Goldilocks and the licensing firm:

Transcription

1 Goldlocks and the lcensng frm: Choosng a partner when rvals are heterogeneous * Anthony Creane and Hdeo onsh We consder how the amount of the technology transferred and the characterstcs of the partner affect lcensng. We fnd that a partal technology transfer can be the ont-proft mnmzng transfer, though under weakly concave demand, a complete transfer always ncreases ont proft f there are at least three frms. We establsh a Goldlocks condton n partner selecton: the optmal lcensee s nether too effcent nor too neffcent. Proftable transfers between suffcently neffcent frms reduce welfare, though a transfer from a suffcently effcent frm ncreases welfare. When makng a complete transfer the effcent frm tends to select an nsuffcently neffcent partner. JEL:D4, L4, L4 ey words: lcensng, technology transfers Mchgan State Unversty Boston College * We thank Jay Pl Cho, Carl Davdson and Thomas Jetschko, as well as partcpants of the Mchgan State theory semnar, for ther comments on a prelmnary draft of ths paper. Of course, all errors are our own.

2 1 1. Introducton nowledge and techncal know-how s transferred between frms n many ways: through lcensng, acquston of rvals, ont ventures, etc. 1 For example, n the auto market, the ont producton venture between GM and Toyota (NUMMI) was partly motvated by gvng GM the opportunty to learn Toyota's effcent manufacturng and management methods, and to apply these technques to other GM facltes (Fenton 005). An ntrgung aspect of the GM-Toyota ont venture s that Toyota actually was ntally n dscusson wth Ford before settlng on GM (The Washngton Post 1980). Ths leads to the queston of why Toyota pcked GM over Ford, or over Chrysler for that matter three non-homogenous companes. An obvous answer s that GM was the proft-maxmzng partner. Ths rases the ssue of what are the characterstcs of the optmal partner among a heterogeneous group when transferrng technology through ont ventures or lcensng. 3 For example, was Toyota choosng the least effcent among the three? On the other hand, snce n ths case the Federal Trade Commsson (FTC) would determne whether the ont venture was allowed, would have Ford or Chrysler or no one been a better partner n terms of welfare? More generally, when approvng lcensng agreements would competton authortes want to nfluence the partner chosen,.e., does the welfare maxmzng partner dffer from the proft maxmzng one? A second ntrgung aspect of ths case s that GM s costs have decreased snce, but have never matched Toyota s. In ths sense, the transfer of Toyota s know-how was not complete, and many mght suspect t could never have been. Ths rases the ssue of whether Toyota wanted to control the amount of knowledge transferred to GM could GM becomng more effcent harm Toyota on the margn more than t benefted GM? 4 Lkewse, when lcensng a technology to a rval the lcensor can control what technology s lcensed. Ths ssue also plays a 1 A ont venture s vewed as a mechansm to transfer knowledge that cannot be done va lcensng (ogut 1988). Such cost mprovements through learnng the rval s knowledge were also a motvatng factor n Ford s long term partnershp wth Mazda (Levn 199) as well as n many other ndustres from smlar ont ventures n the steel ndustry (Cohen 1990) to Sony s conscous strategy (Inkpen 000), as ont ventures are vewed as mechansms to transfer technology (ogut 1988). 3 Lke the costs wth ont ventures, the costs of lcensng technology are often qute hgh, lmtng the number of potental partners. For example, Teece (1976) fnds that the costs assocated wth technology transfers wth lcensng to be on average 19% and as much as 59% of total costs. Caves', et al. (1983) fnd that [t]he preparaton and contract costs nvolved n transferrng technology are not trval, and they strongly qualfy the publc good character that economsts assgn to technology transfer. Astebro (00) also fnds evdence that such costs have real effects on the decson to adopt a technologcal nnovaton. 4 See Roehl and Trutt (1987) for examples of the knowledge transferred beng controlled n ont ventures.

3 role n the ntal queston as the amount of technology that can be transferred could affect the choce of partner or whether an agreement could be reached. These too are all ssues that would concern a welfare-maxmzng competton authorty when approvng lcensng agreements. Though one mght have expected that all of these questons would have already been examned n the well-developed lcensng lterature, surprsngly they have not for the most part, as the maorty of work has been restrcted to analyzng complete transfers n duopoles or wth homogenous rvals, and often assumng lnear demand. 5 In ths paper we analyze a market wth heterogeneous frms to determne whch rval would a frm choose to lcense ts knowledge or technology, how much would t choose to lcense, how lmts n ts ablty to transfer the knowledge affects ts decson, and the welfare mplcatons of these choces. Specfcally, the frms compete n Cournot competton and dffer n ther constant margnal cost of producton and so a technology transfer reduces a frm s margnal cost. We assume that the producton decsons of the frms reman ndependent wth any agreement. That s, we focus on the drect gans from the lcensng and so abstract from any possble benefts from colluson, especally snce outsde of a duopoly, par-wse colluson s not proftable n Cournot competton (Salant et al. 1983). Furthermore, competton authortes typcally mpose condtons when approvng technology agreements so as to prevent colluson from occurrng. We begn by analyzng the effects of a partal transfer between two frms. We fnd that under weakly concave demand f the lcensee s suffcently neffcent then a small technology transfer reduces the ont proft of the two frms (Proposton 3). 6 Thus, we do not expect to see partal technology transfers to have margnal frms as lcensees. In ther semnal paper atz and 5 Wth respect to the amount transferred, the semnal work by atz and Shapro (1985), as well as Rockett (1991) and Cho (00), consder ths but n a duopoly. In the latter two, the focus s on the lcensee usng the technology to mtate or nnovate n the future. Wth respect to heterogeneous rvals, Rockett (1990) consders whch of two potental entrants an ncumbent would lcense so as to deter entry, whch does do not play a role n our model. Hernandez-Murllo and Llobet (006) also consder heterogenety, but snce the monopolst-compettve model of Dxt and Stgltz s used each potental lcensee s a monopolst. Wth respect to lnear demand, the semnal work by atz and Shapro (1985), atz and Shapro (1986) and amen et al. (199) are exceptons to ths assumpton, as well as more recently Gebe and Wolfstetter (007) and Farrell and Shapro (008) though all have homogenous potental lcensees. The mddle three focus on optmal lcensng (aucton) strateges, whle the latter focuses on the welfare effects of potentally nvald patents. For a revew of the lterature see Sen and Tauman (007). 6 Ths also has an nterestng mplcaton regardng the merger paradox (.e., that mergers are usually unproftable): two frms could have a proftable merger under condtons that normally yeld unproftable mergers (Salant et al. 1983) by havng the less effcent frm become even less effcent and leavng the frms as ndependent dvsons (Baye et al. 1996).

