International technology licensing strategy under successive monopoly

Transcription

1 Internatonal technology lcensng strategy under successve monopoly Pe-Cyuan Shh, * Tsung-Han Chou, ** Yan-Shu Ln and Hong Hwang Abstract Assume there s a foregn lcensor who owns a cost-reducng technology whch can be appled to any producton stage of a product manufactured n the home country. Producton of the product comprsed of n producton stages and the maret structure of the ndustry s that of n-stage successve monopoly. We shall use ths model to examne f the foregn lcensor ntends to lcense the technology by means of a two-part tarff contract (.e., a per-unt royalty and a fxed fee) to a frm n the domestc ndustry, what would be the optmal lcensng contract and to whch frm t should lcense. It s found wth surprse that the optmal lcensng polcy of the lcensor s two-part tarff lcensng contract when the lcensee s assocated wth a mddle producton stage. However, when the lcensee s wth the upmost producton stage, a pure fxed fee s called for. Moreover, socal welfare s maxmzed f the lcensng occurs n the upmost producton stage. Ths result mples that a government should encourage nternatonal technology lcensng to tae place n an upper than a lower stage of producton. Key words: Lcensng, Successve Monopoly JEL Classfcaton: D4, D45, L * SHIH: Department of Internatonal Busness and Trade, Mng Chuan Unversty, Emal: pcshh@mal.mcu.edu.tw. ** CHOU: Department of Economcs, Natonal Dong Hwa Unversty, Emal: @gms.ndhu.edu.tw. LIN: Department of Economcs, Natonal Dong Hwa Unversty, Emal: yln@gms.ndhu.edu.tw. HWANG: Correspondng author. Department of Economcs, Natonal Tawan Unversty and RCHSS, Academa Snca, No., Sec. 4, Roosevelt Rd., Tape 067, Tawan; Emal: echong@ntu.edu.tw.

2 Internatonal technology lcensng strategy under successve monopoly. Introducton Technology lcensng s a common practce among ndustres and has grown dramatcally over the last two decades. In the lterature on lcensng, two types of lcensors have been studed extensvely, namely outsde and nsde lcensors. When a lcensor does not (does) compete wth the lcensees n the product maret, t s called an outsde (nsde) lcensor. The lterature on technology lcensng can be dated bac to Arrow (96) who shows that a lcensor can earn more profts by lcensng ts nnovaton to compettve frms than to a monopolst. Recently, many scholars have been nterested n the content of an optmal lcensng contract, namely, a pure royalty, a pure fxed-fee or a two-part tarff lcensng contract. In the lterature of nsder lcensng, Wang (998) and Kamen and Tauman (00), among others, show that a lcensor always prefers a royalty to a fxed-fee contract f the products produced by the lcensor and the lcensee(s) are homogeneous. Moreover, Poddar and Snha (00) fnd that a lcensor may prefer a fxed fee to a royalty lcensng contract f the technology s transferred from a hgh-cost frm to a low-cost frm. On the other hand, most studes show that an oursde lcensor would transfer technology va a fxed-fee lcensng contract (see, for example, Kamen and Tauman (986), Katz and Shapro (986) and Kamen et al. (99), among others). Whle each of these papers has enrched the lterature, t s worth notng that the above analyses are all confned to technology lcensng n a fnal good maret. Nevertheless, Nadr (993) shows that, from 970 to 988, the payments for patents have ncreased by about 400% n Japan and the U.K., 550% n France and the U.S., and by over,000% n West Germany. Accordng to Rostoer (984), royalty lcensng alone was used 39%, fxed-fee lcensng alone 3%, and two-part lcensng 46% of the tme, among the frms surveyed.

