inter-temporal tieins

1357-1516 Print/1466-1829 Online/04/010003-24© 2004 International Journal of the Economics of Business

DOI: 1080/1357151032000172200

Int. J. of the Economics of Business,Vol. 11, No. 1, February 2004, pp. 3–26

Many thanks to Ralph Winter, Norman Siebrasse, Frank Mathewson, Yehuda Kotowitz, theparticipants of the Industrial Organization Workshop at the University of Toronto, anonymousreferees, and especially to Nancy Gallini for their helpful comments. The article has also benefitedfrom comments from officials at the Canadian Bureau of Competition Policy and the US Departmentof Justice, Antitrust Division, although any opinions expressed here are the author’s own. The authorremains the residual claimant for any undetected errors.

Stephen M. Law, Department of Economics, Mount Allison University, Sackville, New Brunswick,E4L 1A7, Canada; e-mail: [email protected]

Inter-temporal Tie-ins: A Case for Tying IntellectualProperty Through Licensing

STEPHEN M. LAW

ABSTRACT Hybrid licences tie trade secret rights (which have no fixed expiration) torelated patent rights (which expire). Although level royalty hybrid licences, which chargea single royalty for both rights, have been prohibited, it can be shown that infinite-termlicensing (ITL) for patent rights may be better than a limited-term patent, when returnsto the licensor are fixed. This article explains hybrid licensing as a means of privatelyimplementing the efficient ITL outcome when returns to the licensor are constrained butnot necessarily fixed, without requiring a change in the length of the patent term.

Key Words: Licensing; Hybrid Licensing; Intellectual Property Rights; Patents;Trade Secrets; Tying.

JEL Classifications: K11, K21, L42.

1. Introduction

Intellectual property rights such as patents and trade secrets permit innovators toreap the rewards of their efforts. This paper analyzes the practice of tyingintellectual property in hybrid licences, which are contracts that package tradesecret rights with related patent rights. Since trade secret contracts for the transferof know-how are not required by law to terminate after a fixed period, unlikepatent contracts, hybrid licences can be a private mechanism for extendinglicences involving patented innovations to periods beyond a limited patent term.The purpose of this article is to demonstrate that tying contracts involvingintellectual property should not be per se illegal; it is better to evaluate hybridlicensing arrangements, alleged to involve misuse of market power provided bythe patent grant, under a rule of reason.1

4 S. M. Law

Earlier research has advanced leveraging and metering arguments for tying,showing that for items without intellectual property protection making tyingarrangements per se illegal is too strict, in that the social benefits from tying canoutweigh the possible anti-competitive effects.2 The results in this paper areconsistent with this conclusion but the arguments concerning efficiency aredistinct. What is at issue here is the means of achieving a more efficient royaltystructure through tying. The model of hybrid licensing developed below indicatesthat where a licensor would offer a licence with royalties that vary with outputand the licensor is constrained (by the outside opportunities of potentiallicensees) to reduce the rate of the hybrid royalty below the rate of thecorresponding patent-only royalty to induce the licensee to accept the licence,then the tying inherent in the hybrid contract can be socially efficient.

A fundamental trade-off in designing an optimal patent policy arises fromconflict between the incentive for invention and the desire for efficient diffusion.However, this problem is partially separable: optimal diffusion mechanisms canbe derived subject to the condition that they provide returns to innovationsufficient to ensure a desired level of research and development. There are (atleast) two ways to pursue this derivation. The first method is to assume, ex ante,a fixed level of return that must be achieved for any innovation and adjust patentpolicy parameters to maximize the efficiency of diffusion subject to thatconstraint. The second is to assume that the prevailing minimum level of rewardinduced sufficient inventive activity to generate a given innovation and adjustlicensing policy for efficient diffusion, while constraining the returns to varywithin the feasible range that arises from market conditions and patentparameters. This paper follows the second, ex post, method of analysis. Oneconclusion, of either route, is that allowing returns for innovation to accrue overa longer period than the limited patent term can be a more efficient way to rewardan innovator.

The logic, following the first route, flows from an application of results fromTandon (1982) and Gilbert & Shapiro (1990).3 These results arise from theobservation that for a given return to an innovator deadweight loss from per-unitroyalties is minimized when the accompanying distortion is spread out over alonger period of time.4 This approach suggests that if returns to the licensor couldbe fixed, infinite-term licensing (ITL) would be the most efficient method ofdiffusion, given the intellectual property rights assigned to innovations.

This article departs from this earlier approach in that returns to the patent-holder are not fixed ex ante at some pre-determined level: the licensor is left freeto select licence terms. In a patent-only licence, the royalty rate must fall to zerowith the expiration of the patent. Efficient licensing can result when the licensor’schoice of licence terms is constrained by the pre-set limit to the patent term andby a potential licensee’s ability to obtain returns without the innovation. Underthese constraints, in setting the terms for a hybrid licence the licensor must reducethe royalty rate during the patent term to raise the rate in the post-patent period.Tying allows the extension of the licence into the post-patent period; however,typically, the licensor must relinquish some returns during the patent-period inorder to gain this licence extension. The model developed below demonstratesthat even without fixing the returns to the patent-holder before licensing occurs,the benefits of the ITL result may be obtained regarding optimal diffusion: if thelicensor charges per-unit royalties, the most efficient licensing structure has thelowest royalty rate and the longest term.

Inter-temporal Tie-ins 5

Current patent rules limit the term of the patent. One way to circumvent thisrestriction without altering patent term is to tie the use of the patent to a tradesecret licence which is not restricted to a finite life. Hybrid licensing can act asa private version of infinite-term licensing of patented rights: where there existsan incentive to write a hybrid licence, this private contract can reach the ITLsolution in the limit (as licence length goes to infinity). The ITL solution has theadvantage that the royalty stream is smoother: without a hybrid licence,royalties are relatively high for the duration of the patent, then drop to zero;under hybrid licensing, if the royalties are lower during the patent periodalthough greater than zero afterward, efficiency losses from distortionaryroyalties can be postponed and reduced. This article does not focus onarguments for or against limiting the length of the patent term; instead, thediscussion here centers on other policy instruments that can be used to adjustfor some of the effects of a limited patent term. These alternate policyinstruments, which may be less complex to administer than compulsorylicensing schemes, are anti-trust regulations (concerning tying) and the rulesgoverning the licensing of IPRs (such as patent misuse provisions). Further,since patent length is unchanged in the analysis here, a hybrid licensingsolution does not reduce future innovative possibilities arising from thediscovery of the patented technology in the hybrid licence, unlike a solutionthat involves an infinite patent length.

Although tying can be found illegal under antitrust laws (when it is shown todecrease efficiency), the tie-in implicit in a hybrid licence is difficult to evaluateunder these laws. Courts have, instead, used the doctrine of patent misuse tocondemn hybrid licensing arrangements: cases in this area have ruled out someforms of licences.5 These judgements imply that a hybrid licence with levelroyalties is equivalent to a tying arrangement where, in the view of the courts,the licensor is using market power granted by the patent to gain leverage in thepost-expiration market by tying a trade secret licence with a long term to apatent licence which will expire.

This article develops a model of the licensing of a process innovation todemonstrate that tying can be socially efficient.6 Typically, the transfer ofknow-how through contractual creation of a trade secret is assumed to be thesale of some valuable technical information that cannot be patented. In thisarticle, in order to focus attention on the choice of licence length, the know-how which is tied to the patented innovation is ‘fictional’, without any value,introduced solely for the purpose of extending the licence beyond the patentterm. In the example scenario developed for the model, the market structure isinitially duopolistic: a licensor, who is not a producer of the final good, isconsidering the prospect of licensing one or both of the producingduopolists.7

2. The Hybrid Contracting Problem

The problem is based on the choices available to a patent-holder decidingwhether to license patented technology and a related trade secret to a potentiallicensee or licensees. Prohibiting tying in this context means that the licensor isrequired to offer a contract involving only the patented technology, that is, thelicensee is not forced to pay for the know-how in the trade secret as a conditionof acquiring the innovation in the patent.