4 3 Shapro (1985) have shown that lcensng could reduce ont proft n a duopoly f the lcensor effectvely has a monopoly because then any transfer would reduce the lcensor s near monopoly proft and hence ont proft. 7 In contrast, our result holds for non-duopoly markets and the lcensor need not have a near monopoly poston (n fact, t could be rather neffcent). Gven our result that small transfers can be unproftable, we then turn to see f any general conclusons can be made regardng complete technology transfers (.e., the transferee s cost equals the transferor s cost). Surprsngly, under the assumpton of weakly concave demand we are able to show that lcensng that nvolves a complete technology transfer s always proftable so long as there are at least three frms n the market (proposton 4). Thus, as long as the transfers s complete (and we have an nteror condton), a technology transfer s always proftable no matter ts absolute sze. Specalzng to lnear demand we are able to derve the range over whch proft s decreasng n the amount of the technology transferred and the range over whch the technology transfer s unproftable, fndng that ths range can be up to eghty percent of the cost dfferences between the frms. Thus, a lcense to an neffcent frm may need to make the lcensee nearly as effcent as the lcensor for t to be proftable. An mplcaton of ths s that an attempted technology transfer that s rsky,.e., ether transfers all of the technology or, wth some probablty, transfers nothng, can be more proftable than one that transfers a fracton of the technology wth certanty, even when ths fracton s greater than the expected amount transferred n the rsky case. We then focus on whch partner would maxmze ont proft. Begnnng frst wth complete transfers, we fnd that for weakly concave demand, t s nether a very neffcent nor a very effcent rval that maxmzes ont proft (proposton 5) the goldlocks condton. Intutvely, wth a complete transfer the less effcent the lcensee, the greater s the transfer. One mght at frst glance expect then that ths mples that the least effcent rval must be the lcensee that maxmzes ont proft. Ths s not necessarly true because wth very neffcent frms, the decrease n proft from beng a lttle less effcent s small profts are convex n cost so the margnal gan from choosng a less effcent frm s small. However, the margnal cost the reducton n the market prce as a result of the transfer, whch harms both the lcensor and the 7 We show elsewhere (009) that wth more than two frms n the market that even a frm wth a nearly monopoly poston may lcense some of ts technology so as to drve-out other frms.

5 4 lcensee s not. So, the frm chooses a partner who s nether too effcent nor too neffcent. Wth nstead, a transfer of a fxed amount (.e., that causes a fxed decrease n margnal cost), the frm would choose the most effcent partner possble under strategc substtutablty (proposton 6) because now the cost (the lower prce) s ndependent of the frm chosen and a more effcent frm benefts more from a gven cost reducton. Gven both the strong nterest and the control that competton authortes have over lcensng and technology transfers, we then consder the welfare mplcatons of such transfers. Our frst welfare result s that f both the lcensor and lcensee are suffcently smlar and neffcent, then proftable transfers are welfare reducng (Proposton 7). Ths s n contrast to atz and Shapro (1985) who found that proftable transfers are never welfare reducng n a duopoly, hence, the mportance of consderng non-duopoly markets. Ths s also n contrast to atz and Shapro (1986) and Sen and Tauman (007) who fnd that wth homogenous frms, lcensng always rases welfare and so heterogenety s also mportant n evaluatng the welfare mplcatons of lcensng. 8 The polcy nference s that t may be better to dscourage lcensng between neffcent frms. On the other hand, we are also able to obtan a condton for transfers to be welfare ncreasng. Specfcally, when the most effcent frm makes a complete transfer, then socal welfare always ncreases under general demand (proposton 10). We are able to obtan further welfare results by assumng lnear demand. Frst, f the lcensor has above average margnal cost, then f a small technology transfer reduces ont proft, t reduces welfare (proposton 8). 9 Second, f the lcensor s suffcently effcent then there are welfare ncreasng transfers that reduce ont proft. 10 Thrd, we show that for complete transfers, f the lcensor s suffcently effcent, then t would choose a more effcent partner than the one that would maxmze welfare (proposton 9), whch can be generalzed to downward slopng demand (proposton 9 ). The concluson for a polcy maker whose obectve s to maxmze socal welfare s that effcent frms should not be dscouraged from lcensng ther technology nor restrcted n the amount of technology they transfer, and f a complete 8 Faulí-Oller and Sandonís (00) have shown that n a duopoly wth prce competton, lcensng by means of a royalty could reduce welfare because, as they put t, the royalty works as a collusve devce. 9 Wth respect to the merger paradox, under these condtons frms that choose the strategy of mergng and rasng a dvson s cost to ncrease ont profts wll actually ncrease welfare. 10 atz and Shapro (1985) also fnd ths s possble, but there t requres that the less effcent frm s not currently producng and only would produce wth the technology transfer.