3 n realty, lcensng actvtes are more prevalent n raw materal or ntermedate goods, as evdenced by Anand and Khanna (000). In ther emprcal paper, they show that most of lcensng actvtes are concentrated on ntermedate goods rather than fnal goods, especally n chemcal, computer, and electroncs ndustres. But n the theoretcal lterature on lcensng, there are few studes focusng on a vertcally related maret, ncludng such as Arya and Mttendorf (006), Muherjee et al. (008), Muherjee (00), Muherjee and Pennngs (0), Dn et al. (03) and Cao and Muherjee (06), among others. Arya and Mttendorf (006) employ a vertcally related maret model to examne lcensng behavors of downstream frms. They found that an upstream frm may adopt dscrmnatory prcng aganst ther downstream frms and the lcensng stll occurs even f the nnovaton s drastc and the goods are homogeneous. Muherjee et al. (008) derve that f there s an nput monopolst and one outsde lcensor n the ndustry, the optmal lcensng contract s that of a pure royalty. Muherjee (00) shows that an nsder lcensng va fxed fee lcensng n the downstream maret s proftable f the technology lcensng ncreases competton n the upstream maret. Muherjee and Pennngs (0) analyze the ncentve for technology lcensng n the fnal goods maret s stronger under a decentralzed rather a centralzed labor unon. In addton, Dn et al. (03) show that the outsde lcensor prefers royalty (fxed-fee) lcensng to fxed-fee (royalty) lcensng when the degree of the upstream producer s monopoly power s small (large) regardless of the nnovaton sze. Furthermore, Cao and Muherjee (06) show that the maret power of an upstream producer may encourage a fnal goods producer to lcense ts technology to a compettor and ths may ncrease consumer welfare. However, to the best of our nowledge, there s no scholarly wor to examne the effects of nternatonal technology lcensng under an n-stage successve monopoly

4 maret. The am of ths paper s therefore to analyze the optmal lcensng contract of an outsde foregn lcensor under a successve monopoly maret. We assume that ths technology can be appled to any of the producton stages of a product. The outsde lcensor has to choose a producton stage and lcense ts technology to the frm assocated wth the stage. We shall show that the content of the optmal contract depends on the ter of the producton stage that lcensng occurs. Specfcally, the lcensor prefers a pure fxed-fee contract f the lcensng occurs n the upmost producton stage; otherwse, t prefers a two-part tarff or a pure royalty contract. Moreover, domestc socal welfare s maxmzed f the lcensng occurs n the upmost producton stage. Ths result mples that the domestc government should encourage a foregn technology to be lcensed to the frm assocated wth the upmost producton-stage. The remander of the paper s organzed as follows. Secton presents the basc model and derves the maret equlbrum wth non-lcensng. Secton 3 analyzes the optmal lcensng contract and the welfare mplcatons. Secton 4 extends the model by assumng the producton technology exhbtng a varable nput coeffcent. Secton 5 concludes the paper.. The Basc Model Assume there s an ndustry comprsng of n producton stages; each producton stage has one frm. The maret structures of the fnal good and all the ntermedate goods are that of monopoly. It means that there s successve monopoly. Furthermore, we denote Frm as the th ter monopoly frm wth = 0,,,, n. Frm 0 s the fnal goods producer, frm s the neghborng upstream frm of frm 0 and frm n s the 3

5 frm assocated wth the upmost producton stage or a raw materal suppler n the ndustry. Furthermore, wthout loss of generalty, we assume that all the producton technology n the entre producton process exhbts one to one relaton,.e., one unt of nput to produce one unt of output. Therefore, the proft functon of frm s = - -, where p s the output prce of frm, p + s the p p p+ c q defned as ( ) nput prce of frm whch s charged by frm +, c s the margnal cost of frm. The fnal demand s assumed to be lnear and tae the followng form: q0 = a- p0. The margnal cost of frm s p+ + c. We start wth a benchmar case n whch technology lcensng does not occur. The game structure of the benchmar case nvolves n+ stages: In the frst stage, frm n determnes the optmal prce to maxmze ts own proft. In the second stage, gven the nput prce, frm n- determnes the optmal nput prce that charges t to frm n-, etc. In the fnal stage, gven the nput prce of the prevous stage and the fnal demand, frm 0 determnes the optmal output (or prce) of the fnal good. From the above dscussons, we can specfy the proft functon of frm as follows: p ( p c p+ ) q = - -. () Frm determnes q to maxmze ts proft and the frst-order condton for proft maxmzaton s dervable as follows: p q = pq + p - c - p = + 0. () The optmal output of frm s dervable from () as follows: q = ( a- c - p + ). (3) From (), we can derve the followng comparatve statc effects: q p + < 0 and p >. The former shows that the output decreases wth the nput prce, p +. + p+ 0 4

