Technology licensing contracts with network effects

Int. J. Production Economics 158 (2014) 136–144

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Int. J. Production Economics journal homepage: www.elsevier.com/locate/ijpe

Technology licensing contracts with network effects Dan Zhao a,b, Hongmin Chen b,n, Xianpei Hong c, Jingfang Liu b a b c

School of Management, Henan University of Science & Technology, Luoyang 471023, China Antai College of Economics & Management, Shanghai Jiao Tong University, Shanghai 200052, China College of Economics & Management, Huazhong Agricultural University, Wuhan 430070, China

art ic l e i nf o

a b s t r a c t

Article history: Received 15 August 2013 Accepted 4 July 2014 Available online 30 July 2014

We study the optimal technology licensing contracts with network effects and investigate the welfare implications when the product innovator is an insider that acts as a Stackelberg leader. We show that (i) the market is fully covered when relatively small network intensity matches quality differentiations that are sufficiently large; (ii) with regard to profit maximization, the optimal licensing strategy varies from one of royalty licensing to two-part tariff licensing as network effects increase (not including fixed-fee licensing); (iii) consumer surplus is optimal under non-licensing conditions in comparison to other licensing strategies, due to the covered market; (iv) depending on network effects, the preferred strategies to achieve social welfare maximization change from no-licensing or fixed-fee licensing to two-part tariff licensing, and royalty licensing is not preferred in this instance; (v) conflict does not always or necessarily occur between the goals of enterprise profit maximization and social welfare optimization. Two-part tariff licensing is preferred both by the licensor and by society when the network effect is large. & 2014 Elsevier B.V. All rights reserved.

Keywords: Network effects Vertical product innovation Technology licensing Stackelberg competition Covered market Social welfare

1. Introduction A network effect, which is generally referred to as a network externality, is a kind of economy of scale economy relating to demand (Katz and Shapiro, 1985, 1994). In markets characterized by networks such as Mobile OS, Videogame and Social commerce, the evaluations made by consumers can be improved as the installed base of the suppliers' products or complementary products increases. Since a network effect can have a significant impact on the willingness of consumers to pay, the conclusions about markets which are subject to network effects may be strikingly different than those of traditional markets. In product markets with network externalities, both incumbents and potential entrants have two choices regarding their choice of technology. They can either attempt to establish their own standards via self-developed products, or they can decide to accept other firms' standards through technology licensing. According to Bloomberg news, after making a one-time payment of in excess of $1 billion to Nokia, Microsoft was able to require Nokia to abandon its own MeeGo system, being developed in cooperation with Intel, in favor of the development of a mobile system based on the Windows phone. As part of the agreement, every sale of a mobile phone made by Nokia requires the payment n

Corresponding author. Tel.: þ 86 21 62933684. E-mail addresses: [email protected] (D. Zhao), [email protected] (H. Chen), [email protected] (X. Hong), [email protected] (J. Liu). http://dx.doi.org/10.1016/j.ijpe.2014.07.023 0925-5273/& 2014 Elsevier B.V. All rights reserved.

of patent royalties to Microsoft. This agreement poses two questions. Why was Microsoft willing to license its own technology to Nokia in this way? In addition, why did Nokia abandon the development of its own system and accept the license offer? One feature of technology licensing is that it does not transfer ownership of the licensed technology. The licensor merely transfers the right to use the technology to the licensee. This feature of retaining ownership leads to strategic behaviors on the part of licensors which in turn generate impacts on licensees in terms of their output and profits. Closely associated with rapid technological changes and increasing degrees of product complexity, technology licensing has gradually come to be viewed by most enterprises (especially high-tech enterprises) as a quick and effective means of enhancing the licensee's technical capabilities. From the perspective of society as a whole, technology licensing is seen as being conducive to the diffusion of advanced technology. Licensing contributes to improvements in technology and innovation in industry as a whole. In highly efficient innovation enterprises, licensing not only helps the company reap early R&D investment and increase profits, but licensing also enables the company to choose “good” competitors and deter potentially aggressive entrants to the market. The licensee can then maintain and enhance their position in the market (Rockett, 1990). For enterprises with lesser innovative and technological capabilities, licensing can be a useful means to shorten a product's or service's development period, reduce R&D risks, learn through the digestion and absorption of new technologies and increase the enterprise's competitive advantage, and finally for the company to form