6 S. M. Law

Know-How

The know-how contained in the trade secret is assumed to be of no value withoutthe patent. This assumption is particularly restrictive and separates this analysisfrom earlier work on tying, in which the tied item has some value to the purchaserindependent of the value of the tying item. The patented technology is a cost-reducing process; the trade secret consists of complementary know-how,unpatented technical information.8 There is no separate market for know-how.Once given access to the patented innovation, the licensee is capable ofdiscovering the know-how costlessly and immediately. The zero cost of learningthe know-how emphasizes the effects of tying: the assumption implies that thetying contract might require the licensee to pay for know-how that could beacquired for free. The trade secret is a ‘fiction’ used to extend the length of thelicence.

Legal Environment

Patent length is finite (T < �). Firms have access to the patented technology atzero cost after the T years of the patent term. However, trade secret protection hasno fixed length. If contract terms include a royalty on the trade secret, the licenseeis obliged to pay Rs indefinitely once the contract is signed.9

Contracting

Contracts have the form (F, Rp, Rs).10 F ≥ 0, is a fixed fee, independent of the levelof output, paid by licensee(s) at the start of the licence.11 Royalties include apatent royalty that is a payment per unit of output produced over the patentperiod of Rp ≥ 0, effective for time t such that 0 ≤ t ≤ T, and a per-unit tradesecret royalty of Rs ≥ 0, for 0 ≤ t ≤ �. Output is fully observable and verifiable:contracts with per-unit royalties can be enforced.12

Production and Competition

The patented technology and the know-how together reduce unit cost from a highlevel, CH, to a low level, CL, (CH > CL).13 Given that development of the know-how is assumed to be costless and immediate, access to the patent implies unitcost can be reduced immediately to CL, P = a – Q is the inverse demand functionwith price, P, market size, a, and total quantity, Q. Production is positive under theold technology, that is, a > CH. Firms produce the same product. Productionrequires specific assets so the number of firms is fixed in the model: there is noentry.14 Competition, if any, in the final (production) stage is Cournot.15

Incentive to Innovate

At t = 0, the licensor has discovered the cost-reducing process and obtained apatent. The analysis is not complicated by the decision to innovate. The minimumreturn available to the innovator in the model is assumed to provide sufficientincentive for innovative activity, in order to focus on the welfare effects from tyingother than generating increased profits to encourage research. Since thebargaining power rests entirely with the licensor in this analysis, he/she will


receive at least the per-unit benefit of the innovation, which is CH – CL, over thelife of the patent, i.e., the present value of the minimum return to licensing is

1 – e–rT

r(CH – CL)Q,

where Q is the total quantity produced under licence, and r is the discount rate.16

Imitation of the patented invention by the potential licensee(s) is assumed to betechnologically impossible.17 This assumption simplifies the discussion byeliminating the complication of infringement.18

Communication and Information

Market conditions (demand), the legal environment, the value of the patentedinnovation, and the value of the trade secret are public knowledge. Thisassumption rules out the exploitation of any information advantage overcompetitors that a user of the innovation may gain as a result of lowering cost toan unknown level.

Innovation Types

It is important to distinguish between degrees of innovation. Arrow (1962)separates innovations into two classes: an innovation is drastic if the monopolyprice with the new technology is below the competitive price with the oldtechnology, or nondrastic, otherwise. Drastic innovations are such that 1⁄2(a + CL)< CH or

a – CH

a – CL

< 1

2.

If the degree of an innovation is measured by

� �a – CH

a – CL

,

then innovations are drastic for 0 < � < 1⁄2 and nondrastic for 1⁄2 ≤ � < 1.Note that the assumptions of the models have been chosen not to create a

realistic scenario or reflect the current landscape of licensing but to generate afield for the analysis of the efficiency effects of hybrid licensing which isdeliberately tilted against a finding of efficiency. Some of the assumptions appearillogical: for example, a potential licensee is assumed to be unable to duplicate thepatented technology but, with that technology, is able to acquire the know-howinstantaneously. On the non-level playing field created by the assumptions,however, hybrid licensing still delivers efficient outcomes for a wide variety ofparameter values.

Consider a licensor who is not a producer of the final good, deciding the termsof licences for two potential licensees. The licensor (Firm 0) makes a take-it-or-leave-it contract offer to one or both of these producers (Firms 1 and 2) who mustthen decide whether to accept. Following these stages, the potential licensees

8 S. M. Law

choose quantities in Cournot competition. Excluding any royalties, during thepatent period, for 0 ≤ t ≤ T, a potential licensee (Firm 1 or 2) produces with unitcost CH without a licence or CL with a licence. After the patent has expired, for T< t ≤ �, Firm 1 or 2 can produce with cost CL, exclusive of royalties.

The licensor must decide whether to license one or both of the potentiallicensees, i.e., must choose n = {1, 2}. For a licensing equilibrium, the licensorchooses n, F, Rp, and Rs to maximize the present value of profits, V0, subject to therelevant constraints. During the patent term the licensor can receive bothroyalties, Rp and Rs, per unit of output multiplied by the output level chosen bythe licensee. With a discount rate of r, revenues during this term, 0 ≤ t ≤ T, arediscounted by (1 – e–rT)/r. After the patent expires, the licensor can receive onlythe trade secret royalty multiplied by the licensee’s output; revenues that accrueduring this period are discounted by (e–rT)/r. A fixed fee is not discounted sincethis amount would be paid at t = 0.

A potential licensee must choose between accepting (H) and not accepting (N)the current licence offer and then set production levels accordingly. Firm i receivesreturns of VHN

i, if firm i accepts a licence while the other, firm j, j ≠ i, does not,i, j = {1, 2}.

There are two participation constraints relevant for the licensor’s decision: VHNi

≥ VNNi, Constraint 1, such that a single firm would receive as much with a licence

as without it given that the other firm is not licensed; and a constraint such thata firm would accept a licence when the other firm had accepted a licence, i.e.,VHN

i ≥ VNHi, Constraint 2. Both constraints are required for a unique equilibrium

when n = 2. If it is optimal for the innovator to license only one firm, only the firstconstraint matters.19 With an exclusive licence, a producing firm would receiveVHN

i and so, the single constraint is VHNi ≥ VNN

i, for n = 1. Along with non-negativity constraints for production quantities, royalties, and the licensor’sreturns at his/her preferred contract, the licensor’s choice of royalties must not behigher than the cost difference, i.e., Rp + Rs ≤ CH – CL. If royalties were higherthan this level, a licensee would prefer to abandon the new technology in favourof the old technology.20

Proposition 1

In equilibrium, with a non-producing licensor offering licences to one or bothproducers, licences are based only upon a fixed fee or a combination of a fixed feeand a patent royalty; there is no equilibrium with hybrid licensing.

Proof of Proposition 1. Choose {n, F, Rp, Rs} to maximize V0 subject to Constraint 1,if n = 1, or subject to Constraint 1 and Constraint 2, if n = 2, where the form ofV0 and the constraints is conditional on the structure of the licensing game withno renegotiation. Details are provided in the Appendix. Equilibrium licences arepresented in Table 1.