6 5 transfer s possble, the effcent frm should be encouraged to pck less effcent partners. In the next secton we ntroduce the basc modelng assumptons. Secton 3 examnes the effect the amount of technology transferred has on proft whle secton 4 examnes the effect of the type of partner. Secton 5 contans the welfare analyss and secton 6 concludes.. The Model We consder the basc Cournot market structure. There s a commodty besdes a numerare good, and ts nverse demand functon s P(Q) whch has P (Q) < 0 for all Q [0, Q]. There are frms n the market wth no fxed cost of producton and we wll consder only equlbra n whch all frms reman actve,.e., the lcensng s not potentally drastc. Frms dffer n ther constant margnal cost c k, and frms 1,,3 are ordered n such a way that c 1 c c 3 Frms are ndexed as k {1,,,} wth k = 1 beng the most effcent frm. Wth a lttle abuse of notaton let the set {1,,,} be denoted by. Each frm k s producton level s denoted by q k. Frm s proft functon s wrtten as: ( ) π ( q, Q ) = P( Q) c q where Q= q. The frst order condton for proft maxmzaton (assumng nteror k = 1 k soluton) s Ths mples Thus, frm s proft s wrtten as P ( Q) q + P( Q) c = 0. (1) ( PQ ( ) c ) q =. P ( Q) ( PQ ( ) c ) π =. P ( Q) We assume the strategc substtute condton throughout the paper: for all P ( Q) q + P ( Q) 0. ()

7 6 Ths condton guarantees the unqueness of equlbrum of ths game. Fnally, let C = denote the aggregate margnal cost. Wth ths we can establsh a standard result, whose dervaton wll be useful for later analyss. k = 1 c k Lemma 1. Under the strategc substtute condton, equlbrum s unque. Moreover, equlbrum total output level Q s a decreasng functon of aggregate margnal cost C. Proof. Snce equlbrum q s are expressed only by the equlbrum total output level Q, f we can show that Q s unque, then we are done. Summng the strategc substtute condtons up over all frms (), we obtan P ( Q) Q+ P ( Q) 0. Equlbrum total output level Q s determned by the sum of the frst order condtons (1): Dfferentatng the LHS of (3) wth respect to Q produces, ( ) D LHS dq P ( Q) Q+ P( Q) C = 0. (3) = P ( Q) Q+ ( + 1) P ( Q) = P ( Q) Q+ P ( Q) + P ( Q) < 0. From (3), then t follows that aggregate output s decreasng n C.// 3. Producton Technologes and Transferablty Each frm has ts own technology of producng the commodty (the margnal cost of producton s c ), and t has the property rght to ts own technology (e.g., t holds a patent). Thus, frm can sell t or some fracton of ts technology (wth an exclusve usage agreement), denoted T, to another frm through a lcensng or a ont producton agreement. As dscussed n the ntroducton, the real world nstances that motvate our study lead us to focus on par-wse agreements and to assume that the output decsons reman ndependent after any transfer as the ndependence of producton decsons s usually a condton mposed by competton authortes (and colluson s proft-reducng n the Cournot settng).

8 7 We can magne a stuaton where technologes that frms and own have complementartes (and n some cases, ncompatbltes: nonsynergy case), but we assume that technologes are ndependent so as to focus on the pure effects of lcensng. That s, f frms and have technologes wth margnal costs c and c, respectvely (assume c < c wthout loss of generalty), then frm s technology s worthless for frm, whle frm can reduce ts margnal cost of producton by T (0, c c ] by adoptng frm s technology through lcensng or some agreement. That s, after the (partal) technology transfer, frm s margnal cost s c T c. 3.1 Partal Technology Transfers Followng prevous work (e.g., atz and Shapro 1985), we focus on how technology transfers affect the ont proft of frms and. By the technology transfer, frm s margnal cost decreases. Ths reduces C (aggregate margnal cost), and there wll be negatve externaltes to other frms through the lower prce snce s fxed. The sum of proft for frms and s ( PQ ( ) c ) PQ ( ) c Π= π + π = +. P ( Q) P ( Q) Recallng that c < c, and treatng T as a contnuous varable (the amount of technology that s transferred from to ), that s, the cost reducton for frm can be made contnuously, t s easy to see from (3) that the equlbrum gven a transfer T s determned by Totally dfferentatng ths equaton, we obtan P ( Q( T)) Q( T) + P( Q( T)) ( C T) = 0. dq 1 = > 0. dt P Q ( + 1) P Thus, the change n ont proft from a small transfer (.e., evaluated at T = 0) s:

9 8 ( ) ( P c ) ( P ) ( PQ ( + 1) P ) Π P c ( P) + P P c ( P) + P c P P c = + P d dt 1 = P c P + P + P c P ( P ) ( PQ ( + 1) P ) ( ) ( P c ) ( ) ( ) P P c P P Q ( + 1) P 1 = ( P c ) + P c PQ ( + 1) P P + ( P c ) P c P c ( PQ ) + +. ( P ) Snce the sgn of the denomnator s postve, f the sgn of the numerator s postve, then we can say that ont proft ncreases as technology transfer T ncreases. We summarze ths as a lemma. Lemma. A margnal technology transfer from frm k to frm mproves ther ont proft f and only f the followng condton holds. P ( P c ) + P c + ( P c ) P c P c ( PQ ) >. ( P ) Surprsngly, the margnal mpact of a technology transfer on ont proft need not be postve. Frst, t s affected by the concavty of demand,.e., the sgn of P. Further, the contents of the frst and second brackets can also take ether sgn. Potentally, then, the margnal technology transfer could reduce ont proft or more mportantly the entre technology transfer may reduce ont proft. Snce the frst bracketed term can take ether sgn, even f demand s lnear (P (Q) = 0), the above condton can be volated that s, the margnal mpact of the technology transfer on ont proft can be negatve. As lnear demand s a standard assumpton n the lcensng lterature (see the dscusson n the ntroducton), t s natural to begn wth ths case when determnng condtons for technology transfers to reduce ont proft and then consder the more general case. From lemma, wth lnear demand the condton for the margnal transfer to ncrease ont proft s (P c ) + (P c ) > 0. We can rearrange ths to the more ntutve condton that frm s proft margn s not too small relatve to the cost dfference between the two frms:

10 9 P c c c. 1 However, as P s a functon of c, whch depends on T, potentally ths condton may not hold for large T. Fortunately, t s straghtforward to check that the aggregaton of the strategc substtute condtons mples that f the condton holds at the ntal costs c and c then t holds at all levels of technology transfers T (0, c c ] (.e., dp/dc k 1). In ths case, ont proft as a functon of the amount transferred takes ts mnmum value at T = 0, and s monotoncally ncreasng. To summarze, T Proposton 1: Wth lnear demand, ont proft of frms and, π + π, ncreases T monotoncally wth T (0, c c ], f and only f the followng condton s satsfed, P c c c. 1 It mmedately follows from ths proposton that for the frms, t s optmal to set the transfer level at the maxmum T = c c when the condton holds. Inspecton reveals that the condton s more lkely to hold the more frms that are n the market (), the more smlar are the frms (c c ) and the more effcent s frm (P c s large). All three turn on the harm the technology transfer causes by reducng the market prce versus the beneft to the recevng frm from havng lower costs (greater output). Frst, as there are more frms n the market (), for a gven ncrease n frm s output (the beneft to ont proft), the harm s spread across more frms the other frms produce less, the busness stealng effect and so less harm to frm. Second, the more smlar are the frms, the smaller the maxmum transfers and hence maxmum harm (snce the condton holds for all T). Fnally, when frm s suffcently neffcent a small technology transfer creates lttle beneft snce ts output s close to zero (n other words, proft s convex n cost). That s, the larger the prce-cost dfference (P c ), the greater the beneft to the lcensee from recevng a small transfer. In the semnal work by atz and Shapro (1985) t was shown that n a duopoly settng an arbtrarly small technology transfer s ontly proftable when the aggregaton of the strategc substtute condton holds and f the frms are suffcently smlar n cost. We see that wth lnear

11 10 demand any sze of transfer (up to makng the frms equally effcent) can be proftable when our condton holds. Further, the condton holds n non-duopoly settngs and the frms need not be suffcently smlar n cost so long as ether there are a large number of rvals or the lcensee s suffcently effcent (P suffcently greater than c ). At the end of ths subsecton we show how our proposton generalzes to weakly concave demand (whch mples that the strategc substtute condton holds). Potentally more nterestng s the case when the condton s volated and a small technology transfer reduces ont proft. That s, f frm chooses a very nferor partner (or only nferor partners are avalable) so that c c s large or P c s small, then a small transfer would decrease ont proft and possbly even a complete transfer would decrease ont proft. That s, no transfer would be optmal. To determne the range of T such that transfers are unproftable, we frst solve for the equlbrum prce, quanttes and proft wth lnear demand. Normalzng the ntercept and slope (whch does not affect the results) to one, wth lnear demand we have P(Q) = 1 Q. Assumng further that constant margnal cost c k (0,1) and lettng Q(C) denote the ntal equlbrum output gven startng aggregate margnal cost C from (3) we have C QC ( ) = C 1+ C PC ( ) = 1 + = C qk( C) = + ck Therefore, wth lnear demand ont proft before lcensng s π + π = C c 1 C ( ) 1 ( ) + c Jont proft after the lcensng gven T (0, c c ] s π T + π T ( ) 1 C T 1 C T = + c + + c T T T = PC ( ) c + PC ( ) c + T,

12 11 where the T superscrpt ndcates a transfer has occurred. Thus, the total benefts from the technology transfer s Δ π = π + π π π T T T T T ( PC ( ) c ) = PC ( ) c + PC ( ) c + T PC ( ) c ( + ) 1 T T ( 1) 1 ( ) = + 1 P( C) c c c. + + (4) Wth these prelmnary calculatons we can obtan the followng proposton (the proof s n the appendx). Proposton. Wth lnear demand, the ont proft of frms k and ntally decreases monotoncally for T (0, T) and then ncreases monotoncally for T (T, c c k ], f the followng condton s satsfed c ck PC ( ) c <. (5) 1 Ths mples that there s a crtcal value T* > T, such that the total beneft from the transfer, Δπ T, takes negatve values for T (0, T*). Snce ont proft s convex wth respect to T, then f the frms are consderng lcensng, the ont proft maxmzng level of transfers wll ether be all or nothng. Thus, f frm cannot make a complete transfer to frm, specfcally, f the maxmum technology that t could transfer T < T*, then a lcensng agreement wll not be reached between the two frms. An example may help clarfy the effects here. Example 1. Consder a market wth three frms ( = 3), wth technologes c 1 = 0, c =. and c 3 =.4. In a lcensng agreement between frm 1 and frm 3, T.16, that s, a technology transfer that only successfully transferred forty percent of the superor frm s technology advantage would maxmze the loss between the two frms. Indeed, to make such a transfer proftable would requre an eghty percent of the technology advantage to be transferred (an eghty percent

13 1 cost reducton for frm 3). As the cost dfferences between frms s usually a multfaceted affar (consder Toyota and GM), a more effcent frm may not be able to transfer the entre cost superorty, and so ths could well be a bndng constrant. If nstead frm 3 s cost le anywhere between.4 and.4, then a small transfer to frm 3 reduces ont proft; a lcensng agreement would not be reached. Interestngly, the same relatve relatonshp holds between frm and 3: for a technology transfer to be proftable requres at least eghty percent of the technology dfference to be transferred. Fnally, f frm were more neffcent (c.9) then a small technology transfer between frm 1 and would also reduce ont proft. In ths case, f only a small amount of the technology were transferable, the most effcent frm would not engage n a technology transfer.// These results are also related to atz and Shapro (1985) who fnd that n a duopoly ont proft decreases wth a technology transfer f the effcent frm s monopoly prce s arbtrarly close to the neffcent frm s margnal cost. That s, when the frms are suffcently dfferent n cost so that before the transfer the effcent frm nearly drves out ts rval. In ths case, the effcent frm loses ts near monopoly poston wth any transfer and so any transfer s ontly unproftable. 11 Here we see from proposton and example 1 that wth lnear demand unproftable transfers can occur n non-duopoly markets and further that there are new and dfferent condtons under whch a technology transfer reduces ont proft. Specfcally, the lcensor need not have a near monopoly poston nor even be the most effcent frm (t could even be the second most neffcent frm). Frst, the lcensor can be very neffcent and a small transfer s stll ontly unproftable when c s suffcently close to P(C). Second, the lcensee s cost can be sgnfcantly less than the market prce and a small transfer s stll ontly unproftable when the two frms are suffcently dfferent n cost. At the end of ths subsecton we show that the former condton (c s suffcently close to P(C)) can be extended to weakly concave demand. A dfferent mplcaton of proposton s that under ths condton the frms ontly beneft f they, nstead of actually transferrng the technology, can rase frm s cost. Ths has an nterestng mplcaton regardng the merger paradox (that n Cournot settngs mergers 11 Creane and onsh (009) show that wth more than two frms, lcensng by a frm wth a near monopoly poston can be proftable (n contrast to atz and Shapro 1985) when t drves other frms out of the market.