D. Zhao et al. / Int. J. Production Economics 158 (2014) 136–144

their own core competitiveness (Cohen and Levinthal, 1989; Chatterji, 1996; Henderson and Cockburn, 1996; Han and Bae, 2014). Therefore, a detailed and in-depth study of technology licensing has important theoretical and practical significance. In reality, establishing a technology standard and negotiating with other parties are highly complex practices, involving not only economic but also technological, legal and public policy issues. In this paper, we do not attempt to capture all the nuances of standard competition. Instead, we focus on the economic issue and, in particular, address the following questions: (i) Should an innovator as an insider develop a proprietary standard, or should the innovator allow others to adopt its technology? (ii) If the innovator licenses technology to others, what pricing strategy should be implemented with network effects? (iii) What are the attitudes on technology licensing with network effects from the viewpoints of enterprise, consumer, and society? (iv) Is there a conflict between profit maximization and social welfare optimization? Without network effects, many theoretical works on the question of optimal licensing strategies exist. Some scholars examine the issue under different market structures (such as Arrow, 1962; Katz and Shapiro, 1985, 1986), proceeding from the competition mode (Kabiraj, 2004, 2005; Erkal, 2005; Filippini, 2005; Mukherjee and Pennings, 2006; Chou et al., 2010), as well as from the information structure point of view (Gallini and Wright, 1990; Macho-Stadler et al., 1996; Beggs, 1992; Choi, 2001; Poddar and Sinha, 2004; Sen, 2005; Van Triest and Vis, 2007; Crama et al., 2008; Lo Nigro et al., 2014). Optimal licensing contracts also depend on the following factors: product differentiation (Kamien and Tauman, 1984, 1986, 2002; Muto, 1993; Wang, 1998, 2002; Stamatopoulos and Tauman, 2008; Li and Wang, 2010; Ye and Mukhopadhyay, 2013), imitation costs (Rockett, 1990; Mukherjee and Balasubramanian, 2001; Kogan et al., 2013), the number of participants (Tombak, 2003; Arora and Fosfuri, 2003) and so on. However, very few published studies exist which deal with the optimal technology licensing contract with network effects. It was only recently that Lin and Kulatilaka (2006) first studied the choice of optimal technology licensing in a homogenous product market from the viewpoint of the incumbent. They find that network intensity can play a crucial role in the optimal choice of licensing strategies. They also find that the incumbent licensor generally changes their choice of optimal licensing from one of royalty per unit to one of a fixed fee as network intensity increases. However, are the conclusions and results of that 2006 study robust? Rostoker (1984) finds that 46 percent of licensing cases use twopart tariff, 39 percent are based on royalties alone, and 13 percent are fixed fees alone. In fact, three deficiencis exist in their study. Firstly, they assume that all consumers or users have the same preferences and that all the products on offer are of equal quality. In the real world, people have different preferences, and products differ in quality. Meanwhile, theoretical studies (e.g. Fudenberg and Tirole, 2000; Gabszewicz and Garcia, 2007; Stamatopoulos and Tauman, 2008; Li and Wang, 2010; Nabin et al., 2012) also find that consumer preferences and product differentiation have significant impacts on market equilibrium. In our paper, we consider and apply the assumptions that more closely match the likelty realities in the marketplace. Secondly, they assume that enterprises compete in a Cournot Quantity Model. In the real world, firms which compete in the market place are asymmetrical in nature, with some firms being dominant and some others being weak (Filippini, 2001, 2005; Kabiraj, 2005). For instance, Nokia and Samsung always price their Smart Phone products using WP or Android systems, following the example of the pricing of IPhones using iOS systems used by Apple, the price leader, in spite of the fact that Samsung has higher global sales than Apple. In the Stackelberg Leadership Structure, we capture partner

137

asymmetry by means of the asymmetry of moves. Thirdly, the researchers cannot consider the impacts of the optimal licensing strategy used by an enterprise on consumers and society, and they cannot investigate whether or not a conflict between profit maximization and social welfare optimization exists. In our paper, we refine and consider the above-mentioned assumptions. Our contributions and conclusions are that (1) Compared to the existing licensing studies that have not taken into account network effects, we find that network effects play a crucial role in deciding upon the optimal technology licensing contracts to be used in network markets: (1a) When the network effect is relatively small (e.g. β o 0:37) or large (e.g. β Z 0:37), pure royalty and two part tariff licensing, respectively, are optimal for licensors. This situation is different from selecting optimal licensing without network effects, which will always be pure royalty licensing under the same settings. (1b) The licensing contract preferred by the licensor does not coincide with society preferences in markets without network effects. However, in markets with network effects, there is an interval relating to network effects (e.g. 0:38 r β o 0:5) so that a two-part tariff licensing contract is preferred by both the licensor and by society. This finding means that network effects can, to a large extent, internalize or offset the externality inevitably caused by the dissemination of technology in technology licensing. (2) In contrast to the existing licensing studies which do consider network effects, our findings are more convincing and more in line with reality. We consider the impacts of such factors as consumer preferences, differences in quality and leadership structure. (2a) We find that the licensing contracts preferred by licensors are pure licensing or two-part tariff licensing. This finding is opposite to the results published by Wang et al. (2012), who concluded that fixed-fee licensing is always optimal for the licensor when the network effect is large. At the same time, the participation constraint of the licensee is always binding. Again, this is contrary to the findings of Lin and Kulatilaka (2006). (2b) We comprehensively examine the role of network effects and their impact on optimal technology licensing contracts from the views of the licensor, consumers and society. See the details contained from Proposition 1 to Proposition 7. The remainder of our paper is organized as follows. In Section 2, we present the model and derive the benchmark status quo for non-licensing in the covered market. In Sections 3–5, we examine the effects on profitability of fixed-fee licensing, royalty licensing and two-part tariff licensing. In Section 6, we discuss the implications of the availability of different licensing contracts in terms of the licensor's profit, consumer surplus and social welfare. Hence, we also examine whether or not there exists a contradiction between profit maximization and social welfare optimization. Finally, we make a number of conclusions in Section 7.

2. Model descriptions and no-licensing for the covered market 2.1. Model descriptions Consider an industry which consists of two firms in which the goods have network effects. Firm 1 produces a product of high quality s1 , Firm 2 produces a product of low quality s2 , and s1 4 s2 . Let s1 ¼ 1, and s2 ¼ ts1 ¼ t, where t A ð0; 1Þ. The parameter t captures the degree of product quality differentiation. A larger t implies closer substitutability between the two products and that they are more homogeneous. A smaller t indicates a larger quality difference between the products and that they are more heterogeneous. For consumers with different preferences, when they buy nothing, the utilities are zero. If they buy a product with quality si at most, the utility function is U i ¼ θsi þ vðqe Þ  pi , i ¼ 1; 2. Here, θ is a marginal utility regarding quality, and it reflects consumer

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preferences assumed with uniform distribution [0, 1]. The density function is one. The larger the θ, the higher is the quality that consumers prefer. The term vðqe Þ means a sole consumer's evaluation of a network product or the incremental utility of an individual consumer regarding network effects (regardless, it is an added willingness to pay for the network value of the product), and is an increasing function of qe , where qe is the consumers' expectation of the size of the network. According to the Metcalfe Law,1 let vðqÞ ¼ β q, where β A ½0; 1Þ denotes network intensity, reflects network effects or reflects network externalities. The larger β is, the higher will be the consumers' willingness to pay. When the network intensity is equal to zero, network goods degenerate to normal goods, whereby consumers only enjoy the standalone value. The marginal cost of production is independent of the quantity produced and the product's quality. As for a product with network effects, its development often requires an initial large financial lump sum. However, once the product succeeds in the marketplace, the marginal production cost is nearly zero. Therefore, we assume the zero marginal production cost in this paper. The timing of licensing games consists of three stages. In the first stage, the high-quality Producer-Firm 1 acts as a Stackelberg leader and makes a licensing decision in setting a fixed fee, royalty rate or both. In the second stage, the low-quality Producer-Firm 2 acts as a Stackelberg follower in deciding whether or not to accept the take-it-or-leave-it offer from Firm1. In the third stage, the two firms engage in non-cooperative Stackelberg competition in terms of the quantities of their products sold. If the two firms cannot come to an agreement on licensing, there are two small and incompatible markets using two technology standards. However, if technology licensing occurs, the two firms conform to the same standard, and the consumers of both firms' products form a large network, leading to higher network value. 2.2. No-licensing for the covered market We start our analysis by considering a status quo where licensing does not occur. In this case, two firms produce their goods with different respective qualities. The consumer who is indifferent when deciding whether to buy high quality goods or low quality goods has a taste parameter θ1 (let U 1 ¼ U 2 ) such that:

θ1 ¼

NL e e pNL 1  p2  β ðq1  q2 Þ 1t

ð1Þ

All the consumers for whom θ Z θ1 will buy the high quality goods produced by Firm 1. The consumer who is indifferent when 1

Metcalfe as one of the founders of 3com thought that the total value of a network increases in proportion to the number of end-users in the network. And the value of general network externality function is always taken to be twice continuously differentiable, where v0 4 0, v″ r 0. Satisfying the feature, we denote the general network externality by vðQ e Þ ¼ β ðQ e Þα , where 0 o α r 1, and there are two perspectives to set up the network effect function in economics: from network intensity (α ¼ 1) or elasticity about network size (β ¼ 1). From the network intensity's view, the network effect function can be expressed by v ¼ βQ e , where β is the network intensity, and is an increase of network value caused by a unit increase of the expected size of users Q e , reflecting the magnitude of network effects. The expression of the network effect function is adopted by many scholars, such as De Palma and Leruth (1996); Rochet and Tirole (2003); Schiff (2003), Armstrong (2006); Lin and Kulatilaka (2006); Economides and Katsamakas (2006); Li et al.,(2010). From the viewpoint of the elasticity of network effects relating to network size, the expression v ¼ ðQ e Þα is constantly used for the network effect function. Where α r 1 is the logarithmic elasticity of the network value about the expected size of users Q e , and measures the percentage change in the network value in response to a one percent change in Q e , similarly reflects the magnitude of network effects, but just with different emphasis! Therefore, with the emphasis on network intensity as well as simplicity, we also adopt the former formula. However, the simulation to the latter formula or the general formula for β A ð0; 0:5Þ can be obtained from the authors upon request.

choosing between buying the differentiated goods and not buying e at all has the taste parameter θ^ 1 ¼ ðpNL 2  β q2 Þ=t. For this consumer, the purchase of the low quality product will imply a zero utility level. All those described by θ^ 1 r θ o θ1 will buy the low quality product made by Firm 2, and those described by θ o θ^ 1 will not buy at all. Given θ1 and θ^ 1 , the quantities demanded of the high and low quality firms are given respectively in no licensing by (superscript NL represents the no-licensing status quo) Z 1 e e pNL  pNL 2  β ðq1  q2 Þ qNL ¼ dθ ¼ 1  1 1 1 t θ1 Z θ1 e e NL e pNL  pNL 2  β ðq1 q2 Þ p2  β q2 ð2Þ dθ ¼ 1  qNL 2 ¼ ^θ t 1  t 1 The inverse demands are: e NL NL pNL 1 ¼ 1 þ β q1  q1  tq2 e NL NL pNL 2 ¼ t þ β q2 tq1 tq2

ð3Þ

The profit functions are: e NL NL NL π NL 1 ¼ ð1 þ β q1  q1  tq2 Þq1 e NL NL NL π NL 2 ¼ ðt þ β q2  tq1  tq2 Þq2

ð4Þ

In the Stackelberg quantity competition stage, Firm 2 as a follower chooses its output for any product given the leader Firm 1's output. We assume that the innovator is the leader. Solving NL the firms' profit maximization problems2 satisfying ð∂π NL 1 ðq1 ; NL NL NL NL qNL ðq ÞÞ=∂q Þ ¼ 0, ð∂ π =∂q Þ ¼ 0, and imposing a fulfilled expec2 1 1 2 2 tation equilibrium (FEE) condition3 satisfying qe1 ¼ qNL and 1 qe2 ¼ qNL 2 , equilibrium output, and pricing in no-licensing are: 2t  t 2  β 2t  t 2  β NL ; pNL q1 1 ¼ 2 2t  β ð2  β Þð2t  β Þ  2t   t 2t t 2  β NL qNL 1 ; pNL 2 ¼ 2 ¼ tq2 2 2t  β ð2  βÞð2t  βÞ  2t qNL 1 ¼

ð5Þ

Because every consumer for whom θ A ½0; 1 buys one product NL at most, the above Eq. (5) needs to satisfy qNL 1 þ q2 r 1. For simplicity, we assume that the market is covered in noNL licensing.4 Therefore, if satisfying qNL 1 þ q2 ¼ 1 such that β ¼ t, we can ensure full market coverage and that all the firms have positive outputs. Then, the equilibrium outputs, prices and corresponding profits can be rewritten as: qNL 1 ¼

1  β NL ð1  β Þ3 NL ; p1 ¼ ð1  βÞqNL 1 ; π1 ¼ 2  3β ð2  3β Þ2

qNL 2 ¼

1  2β NL βð1  2βÞ2 NL ; p2 ¼ βqNL 2 ; π2 ¼ 2  3β ð2 3β Þ2

ð6Þ

2 NL NL 2 NL 2 We omit the SOC: ð∂2 π NL 1 =∂ðq1 Þ Þ ¼  2 o 0 and ð∂ π 2 =∂ðq2 Þ Þ ¼  2t o 0. FEE means that the consumer expectation of market size equals the market outputs in equilibrium (Katz and Shapiro, 1985). Leibenstein (1950) shows how to derive the demand curve in the presence of network effects under FEE. Those who are interested in this can read it. 4 Before the technology licensing occurs, the gap between Nokia mobile OS and Microsoft mobile OS in terms of OS quality perceived from the functionality, fluency and operability is relatively large, and the small expected user size leads to relatively small network effects. That means the scenario before licensing is that the relatively large quality difference and relatively small network effects coexist. To simulate the scenario, we assume that the market is covered before licensing so that sufficiently large quality difference and the relatively small network effect appear and match each other (e.g. t ¼ β o 0:5). When technology licensing occurs, the licensing parties make an agreement on technology standards, and both firms use the same OS with the same quality and form a larger network than ever, which means a larger network effect. According to Proposition 3 and Proposition 4, the technology licensing contract with network effects referred to royalty is optimal. Hence, it explains the event properly. 2 3