6 On the other hand, the latter shows that the optmal prce of frm ncreases wth the nput prce, p +. Smlarly, we can defne the proft functon of frm n as follows: p = ( p - c ) q. (4) n n n n The frst-order condton for proft maxmzaton of frm n and the optmal nput prce are as follows: dp n dp n qn = qn + ( pn - cn) = 0, (5) p n n- æ ö pn = ç a- å cj + cn. (6) è j= 0 ø We can substtute (6) to p n- to derve the equlbrum nput prce of frm n-. Proceedng as before, we derve the equlbrum prce and output of frm as follows: p = n- + ( ) - n æ ö - ç a- å cj + å c è j= 0 ø j= n- + j, a q =, (7) n + where æ a º ç a- è n å j= 0 c j ö ø s the effectve demand. It s straghtforward to show that all the n+ successve monopoly frms produce the same equlbrum quantty due to the one nput for one output technology. The equlbrum ndustry proft s dervable as follows: = 0 n+ ( - ) n a Õ = å p =. (8) n+ Socal welfare, whch s the sum of the ndustry profts and consumer surplus, s defned as follows: SW = CS +P, where CS n+ = a ( ). 3. Optmal Lcensng Contract In ths secton, we examne the optmal contract of the outsde lcensor. Assume that 5

7 ths technology can be appled to any producton stage and can only be used once. The game now conssts of n+ stages. In the frst stage, the lcensor determnes the optmal contract. In the second stage, gven the optmal contract, frm n determnes the optmal prce to maxmze ts own proft. In the thrd stage, gven the optmal contract and the nput prce, frm n- determnes the optmal nput prce that s charged to frm n-, etc. In the fnal stage, gven the nput prce of the prevous stage, frm 0 determnes the optmal output. The lcensng contract s assumed to be a two-part tarff contract: A per-unt royalty, r, and a fxed fee, F. Gven the patent holder lcenses ts technology to frm, the margnal cost of frm, remans the same as c, ¹. The margnal cost of frm who s the lcensee frm becomes c - e + r, where e stands for the nnovaton level. 3 By substtutng c- e + r nto (7), we can derve the equlbrum output of the lcensee,.e., frm, under technology lcensng follows: q= + -. n + ( a e r) Moreover, the proft functon of the foregn lcensor s as follows: Max W = rq + F( ), subject to ( a + e - r) a F ( ) = -, (9) n+ - n+ - where F() s a functon of and represents the fxed-fee charged by the outsde foregn lcensor. The optmal fxed fee s subject to the lcensee frms ncentve constrant-- the proft of the lcensee frm after lcensng s no less than that before lcensng. As the proft functon of the lcensor frm ncreases wth the fxed fee, the 3 In ths paper, the nnovaton level s the same for all the ters. However, t s of nterest to extend the analyss to dfferent nnovaton level among ters, that s e. Wth ths extenson, we could examne the optmal lcensee and how the optmal contract form s affected by the dfferent nnovaton levels. These extensons are reserved for future research. 6

8 optmal fxed fee has a corner soluton. 4 The foregn lcensor chooses r and F to maxmze the lcensng revenue and the frst-order condton for ths proft maxmzaton s as follows: 5 ( a + e - r) - r - ( a + e - r) dw = + + = 0. (0) n+ n+ n+ - dr From (0), the optmal royalty rate s dervable as follows: n- ( - )( a + e ) r ( ) =, () n- + - It ndcates that the royalty rate s a functon of. The equlbrum output and proft of frm are as follows: q ( ) = a + e + n- + ( )( - ) ( ) and ( a + e ) p ( ) = ( )( - ) + - n- +, () where varables wth a subscrpt denotes that they are assocated wth frm. If =, p s the proft of the lcensee. Moreover, t s also mportant to note that gven the restrcton that r e, the optmal royalty rate has a corner soluton: r = e, f n- ( - ) a e º ˆ e. n- We can derve the optmal lcensng contract as follows: ì ( a + e ) a ï r = 0, F = - f = n n+ n+ ï n- ï ( - )( a + e ) ( a + e ) a í r( ) =, F( ) = - f j < < n. n- + + n- + n+ - ï - ( )( - ) ï r = e, F = 0 f 0 j ï î 4 For smplcty, we assume the outsde lcensor has full barganng power, and the fxed-fee payment of frm s the proft dfference between acceptng and rejectng the lcensng offer. 5 Furthermore, the second-order condton for proft maxmzaton s negatve as: W r - = + < 0. n+ n+ - 7

