The Role of Fixed Fee and Royalty in Patent Licensing

Transcription

1 Department of Economics Working Paper No. 011 ttp:// Te Roe of Fixed Fee and Royaty in Patent Licensing Sougata Poddar Nationa University of Singapore Uday Banu Sina Indian Statistica Institute Abstract: We consider a monopoistic screening mode of patent icensing. Tere is one patentee and one icensee and te patentee wises to se a patent of cost reducing tecnoogy to te icensee. Te patentee is an outsider and te icensee is te ony firm in te product market. Te icensee possesses private information about te market demand wic is unknown to te patentee except for some prior beief about it. In tis scenario, we find te inear optima icensing contract. Key words: JEL Cassification: icensing, fixed fee, royaty, adverse seection D3, D5, L13, L1 00 Sougata Poddar and Uday Banu Sina. Sougata Poddar, Department of Economics, Nationa University of Singapore, 10 Kent Ridge Crescent, Singapore 11960, Fax: ( , E-mai: ecssp@nus.edu.sg. Uday Banu Sina, Economic Researc Unit, Indian Statistica Institute, 03, B. T. Road, Kokata , India, E-mai: sinauday@yaoo.com. Views expressed erein are tose of te autors and do not necessariy refect te views of te Department of Economics, Nationa University of Singapore.

2 1. Introduction Patent icensing is fairy common tat takes pace in amost a industries. It is a source of profit for te inventor (aso caed patentee wo earns rent troug icensing a patent. Te common modes of patent icensing are: a royaty on per unit of output produced wit te patented tecnoogy, a fixed fee tat is independent of te quantity produced wit te patented tecnoogy, or a combination of fixed fee and royaty. Te patentee can coose wic of tese modes of icensing to empoy. Tat is, se can decide on weter to set a royaty rate and/or a fixed fee for wic any firm can purcase a icense or auction a fixed number of icenses. Te objective of te patentee is to maximize profits troug icensing. In te patent icensing iterature, depending on patentee s position in te market, generay two cases are discussed. One, were te patentee is outside te market of operation i.e. te patentee is not a competitor in te product market and two, were te patentee is inside te market of operation and naturay becomes a competitor in te product market. Given tese two possibe situations, te resuts regarding optima icensing is rater interesting. In a compete information framework, if te patentee appens to be an outsider, a fixed fee icensing is better tan per unit royaty icensing (see Kamien and Tauman (1986, Katz and Sapiro (1986, Kamien et. a. (199, Kamien (199 among oters and te reverse appen wen te patentee is an insider i.e. a competitor (see Wang (1998, Poddar and Sina (001. Given tis teoretica finding, in reaity, ten one soud expect tat eiter a fixed icensing or a per unit royaty icensing contract is being offered by te patentee to te icensee depending on weter te patentee is an outsider or insider. But empirica facts say oterwise 1, e.g. Rostoker (1983 in a firms survey finds out royaty pus fixed fee icensing accounts for 6 percent of te icens ing arrangements, royaty aone 39 percent and fixed fee aone 13 percent. Simiar studies by Tayor and Siberston (1973 find tat arrangements wit royaties or a mixture of fixed fee and royaty are far more common tan a simpe fee. In tis paper, we try to find out a pausibe teoretica expanation of tis empiricay observed fact in icensing arrangements. We consider a simpe mode of asymmetric information wit adverse seection. Tere is one patentee and one potentia icensee. Te patentee ods a patent for a cost reducing tecnoogy and wises to icense it wit an objective to maximize its own profit. Te icensee is te ony firm operating in te product market. Te patentee is an outsider. Te icensee as te private information regarding te market demand (weter it is ig or ow wereas te 1 See aso Caves et a. (1983, Maco-Stader et a. (1996, Jensen and Tursby (001 among oters. 1