D. Zhao et al. / Int. J. Production Economics 158 (2014) 136–144

When the quality differentiation is relatively small (e.g. t ¼ β Z 0:5), the low quality Producer-Firm 2 will get out of the market, and the high quality Producer-Firm 1 will set a monopoly price 1=ð2  βÞ5 and produce 1=ð2  β Þ. That condition 1=ð2  β Þ o 1 holds shows the market is not covered. The paper assumes the covered market, so the case of Firm 1 setting the monopoly price will not be considered. By Eq. (6), we reach the condition where the market is covered is t ¼ β o 0:5. In this condition, the two firms have positive outputs, and the number of consumers who purchase the high quality product made by Firm 1 is much larger than NL those buying the low quality product made by firm 2 ðqNL 1 4 q2 Þ. NL By Eq. (6), the consumer surplus CS in no-licensing is: CSNL ¼ ¼ ¼

Z

1

θ1

U 1 dθ þ

1  2ð1  2β

Z θ1 θ^ 1

β

2 ÞðqNL 2 Þ

2 2ð2  3βÞ2  ð1  2β Þð1  βÞð3  4βÞ

ð7Þ

2ð2  3β Þ2

By Eq. (11), the corresponding payoffs are:

π F1 ¼

1

þ F; π F2 ¼

ð2  βÞ3

1 ð2  βÞ4

F

ð12Þ

At the fixed-fee licensing stage, Firm 1 as the licensor maximizes its payoff through the acceptance of Firm 2 as the licensee. In other words, the optimal fee is the solution to the following constrained maximization problem: h i Max π F1 ¼ Max ð2 1βÞ3 þ F F

F

NL NL W NL ¼ π NL 1 þ π 2 þ CS 2 NL 2 1 þ 2β ðqNL 14β  11β  3β þ 3 1 Þ ð1  3β Þðq2 Þ ¼ ¼ : 2 2ð2 3β Þ2 3

2

ð8Þ

3. Fixed-fee licensing status quo Once an agreement is made on the technology licensing, the two firms conform to the same standards. Thus, their products are of the same quality ðs1 ¼ s2 ¼ 1Þ. At the same time, the consumers using both firms' products form one large network, leading to a higher network value. When Firm 1 licenses its technology to Firm 2 for a fixed fee, the two firms again engage in Stackelberg competition. The consumer who is indifferent about buying the homogenous good and not buying at all has the taste parameter θ2 ¼ pF  βðqe1 þ qe2 Þ from U 1 ¼ U 2 ¼ θ þ βðqe1 þ qe2 Þ  pF ¼ 0. The con-

sumers described by θ Z θ2 ¼ pF  βðqe1 þ qe2 Þ will buy goods from Firm 1 or Firm 2. Therefore, we can meet the demands by R1 qF1 þ qF2 ¼ θ2 dθ ¼ 1  pF þ βðqe1 þqe2 Þ, and the inverse demands are:

pF ¼ 1 þ β ðqe1 þ qe2 Þ  qF1  qF2

ð9Þ

In this case, Firm 2 has to pay Firm 1 a lump sum F in order to use the technology standard of Firm 1. Then, the two firms' payoffs under fixed-fee licensing are given by (superscript F represents the Fixed-fee licensing status quo):

π F1 ¼ pF qF1 þ F ¼ ½1 þ βðqe1 þqe2 Þ  qF1  qF2 qF1 þ F π F2 ¼ pF qF2  F ¼ ½1 þ βðqe1 þ qe2 Þ qF1  qF2 qF2  F

ð10Þ

Similar to no-licensing, in the Stackelberg quantity competition stage, solving the two firms' optimal production decisions, we get the outputs and price in equilibrium: 1 1 1 ; qF ¼ ; pF ¼ 2  β 2 ð2  β Þ2 ð2  βÞ2

ð11Þ

ð13Þ

Recall the assumption that Firm 1, with perfect bargaining,6 makes a take-it-or-leave-it offer to Firm 2, and Firm 2 agrees to the license offer, even if it is indifferent to licensing or not licensing. This means the maximum license fee F is determined by π F2 ¼ π NL 2 , as follows: F n1 ¼

The social welfare W NL is:

qF1 ¼

F F To satisfy pffiffiffi the constraint q1 þ q2 r1, we need the condition

β r ð3  5Þ=2  0:38 holding.

s:t:π F2  π NL 2 Z0

U 2 dθ

2 ÞðqNL 1 Þ ð1 

139

1 ð2  βÞ

4



ð1  2β Þ2 β ð2 3β Þ

2

¼

ð2  3β Þ2  ð1  2βÞ2 ð2  βÞ4 β ð2 3β Þ2 ð2  βÞ4

ð14Þ

In fact, solving the above problems is not sufficient. The condition that fixed-fee licensing is profitable for Firm 1 as a licensor also needs satisfying π F1 Z π NL 1 . The following Proposition 1 deals with the above statement. Proposition 1. Compared to the no-licensing status quo for the covered market ðβ ¼ t o0:5Þ, fixed-fee licensing for a licensor is profitable if and only if the network intensity is moderate ð0:3 r β r 0:38Þ. Proof. π F1 Z π NL and π F2 Z π NL is equal to the optimal fixed fee 1 2 n F 1 40 and the incremental industrial profit Δπ F Z 0. See the details in Figs. A1 and A2 in the Appendix. When licensing occurs under a fixed-fee contract, consumer surplus CSF is: Z 1 ðqF þqF2 Þ2 ð3  β Þ2 CSF ¼ ¼ ½θ þ β ðqe1 þ qe2 Þ  pF dθ ¼ 1 ð15Þ 2 2ð2  β Þ4 θ2 By the value of θ2 and Eqs. (12), (14) and (15), social welfare W F is: W F ¼ π F1 þ π F2 þCSF ¼