Discussion of Proposition 1. For a drastic innovation, 0 < � < 1⁄2, a single licenseecan become a monopolist: the other firm is unable to compete and exits themarket for 0 ≤ t ≤ T. The licensor cannot do better than to license a monopolistand so creates one (during the patent period) with an exclusive licence, extractingthe additional returns from the licensee.21 Given that it is not optimal for thelicensor to distort the output choice of the licensee by charging a per-unit royalty,


the licensee sets a fee, Fd, arising from the single participation constraint, whichis VHN

i ≥ VNNi, to extract the difference between monopoly and duopoly

profits.For a nondrastic innovation, the licensor is not able to create a monopolist with

an exclusive licence. For relatively modest innovations such that 3⁄4 ≤ � < 1, thelicensor offers a licence with only a fixed fee, Fm, to both licensees, capturing thereturns to the Cournot firms from the decrease in unit costs. The licence term isnot extended beyond the patent term by licensing; there is no tying. With a fixedfee, compensation for the innovation is settled at the start of the patent period.There are no distortionary royalties: the patent-holder has simply used thefreedom to contract provided by the patent grant to extract the maximum rewardfrom the market as a lump sum. For the remaining innovations, 1⁄2 ≤ � < 3⁄4. Theseinnovations provide a cost reduction that is more than modest, yet less thandrastic. For these substantial innovations, the maximization of V0, yields a licencewith both a fixed fee, Fs, and a patent royalty. The licensor would like to haverelatively high royalty rates since a higher royalty pushes the output level chosenby the licensees closer to the monopoly output. Monopoly output with unit costof CL is 1⁄2(a – CL). The patent royalty that would induce this level of output fromthe two Cournot duopolists is 1⁄4(a – CL) such that each firm produces 1⁄4(a – CL)during the patent period. Once the licensees have been pushed as close to themonopoly level of output as is feasible (or desirable, from the viewpoint of thelicensor), the licensor could then set the fixed fee to extract any remaining surplusfrom the use of the innovation. But a higher royalty increases the potentiallicensee’s opportunity profit of operating without a licence while his/hercompetitor is constrained to pay royalties. This represents a rather unique featureof the licensor’s problem: the outside opportunity of a licensee depends upon thelicensor’s choice of Rp. An increase in opportunity profit (from a higher Rp,chosen to induce an output closer to the monopoly output) implies a reduction inthe amount that a licensee would be willing to pay as a fixed fee. Thus, inchoosing the terms of the licence, the licensor must balance the marginal benefitof having a higher royalty against the marginal reduction in licensing revenues(from a reduced fixed fee) that setting a higher royalty rate involves. This trade-off implies that the royalty rate that achieves the monopoly output is too highfrom the licensor’s point of view: this high royalty diminishes the fixed fee thatcan be extracted more than is optimal for the licensor. When Constraint 2 isbinding, the licensor can charge only that royalty that leaves the potential licenseeindifferent between accepting the license and producing without a license whilehis/her competitor is constrained to pay royalties. In this case, reducing theroyalty has two effects: it increases the number of units upon which the royalty ispaid and makes producing without a licence less attractive.

Table 1. License types (no renegotiation)

Degree of innovation Condition Equilibrium licence type

Modest 3⁄4 ≤ � < 1 {n = 2, Fm > 0, Rp = 0, Rs = 0}Substantial 1⁄2 ≤ � < 3⁄4 {n = 2, Fs > 0, Rp > 0, Rs = 0}Drastic 0 < � < 1⁄2 {n = 1, Fd > 0, R p = 0, Rs = 0}

10 S. M. Law

The licensing equilibrium does not yield a hybrid.22 A number of refinementsto the model could deliver tying in the form of hybrid licensing for wider rangesof the parameters. Examples include the unavailability of fixed fees (which is notdiscussed here), and the possibility of renegotiating the licences after an initialround of offers (developed below).23

Renegotiation

The constraints in the problem above arise from a subgame perfect Nashequilibrium to a two-stage game. Contract offers are made and accepted orrejected in the first stage; production occurs in the second stage with coststructures conditional upon the licensing in the first stage. If there can be norenegotiation, contracts are binding on a licensor and a licensee even when itmight be in the interest of both to renegotiate. If renegotiation is possible, thenthe licensor may be able to induce licensees to accept a hybrid licence.

To obtain this result, a potential licensee must believe that if he/she rejectsthe initial licence offer then they will be placed at a competitive disadvantage asthe licensor will offer the other firm a (renegotiated) favourable licence: theother licensee could be offered a zero-royalty contract, for example. Thesebeliefs correspond to the wary beliefs discussed by McAfee and Schwartz(1994). There are three stages to this game: the first round of contract offers,renegotiation if needed, and finally production of the final good. The initialchoice of a potential licensee is to accept or reject the offered licence.Renegotiation does not occur in equilibrium.

For drastic innovations, exclusive licensing is the preferred outcome for thelicensor. For nondrastic innovations a licensor would prefer to licence bothfirms and so she would use the threat of renegotiation to induce both potentiallicensees to accept the hybrid licence that provides her with the highestreturns.

If one firm accepts while the other rejects, the firm that accepts will renegotiatecontract terms with the licensor. For n = 1, the exclusive licence that is the threatcontains a fixed fee but no output royalties where the fixed fee is the increase inreturns from operating with the lower cost of CL while the competitor continuesto face the higher cost of CH.

Two pressures shape the equilibrium in which a licence for a nondrasticinnovation is accepted by both producing firms. For each of the potential licenseesthere is the hope of gaining a competitive advantage by accepting a licence whilethe other rejects – thus becoming the firm that receives a favourable exclusivelicence – and the fear of being placed at a competitive disadvantage by rejectingthe current offer, leading the licensor to renegotiate with the other firm. This gameshares some features with a prisoner’s dilemma game: although both licenseesmight be better off if they both rejected the initial licence offered by the licensor,and simply waited to produce in the post-patent period, in equilibrium bothlicensees accept the licence offer of the licensor.

Proposition 2

If renegotiation is possible and the potential licensees have wary beliefs, theequilibrium licence for nondrastic innovations is a hybrid licence with levelroyalties.


Proof of Proposition 2. Choose {n, F, Rp, Rs} to maximize V0 subject to Constraint1, if n = 1, or subject to Constraint 1 and Constraint 2, if n = 2, where the formof V0 and the constraints is conditional on the structure of the licensing gamewith renegotiation. Details in the Appendix. Equilibrium licences are providedin Table 2.

Discussion of Proposition 2. The initial offer of the licensor is accepted by both firmsin equilibrium. The parameter boundaries for the equilibrium licences aredepicted in Figure 1.

If innovations are drastic, as in Region 1 of Figure 1 where 0 < � < 1⁄2, thelicensor extracts from a licensee the difference between the monopoly profitsavailable with the licence over the patent term and the profits that would haveaccrued to the licensee under Cournot competition with unit cost CH.

For nondrastic innovations, the licensor cannot create a monopoly during thepatent term: in equilibrium, both producing firms are licensees. The licensor usesper-unit royalties to alter the cost structure of the industry and thus an equilibriumlicence specifies a royalty rate. It is not in the licensor’s interest to have both a patentroyalty and a trade secret royalty in the hybrid licence and Rp = 0 is optimal giventhe game structure in this case. Without a licence, a potential licensee faces CH whilethe other licensee has a lower unit cost and pays no output royalties under thethreatened exclusive licence for the other licensee. This outside opportunity is notdependent on the level of per-unit royalty chosen by the licensor for the two-firmlicence, unlike the situation in the basic game described at the start of this section: ahigher royalty rate does not increase the opportunity profits of rejecting the licence.In selecting a royalty rate, the licensor need only consider the maximization ofroyalty revenues – raising the royalty rate increases the rate per unit, but decreasesthe number of units of output chosen in equilibrium by the licensees – subject to theparticipation constraint. The licensor does not need to evaluate the effect of theroyalty rate on the returns to rejecting the licence.