14 13 wthout large cost synerges are not proftable, see Salant et. al 1983). Specfcally, f the two frms merge, but keep ther producton decsons ndependent (see, e.g., amen and Zang 1990) and have frm s cost ncrease, then the merger becomes proftable. Rasng a dvson s cost would seem to almost always be feasble. The prevous example can be used to show how rasng one s dvson s cost can make a merger proftable. Specfcally, consder a market wth three frms and c 1 = 0, c =. and c 3 =.4. Consder a merger between frms 1 and 3 n whch they leave ther output decsons of each frm (now called dvsons) ndependent. In ths case any ncrease n the hgh cost dvson s cost rases ont proft. More broadly, f c 3 >.09, then a merger that keeps the dvsons ndependent but rases the neffcent dvson s cost suffcently rases ont proft. We brng to a close ths subsecton by consderng what conclusons we can arrve to under more general demand. Propostons 1 and partally extends to weakly concave demand case. 1 The proof of proposton 3 s found n appendx. Proposton 3: If demand s weakly concave, then A. when the frms have suffcently smlar costs (c c ), a small technology transfer ncreases ont proft. B. when the less effcent frm s suffcently neffcent (c s suffcently to close to the market prce: P(C) c 0), a small technology transfer decreases ont proft. Part B of proposton 3 ndcates that we should not expect to see margnal frms (.e., hgh cost/low output frms) obtanng lcenses that yeld only small cost mprovements from ther rvals. Further, f transactons cost assocated wth technology transfers s hgh (Teece 1976, Caves', et al. 1983), then even proftable transfers for more effcent frms may stll yeld negatve net proft once the transacton cost s consdered. Indeed, Astebro (00) fnds evdence that such transfer cost help to explan why technology adopton s less lkely when frms have smaller plants (smaller output). Part A of proposton 3 together wth part B suggests that the lcensng of small nnovatons s more lkely to be observed between smlar frms 1 Case A of Proposton 3 corresponds to the last part of convex functon Δπ T (c c ), whle case B corresponds to the ntal part of t (condton P(C) c 0 corresponds to P(C)- c < (c - c )/(-1) n lnear demand case).

15 14 brds of a feather. 3. Complete Technology transfers Propostons and 3 show that a partal technology transfer from a frm to a suffcently neffcent partner can reduce ont proft. We now consder the extent to whch these results extend to complete technology transfers. Somewhat surprsngly gven those results, we show that under weakly concave demand (whch ncludes lnear demand) a complete technology transfer s always proftable as long as there s a thrd frm. The proof s nvolved, and found n the appendx. Proposton 4. Assume nteror solutons (no frm chooses zero producton). Then, for any par of frms and wth c < c, a complete technology transfer from frm to frm s ont proft mprovng, f 3 and P (Q) 0 for all Q. Ths result combned wth propostons and 3 ndcate that the only tme we should expect to observe technology transfers to neffcent frms s when the transfer s complete, that s, brngs the neffcent frm s cost to the lcensor s level. One thng that Proposton 4 does not state s whether a complete technology transfer s more proftable than any partal technology transfer. It appears unlkely that a partal transfer domnates a complete transfer snce by proposton 3 when frm s technology approaches frm s, ont proft s ncreasng from a small transfer. In fact, t can be shown that under lnear demand (P = 0), a complete transfer domnates any partal transfer. 4. Transfers of Technology and the Choce of a Partner Whle n the prevous secton we consdered the effect that the amount of technology transferred has on ont proft gven some partner, n ths secton we consder whch partner would maxmze ont proft. That s, for frm, whch frm would create the greatest ncrease n ont proft from a technology transfer? Gven proposton 4 we begn by consder the case when frm

16 15 can transfer all of ts technology so that ts partner s cost equals ts cost ex post (or equvalently the amount transfer s a constant fracton of the cost dfference). That s, when T = c c, whch we know wll be proftable. Hence, choosng a less effcent partner leads to a larger technology transfer. We then wll consder whch partner would be chosen when only a fx amount of ts technology can be transferred. That s, the rval s cost s reduced by the same amount regardless of the rval chosen. 4.1 The Optmal Partner for a Complete Technology Transfer Recall that Q(C) denotes the ntal equlbrum output gven startng aggregate margnal cost C from (3). Therefore, let Q(C ) be the equlbrum output gven aggregate margnal cost C after frm makes a complete transfer to frm,.e., C = C c + c, and T denote the amount of technology transferred (T = c c T ). The total beneft (.e., change n ont proft) from a complete technology transfer from frm to frm s T T T Δ π = π + π π π PQC ( ( ) c PQC ( ( )) c ( PQ ( ) c ) PQ ( ) c = +. P ( Q( C )) P ( Q( C )) P ( Q) P ( Q) Let us consder whch partner would maxmze ont proft from a transfer of technology from frm. Notng that dc /dc = -1 (selectng a less effcent frm decreases aggregate cost after the transfer), so dq(c )/dc = -dq/dc [ P Q ( + 1)P ] -1 > 0, we take the dervatve of π T Δ wth respect to c : T Δπ PQC ( ( )) c dq PQ ( ) c = ( P ( Q( C ))) P ( Q( C ))( P( Q( C )) c ) + c [ P ( Q( C ))] dc P ( Q) PQC ( ( )) c dq P ( Q( C ))( P( Q( C )) c) PQ ( ) c = ( ( )) P Q C ( ( )) [ P ( Q( C ))] dc P P Q C + ( QC ( )) P ( Q) PQC ( ( )) c dq PQ ( ) c [ ]. P P q P = + + [ P ( Q( C ))] dc P ( Q)