ð3  β Þð5  β Þ 2ð2  β Þ4

:

ð16Þ

4. Royalty licensing status quo In this section, we consider licensing solely by means of a royalty per unit. Under this licensing status quo, Firm 1 licenses its technology to Firm 2 at a fixed royalty rate r A ð0; 1Þ. Those amounts depend on the quantity of Firm 2's production. The inverse demands in this case are just the same as Eq. (9) in fixed-fee licensing, namely, pR ¼ 1 þ β ðqe1 þ qe2 Þ  qR1  qR2 . The two firms' payoff functions become (superscript R denotes the royalty licensing status quo):

π R1 ¼ pR qR1 þ rqR2 ¼ ½1 þ βðqe1 þ qe2 Þ  qR1  qR2 qR1 þ rqR2

ð17Þ

π R2 ¼ pR qR2  rqR2 ¼ ½1 þ βðqe1 þ qe2 Þ  qR1  qR2 rqR2

ð18Þ

5

For cost-reducing innovation by Stackelberg leader, there are three probable results for Stackelberg followers: entry of accommodating, deterring and blocking, and then the Stackelberg leader can set competitive pricing, restricted monopoly pricing and monopoly pricing (Filippini, 2005, Kabiraj, 2005). However, for qualityimproving innovations, as opposed to cost-reducing innovations, whether normal goods or network goods, only issues of entry of accommodating and blocking arise. Also, a Stackelberg leader has the option of two pricing acts: competitive pricing or monopoly pricing.

6 Pricing mechanisms can be categorized mainly into three types: fixed price (take it or leave it offer in our paper), bargain and auction. This paper only investigates the fixed price option, with the clear goal of examining what impacts network effects and consumer preferences have on choices of technology licensing in a Stackelberg structure. Apparently, the other two types also require further study.

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At the stage of Stackelberg quantity competition, by solving profit-maximizing choices of output satisfying ð∂π R1 ðqR1 ; qR2 ðqR1 ÞÞ= ∂qR1 Þ ¼ 0, ð∂π R2 =∂qR2 Þ ¼ 0 and the FEE conditions of qe1 ¼ qR1 and

qe2 ¼ qR2 , the equilibrium quantities under the optimal production decisions are: 1  βr R 1  ðβ  2β þ2Þr R 1 þ 2ð1  βÞr ; q ¼ ; p ¼ qR1 ¼ 2β 2 ð2  βÞ2 ð2  βÞ2 2

ð19Þ

Firm 2's output as a follower is decreasing with Firm 1's output as a leader. When choosing its output, the leader attempts to foresee the follower's best response to its output levels and takes into account that the lower qR1 , the higher qR2 and hence, for any given royalty rate, the higher its royalty revenue. By Eq. (19), the leader's output is decreasing in terms of royalty rate, and the follower bears the royalty cost. To ensure qR2 40 so that 2 r o ð1=ð2 2β þ β ÞÞ. At the same time, to ensure qR1 þ qR2 r 1, we 2 have to satisfy a restriction that r Zð  β þ 3β  1Þ=2. For β r 0:38, the above restriction always holds for any r A ð0; 1Þ. Also, for β 4 0:38, then the above restriction is binding. By inserting Eqs. (17) and (18) into Eq. (19), we see the corresponding payoffs for the two firms are:

π R1 ¼ π R2 ¼

ð1  β rÞ½1 þ 2ð1  βÞr ð2  β Þ

3

1  ðβ  2β þ2Þr 2

þ

ð2  βÞ2

r

½1  ðβ  2β þ 2Þr2 2

ð20Þ

ð2  βÞ4

At the royalty licensing stage, Firm 1 as a leader chooses r in order to maximize its profits, subject to the follower's participation constraint, i.e. h i 2 þ 2ð1  βÞr 1  ðβ  2β þ 2Þr Max π R1 ¼ Max ð1  βrÞ½1 þ r ð2  βÞ3 ð2  βÞ2 r

r

s:t:π R2 Z π NL 2

By Eq. (21), the maximum royalty rate r n2 chosen by Firm 1 under the unconstrained payoff maximization conditions, regardless of Firm 2's acceptance, is: 2ð1  βÞ 4  4β þ 2β  β 2

ð23Þ

3

According to Eqs. (22) and (23), it is the optimal rate that is determined by taking the minimum of the rates r n ¼ Minfr n1 ; r n2 g. In fact, for β o 0:5, we always get r n1 4 r n2 4 0 (see Figs. A3 and A4 in the Appendix). That is to say, r n ¼ r n2 . Meanwhile, we find that r n2 4 ð  β þ 3β  1Þ=2 and r n2 o1=ð2  2β þ β Þ hold for any β o 0:5. In what follows, we give the condition that licensing by means of royalty is profitable to the licensor. 2

Standard calculations yield the consumer surplus and social welfare under licensing by means of royalty per unit: Z 1 ðqR þ qR2 Þ2 CSR ¼ ½θ þ β ðqe1 þ qe2 Þ  pR dθ ¼ 1 2 θ2 ¼

ð3  β  2r n2 Þ2

2

Proposition 2. Compared to the no-licensing status quo for the covered market ðβ ¼ t o 0:5Þ, royalty licensing for the licensor is preferable if and only if the network intensity is relatively small ðβ r 0:45Þ. Proof. Only when both of the two firms are willing to license or accept the license agreement, will royalty licensing occur. We know Firm 2 always accepts royalty licensing, so we just compare Firm 1's payoff under royalty licensing with what they would receive under no-licensing conditions, in order to find the

ð24Þ

2ð2  βÞ4

W R ¼ π R1 þ π R2 þ CSR ð3  β  2r n2 Þ½5  β þð2 4β Þr n2  ¼ 2ð2  βÞ4

ð25Þ

5. Two-part tariff licensing status quo Under two-part tariff licensing, Firm 1 as the licensor not only charges a fixed fee F to Firm 2, but also receives a fixed rate r revenue per output from Firm 2. When Firm 1 licenses its technology, the goods of both firms have the same quality. In such cases, consumers form a large market using the same standard, and the inverse demands are similar to those in fixed-fee licensing and royalty licensing cases. The two firms' payoff functions are (superscript FR denotes the royalty licensing status quo): R π FR 1 ¼ π1 þ F ¼ R π FR 2 ¼ π2  F ¼