For substantial innovations, nondrastic innovations such that 1⁄2 ≤ � < 3⁄4, thelicensor can use the royalties in the hybrid licence to push the licensees to produce,jointly, the level of output that a monopolist with unit cost CL would produce,extracting any additional surplus by means of a fixed fee. Since we restrict the fixedfee to be non-negative, this license is only feasible in Region 2 of Figure 1 where the

Table 2. Hybrid license types (renegotiation possible; tying permitted)

Degree of Innovation Discounting: e–rT Equilibrium Licence Type

Modest 0 ≤ e–rT < M(�) {n = 2, Fm > 0, Rp = 0, Rs > 0}3⁄4 ≤ � < 1 M(�) ≤ e–rT ≤ 1 {n = 2, F = 0, Rp = 0, Rs > 0}

Substantial 0 ≤ e–rT < s(�) {n = 2, Fs > 0, Rp = 0, Rs > 0}1⁄2 ≤ � < 3⁄4 s(�) ≤ e–rT ≤ 1 {n = 2, F = 0, Rp = 0, Rs > 0}

Drastic 0 ≤ e–rT ≤ 1 {n = 1, Fd > 0, Rp = 0, Rs = 0}0 < � < 1⁄2

Notes and definitions: M(�) = 64(1 – �) – 7

64(1 – �)s(�) =

3� – 1

4�

12 S. M. Law

innovation is such that 1⁄2 ≤ � < 3/4 and the discount rate is high enough, that is, 0 ≤e–rT < S(�). For the remaining substantial innovations, Region 3 of Figure 1, thelicence contains a level royalty and a fixed fee of zero.

For modest innovations, 3/4 ≤ � < 1, the licensor is not able to induce thelicensees to produce the monopoly output for any feasible values of � or r. Thehighest royalty rate available to the licensor is simply the decrease in unit costsconferred by the new technology. A nonnegative fixed fee is possible for 0 ≤ e–rT <M(�) in Region 4 of Figure 1; for the remaining modest innovations, in Region 5, thefixed fee is zero and the licensor collects revenue only through a level hybridroyalty.

For nondrastic innovations, then, the equilibrium to the licensing game whentying is permitted involves a hybrid royalty with level royalties.

Proposition 3

When the equilibrium licence is a hybrid licence with royalties that are lower thanthe corresponding patent royalty were tying prohibited (i.e., when the conditions

Figure 1. Licence offers from a non-producing licensor to a Cournot duopolist when renegotiation ispossible: Feasibility conditions and efficiency comparisons. Efficiency is reduced by tying within theshaded area. (Notes in the Appendix)


that establish Region 2 and Region 4 of Figure 1 are not satisfied), permittinghybrid licensing is socially more efficient than its prohibition.

Proof of Proposition 3. For equilibrium licence terms, since Rs = 0 if tying isprohibited, choose {n, F, Rp} to maximize V0 subject to Constraint 1, where n = 1,or subject to Constraint 1 and Constraint 2, where n = 2, where the form of V0 andthe constraints is conditional on the structure of the licensing game withrenegotiation. Sum consumer surplus and total profit under these licence termsand compare to the sum of surplus obtained when Rs is not restricted to zero (asfor Proposition 2) to find that Rs > 0 yields higher surplus except where F > 0.Details in the Appendix.

Discussion of Proposition 3. The prohibition of tying amounts to requiring thelicensor to offer a licence for the patented technology alone. The assumption thatthe development of the know-how is costless and immediate upon acquisition ofthe patented technology implies that there would be no separate licence for theknow-how with Rs > 0. Note that for substantial innovations, in Region 2 ofFigure 1, the royalty rate which is paid only during the patent term when tyingis prohibited, that is, 1⁄4(a – CL), is the same royalty rate that is paid forever underthe hybrid licence and for modest innovations, in Region 4 of Figure 1, the patentroyalty, CH – CL is the same royalty rate as the hybrid royalty when tying ispermitted; however, the hybrid licence extends indefinitely.

Using a common social discount factor, that is, abstracting from distributionalissues to consider efficiency alone, the present value of the sum of licensor,producer and consumer surplus under the hybrid licences (tying permitted) ofRegions 2 and 4 is lower than the present value of the sum of surplus under thepatent-only licence (tying prohibited).24 This result arises since there is nocountervailing social benefit derived from extending the length of the licence: theroyalty rate is not lower under the hybrid licence to compensate for the greaterperiod during which royalties are paid.

For Regions 3 and 5, the present value of the sum of licensor, producer, andconsumer surplus is higher when tying is permitted than when it is prohibited. Ifthe licensor wishes to smooth the royalty stream – instead of charging a patentroyalty followed by a zero royalty – by decreasing the royalty rate during thepatent period and increasing post-patent royalties to compensate, then efficiencyis increased by permitting the hybrid licences that accomplish this smoothing.25

For the parameter values for which this hybrid licence obtains, the hybrid royaltyrate is lower than the royalty rate in the corresponding patent-only licence. Thus,although the hybrid licence extends the length of time over which royalties mustbe paid, the reduction in rate over the patent term is sufficient to generate theefficient ITL result. To put the efficiency results into perspective, when thediscount rate is 3% and the patent term is 17 years, e–rT = 0.6. For this discountfactor, for all nondrastic innovations, permitting tying is more efficient than itsprohibition.

Note that the primary feature that distinguishes the hybrid licences that reducesocial surplus, in contrast to those that enhance social efficiency, is the presence ofa fixed fee. Given that the opportunity returns of the potential licensees do notdepend on the royalty rate chosen by the licensor in their optimal contract, for asufficiently high value of r, the licensor retains the same royalty rate in the tyinghybrid licence as the patent-only licence but reduces the fixed fee to compensate

14 S. M. Law

for the extension of licence length, holding the licensees to their opportunityprofits. The efficient ITL result depends on a reduction in royalty rate. In thisversion of the model, where the licensor can threaten a potential licensee whorejects a licence with the prospect of competing against a licensee who accepts acontract and then renegotiates a licence with a fixed fee and zero royalties, asufficiently low discount factor implies that it is the fixed fee that is reduced withthe extension of the length of the licence, not the royalty rate. If this compensatoryshift in the fixed fee is unavailable, the licensor must reduce the royalty rate tosecure a hybrid licence, provided her choice of contract terms is constrained bythe opportunities of a potential licensee.

When the licensor chooses a hybrid royalty rate that is smaller than thecorresponding patent-only royalty rate, the present value of social surplus ishigher when extending the licence length through a hybrid licence is permitted.This result occurs for most of the practical values of � and e–rT and arises from theeffects discussed earlier in the paper: a lower royalty rate during the patent perioddecreases the distortion ensuing from the use of per-unit royalties. To achieve thislower royalty rate during the patent period without reducing the rents that accrueto the patent-holder, the length of the licence needs to be increased. Althoughroyalties are paid for a longer period, the increase in surplus during the patentperiod outweighs the decrease in the post-patent period.