17 16 Snce P + P q < 0 by the second order condton, the frst term s negatve and the second term s postve. In words, the frst term s the effect of a slghtly more neffcent frm beng selected on the lcensor and lcensee s proft after the lcensee receves the transfer. A less effcent lcensee means a greater output after the transfer whch harms the lcensor. Snce the lcensee wll also have margnal cost c after the transfer, the lcensee s proft s the same as the lcensor s after the transfer. Thus, the lcensee s proft after the transfer also decreases as a more neffcent frm s selected. The second term s the effect of a slghtly more neffcent frm beng selected on that frm s proft before the transfer. Ths s ncreasng n c : a more neffcent frm has lower proft beforehand, whch means a greater ncrease from the transfer. Interestngly, ths formula says that there s (potentally) an nteror optmal. The best partner s not too close to frm but not too far from frm as well. The proof s n the appendx. Proposton 5. Wth a complete transfer, the ont-proft maxmzng partner for a frm s nether too effcent nor too neffcent relatve to the frm under weakly concave demand. We note that for these condtons the number of rvals s fxed. 13 Ths goldlocks condton s ntutve: you cannot make a rval who s that effcent much more effcent. Thus, there s a beneft from pckng less effcent rvals as there s a greater ncrease n proft from the transfer. However, you can pck too neffcent of a rval. The reason s that as you pck a more neffcent rval the prce falls more, harmng you as well as the rval. At the same tme, when consderng suffcently neffcent frms, a slghtly more neffcent frm does not have much less proft (snce ts output s approachng zero,.e., margnal cost s approachng the prce) and the gan from selectng a slghtly more neffcent rval approaches zero. These trade-offs also exst f one consdered nstead whch rval would bd the most for the complete technology transfer n a smple aucton A possble varaton of the partal transformaton case would have the fracton of technology s proportonal to the technology dfferences,.e., T(α) = α(c c ), α (0,1]. However, because the fracton s proportonal, the characterzaton s analogous to the complete technology transfer wth c now dependng on α. In ths case, as α ncreases the optmal partner s always more neffcent than frm even though wth complete technology transfer frm would never choose a suffcently neffcent frm. 14 In ths case, snce the rval does not nternalze the harm to the lcensee a more neffcent frm would obtan the lcense as compared to the rval that maxmzes ont proft.

18 17 If we restrct demand to be lnear (P = 0) then the ont proft maxmzng lcensor can be explctly determned, as the dervatve above then takes ts peak at c c + ( 1) P( C) c = + 1 ( P( C) c ) = PC ( ). ( ) + 1 As an example, consder a market wth four frms wth costs c 1 = 0, c =.1, c 3 =. and c 4 =.3. In ths case the most ontly proftable partner for the most effcent frm s to select s the ntermedate cost rval (frm 3) wth margnal cost.. 15 Interestngly, even though a small technology transfer to the least effcent rval (frm 4) would reduce ont proft, a complete transfer ncreases ont proft more than a transfer to the most effcent frm (frm ). 4.. The Optmal Partner for Partal Technology Transfers We now turn to the case when frm can only make a partal transfer. Specfcally, whchever partner frm selects, the partner gets exactly the same cost reducton:.e., T s common to every frm. Thus, the prce after transfer s ndependent of whch frm receves the transfer and so the harm to the lcensor s the same. The ont proft maxmzng partner then s the one who benefts most from a cost reducton. The total benefts from lcensng n ths case s Δ π = π + π π π T T T T T PQC ( ( ) c PQC ( ( )) c + T ( PQ ( ) c ) PQ ( ) c T T = + P ( Q( C )) P ( Q( C )) P ( Q) P ( Q), where C T ndcates aggregate cost after the transfer,.e., C T = C T. Takng dervatve wth respect to c, Δπ T monotoncally decreases (see the appendx) and so we can conclude, Proposton 6. Wth a fxed amount of technology to be transferred, the frm chooses the 15 In ths case, when frm 1 selects frm 3, the least effcent frm (4) does not produce. The example can easly be adusted so that frm 4 does produce (c 3 =.75) n ths case wth no change n the qualtatve results (.e., frm. s stll the partner that maxmzes ont proft).

19 18 closest partner possble under strategc substtutablty. Thus, frm would choose the closest partner (lowest cost of possble partners) f t s proftable (and f the partner s suffcently close to frm, then the transfer s guaranteed to be proftable). Proposton 6 however allows for the possblty that there s super-addtvty, that s, f T > c c, frm becomes more effcent than frm (or ndeed frm s already more effcent than frm ). Ths s certanly possble f frm has some propretoral technology that frm does not have. On the other hand, t s readly concevable that frm does not have any specal technology, n whch case T must be constraned so that T c c. Defne then the most effcent frm that gets the complete amount of transfer T as c T : T = T c c. In ths case, for any frm k more effcent than c T (c k < c T ) we are back to the realm of proposton 5 (a complete technology transfer equal to T = c k c < T c c ). 5. Welfare Effects We now nvestgate the effect of technology transfers on socal welfare whch we defne as the sum of the frms proft and consumer surplus. Snce technology transfers reduce producton cost, socal welfare tends to ncrease n the amount of technology transferred. Indeed, atz and Shapro (1985) show that wth a duopoly, lcensng that ncreases ont proft always ncreases welfare (and welfare decreasng lcensng always decreases ont proft). Lkewse Sen and Tauman (007) fnd lcensng to be welfare mprovng under general lcensng schemes. Here we extend the welfare analyss to when there are more than two frms and those frms are heterogeneous. Despte prevous results, we fnd that proftable lcensng could reduce welfare. Ths possblty arses because f a very neffcent frm obtans a technology transfer that reduces ts cost only slghtly, socal welfare s reduced because ts resultng ncrease n producton wll dsplace the producton of more effcent frms. Ths mechansm has already been noted by Lahr and Ono (1988) who show that makng a suffcently neffcent frm more effcent reduces welfare. The queston here s whether ths mples that ontly proftable lcensng can reduce welfare contrary to pervous results. By the use of proposton 3 combned wth Lahr