9 It s found that the outsde nnovator charges a pure fxed-fee f the lcensee s the frm assocated wth the upmost producton stage and charges a pure royalty f the lcensee s the frm assocated wth a low producton stage. Thus, we can mae the followng proposton. Proposton. Under a successve monopoly maret structure, the optmal lcensng polcy of the outsde lcensor s two-part tarff lcensng contract when the lcensee s assocated wth a mddle producton stage. However, when the lcensee s wth the upmost producton stage, a pure fxed fee s called for. Ths s n contrast to earler results n the lterature such as Kamen and Tauman (986) and Katz and Shapro (986). They all conclude that an outsde lcensor would charge a pure fxed-fee. Our result also dffers from those n Muherjee et al. (008) and Dn et al. (03). They all show that an outsde lcensor may prefer royalty lcensng to fxed-fee lcensng f the maret n queston has two ters wth one upstream frm vs. one downstream frm and the outsde lcensor adopts a one-part tarff contract. In ths paper, we examne the optmal two-part lcensng contract when the ndustry has n successve producton stages. To the best of our nowledge, ths has never been dscussed n the lterature. It s also worth mentonng that our fndng s smlar to that of Poddar and Snha (00), even though the two models are very dfferent. They employ an nsde lcensor model and conclude that the optmal lcensng contract could be that of a pure fxed fee, two-part tarff or pure royalty, dependng on the ntal cost dfference between the lcensor and the lcensee. Our model examnes the optmal lcensng contract for an outsde lcensor and concludes that the lcensor may also choose a pure fxed-fee, two-part tarff or pure royalty, dependng however on the producton stage 8

10 wth whch the lcensee s assocated. The ntuton for the aforementoned result s as follows. Note that there are two effects arsng from the lcensng. The frst effect s the effcency gans from the new technology and the second effect s the rent-extractng effect by an upstream frm. If the lcensee s assocated wth the upmost producton stage, the effcency gan s most sgnfcant, but the rent-extractng effect s nl. The outsde lcensor chooses a fxed fee to approprate the effcency gans. On the other extreme case, f the lcensee s assocated wth a lower producton stage, then the gans from the ndustry effcency s small, but the rent-extractng effect s sgnfcant. Under such a crcumstance, the outsde lcensor should charge a pure royalty so as to reduce the rent extracted by all the upstream frms. If the lcensee s assocated wth a mddle stage of producton, a mxture of a fxed-fee and a royalty s called for. By substtutng () nto (9), we obtan that: n- dr( ) - ln() ( a + e ) = < 0, n- + d ( - ) n- + df( ) ln()( )( a + e ) ln() a = - > 0. + n- + n+ - d ( - ) It s straghtforward to show that the royalty rate (fxed fee) decreases (ncreases) wth the producton ter of the lcensee. Furthermore, the corner soluton of whch the optmal royalty rate s set equal to the nnovaton level,.e., r happen f the lcensee s assocated wth a lower producton stage. = e, s more lely to The ntuton behnd ths result s as follows. Technology lcensng lowers the margnal cost of the lcensee, expandng the derved demand and ncreasng the nput prce. The gans from lcensng wll spllover to upstream frms and lower the lcensng revenue of the lcensor. The lcensor, beng a frst mover n the game, can 9