3 patentee as ony a prior beief about it. Te patentee wants to offer an optima inear icensing contract for two possibe demand situations (ig or ow to te icensee, and ence faces an adverse seection probem. Te icensee as aways an incentive to convince te patentee tat te demand condition is ow in order to pay ower price for te icense as compared to te ig demand situation (since ig demand state generates more surpus to te icensee, wic in turn increases te icense fee. Given tis adverse seection probem, we expore wat woud be an optima as we as an efficient inear icensing contract offered by te patentee. We beieve many rea-ife icensing arrangements are simiar to te situation described ere. Notice tat witout any asymmetric information, i.e. in a compete information framework of te mode, carging a fixed fee (i.e. ig fee for te ig demand and ow fee or te ow demand woud be ceary optima for te patentee. However, wit adverse seection, we sow tat te optima icensing invoves royaty, fixed fee and a combination of bot depending on te parameter configurations of our mode. Te studies wic aso try to expain te prevaence of per unit royaty or a mixture of royaty and fixed fee as a icensing contract wen te patentee is an outsider are Beggs (199, Gaini and Wrigt (1990, Coi (001 3 among oters. Beggs (199 examined a situation were te icensee as a very cear idea of te market for a new product or te reduction in costs from a new process, ence possesses private information about te actua vaue of te patent wic te patentee does not know. In tis context e mainy considers a signaing game and sows tat royaty contracts make a separating equiibrium possibe, and may aow a more efficient outcome tan a fixed fee icensing. However, our mode is one of screening one (not signaing, were te patentee offers icensing contract to te icensee wie facing te probem of adverse seection. Wie in Beggs, te icensee makes a singe offer to te patentee in order to signa about te possessed private information of te true vaue of te patent. On te oter and, Gaini and Wrigt (1990 considers anoter signaing game were te patentee as private information about te actua vaue of te patent and expained tat royaty rate in te contract can act as a signaing device for te patentee. Tis is again in contrast to our mode, were te private information about te market demand in From empirica facts and observations, it is quite evident tat inear sceme of tecnoogy icensing is very muc prevaent in reaity (see previous discussion. 3 Very recenty, Coi (001 considered a mora azard probem in a icensing reationsip were effective transmission of knowedge (i.e vaue of te patent requires costy inputs by bot dispensing and receiving parties wic may not be observabe to any oter party, and expains te prevaence of royaty contract in te icensing reationsip. Bousquet et. a. (1998 considered a icensing arrangement under demand or cost uncertainty and justified te use of royat y in addition to fixed fee using risk-reated considerations. In teir mode tey do not ave any asymmetric information.

4 our case ies wit te icensee and patentee as ony some prior beief about it. Finay, to te best of our knowedge in te patent icensing iterature, tis kind of screening probem of te patentee is never considered expicity. Here we make an attempt to fi tis gap. Te pan of te paper is as foows. Section describes te basic framework. Section 3 describes two pooing icensing contracts: fixed fee and fixed fee pus royaty. Section improves upon te previous contracts and describes a separating icensing contract. Finay, section 5 concudes.. Te Basic Mode We consider a mode of tecnoogy icensing wit one patentee and one icensee. Te patentee ods a patent for a cost reducing tecnoogy. Tere is an incumbent firm in te market, wic is te potentia icensee for tis tecnoogy. Te patentee cannot enter into te market and produce te product. Tus we consider te case of an outside patentee, for exampe an R& D Laboratory. We are interested in te inear optima icensing strategy of te outside patentee wit one potentia icensee, wo as private information about te market demand condition. Te market (inverse demand function is given by p = A q, were p and q denote price and quantity respectivey wereas A is te demand intercept. Tere can be two states of demand of te product under consideration: ig or ow. We capture tis fact by assuming tat te intercept term A can take two vaues A and A depending on weter te demand is ig( and ow( (naturay A > A. Te incumbent firm as private information about tis demand conditions i.e., it knows for sure weter te market demand is ig or ow. On te oter and te patentee being an outsider does not know te actua demand but as a prior beief about tese demands. Wit probabiity θ, te patentee beieves tat te demand is ow and wit probabiity ( 1 θ it beieves te demand is ig. θ is common knowedge to bot parties. Suppose te incumbent firm can serve te market wit its existing tecnoogy for wic te margina cost of production is c. However te patentee as a new tecnoogy wic is more efficient and it reduces te cost of production by ε (ε>0. Tus, if tis new tecnoogy is used for te production, te margina cost of production woud be ( c ε. We consider te icensee to be ig type or ow type depending on weter it knows te demand to be ig or ow respectivey. 3