20 19 and Ono s result we are able to show that the prevous results do not generalze to when there are more than two frms and frms are heterogeneous: proftable lcensng can be welfare reducng lcensng. Gven ths result one may wonder f there are condtons that guarantee that a technology transfer rases welfare. We then show that f the most effcent frm makes a complete technology transfer, then welfare ncreases. The polcy mplcatons of these results appear straghtforward: competton authortes should be scrutnous of technology transfers (through lcensng, ont venture, or merger) between margnal frms (n the technologcal effcency sense) n an ndustry, especally small transfers. On the other hand, the most effcent frm wthn an ndustry should not be dscourage from makng a technology transfer to a rval and moreover should be encourage to make the technology transfer complete. 5.1 Welfare-reducng proftable lcensng To show that a proftable transfer can reduce welfare, we begn by presentng Lahr and Ono s condton for when an mprovement n the margnal cost of an neffcent frm reduces socal welfare. Lemma 3. (Lahr and Ono 1988): When frm s margnal cost (c ) decreases, socal welfare decreases f c s suffcently hgh, though consumer welfare (surplus) ncreases. We now combne lemma 3 wth Proposton 4 to obtan a new result: there are proftable technology transfers that reduce total welfare though beneftng consumers. Proposton 7: Suppose that demand s weakly concave and that there are more than two frms. Then, f frm has suffcently hgh margnal cost (c ) and frm s margnal cost s suffcently close to frm s, then welfare decreases though consumer welfare (surplus) ncreases by a proftable lcensng between and. The prevous example can be used to llumnate when ths can happen. Recall that n that example there are four frms wth costs c 1 = 0, c =.1, c 3 =. and c 4 =.3. In ths case, a

21 0 complete technology transfers between frm. and.3 s ontly proftable and welfare reducng. As a second example consder a market wth fve frms wth costs c 1 = 0, c =.075, c 3 =.15, c 4 =.5 and c 5 =.9 (so the least effcent frm produces n the ntal equlbrum). In ths case, a complete technology transfer from ether frm 3 or 4 to the least effcent frm (frm 5) s ontly proftable and welfare reducng. Though ths result s novel to the lcensng lterature, there are prevous results n the lterature that may at frst glance appear to be smlar even though they are qute dstnct. Frst, atz and Shapro (1985) have shown that n a duopoly a technology transfer can reduce welfare, but only when t reduces ont proft. Hence, such transfers would never occur. In contrast, here there can be technology transfers that reduce welfare, but ncrease ont proft. Second, Faulí-Oller and Sandonís (00) have shown that n a duopoly that proftable lcensng can reduce welfare, but ths requres the use of a royalty (rasng the recpent s margnal cost) and only occurs n prce competton. As they note, the royalty works as a collusve devce and so reduces welfare. More generally, lcensng contracts can reduce welfare through ther collusve effects (Shapro 1985 and others), whch do not exst here. We have seen that technology transfers can reduce ont proft and welfare. A natural queston s the relatonshp between these two condtons. Snce welfare decreases because the harm to aggregate proft (from the effcent frms producng less) outweghs the beneft to consumers, one mght suspect that when technology transfers reduce ont proft, then t reduces welfare. To obtan more explct results, we specalze to the case of lnear demand so as to use the specfc condton (5) for ont proft to decrease from technology transfers. We can then obtan an explct condton for a technology transfer to reduce welfare when demand s lnear (see the appendx for the proof): Lemma 3. Wth lnear demand socal welfare decreases when frm s margnal cost decreases f + + 3C+ C + 0. c > ( + 1) (6) A suffcent condton for ths s that frm has margnal cost (c ) greater than 1 C +.

22 1 Snce the market prce under lnear demand s P(C) = (1 + C)/( + 1), clearly the above condton s satsfed for relatvely neffcent frms. Now we can turn to the comparatve analyss. Rewrtng equaton (5) the condton for a transfer to be unproftable as (1 + C)( 1) c + < c, (5 ) ( + 1) t s smple to show that f c C/ (.e., above average margnal cost) then (5 ) mples (6) so long > ; when a small technology transfer between relatvely neffcent frms reduces ont proft, then t reduces welfare. To summarze: Proposton 8: Wth lnear demand, f a small technology transfer reduces ont proft, then t reduces welfare when the transferrng frm has above average cost technology and >. An nterestng mplcaton of ths result related to the merger paradox s that f a merger between two neffcent frms that rases the less effcent dvson s cost s proftable, then t also rases welfare. Perhaps more nterestng s that when frm s suffcently effcent, transfers that reduce ont proft can ncrease welfare. That s, even though a technology transfer would reduce ont proft t could stll ncrease welfare. Roughly ths s true when there are relatvely few frms (small ) or relatvely hgh aggregate cost (large C). An example wll perhaps make ths clearer. Consder a market wth four frms ( = 4) wth costs c 1 = 0, c =.15, c 3 =. and c 4 =.5 (C =.6). It s straghtforward to verfy that a small technology transfer between the most effcent frm (frm 1) and the least effcent frm (frm 4), reduces ont proft, but ncreases welfare. 16 Ths result s also suggestve technology transfers from the most effcent frm mght always be welfare ncreasng under certan condtons. We fnd that the needed condton s qute smple: that the technology transfer s complete. 16 The ntuton behnd ths s as follows. If the transferrng frm s relatvely neffcent, then ths mples all the more effcent frms are also harmed by the transfer more than the recevng frm benefts. The harm to aggregate proft s large (or alternatvely the amount of producton shft from more effcent frms to the less effcent frm s large). On the other hand, f the transferrng frm s very effcent, then the harm to the other frms n the market s relatvely small and so the consumer surplus beneft can outwegh the loss n aggregate proft.