11 use royalty rate to suppress the rent to be extracted by upstream frms of the lcensee. Therefore, t s optmal to apply a royalty rate f the lcensee s assocated wth a lower producton stage. Ths result s dfferent from those n Muherjee et al. (008) and Muherjee (00). They show that f there s an nput monopolst and one outsde lcensor n the ndustry, the optmal lcensng contract s that of a pure royalty. However, they consder a maret wth only two-ter rather than n-ter successve monopoly. By substtutng () and () nto (9), the equlbrum proft of the foregn lcensor s as follows: n- n- ( - )( a + e ) ( ) ( a + e ) a W ( ) = r( ) q( ) + F( ) = + [ - ] + n- + n+ - n- + n+ - ( )( - ) ( )( - ) ( ). (3) By dfferentatng (3) wth respect to, we can derve the frst-order condton for proft maxmzaton as follows: dw ( ) ln( a + e ) ln() a = - > 0 f j< < n. + n- + n+ - d ( )( - ) It means that the proft of the lcensor ncreases f the lcensee s assocated wth an upper ter producton stage. From the above dscussons, we can mae the followng proposton. Proposton. The proft of the lcensor s maxmzed f the lcensee s assocated wth the upmost producton stage. The ntuton s as follows: The gans from the technology lcensng spllover to upstream monopolsts as t expands ther derved demands whch results n a hgher nput prce and lowers the proft of the outsde nnovator. As s larger, the rent-extractng effect by the upper upstream monopolsts s smaller. As a result, the 0

12 outsde lcensor can mae a hgher proft f the lcensee s assocated wth an upper producton stage. The ndustry proft under technology lcensng s as follows: ( - )( a + e ) P ( ) = ( - ) n+ + n- + From the proft, we can obtan:. n+ dp ( ) ln( - )( a + e ) = > 0 f j< < n. + n- + 3 d ( )( - ) It shows that the ndustry proft ncreases wth the stage of producton wth whch the lcensee s assocated. That s to say, other ter frms except the lcensee beneft the most from the lcensng f the lcensng occurs n the upmost producton stage. We summarze the result as the followng proposton. Proposton 3. The proft of the ndustry reaches the hghest level f the lcensng occurs n the upmost producton stage. The ntuton s as follows. Accordng to Proposton, the content of the optmal lcensng contract vares by the producton ter wth whch the lcensee assocated and the lcensor charges a lower royalty rate for an upper ter producer. The cost-reducton beneftng from the technology lcensng spreads to all the lower ter producers by means of a lower nput prce. If the lcensee s assocated wth the topmost producton-stage, the royalty rate charged by the outsde lcensor becomes zero. Therefore, the whole ndustry reaches the hghest proft. 6 We now explore the effects of lcensng on the ndustry profts, consumer surplus 6 In ths paper, we assume there s no ndustry proft allocaton. However, accordng to Proposton 3, other ter producers except the lcensee beneft the most from the lcensng f the lcensee s assocated wth the topmost producton stage. Under such a crcumstance, the upmost producton stage producer may reject ths technology lcensng offer. In order to avod ths stuaton, the frms may engage n proft allocaton. Ths extenson s reserved for future research.

13 and socal welfare. By dfferentated () wth respect to, we can derve the comparatve statc effect as follows: dq( ) ln()( a + e ) = > 0. (4) + n- + 3 d ( )( - ) It shows that the output and consumer surplus ncrease wth the ter whch lcensng occurs. Furthermore, socal welfare s defned as follows: SW = CS( q( )) +P ( ). (5) From the above dscussons, t s found that both the ndustry proft and consumer surplus ncrease wth the lcensng ter of the producton. It mples that socal welfare s the hghest f the lcensng occurs n the topmost producton stage. Based on the fndng, we can establsh the followng proposton. Proposton 4. Socal welfare s maxmzed f lcensng occurs n the upmost producton stage. In Proposton, we show that the lcensor would prefer pure fxed fee lcensng f the lcensee s assocated wth the upmost producton stage. Otherwse, the lcensor would adopt a two-part tarff or even a pure royalty contract to suppress the rent to be extracted by the lcensee s upstream frms. If the lcensee s the raw materal suppler, the rent-extractng effect does not exst, but the cost-reducng effect s the most sgnfcant. Ths s why socal welfare reaches the hghest level f lcensng occurs n the upmost producton stage. 4. Varous Input Coeffcents We have so far assumed that one unt of nput s requred to produce one unt of