ð1  β rÞ½1 þ 2ð1  β Þr ð2  β Þ

3

½1  ðβ  2β þ 2Þr2

1 ðβ  2β þ 2Þr 2

þ

ð2  β Þ2

r þF

2

ð2  βÞ4

ð21Þ

By Eq. (20), we can easily prove that the payoff of Firm 2 as the follower, is decreasing in the royalty rate r, so the payoff when Firm 2 accepts the licensing agreement should not be less than under a no-licensing situation. Thus, the highest rate paid by Firm 2 is decided by π R2 ¼ π NL 2 which is: pffiffiffiffi ð2  3β Þ  ð1  2βÞð2  βÞ2 β ð22Þ r n1 ¼ 2 ð2  3β Þð2  2β þ β Þ

r n2 ¼

condition that royalty licensing is deserved by Firm 1. If π R1 Z π NL 1 is satisfied, we can ensure that royalty licensing occurs. When the network intensity is relatively small ðβ r 0:4537  0:45Þ (see Fig. A5 in the Appendix), we get π R1 Z π NL 1 .

F

ð26Þ

At the two-part tariff licensing stage, Firm 1 chooses its optimal fixed-fee F and royalty rate r to maximize its payoff under Firm 2's acceptance constraint: h i 2 ð1  βrÞ½1 þ 2ð1  βÞr 1  ðβ  2β þ 2Þr Maxπ FR þ r þF 1 ¼ Max ð2  βÞ3 ð2  βÞ2 F;r

s:t:π

F;r

FR 2

¼π

R 2 F Z

π NL 2

ð27Þ

Solving the above problem yields the maximum fixed fee F n2 paid by firm 2: ½1 ð2 2β þ β Þr2 2

F n2 ¼

ð2  β Þ

4



ð1  2β Þ2 β ð2 3β Þ2

ð28Þ

Substituting Eq. (28) into Eq. (27), the optimal royalty rate is: 8 2 pffiffiffi < β  4β þ 2 β o 2  2  0:59 n 4ð1  β Þ ð29Þ r3 ¼ :0 β Z 0:59 When the network's intensity is high ðβ Z 0:59Þ, the optimal royalty rate is equal to zero, and two-part tariff licensing degenerates to fixed-fee licensing alone. However, fixed-fee licensing occurs when the network's intensity is moderate ð0:3 r β r0:38Þ from Proposition 1. Therefore, two-part tariff licensing occurs, and the royalty rate is positive, if and only if the network intensity is not too large (β o 0:59). The following Proposition 3 gives conditions under which two-part tariff licensing occurs both in cases of constrained fixed fees and unconstrained fixed fees. Proposition 3. Compared to the no-licensing status quo for the covered market ðβ ¼ t o0:5Þ, licensing by means of a two-part tariff for the licensor always holds, and: (1) When the network intensity is relatively small ðβ o 0:32Þ, the fixed fee is unconstrained, namely, F n2 o 0;

D. Zhao et al. / Int. J. Production Economics 158 (2014) 136–144

(2) When the network intensity is relatively large ðβ Z 0:32Þ, the fixed fee is constrained, namely, F n2 Z 0. See the proofs in Fig. A6 in the Appendix. By standard calculations, we can get the consumer surplus CSFR and social welfare W FR under licensing by means of a two-part tariff: CSFR ¼

ð3  β 2r n3 Þ2

ð30Þ

2ð2  βÞ4

FR FR W FR ¼ π FR 1 þ π 2 þ CS

¼

ð3  β  2r n3 Þ½5  β þ ð2  4βÞr n3 

ð31Þ

2ð2  β Þ4

6. The optimal licensing for the enterprise, consumers and society In Sections 2–5, this paper has already analyzed the equilibrium quantities, prices, consumer surplus and social welfare conditions under no-licensing, fixed fee licensing, royalty licensing and two-part tariff licensing agreements. In order to accurately analyze the optimal licensing strategy from the perspectives of the licensor, consumers and society, the strategies need to be compared under the same conditions. Based on the benchmark status quo of no-licensing for the covered market, it is comparable under β ¼ t o 0:5. The results in Propositions 1–3 show that fixed-fee licensing occurs when 0:3 r β r 0:38, royalty licensing happens if β r 0:45, and two-part tariff licensing is always profitable under β ¼ t o 0:5. We compare the payoff functions for Firm 1 under the conditions of each of the above strategies and obtain the optimal licensing strategy for given parameter values as shown in Fig. 1. According to Fig. 1, we summarize the following Proposition 4: Proposition 4. From the perspective of the licensor, pure royalty licensing is optimal when the network effect is relatively weak R (0 o β o0:37, derived from π FR 1 ¼ π 1 ). Two-part tariff licensing is dominant when the network effect is relatively large ðβ Z 0:37Þ. Proposition 4 illustrates that from the perspective of enterprise profit maximization, the optimal licensing strategy changes from pure royalty licensing to two-part tariff licensing as the network intensity increases. The intuition behind Proposition 4 is as follows: if licensing occurs, the two firms' products have the same standard, and consumers form a larger network accompanied by higher industrial output than occurs under no-licensing conditions. The increase in industrial outputs has two countervailing effects on the price of the network product. On the one hand,