5 We consider te foowing game. Te patentee makes an offer of te new tecnoogy by carging some payment scedue. Te icensee can accept or reject te offer. After tis te production is undertaken by te icensee eiter wit te new tecnoogy (if it as accepted te offer or wit te existing tecnoogy (in case it as rejected te offer. Te profit is reaized at te end of te game. Let us note some of te variabes, wic woud be usefu for subsequent cacuations. Since te icensee is te ony one firm in te market so te market is served under monopoy. Te reservation payoff for eac type of te icensee is te payoff it receives witout te new tecnoogy, i.e., R i = ( A i c And te corresponding output is q i = for eac i = or (1 ( A i c for i = or. Suppose te new tecnoogy is used for production ten te profit of te firm woud be ( A i c + ε for i = or On te oter and, if some per unit royaty r is carged ten te profit of te icensee woud be ( A i c + ε r ( A c r q i (r = i + ε for i = or. and te corresponding output woud be It is we known in te iterature tat te royaty is distortionary as it increases te margina cost of production eading to ower overa surpus tat can be divided between te patentee and te icensee. Suppose bot te patentee and te icensee knows te actua demand in te market. Ten te game is one of compete information. Ten te optima icensing strategy in tis case is to carge a fixed fee suc tat te icensee receives its reservation payoff. Tus te optima fixed fee is given by: T i = ( A i c + ε ( A i c depending on i = or. ( 3. Pooing contracts 3.1 Fixed Fee Let us consider te asymmetric information probem were te icensee as te private information about demand and te patentee as ony prior beief about tat. Due to tis

6 asymmetric information te patentee wi face an adverse seection probem in icensing te tecnoogy as te ig type icensee woud ike to ide its private information and pretend to be ow type in order to pay ower amount for te tecnoogy. First consider te simpest contract wic is te fixed fee icensing contract. If te patentee carges ony fixed fee for its icense, ten eiter it as to carge T and in tat case bot type of te icensee wi accept te icense, or it as to carge T, in tat case ony ig type wi accept te tecnoogy, and te ow type wi reject te offer. Tus, if te patentee carges T, ten te tota payoff it receives is T. On te oter and if te patentee carges T, ten ony te ig type accepts te offer and te ow type wi not accept te icense. Tus, te expected payoff woud be: θ.0 + (1-θT = ( 1 θ T Now depending on te prior beief about te type of te icensee, te patentee wi coose eiter of tese two icense fees wic maximize its payoff. A simpe cacuation sows tat tere exists a θ* = (1- T suc tat for θ θ* bot types of te icensee is offered te T tecnoogy and te ow fixed fee is carged. And for θ < θ* ony ig type is offered te icense and te ig fixed fee is carged. Tus, for θ < θ* te market is not going to be served wit te new tecnoogy if te market demand is truy ow. Ony te ig type of te icensee accepts te offer and serves te marke t. So tere is an inefficiency due to asymmetric information as te market is not served by new tecnoogy wit probabiity θ for te prior beief θ < θ*. Te patentee s payoff π =Max. [T, (1-θT ]. In tis context, we define efficiency as a situation were te new tecnoogy is used to serve te market irrespective of te prior beief of te patentee. 5 Tus, we ave our first proposition, Proposition 1 Suppose te patentee carges ony fixed fee for icensing its tecnoogy. Ten, for θ θ* te patentee carges T as fixed fee and bot types of te icensee accept te offer. For θ <θ*, te patentee carges T and ony te ig type icensee accepts te offer, and as a resut te market is not served by new tecnoogy wit a prior beief θ < θ* i.e. wen te market demand is truy ow. 6 5 Note tat tis is different from te notion of socia efficiency (i.e. socia surpus maximization. However, te reationsip betw een te two wi be discussed at te end of section. 6 Tis case is simiar to wat is mentioned in Beggs (199, page 17. Te ony difference wit Beggs is tat wen te icense is offered wit ig fixed fee in case of rejection by te ow type, te patentee as a fa back payoff wic is nonzero (unike zero in our case as te patentee can turn to some oter aternative icensee as assumed tere. Atoug Beggs ad mentioned about te royaty contract wic is contingent on te output 5