The standard argument in favour of tying relies on the idea that there is anupper bound to the amount that a seller can extract from a buyer, i.e., that thebuyer evaluates the package of goods offered by the seller and thus an increase inthe effective price of one good in the package must be matched by a decrease inthe effective price of another. The optimal patent length argument of Tandon(1982) or Gilbert and Shapiro (1990) involves holding constant the return to thepatentee while extending the period of compensation in order to secure areduction in price. The argument in this article would suggest that for efficiencygains from permitting tying, it is necessary that there be some reduction in the‘price’ or royalty rate during the patent period, although it is not necessary to fixthe returns to the licensor to obtain this result. However, without a sufficientreduction in royalty rate, there can be a reduction in efficiency: royalty rates canbe ‘too high for too long’ from a social perspective. The examples developed heresuggest that privately chosen per-unit royalties will increase efficiency, unlessinnovations are nondrastic and the discount rate is high. The potential licenseewas assumed to be incapable of imitating the patented technology: recognizingthe possibility of imitation would further constrain the contract terms available tothe licensor, reducing the range for which hybrid licensing would be inefficient.This effect would be particularly pronounced in the worst case considered above,that is, with ‘impatient’ agents (e–rT near 0) who would not want to wait for theexpiration of the patent to gain access to the technology. See also Gallini (1992).

3. Conclusions

Courts have expressed concern that hybrid licences allow a patent-holder toleverage any market power afforded by the patent into the post-patent period. Asthe licensing example with renegotiation shows, this concern is not unfounded.The leveraging of market power relies on a particular set of parameter values andthe credibility of a threat of re-contracting such that the threat would lead apotential licensee to accept an unfavourable hybrid licence to avoid the


competitive disadvantage of producing without a licence while their competitorreceived a very favourable exclusive licence. For other parameter values – lessdrastic innovations, essentially – or in the absence of a credible threat, hybridlicences can enhance efficiency. To write a hybrid licence when constrained by theopportunities of the licensees, the licensor must exercise less market power for theduration of the patent in order to secure royalties in the post-patent period. Thecountervailing benefit to society from allowing the licensor greater freedom tocontract is the reduction in royalty rate, and hence prices, during the patentperiod that occurs as the licensor adjusts the licence to induce a licensee to acceptthe longer term. With a hybrid licence there are higher prices after the patentperiod but the loss from these higher prices is not so large as to outweigh thegains during the patent period.26

When hybrid licensing is privately efficient, the present value of licensor,producer, and consumer surplus is typically higher under hybrid licensing thanwhen it is prohibited. Tying can increase efficiency because the licensor is able tosmooth the distortionary royalty stream.27 Note that when the licensor can inducea licensee to accept the same royalty rate under a (tying) hybrid licence as undera (no-tying) patent licence, the sum of surplus is lower with tying, since the longerterm of the tying contract is not accompanied by a countervailing reduction in theroyalty rate, i.e., there is no ‘smoothing’ of the royalty stream. This result holds,e.g., for a limited set of parameter values (market size, degree of innovation,discount rate) when the licensor is capable of renegotiating licence terms. SeeProposition 3.

Although hybrid licences have escaped per se illegality under antitrust rules,American courts applying the doctrine of patent misuse to condemn this form oftying have arrived at decisions that are excessively harsh. In the absence of acredible threat of exclusive licensing, or when the licensor is herself a producer ofthe final good, efficiency is generally enhanced by hybrid licensing, even whenthe know-how tied to the patent is a ‘fiction’ without inherent value of any kind.Further, the results above suggest that a rule that makes level royalties illegal isan excessive restriction.

How should we respond to the result that permitting tying of IPRs mayenhance welfare? In the US, courts have applied patent misuse provisions in casesinvolving patents and tying. The evaluation of tying cases under a rule of reasonrather than under a per se illegal rule, should be echoed for the tying of IPRs.Further, laws concerning level royalties in hybrid licences should be morepermissive: if the tying element of a particular hybrid licence has not beenfound to be harmful, it is hard to see why level royalties (if used) would beprohibited.

The message here is that tying is generally welfare enhancing unless thelicensor can get the licensee to accept a contract under tying with royalties that areno lower than no-tying. The primary cause of this bad outcome would be that thediscount factor is very low (discount rate is high) such that the licensee does notcare about the post-patent period. If the license includes a fixed fee then thissituation might present a problem in terms of efficiency. If it does not, then thelicensor does not have a way to reduce efficiency using the tying contract.28 Ifthere is a fixed fee, then the courts could consider constructing terms that includea patent-only royalty that would have been equivalent for the licensor at the startof the contract to the actual hybrid licence (that is, estimate the Rp that might havebeen offered). If the estimated Rp and the observed Rs are not significantly

16 S. M. Law

different, and there is a fixed fee, then the licence will introduce inefficiency andpost-patent royalty obligations should be found unlawful.29

The central point of much licensing literature is that an arbitrarily fixedpatent length is not necessarily the best policy. The hybrid licensing examplepresented here is meant to provide some insight into the consequences of somemore flexible arrangements. The argument does not establish reasons foraltering patent length, generally, concluding instead that since some licences canincrease efficiency the practice of hybrid licensing should not be per se illegal,that allowing some of these licences for reasons of efficiency may be a betterpolicy. However, retaining the judicial tools to assess them would be worth-while since it is equally true that some licences may reduce efficiency. Theprivate nature of hybrid licensing arrangements provides policy-makers withthe opportunity to retain limited length patents if these are desirable for otherreasons and use licensing restrictions (or the lack of restrictions) to encourageprivate licensors to select the licence terms that achieve the efficiency-enhancingeffects discussed here.

Notes

1. The US Supreme Court appears to disagree. See Sandonato & Shatz (2002) and the Appendix.2. See Bowman (1957); Blackstone (1975); Adams & Yellen (1976); Blair & Kaserman (1978); Tirole

(1988: 146–148; 333–336); Whinston (1990); and Mathewson & Winter (1997).3. The social problem is to minimize any deadweight loss associated with the patent grant.

Assuming that the innovator receives profit during the patent term, the problem can be solved byminimizing the ratio of deadweight loss to profit, given a fixed return to the innovator. Tominimize this ratio, reduce the royalty rate to its lowest level. Since total profits of the patent-holder are fixed by assumption, the lowest royalty rate obtains where the length of the patent islongest. These results have a parallel in the literature on optimal taxation. For other discussions ofthe issue of optimal patent design see, for example, Green & Scotchmer (1989), Klemperer (1990),or Denicolo (1996).

4. Provided imitation of the patented innovation is impossible or prohibitively costly. See Gallini(1992).

5. See the discussion of legal issues surrounding hybrid licensing provided in the Appendix.6. The model and results presented here are in no way intended to span the space of licensing. There

is a large and growing literature covering the economics of licensing. See, inter alia, Tandon (1982),Rostoker (1983), Gallini (1984), Tandon (1984), Gallini & Winter (1985), Katz & Shapiro (1985),Kamien & Tauman (1986), Katz & Shapiro (1986), Katz & Shapiro (1987), Rockett (1990), Beggs(1992), Eswaren (1994), Macho-Stadler et al. (1996), Wang (1998), Erutku Richelle (2000), Costa &Dierickx (2002), Filippini (2002), Hollis (2002), Saracho (2002), Sen & Tauman (2002), and Eang(2002).

7. A second variant of the model was developed to consider a situation similar to existing work onlicensing in which the licensor is a producer of the final good. Tying is socially efficient in this case.See Law (1997).

8. This assumption implies that these instructions are of no benefit to a user of the old technology.While it might be convenient to suppose that the trade secret could consist of instructions detailingthe most efficient use of the patented technology, this supposition would violate ‘best use’provisions found in most countries’ patent laws which oblige patent applicants to reveal the bestuse of their innovation before a patent is granted. A successful applicant who fails to disclose thisinformation runs the risk of having the patent ruled invalid at a later date.

9. It might be anomalous to posit an innovation that is valuable forever in an innovative environmentthat might generate a superceding discovery but this problem poses no difficulty for the analysis. Bylinking the know-how inextricably to the patent in a hybrid licence, the licensor risks receiving noroyalties for the know-how should the licensee abandon the use of the patent for a subsequentinnovation but it is hard to see why antitrust authorities would be concerned to protect the royaltystream of the licensor in such a case. If there is substantial risk of subsequent innovation, that is likelyto be reflected in a higher discount rate for the licensor. See also the Appendix.