increased output will cause the price to fall, due to the same supply-and-demand conditions that apply to normal products. Apparently, the decline in price arises from the supply side, and we can call it a “supply side effect.” On the other hand, firms can charge a higher price when their product is more highly evaluated by consumers. This view arises from the demand side, and is obviously caused by the network effect. Besides the two effects named above, we also must consider the incentive for the licensor. It is explicitly accepted that the licensor has a much greater incentive to retain its leadership in quantity of production under Stackelberg competition than under Cournot or Bertrand structures. The royalty rate can add to the licensee's marginal costs, and thus lead to asymmetrical quantities being produced by the two firms. Therefore, retaining production leadership is a point the licensor always focuses upon under Stackelberg competition. The optimal licensing contract also always refers to a royalty fee. Now, let us consider the two effects. When network intensity is sufficiently high (e.g. β Z 0:37), this means the network effect dominates the supply-side effect. This in turn suggests that we should add a lump sum fee which cannot influence quantity equilibrium and reduce the royalty rate, so two-part tariff licensing occurs. When the network intensity is small (e.g. 0 o β o 0:37), it suggests the network effect is dominated by the supply-side effect, and therefore keeping Stackelberg leadership and decreasing industrial supply is more important for the licensor, which in turn means that pure royalty licensing is the more profitable option. As depicted in Fig. 2, we compare the consumer surpluses under different licensing strategies and summarize the following Proposition 5: Proposition 5. From the perspective of consumer surplus, choosing no licensing is always the optimal strategy, whatever the network intensity or quality differentiation. Pure royalty licensing and twopart tariff licensing of the licensor are always dominated by others' licensing strategies. Proposition 5 shows that consumer surplus is optimal when the two firms do not come to any agreement on licensing. Without licensing, consumers with a preference for high quality can choose high-quality products, and consumers described as having lowquality tastes can choose low-quality products. Hence, all consumers can buy what they want, which means the market is fully covered. Higher yields and lower prices thus lead to the nolicensing status quo preferred by consumers with different tastes. The comparisons of social welfare in each case, as depicted in Fig. 3, can be summarized in the following Proposition 6: Proposition 6. From the point of view of social welfare optimization, assuming that the market is covered in pre-licensing ðβ ¼ t o0:5Þ, no licensing is optimal if and only if the network effect is weak ð0 o β o 0:3Þ. Fixed fee licensing is optimal if and only if the network

0.5

1

0.45

0.9

FR

0.4

0.8

β=0.3683

0.35

141

0.7 CS

R

0.3

F

0.6 0.5

NL

NL

0.4

0.25

0.3

F

0.2

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

β

Fig. 1. The optimal decision for given parameter values.

0.45

0.5

0.1

R

FR

0.2 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

β

Fig. 2. Consumer surpluses under different licensing strategies.

0.5

142

D. Zhao et al. / Int. J. Production Economics 158 (2014) 136–144 1.3 1.2 1.1 β=0.38

W

1

F

0.9

FR

β=0.3

0.8

β=0.3088

0.7 0.6 NL

0.5

R

0.4 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

β

Fig. 3. Social welfare under different licensing strategies.

effect is moderate ð0:3 r β o 0:38Þ. In addition, two-part tariff licensing is optimal if and only if the network effect is relatively large ð0:38 r β o 0:5Þ. Is there a conflict between enterprise profit maximization and social welfare optimization for any given licensing strategy? From Proposition 4 and Proposition 6, we summarize the following Proposition 7: Proposition 7. Assuming that the market is covered in no-licensing ðβ ¼ t o 0:5Þ, when the network effect is relatively small ð0 o β o 0:38Þ, a conflict exists between enterprise profit maximization and social welfare optimization for optimal licensing. When the network effect is relatively large ð0:38 r β o 0:5Þ, the optimal licensing strategy preferred by society is the same as that preferred by the licensor. Proposition 7 illustrates that neither conflict nor consistency always exists between social welfare goals and enterprise profits. When the network effect is very small (e.g. 0 o β o0:3), there is a conflict with optimal licensing, in that society prefers no licensing, while the licensor prefers pure royalty licensing. When the network effect is relatively small (e.g. 0:3 r β o 0:37), society prefers fixed-fee licensing, while the licensor prefers pure royalty licensing. When the network effect is relatively large (e.g. 0:37 r β o 0:38), society prefers fixed-fee licensing, and the licensor prefers two-part tariff licensing. When the network effect is large (e.g. 0:38 r β o 0:5), there is a consistency in optimal licensing, in that both society and the licensor prefer two-part tariff licensing. Technology licensing is conducive to technology dissemination and product quality improvements, but we can see from Proposition 7 that not all licensing strategies are helpful in terms of improving social welfare. The cause of this contradiction may lie in the licensing strategy itself. In fact, the nature of the distinction between fixed-fee licensing and royalty licensing, as well as two-part tariff licensing, is the extent of each licensing strategy's impact on equilibrium in market production. Under royalty licensing or two-part tariff licensing, the licensor will receive a royalty for each unit sold by the licensee (the royalty rate is higher in the royalty contract than in the two-part tariff contract). Through the royalty rate, the licensor can increase the marginal costs of the licensee, but weaken the incentive for the licensee to undertake higher production, thus allowing the licensor to attain a higher market share and achieve the double benefits of “costproduction” leadership. Higher product quality and a higher market price, together with relatively lower total production quantities, when accompanied by a weak network effect, will inevitably reduce the consumer surplus. A weak network effect indicates that the incremental industrial profit is much lower than when the network effect is large, even when licensing occurs. A greater reduction in consumer surplus and a lesser increase in industrial profits will eventually result in lower social welfare. In this case, the no-licensing status quo for the covered market is preferred by society.

However, as the network effect increases (e.g. β Z 0:3), a higher product quality (where licensing occurs) and a higher evaluation of the product by consumers will lead to far greater industry profits. At the same time, only the fixed-fee licensing of the three licensing strategies yields the minimum production distortion for the licensee, and thus does not affect the total equilibrium of quantity, thus resulting in a higher consumer surplus. Therefore, higher industrial profit coupled with greater consumer surplus makes fixed-fee licensing the optimal option from the social welfare perspective. However, for the licensor, retaining double leadership in the areas of both cost and production is the primary goal. Pure royalty licensing yields a greater distortion in the licensee's production quantities than do other licensing strategies, and therefore royalty licensing is preferred by the licensor. Due to higher consumer expectations of market size and the larger network intensity jointly resulting in the consumers' greater willingness to pay, the licensor has a strong incentive to raise the total quantity of production (the network effect dominates the supply-side effect). The licensor also has the goal of retaining leadership in both cost and production when the network effect is relatively large ðβ Z 0:38Þ. Under these conditions, the licensor will choose the second highest royalty rate, which has a lesser effect on the licensee's production quantities. Hence, two-part tariff licensing is preferred both by the licensor and by society.