14 output. However, t s of nterest to dscuss the case under a dfferent nput coeffcent. In ths secton, we assume one unt of nput can produce h unt of output. That s, the nput coeffcent s h. For smplcty, we begn our analyss by consderng the case where the maret structure s of two-ter successve monopoly wth one upstream frm vs. one fnal good producer and the nput coeffcent s two. Accordng to ths the settng, the proft functons of the fnal good producer and the upstream frm are as follows: p p 0 = [ p0( q) - c0 - ] q, p = [ p ( q) - c ] q, where q s the fnal output. Proceedng as before, we can compare the profts of the lcensor f she lcenses her technology to the upstream frm and the fnal good producer as follows: [ ( a c ) c ] ì e (4a- 4c0 - c+ e ) e ï - < 0 f e < ˆ e ï D W = W () - W (0) = 3 8 í ï e (4a- 4c0 - c+ e ) (a- c0 - c+ 4 e ) + 8 e (a- c0 - c) - < 0 f e ³ ˆ e, ï î 3 9 where Ω() s the lcensng revenue f the lcensee s the upstream frm and Ω(0) s the lcensng revenue f the lcensee s the fnal good producer. It s found that lcensng revenue s maxmzed f the lcensor lcenses her technology to the fnal good producer. We can use Fgure to llustrate ths outcome. 7 7 It s nown that Ω s postve (negatve) f the nput coeffcent s one (two). Dfferentatng Ω(0) and Ω() wth respect to h and evaluatng at h=(h=) yelds postve(negatve). Therefore, we derve that there exsts an nput coeffcent, h-hat, to mae Ω=0. 3

15 W W (0) ĥ Fgure. Lcensng revenue and nput coeffcent W () Input coeffcent As shown n the fgure, the proft of the lcensor ncreases wth the nput coeffcent f she lcenses her technology to the fnal good producer, but decreases wth t f she lcenses her technology to the upstream producer. The two curves ntersect at the pont at whch the nput coeffcent falls between and. If the nput coeffcent s equal to, the lcensng proft s necessarly hgher f the lcensee s the fnal good producer than the upstream frm. Thus, we can arrve at the followng proposton. Proposton 5. The proft of the lcensor s hgher f the lcensee s the fnal good producer than the upstream frm and the nput coeffcent of the producton technology s two. 5. Conclusons Over the past two decades, technology lcensng has been studed extensvely. However, there s no lterature to examne the effects of nternatonal technology 4

16 lcensng under an n-stage successve monopoly maret. Ths paper has found that the content of the optmal contract depends on the ter of the producton stage that lcensng occurs. The lcensor prefers a pure fxed-fee contract f lcensng occurs n the upmost producton stage; otherwse, t prefers a two-part tarff or a pure royalty contract. Ths s because the lcensor, beng a frst mover n the game, can use a royalty rate to lower the rents to be extracted by all the upstream frms of the lcensee. Moreover, the proft of the ndustry and socal welfare are both maxmzed f lcensng occurs n the upmost producton stage. Fnally, the lcensor prefers to lcense her technology to the fnal good producer f the maret s that of successve monopoly wth one upstream frm vs. one fnal good producer and one unt of the nput can produce two unts of the fnal good. These results bear a polcy mplcaton and mply that a government should encourage nternatonal lcensng to tae place n an upper than lower stage of producton as the proft of the lcensor, the profts of domestc ndustry and socal welfare are all maxmzed f lcensng occurs n the upmost producton stage. References Anand, B. N., and Khanna, T. (000), The structure of lcensng contracts, Journal of Industral Economcs, 48, Arrow, K. J. (96), Economc welfare and the allocaton of resources for nnovaton, The Rate and Drecton of Incentve Actvty: Economc and Socal Factors, Prnceton Unversty Press. Arya, A. and Mttendorf, B. (006), Enhancng vertcal effcency through horzontal lcensng, Journal of Regulatory Economcs, 9, Cao, J. and Muherjee, A. (06), Maret power of the nput suppler, technology 5

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