10. A survey concerning methods of licensing compensation found that ‘a down payment withrunning royalties was used 46% of the time, while straight royalties and paid-up licencesaccounted for 39% and 13% respectively. Other forms of compensation such as periodic lump sumpayments, cross licensing, stock equities and royalty free licences . . . were used an insignificantportion of the time (2%)’ (Rostoker 1983: 64). The data of a study of licence design in Spain,‘confirm that most of the contracts have a very simple structure: . . . 86.3% of the contracts arelinear (in many cases degenerated, in the sense that they are based either on fixed fees or variablepayments only)’ (Macho-Stadler et al., 1993:4). Of the simpler contracts, 59.3% have only royaltypayments, 27.8% have only a fixed fee, and the remaining 12.9% have both. Only 15.8% of thesecontracts involved patents; the rest covered transfers of property rights such as franchises, trademarks, and industrial designs.

11. A licensor’s preference for royalties over fixed fees could arise from recognition of the strategicimplications of licensing which alters the cost structures of producing firms. The cost structure canbe changed for the entire industry, such as when a licensor chooses to increase the marginal costsof their licensees in order to induce the licensees to restrict output to an amount closer to themonopoly level, raising industry profits while the licensor extracts these higher profits through theroyalty and perhaps also a fixed fee. The licensor can also threaten to use royalties to affect therelative cost structure within an industry. For example, a potential licensee may accept a lessfavourable licence with a higher royalty rate than they would have in the absence of strategicconsiderations from fear of the threat of a competitor receiving a very favourable exclusive licencewith a low royalty rate that confers a cost advantage. The strategic licensing motivation for the useof per-unit royalties is explicitly considered in the analysis here. Interested readers can find furtherdiscussion of this issue in Law (1997).

12. See the legal notes in the Appendix.13. The innovations considered here relate only to the production process and are not new consumer

goods.14. For further discussions of the effect of entry on licensing arrangements, see, inter alia: Katz &

Shapiro (1985), Kamien & Tauman (1986), and Sen & Tauman (2002).15. However, note that in a situation where the innovation was patented by a producer of the final

good, in the pre-production (contract-setting) stage the licensor can act as a Stackelberg leadersince equilibrium quantities depend on contract terms. This case is analysed further in Law(1997).

16. Discount rates, implicitly incorporating attitudes toward risk, for licensor and licensee(s) areassumed to be equal. However, differences between licensor and licensee regarding the value orthe risk of obsolescence of the patented technology would impact equilibrium contract terms. Theeffect of differential discount rates would be mixed. Consider a licensee who has a higher discountrate because he believes an innovation that would substitute for the licensor’s patentedtechnology is soon to be developed. Given the higher discount rate of the licensee, the equilibriumlicence that incorporates the tying element is more likely to be welfare-reducing if it continues pastthe patent period (see the discussion of Proposition Three) but it is unlikely to so continue since withthe discovery of the substitute innovation, the licensee will abandon the licence. For interestingdiscussions of the choice of fixed fees or royalties under uncertainty and of issues of franchisingcontracts, or licences, and market power more generally, see Inaba (1980), Blair & Kaserman(1981), Inaba (1981), Blair & Kaserman (1982), Blair & Kaserman (1985), and Fratrik & Lafferty(1985).

17. Without this assumption, equilibrium licence terms would depend on the expectations of thelicensor and licensee(s) regarding the probability of discovery of an invention that would renderthe patented technology obsolete and, in turn, the licence terms would influence the incentive ofa potential or actual licensee to exert effort toward such a discovery. If the licensor feels that‘inventing around’ is likely, she is less likely to want to extend the licence past the patentexpiration and, hence, would be less likely to write a tying contract.

18. For a discussion of the impact of infringement remedies on the choice of royalty rates, see Law(1997).

19. In this initial case, without renegotiation or other strategic adjustment of licence terms, if it isoptimal to license only one firm, the licensor randomly selects one of the two identical firms.

20. Although the use of the patented innovation is verifiable, and thus abandonment of thetechnology under a patent-only licence would relieve a licensor of further royalty payments, theuse of the trade secret is not verifiable since it is a fiction constructed for the purpose of extendinglicence length. A licensee may therefore be obligated by the terms of the contract to pay for theknow-how in the licence indefinitely, as long as they continue to produce the good covered by the

18 S. M. Law

trade secret. See the assumptions, and the Appendix, for conditions necessary for this kind ofcontracting. In particular, output must be observable and verifiable.

21. In an auction, or when the licensor can threaten to licence the other producing firm, a potentiallicensee would be willing to pay more than this difference between monopoly and duopoly profitsas a fixed fee since if they do not gain access to the new technology, the other firm will, and thusthe consequence of rejecting the license is to receive less than the duopoly profit. See thediscussion below.

22. See also Kamien and Tauman (1986) who show that the private value of a patent is highest withthe use of fees only, or Katz & Shapiro (1986) who derive profit-maximizing patent licensing feesunder the assumption that output is not observable.

23. See also Law (1997) in which results from this model are derived under conditions where fixedfees not available and there is no possibility of renegotiation.

24. See Law (1997) for further details.25. While it might appear that two policy variables are changing (the illegality of tying and of level

royalties), the inclusion of level royalties is a minor point. If it is permissible to tie but not to use levelroyalties, then the licensor could choose a small patent royalty that is just sufficient to avoid illegalitywhich would have no impact on profits (to the first order). The crucial issue is the availability of ameans to extend the length of the licence in the presence of a time limit on patent protection.

26. The results have implications for tying of other intellectual property rights. For example, ifarrangements are made for royalties for repeated use of copyright material instead of the morecommon practice of charging a single fee, the results carry through for the tying of patentedtechnology to copyrighted instructions since copyrights last longer than patents. The smoothingeffect would not be as pronounced as in the model since the term of a copyright licence is notpotentially infinite, unlike a trade secret licence, but some reduction of the royalties during thepatent term could be gained. Tying intellectual property to an item without intellectual propertyprotection may yield the same results: a licensor could conceivably tie an intellectual propertylicence to a land rental contract with automatic renewal and hence indefinite length.

27. For another discussion of this effect of inter-temporal Ramsey pricing, see Ayres & Klemperer(1999).

28. Note that a fixed fee that is not explicitly in the licence, such as an implicit fixed fee embodied inthe transfer price of some other asset, might be difficult for courts to detect.

29. Although final determination of the optimality of applying a rule of reason to the tying componentof a hybrid licence must await a careful empirical comparison of the additional information costsincurred by the courts versus the efficiency benefits which arise from not prohibiting hybridlicences, there is at least some support in the judiciary for a change to rule of reason. ‘In JudgePosner’s view, it is a mere detail whether the patentee extracts royalties at a higher rate over ashorter period or lower rate over a longer period and the latter should not constitute a patentmisuse’, (Sandonato & Shatz, 2002).