7 Now, we woud ike to introduce more genera kind of contract, wic is a inear function of output aving bot fixed and a variabe component. Tis kind of inear contract is very common in te context of tecnoogy icensing in practice. 3. Fixed fee pus Royaty Contract We consider royaty as per unit fee carged on te output produced by te icensee and te fixed fee is a ump sum payment independent of output. We consider a uniform payment sceme te patentee designs for icensing te tecnoogy. Suppose te patentee designs a inear contract F + r q were F is te fixed fee and r is te royaty per unit of output produced. Tis payment scedue is uniform irrespective of te icensee s type. However, if te icensee produces more output wic is expected in case of ig demand ten te ex-post payment to te patentee is more because of te royaty rate r. Tis is a pooing contract as te same contract ( F, r is offered to bot types of te agent (icensee. Wit te pooing contract te patentee s probem is to maximize its payoff π = θ( F + rq ( r + (1 θ ( F rq ( r (3 + subject to te participation constraints of bot types of te icensee given by (using (1, - F + ( A i c + ε r ( A i c for i = and. (PC Given tis probem it is easy to see tat te ig type icensee woud receive some rent and te participation constraint of te ow type woud be satisfied wit equaity under tis pooing contract. To sove for te payoffs first note tat te optima fixed fee F = ( A c + ε r - ( A c. Substituting tis F and aso q (r, q (r into patentee s payoff p (from 3, we find patentee s payoff becomes a function of r ony, and tus we write: ( p(r = A c + ε r - ( A c ( A c r + θ r. + ε ( A + (1-θ.r. c + ε r Now maximizing p (r wit respect to r we get optima royaty under pooing contract as r = (1-θ (A A. Since te fixed fee can never be negative (i.e. F 0 so given te participation constraint (PC te royaty rate can never be greater tan ε. ( produced, in te simiar set up ike ours, but is non-inear royaty contract utimatey in tis simpe case turned out to be ike fixed fee contract as anayzed above. 6

8 Tus te optima royaty rate under pooing contract r* = Min.[(1-θ (A A, ε]. As a resut, F is aso determined. Putting te vaue of r* and F, we get te patentee s payoff under pooing contract p (r*. Te foowing emma caracterizes te royaty sceme r* under pooing contract. Lemma 1 Tere exists θ 1 = A A ε suc tat for θ 1 A A θ te optima royaty rate is ε and for θ > θ 1 te optima royaty rate is 1 θ ( A A < ε. ( Aternative to te above pooing contract te patentee can ony offer icense to te ig type icensee and carge te ig fixed fee T (using (. In tis case te patentee s payoff woud be (1-θ T. Now comparing te payoffs we get te optima strategy of te patentee. Note tat π (r* tere exists θˆ = (1- suc tat for θ θˆ bot types of te icensee is offered te T tecnoogy wit bot fixed fee (F 0 and royaty payment (r* 7. And for θ <θˆ ony ig type is offered te icense and te ig fixed fee (T is carged. Te patentee s payoff under P * tis pooing contract is: π = Max. ( π ( r, ( 1 θ T Tus, te foowing proposition caracterizes te icensing strategy under pooing contract. Proposition (i Wen te tecnoogy is offered under pooing contract of royaty pus fixed fee ten for θ θˆ te patentee offers te new tecnoogy to bot types of te icensee. And for θ <θˆ te patentee offers te tecnoogy to te ig type ony by carging (ii (iii te ig fixed fee. Wen te tecnoogy is offered to bot types, expected profit of te patentee under te pooing contract of royaty pus fixed fee, is iger tan te earier simpe fixed fee contract. Formay, p(r* > T. Under te pooing contract of royaty pus fixed fee inefficiency is reduced as compared to te situation wen ony te fixed fee icensing is offered sinceθˆ <θ*. 7 Note tat if r* = ε, ten F=0; oterwise F>0. 7