23 We next consder whch partner for frm would maxmze welfare. Recall that when consderng whch partner would maxmze the ncrease n ont proft (secton 4.1), the choce of the partner affects the ont proft before the transfer (a less effcent partner chosen means smaller ont proft before the transfer). However, when consderng whch partner would maxmze the ncrease n welfare, welfare before the transfer occurs s not affected by the choce of partner snce welfare ncludes the sum of all frms operatng cost. For ths reason, when consderng welfare, the choce of a partner s equvalent to the choce of amount of technology transferred. It can be shown that f the lcensor s suffcently neffcent then dervatve wth respect to c s ntally negatve: as we know welfare can decrease wth a complete technology transfer when both frms are suffcently neffcent. A lttle more nsghtful s that snce the functon s convex, then f there s a partner that would ncrease welfare, then the least effcent partner would ncrease welfare the most. Specfcally, t can be shown that f frm s suffcently effcent (c 0), then the dervatve at c = c s postve and so snce welfare s convex n c t s welfare optmal that frm chooses the least effcent frm to make a complete transfer. When consderng prvate ncentves nstead, we saw that for ont proft maxmzaton there was an nteror soluton (proposton 5): the best partner was not too neffcent. Thus, wth complete transfers the effcent frms may choose an overly effcent frm as a partner. Proposton 9: Wth lnear demand, the proft maxmzng partner for a suffcently effcent frm to make a complete transfer to s more effcent than the welfare maxmzng partner. We brng to a close ths subsecton by consderng the case of a fxed technology transfer. We saw that the ont-proft maxmzng choce would be to choose the most effcent frm possble. It turns out that n ths case, the welfare calculus yelds the same result. The reason s smple. Frst, a gven reducton n aggregate margnal cost has the same effect on consumer surplus ndependent of the frm recevng the cost reducton. Second, the only effect ths change has on aggregate proft s on the lcensee s change of proft snce the market prce after the transfer depends only on aggregate margnal cost (and so s ndependent of whch frm receves the transfer). However, ths s the same calculaton for maxmzng ont proft and so the two questons yeld the same answer.

24 3 5. Welfare-mprovng proftable lcensng The prevous subsecton provded condtons for technology transfer to reduce welfare even when such transfers are proftable. The fnal result though was that, wth lnear demand, f frm s suffcently effcent then a complete transfer rases welfare. The leads to the queston of whether ths would hold under more general demand and how effcent must frm must be. Indeed, we can show that f frm s the most effcent frm, then a complete transfer s always welfare ncreasng. For ths result, we need no condton on demand functon (see the appendx for the proof). Proposton 10. Suppose that the most effcent frm 1 makes a complete transfer to frm (c 1 c c c ). Then, the socal welfare mproves. Thus, a complete technology transfer by the most effcent frm always rases welfare. Actually, from the proof n the appendx, t s clear that a complete technology transfer to the least effcent frm from the most effcent frm acheves the hghest socal welfare gan (n contrast to the case of a fxed technology transfer when a transfer to the most effcent frm possble acheves the hghest socal welfare gan). Thus, we can make a weaker statement of Proposton 9 wthout the lnear demand assumpton. Proposton 9 : The proft maxmzng partner for the most effcent frm to make a complete transfer to s more effcent than the welfare maxmzng partner, snce the latter s the least effcent frm. The results here suggest that for complete transfers (or those proportonal to the technology gap between the frms), polcy makers may want to encourage the domnant frm n an ndustry to lcense ts superorty to a partner less effcent than the frm would fnd most proftable. On the other hand, for fxed technology transfers, the domnant frm s ncentves would be n lne wth socal ncentves. Thus, n consderng polcy, a crtcal fact s whether the transfer s ndependent of the effcent dfferences.

25 4 6. Concluson We explore technology transfers (through lcensng or ont venture agreements) n a market wth frms heterogeneous n cost. We begn by consderng the proft maxmzng amount of technology to be transferred. We fnd that wth weakly concave demand (whch ncludes lnear demand) a small (partal) technology transfer s unproftable when the recevng frm s suffcently neffcent, but proftable when the two frms are suffcently smlar. Thus, f only part of the effcency dfferences between frms s approprable (so that the less effcent frm cannot be made as effcent as the superor frm) then we expect to see transfers between effcent frms only. An mplcaton of ths result s that a merger between two neffcent frms can be proftable under condtons n whch they normally are not proftable (Salant, et al. 1978) f the output decsons reman ndependent (amen and Zang 1990) and the less effcent frm becomes even less effcent. That s, a merger can be proftable by rasng a dvson s cost. We then turn to examne the case of complete transfers (.e., the recevng frm becomes as effcent as the lcensor). Even though partal transfers can reduce ont proft, we fnd that under weakly concave demand, any complete technology transfer between frms ncreases ont proft (that s, lcensng complete transfers s proftable) so long as there are at least three frms n the market. Thus, to the extent that the Toyota-GM ont venture was drven by the technology transfer, a suffcent condton for t to have been successful would have been that GM lowered ts cost to Toyota s level, whch recent events suggest have not occurred. From our results regardng partal transfers, we see that f GM s cost reducton was small enough then ther ont proft could well have decreased from the venture. An mplcaton of these results s that an attempted technology transfer that wll ether be complete or, wth some probablty, transfers nothng s more proftable to one that transfers only a partal amount wth certanty, even f the expected amount of technology transferred s greater n the certanty case. We then consder whch partner a frm would choose to lcense ts technology. Our frst result s that wth complete transfers the optmal partner s nether too close to the frm n terms of effcency nor too neffcent. Work by Leberman and Dhawan (005) suggests that GM and Ford were equally effcent at that tme, whle Chrysler was the least effcent (Toyota s dscussons wth Ford but not Chrysler then s potentally consstent wth ths). We then consder a transfer of a fxed amount of technology, whch corresponds to the case when the frm has made an advance