7. Discussion and concluding remarks In this paper, we have analyzed the optimal technology licensing contracts to be made by a vertical product innovator as a Stackelberg leader and the implications of that choice on welfare when the goods demanded by the consumers who have different quality preferences have network effects. We have shown that when the relatively weak network intensity is equal to the large quality differentiations, the market can be fully covered. This is because, when they buy, the consumers will make a trade-off between quality differentiation and the network effect. Increases in quality differentiation will lead to more low-quality goods being consumed (e.g. ð∂qNL 2 =∂tÞ o 0), and the existence of the network effect will increase consumers' willingness to buy high-quality goods (e.g. ð∂qNL 1 =∂β Þ 4 0). Only when the balance between the quality differentiation and the network effect arises will all the consumers described as having different quality tastes buy the two firms' goods. Under those circumstances, the market is covered. The impacts and implications of the optimal technology licensing contracts with network effects chosen by the innovator as a leader in profits, consumer surplus and social welfare are summarized into the following three points: From the perspective of enterprise, when the network effect is weak, the licensor prefers pure royalty licensing as shown in Proposition 4. The result from Proposition 4 is similar to Rockett (1990) in the case of no imitation; Poddar and Sinha (2004) in the covered market status quo, and Lin and Kulatilaka (2006) in a largesized market when the goods have network effects. However, the result in a network-good market also differs from that in a normalgood market (e.g. Mukherjee and Pennings, 2006; Li and Song, 2009). Mukherjee and Pennings (2006) argue that the optimal licensing option is fixed-fee alone, owing to the strategic trade considerations in the international transfer of technology. In addition, Li and Song (2009) find that pure royalty licensing is always optimal, regardless of differences in quality. However, from Proposition 4, when the network effect is large, the licensor prefers two-part tariff licensing. The result is different from that proposed by Lin and Kulatilaka (2006). In our paper, the participation constraints on the licensee are always binding, and this is not the same as in the Lin and Kulatilaka (2006) study. At the same time, when the network effect is very large (e.g. β Z 0:59), two-part tariff licensing degenerates to a pure

D. Zhao et al. / Int. J. Production Economics 158 (2014) 136–144 4 3.5 3

F1

2.5 2 1.5 1 0.5

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

β

Fig. A1. F1 40.

0.5 0 -0.5 β=0.2996

∆πF

-1 -1.5 -2 -2.5 -3 -3.5 -4

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

β

Fig. A2. The incremental industry profit Δπ F in fixed-fee licensing.

0.51 0.5 0.49 0.48 r2

fixed-fee licensing agreement, which occurs if and only if 0:3 r β r0:38 from Proposition 1, and under which the licensor will NL choose no licensing ðπ FR 1 o π 1 Þ, so pure fixed-fee licensing does not occur. However, this point is omitted and not even considered by Lin and Kulatilaka (2006). From the consumers' perspective, as described in Proposition 5, the order of the preferred licensing strategies from high to low is: no-licensing, fixed-fee licensing, two-part tariff licensing and royalty licensing. This finding differs from those of Kabiraj (2005), Li and Song (2009). Fixed-fee licensing is considered by Kabiraj (2005) to be optimal to consumers in a Stackelberg structure, but the study does not investigate the impacts of quality differentiations and network NL effects (e.g.ð∂qNL 2 =∂tÞ o 0, ð∂q1 =∂β Þ 4 0). Nor do Li and Song (2009) investigate these impacts in a vertical differentiated Cournot structure which studies conditions under the uncovered market. Therefore, the fixed fee which is considered the first/best in Kabiraj (2005) and Li and Song (2009) becomes second best in our paper. Contrary to what is said in existing studies, such as those conducted by Poddar and Sinha (2004), Kabiraj (2005), Erutku and Richelle (2007), Stamatopoulos and Tauman (2008), Li and Song (2009), Mukherjee (2010) and Wang et al. (2012), when the network effect is sufficiently large and the quality differentiation is relatively small (e.g. 0:38 r β ¼ t o0:5), as shown in Proposition 6 and Proposition 7, two-part tariff licensing is preferred both by society and the producing enterprise. This means that the optimal licensing strategy preferred by the licensor does not always conflict with that preferred by society. Such effects and the parameters of network effects, supply-side effects, competition structures and consumer preferences in terms of quality all play joint roles in optimal licensing decisions. Discussions in detail are contained below in Proposition 4 and Proposition 7. This study inevitably has several limitations which could be addressed in further research. Firstly, we assume that goods of different qualities have the same network effects. Indeed, highquality goods probably have a weaker network effect at the initial stage than do the low-quality goods. Therefore, the licensing issues with asymmetric network effects is worthy of further study. Secondly, we assume that network effects will be generated once goods are sold. However, the generation of network effects involves a significant time lag, and only consumers in the period following the product launch can feel such network externalities. Thirdly, at the initial R&D stages, the outcomes are full of uncertainty, and if there is government intervention in R&D, then the optimal licensing strategy under R&D intervention is also one of the interesting topics worthy of further study.

143

0.47 0.46 0.45 0.44 0.43 0.42

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.4

0.45

0.5

β

Fig. A3. The constrained royalty rate r2 40.

Acknowledgments

0.4 0.35 0.3 r1-r2

The authors are very grateful to the editor and the anonymous referees for their insightful comments that have significantly improved this paper, and thank seminar participants at Antai College of Economics and Management, Shanghai Jiao Tong University for their helpful comments. This research was supported in part by the National Natural Science Foundation of China (Grant nos. 71271077 and 71301102), and Humanity and Social Science Youth foundation of Ministry of Education of China (Grant no. 11YJC630058).

0.25 0.2 0.15 0.1 0.05 0

Appendix See Figs. A1–A6.

0

0.05

0.1

0.15

0.2

0.25

0.3

β

Fig. A4. Curve of r1–r2.

0.35

144

D. Zhao et al. / Int. J. Production Economics 158 (2014) 136–144

0.06 0.04 0.02 0 β=0.4537

-0.02 -0.04 -0.06 -0.08

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

β

Fig. A5. Curve of π R1  π NL 1 under royalty licensing.

2 0 β=0.3182

F2

-2

β=0.5821

-4 -6 -8 -10

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

β

Fig. A6. Curve of F2 under two-part tariff licensing.

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