9 In oter words, under te pooing contract of royaty pus fixed fee, te market is being served for greater range of prior beief tan simpe fixed fee contact. Proof (i Foows from above discussion. (ii Note tat p(0 = T and p(r is a positive function of r wen 0 r < r * <. (iii Notice te fact tat p(r* > T. Coroary 1 (consistency wit compete information : Observe tat under pooing contract wen θ =1 (i.e., te demand is known to be ow ten r * = 0 and π ( r * = T ; wereas wen θ = 0 (i.e., te demand is known to be ig ten ( θ T = T 1. Now te question is weter te patentee can do any better by designing a separating contract and wat appens to te efficiency as a resut of tat.. Separating Contract Suppose te patentee can offer a discriminatory contract between te two types of icensee. Note tat tis kind of separating contract must satisfy anoter two constraints apart from te participation constraints (PC. Tese are incentive compatibiity constraints. Suppose, te contract offered to te icensee is (F, r and (F, r to ow type and ig type respectivey and te respective type accepts te offer. Now te incentive compatibiity means tat neiter type woud mimic and accepts te contract meant for te oter type. So we write te foowing incentive compatibiity constraints for te ow type (IC1 and te ig type (IC respectivey. ( A c + ε - F + ( A c + ε - F + r r ( A - F + ( A - F + c + ε r c + ε r (IC1 (IC First note tat any (F, r must satisfy te participation constraint of te ow type. Now by mimicking to be ow type te ig type icensee woud get te RHS of (IC. It is easy to ceck tat ig type gets a rent above its reservation payoff by mimicking to be ow type icensee. Tus, to separate out te ig type, (F, r must be suc tat te ig type gets tat rent in equiibrium. Since royaty as distortionary effects on surpus, so reducing r to zero 8

10 and increasing F (subject to IC woud increase te surpus extracted by te patentee. Tis ( A c + ε mecanism does not vioate te (IC1 aso. As a resut, F = F + - ( A c + ε r satisfied wit equaity we get F = ( A c + ε r (from (IC. Since te participation constraint of te ow type wi be - ( A c Tus, te patentee s payoff π becomes a function of r ony, and we write: π ( r = θ[ F + r q ( r ] + (1 θ F (6 Terefore, te maximization of π ( r wit respect to r woud yied r = However, we ave aready noted tat r cannot exceed ε. Tus, te optima r * = Min.[ ( 1 θ ( A A, ε]. θ ( 1 θ ( A A. θ As a resut te corresponding F * and F * are aso determined. Hence te Patentee s payoff under separating contract is acieved from (6. Te foowing emma caracterizes te royaty sceme r * under separating contract wit fixed fee pus royaty. (5 Lemma Tere exists θ = A A A A +ε suc tat for θ θ te optima royaty rate is ε and for θ > θ te optima royaty rate is ( 1 θ ( A A θ < ε. Tus, for θ θ, F* = 0 and F* = ( A c + ε ( A - c wic is te maximum fixed fee carged under compete information. Aso for θ > θ, F * > 0 and F * is ess tan te compete information fixed fee. In particuar wen θ = 1 ten te royaty rate is zero. And ow type is carged ony wit te fixed fee equivaent to te entire surpus as it soud be ike under compete information. Te above separating contract is te best for te patentee under te inear contract sceme we are considering in te present paper. 9