30. Additional details of this proof are available in Law (1997), Appendix to Part 1.

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Appendix

Proof of Proposition 1

For a drastic innovation, 0 < � < 1⁄2, the licensee sets a fee arising from theparticipation constraint which is VHN

i ≥ VNNi, when n = 1, or:

1 – e–rT

r � a – CL

2 �2

+ e –rT

r � a – CL

3 �2

– F ≥

1 – e–rT

r � a – CH

3 �2

+ e–rT

r � a – CL

3 �2

, (1)

and so, from the maximization of Vo subject to Constraint 1, the licence has theform:

n = 1, F =1 – erT

r � a – CL

2 �2

– 1 – e–rT

r � a – CH

3 �2

, Rp = 0, Rs = 0, (2)

Constraint 1 does not have the form VHNi ≥ VNH

i due to symmetry, especially ininformation. The licensor is unable to induce a licensee to accept a punishingcontract by threatening to licence the other firm at favourable terms because sucha threat would not be credible. If VHN

i = VNNi, for the current offer, both potential

licensees know that this offer is the best that the licensor can do. Instead, if VHNi

> VNNi, then the licensor cannot do better than to offer a license that maximizes

their royalty revenue. VHNi ≥ VNH

i would be the form of the relevant constraintif the licence were offered by auction (not considered here) or if the licensor were


able to secretly renegotiate licences with one or both of the licensees after theinitial licence offer. Licence terms under this latter possibility, of renegotiation, arederived below for Proposition 2.

For modest innovations such that 3⁄4 ≤ � < 1, from the maximization ofV0subject to Constraint 2, the licence chosen by the licensor is:

n = 2, F =1 – e–rT

r � a – CL

3 �2

–1 – e–rT

r � a – 2 CH + CL

3 �2

, Rp = 0,

Rs = 0. (3)

For substantial innovations, 1⁄2 ≤ � < 3⁄4, the maximization of V0, given by:

1 – erT

r � a – CL – Rp – Rs

3 � 2 (Rp + Rs) + e–rT

r � a – CL – Rs

3 � 2 Rs + 2F, (4)

when n = 2, subject to Constraint 2, VHHi ≥ VHN

i, or:

1 – e–rT

r � a – CL – Rp – Rs

3 �2

+ e–rT


3 �2

– F ≥

1 – e–rT

r � a + CL – 2CH + Rp + Rs

3 �2

+ e–rT

r � a – CL + Rs

3 �2

, (5)

yields a licence with both a fixed fee and a patent royalty:

n = 2, F =1 – e–rT

r � a – CL – Rp

3 �2

– 1 – e–rT

r � a – 2CH + CL + Rp

3 �2

,

Rp =4 (CH – CL) – (a – CL)

6, Rs = 0. (6)


Choose to F, Rp, and Rs maximize V0 subject to Constraint 1, where n = 1, orsubject to Constraint 1 and Constraint 2, where n = 2, where the form ofV0 andthe constraints is conditional on the structure of the licensing game withrenegotiation.

If innovations are drastic, as in Region 1 of Figure 1 where 0 < � < 1⁄2,the licensor extracts from a licensee the difference between the monopolyprofits available with the licence over the patent term and the profits thatwould have accrued to the licensee under Cournot competition with unit costCH.

For nondrastic innovations, the licensor cannot create a monopoly during thepatent term. The licensor chooses F and Rs to maximize Vo subject to the

22 S. M. Law

constraint that the licensee makes as much with the licence as without it. Theparticipation constraint is given by:

1


3 �2

– F ≥ 1 – e–rT

r � a + CL – 2 CH

3 �2

+ e–rT

r � a – CL

3 �2

. (7)

Under the structure of the licensing game, if one firm accepts while the otherrejects, the firm that accepts will renegotiate contract terms with the licensor. Forn = 1, the exclusive licence that is the threat contains a fixed fee but no outputroyalties. For most nondrastic innovations, that licence would be:

n = 1, F =1 – e–rT

r � a + CH – 2CL

2 �2

– e–rT

r � a – CH

2 �2

,

Rp = 0, Rs = 0. (8)

In equilibrium, however, both firms will be licensed. The licence for substantialinnovations, such that 1/2 ≤ � < 3⁄4, is:

n = 2, F =1

r � a – CL

4 �2

– 1 – e–rT

r � a + CL – 2CH

3 �2

– e–rT

r � a – CL

3 �2

,

Rp = 0, Rs =1

4(a – CL). (9)

This licence is not feasible for modest innovations, such that 3⁄4 < � < 1, since Rs= 1⁄2(a – CL): the hybrid royalty rate would exceed the reduction in unit costs, CH– CL, for these innovations. However, for this licence to satisfy the condition thatF ≥ 0, it must be the case that:

� (1 – �)(1 – e–rT) > 7

64, or e–rT <

64(1 – �) – 7

64 (1 – �). (10)

The extreme values for this condition are {� = 1⁄2, 0 < e–rT ≤ 9/16} and {1⁄2 < � ≤7/8, e–rT = 0}. Thus, the licence in (9) is only feasible in Region 2 of Figure 1 where1/2 ≤ � < 3/4 and the discount rate is high enough for the condition in (10) tobe satisfied. If this condition is not satisfied, i.e., for the remaining substantialinnovations, the licence is:

n = 2, F = 0, Rp – 0, Rs = a – CL – (1 – e–rT) CL – 2CH)2 +

e–rT (a – CL)2]12 = a – CL – [9 rVNE]

12. (11)

where VNE is the return to producing without a licence while the other firm hasan exclusive licence from renegotiating with the licensor. This licence is theequilibrium contract for the parameter values in Region 3 of Figure 1.


The equilibrium licence for modest innovations, such that 3/4 ≤ � < 1, is:

n = 2, F =1

r � a – CH

3 �2

– 1 – e–rT

r � a + CL – 2CH

3 �2

– e–rT

r � a – CL

3 �2

,

Rp = 0, Rs = CH – CL. (12)

For F ≥ 0, the discount rate must be sufficiently high such that:

e–rT < 3� – 1

4 �. (13)

The licence in (12) is the equilibrium contract for parameter values as in Region 4 ofFigure 1. For the remainder of modest innovations, Region 5, where the discountrate is low enough that the condition in (13) fails to hold, the equilibrium licence isas given in (11): a contract with a royalty on the trade secret and no fixed fee.


We need only consider cases where tying matters, that is, nondrastic innovations,and thus the optimal licences are such that n = 2. If tying is prohibited, then thelicensor chooses F and Rp to maximize licensing returns:

V0 =1 – e–rT


3 � 2 Rp + 2F. (14)

subject to:

1 – e–rT


3 �2

+ e–rT

r � a – CL

3 �2

– F ≥

1 – e–rT

r � a + CL – 2 CH

3 �2

+ e–rT

r � a – CL

3 �2

. (15)

For substantial innovations, 1/2 ≤ � < 3/4, the equilibrium licence when tyingis prohibited is:

n = 2. F =l – e–rT

r � a – CL

4 �2

– 1 – e–rT

r � a + CL – 2 CH

3 �2

,

Rp = 14 (a – CL), Rs = 0. (16)

This licence is feasible for Regions 2 and 3 in Figure 1. Note that in Region 2, theroyalty rate which is paid only during the patent term under the licence in (16),

24 S. M. Law

that is, 1⁄4(a – CL), is the same royalty rate that is paid forever under the hybridlicence as in (9). For modest innovations, the royalty rate must not exceed thedecrease in cost from the patented innovation, and so when 3⁄4 ≤ � < 1 theequilibrium licence is:

n = 2, F =1 – e–rT

r � a – CH

3 �2

– 1 – e–rT

r � a + CL – 2CH

3 �2

,

Rp = CH – CL, Rs = 0. (17)

which includes the same royalty rate as the hybrid licence of (12); however, thehybrid licence extends indefinitely.

