's research nterests nclude technologcal strategc allances, manageral economcs, economcs of technolog and nnovaton, ndustral organaton, econometrcs, and development, and he has publshed hs papers n such journals as Manageral and Decson Economcs, Journal of Economcs and Busness, S.A.M. Advanced Management Journal, Appled Economcs Letters, The Journal of Amercan Academ of Busness, Cambrdge, Journal of Internatonal Busness and Economcs. Dr. Km's paper has been selected as one of the Best Papers from the 64th Academ of Management Annual Meetngs. 0