11 * * Aso observe tat optima royaty rate r under separating contract is iger tan tat of r in te case of fixed fee pus royaty pooing contrac t. See figure beow. [Insert Figure 1 about ere] Now, comparing Eqns.(3 and (6, we state te foowing emmas. Lemma 3 For a r = r, we must ave F F = and ( π( r π >. r Proof: From (3, note tat π ( r = θ (F + r q(r + (1-θ ( F + r q(r were, F = ( A c + ε r - ( A c From (6, note tat π ( r = θ[ F + r q ( r ] + (1 θ F were, F = ( A c + ε r It is easy to see tat wen - ( A i c r = r, ten F F = and aso ( r q ( r q =. Tus, te first term of π ( r and π ( coincides. Hence remains to sow te second term of ( r second term of π ( r. Leaving aside te common term (1- θ, second term of ( π, r π is bigger tan r ( A c + ε F = F + ( A c + ε - Since, F = F, it is enoug to sow r ( A c + ε ( A c + ε - r > r q (r Now putting te vaue of q (r and simpifying, we get: r > r, wic is true for r = r. Hence te resut. Lemma * P * It is true tat π ( r > π = Max. ( π ( r, ( 1 θ T Proof: First observe tat ( ( * π r * π > for a θ θˆ. Tis foows directy from emma 3. r 10

12 π r * > 1 θ T for a θ < θ ˆ. To sow ( ( Consider a feasibe separating contract as foows: Note tat tis contract is accepted by bot types. r = ε, F = 0, F = T. Tis contract acieves a payoff of π ( r = θ ( 0 + εq ( ε + ( 1 θ T > ( 1 θ T Now since, π ( r π ( * r as * Tus, we state our fina proposition. r is optima. Hence te resut. Proposition 3 (i Expected payoff of te patentee under te separating contract is greater tan tat (ii (iii π r > π of fixed fee pus royaty pooing contract. Formay, ( P *. Wen te icensee offers te tecnoogy under separating contract, ten for a prior beief, te tecnoogy is offered to bot types of te icensee, ence it is aso efficient. Te ig type of te icensee is aways carged wit fixed fee. In case of ow type icensee, for θ θ te optima royaty rate is ε wit zero fixed fee and for θ > θ te optima royaty is ess tan ε and aso some fixed fee is carged. Proof: (i foows directy from emma. (ii Note tat an aternative option of te patentee is to offer icensing contract ony to te ig type (wic is actuay optima in te earier pooing contract under some prior beief, see proposition (i. Using tat option te patentee receives ( 1 θ T. * P However, from emma, we note tat π ( > π = Max( π ( r, ( 1 θ T r 1 θ T. *. ( So under te separating contract, it is aways optima for te patentee to offer te patent to bot types of te icensee irrespective of te prior beief. (iii foows from emma and te discussion after tat. Tis finding is interesting as it estabises tat under adverse seection te optima icensing arrangement can be found wit a separating contract. Reca tat in te pooing contract wit royaty, wen icensing is offered to bot types ten, π * P find tat π ( r > π P π ; now under separating case, we, ence te optima icensing contract for te patentee is a separating contract as described above. Tis optima contract coud invove ony fixed fee, ony royaty 11

13 and a mixture of fixed fee and royaty depending on te parameter configurations. Te royaty is never used for te ig type of icensee under separating contract and it is used ony for ow type of icensee. 8 Aso note tat unike te pooing contracts described before were bot types are offered wit new tecnoogy over a restricted range of prior beief of te patentee, in te separating contract case irrespective of te prior beief of te patentee, new tecnoogy is aways offered to bot types. Tus, te opt ima icensing contract is more efficient in nature as compared to te pooing contract case. However, it soud be noted ere tat tis separating contract is sti not te first best contract from te point of view of socia surpus maximization. Te socia surpus is maximized wen te tecnoogy is used for bot types of demand and production taking pace according to te true margina cost of production associated wit te tecnoogy. In te separating contract anayzed above atoug te market is being served in bot states of demand but te presence of royaty per unit of output distorts te socia surpus avaiabe in te reationsip. Tus we find a second best contract from te socia wefare point of view wit a inear contract sceme. Coroary (consistency wit compete information : Observe tat under separating contract wen θ =1 (i.e., te demand is known to be truy ow ten * = 0 * r and ( r = T π ; wereas wen θ = 0(i.e te demand is known to be truy ig ten * r = ε wic impies F = 0 and ence F = T. 5. Concusion In tis paper, we ave considered a simpe mode of patent icensing wit a feature of adverse seection. Tere is one patentee and one icensee and te patentee wises to se a patent of cost reducing tecnoogy to te icensee. Te patentee is an outsider and te icensee is te ony firm in te product market. Te icensee possesses private information about te market demand wic is unknown to te patentee except tat te patentee as some prior beief about it. Te patentee as an option to carge a fixed fee, a per unit royaty fee or a mix of fixed and royaty fee in order to maximize profit. In a compete information framework of tis mode, te optima icensing contract woud be to carge a fixed fee contingent upon te state of demand. But due to asymmetric information, were te icensee as private information about te true demand, an adverse seection probem arises. In tis scenario, we 8 Tis finding appears to be consistent wit empirica observation in icensing arrangements tat royaty rate decreases wit output (Tayor and Siberston,