To derive the efficiency results, compare the present value of the sum ofconsumer and producer surplus, under ‘tying permitted’ with Rs ≥ 0 (and Rp =0) to the sum of surplus under the sum of surplus under ‘tying prohibited’ or Rs= 0 (and Rp > 0). Rs < Rp is required for a finding that welfare increases withtying permitted.30

Notes for Figure 1

Figure 1 depicts feasibility conditions and efficiency comparisons for licenceoffers from a non-producing licensor to a Cournot duopolist when renegotiationis possible. The fixed fees in Table A1 are given by:

Table A1. Licence structures (renegotiation possible)

Region Conditions ‘Tying’ licence ‘No-tying’ licence

1 1⁄2 > � > 0 n = 1 n = 1F = Fd F = Fd

2 3⁄4 > � ≥ 1⁄2 n = 2 n = 2and F = F(Rs = 1⁄4(a – CL)) F = F(Rp = 1⁄4(a – CL))�(1 – �)(1 – e–rT) ≥ 7⁄64 Rp = 0 Rp = 1⁄4(a – CL)

Rs = 1⁄4(a – CL) Rs = 0

3 3⁄4 > � ≥ 1⁄2 n = 2 n = 2and F = 0 F = F(Rp = 1⁄4(a – CL))�(1 – �)(1 – e–rT) < 7⁄64 Rp = 0 Rp = 1⁄4(a – CL)

Rs = a – CL – [9rViNE]

1⁄2 Rs = 0

4 1 > � ≥ 3⁄4 n = 2 n = 2and F = F(Rs = CH – CL) F = F(Rp = CH – CL)4�(1 – e–rT) – � ≥ 1 Rp = 0 Rp = CH – CL

Rs = CH – CL Rs = 0

5 1 ≥ � ≥ 3⁄4 n = 2 n = 2and F = 0 F = F(Rp = CH – CL)4�(1 – e–rT) – � < 1 Rp = 0 Rp = CH – CL

Rs = a – CL – [9rViNE]

1⁄2 Rs = 0


F(Rp =1

4(a – CL)) =

1 – e–rT

r � a – CL

4 �2

– 1 – e–rT

r � a + CL – 2CH

3 �2

; (18)

F(Rp = (CH – CL)) =

1 – e–rT

r � a – CH

3 �2

– 1 – e–rT

r � a + CL – 2CH

3 �2

; (19)

F(Rs = 14 (a – CL)) =

1

r � a – CL

4 �2

– 1 – e–rT

r � a + CL – 2CH

3 �2

– e–rT

r � a – CL

3 �2

; and (20)

F(Rs = (CH – CL)) =

1

r � a – CH

3 �2

– 1 – e–rT

r � a + CL – 2CH

3 �2

– e–rT

r � a – CL

3 �2

. (21)

Legal Notes and Cases

For an example of an important hybrid licensing decision in the United States seethe Duplan case in which ‘purchasers of machinery for false twist yarn texturingof synthetic yarns, in being required to take out patent use licences, were requiredalso to pay for unpatented technical information tied to such machines andnonapplicable patents and unpatented technical information tied to other patents’Duplan Corp. v. Deering Milliken, Inc., 444 F. Supp. 648, 649 (1977). See also St. RegisPaper Co. v. Royal Industries, 522 F.2d 309, 315 (1979), Pitney-Bowes, Inc. v. Mestre,701 F.2d 1365, 1370–1373 (1983) and Brulotte v. Thys Co., 379 U.S. 29, 32 (1964).

Pooley (2000), §8.06[3], contains a legal discussion of limitations on trade secretcontracting imposed by antitrust and patent law. In particular, licensors areprohibited from charging a royalty over the length of the licence that does notdecline with the expiration of the patent, i.e., level royalties are illegal.

Jurisprudence developed from a number of cases concerning hybrid licensinghas led to the following rules from Jager (1986: 186, emphasis added):

(1) In a hybrid agreement in which the royalty obligations for patent andtrade secret rights are inseparable . . . the royalty provisions of theagreement become unenforceable upon expiration of the patent under theBrulotte rule; (2) in such a case, a licensor may still be eligible forcompensation for trade secrets transferred, most likely on the basis of anunjust enrichment theory; and (3) if a hybrid agreement allocates royaltyobligations between patent and non-patent rights, the non-patent royaltyobligations may survive patent expiration or invalidity.

26 S. M. Law

The unjust enrichment doctrine is the

principle that one person should not be permitted unjustly to enrichhimself at the expense of another, but should be required to makerestitution of or for property or benefits received, retained or appro-priated, where it is just and equitable that such restitution be made, andwhere such action involves no violation or frustration of law oropposition to public policy, either directly or indirectly. Tulalip Shores, Inc.v. Mortland, 9 Wash.App. 271, 511 P.2d 1402, 1404. (Black, 1990: 1535).

Note that the unjust enrichment doctrine as applied to trade secrets is notuniversally accepted as mainstream law. See also Hill (1999) for a discussion of theconnection between trade secrets and unjust enrichment.

The three rules for hybrid licensing imply that contracts must be written so asto ensure that patent royalties are distinct from trade secret royalties (see alsoO’Reilly and Pula (1984)). Otherwise, the licensor cannot depend on the contractto recover trade secret royalties when the patent expires or if the patent is foundinvalid. At best, the licensor will receive some court-ordered compensation fortransfer of the trade secret. Further, in the Brulotte case, the court concluded that‘a patentee’s use of a royalty agreement that projects beyond the expiration dateof the patent is unlawful per se’. The Brulotte case closes the door on the possibilitythat a licensor could justifiably claim that a hybrid licence with level royalties isa trade secret agreement with the patent segment provided for free.

Enforcement of the licence, especially the trade secret component, could beundertaken through contract law. See, for example, Pooley (2000). For an exampleof a long trade secret contract, see Warner–Lambert Pharmaceutical Co. v. JohnReynolds, Inc., 178 F.Supp. 655, 123 U.S.P.Q. 431 (S.D.N.Y. 1959), aff’d, 280 F.2d 197(2nd Cir. 1960). After Warner–Lambert most licensees have insisted on language intrade secret contracts that would terminate royalty obligations if the trade secretbecomes public knowledge and licensors protect themselves with non-disclosureclauses. Enforcement of the kind of hybrid contract we envisage here would beconditional on a licencee continuing to use the licensor’s technology, regardless ofwhether that technology were covered under a patent or not. In addition to casescited above concerning the length of trade secret royalty obligations, see Span–Deck, Inc. v. Fab–Con, Inc., 677 F.2d 1237, 215 U.S.P.Q. 835 (8th Cir. 1982), cert.denied, 459 U.S. 981 (1982), and Chromalloy American Corp. v. Fischmann, 716 F.2d683, 221 U.S.P.Q. 311 (9th Cir. 1983) which further set out requirements for licenceswith royalty rates. However, the contract must specify separate rates on the patentand the know-how: see Boggild v. Kenner Products, 576 F.Supp. 533, 222 U.S.P.Q.393 (S.D. Ohio 1983).

The fundamental implications of these cases for hybrid licensing have not beenoverturned by the US Supreme Court despite an opportunity to overturn in 2003.See Scheiber v. Dolby Labs, Inc., 02–689, Supreme Court of the United States, 123S.Ct. 853; 154 L.Ed. 2d 781; 2003 U.S. LEXIS 652; 71 U.S.L.W. 3471, January 13,2003, Decided; Scheiber v. Dolby Labs, Inc., No. 01–2466, US Court of Appeals forthe 7th Circuit, 293 F.3d 1014; 2002 U.S. App. LEXIS 11878; 63 U.S.P.Q.2D (BNA)1404, December 3, 2001, Argued, June 17, 2002, Decided, Rehearing and RehearingEn Banc Denied August 1, 2002, Reported at: 2002 U.S. App. LEXIS 15741. Writ ofcertiorari denied: Scheiber v. Dolby Labs, 2003 U.S. LEXIS 652 (U.S. Jan. 13,2003).

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