14 sowed tat an optima icensing contract of te patentee is to offer a separating contract, one for te ow demand type and te oter for te ig demand type. A ow demand type is offered wit a contract wic is eiter ony royaty or a combination of fixed fee and per unit royaty and te ig demand type is offered wit a contract wit ony fixed fee. We proved tat te expected payoff to te patentee from te separating contract is iger tan any pooing contract. We aso sowed tat irrespective of te prior beief of te patentee, new tecnoogy is aways offered to bot types under te separating contract. In oter words, te market is aways served by te new tecnoogy irrespective of te prior beief of te patentee, unike te pooing contracts were bot types are offered wit new tecnoogy over a restricted range of prior beief of te patentee. Tus, te optima inear separating icensing contract aso turned out to be more efficient tan an optima pooing contract. However, te optima separating contract is not te first best contract from te socia wefare point of view. Neverteess, tis kind of inear sceme is indeed observed in practice. References Beggs, A. W., 199. Te icensing of patents under asymmetric information, Internationa Journa of industria Organization, 10, Bousquet, A., Cremer, H., Ivadi, M., and Wokowicz, M., Risk saring in icensing, Internationa Journa of industria Organization, 16, Caves, R., Croke, H., and Kiing P., Te Imperfect Market for Tecnoogy Licenses, Oxford Buetin of Economics and Statistics, 5, Coi, J. P., 001. Tecnoogy transfer wit mora azard, Internationa Journa of Industria Organization,19, Gaini, N. and Wrigt, B. D., Tecnoogy transfer under asymmetric information, Rand Journa of Economics, 1, Jensen, R. and Tursby M., 001. Proofs and Prototypes for Sae: Te icensing of University Inventions, American Economic Review, Kamien, M., 199. Patent Licensing, In Aumann, R. J., and Hart, S. (Eds., Handbook of Game Teory, Capter

15 Kamiem, M. I. and Tauman, Y., Fees versus royaties and te private vaue of a patent, Quartery Journa of Economics, 101, Kamien, M., Oren, S., and Tauman, Y., 199. Optima icensing of cost reducing innovation, Journa of Matematica Economics, 1, Katz, M. and Sapiro, C., How to icense intangibe property, Quartery Journa of Economics, 101, (3, Maco-Stader, I., Martinez, X., Prerez-Castrio, D., Te Roe of Information in Licensing Contract Design, Researc Poicy, 5, Poddar, S. and Sina, U. B., 001, Licensing poicy in Bertrand spatia competition, mimeo. Dept. of Economics, NUS. Rostoker, M., A survey of corporate icensing, IDEA-Te Journa of Law and Tecnoogy, PTC Researc Report, Tayor, C. T. and Siberston, Z., A., Te Economic Impact of te Patent System, Cambridge, Cambridge University Press. Wang, X. H., Fee versus royaty icensing in a Cournot duopoy mode, Economics Letters, 60,

16 r, r A - A r * r* 0 θ1 θ 1 θ Figure 1