雙占競爭下管理授權與技術移轉之研究

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(1)國立高雄大學經濟管理研究所碩士論文. 雙占競爭下管理授權與技術移轉之研究 Studies on Managerial Delegation and Technology Transfer under Duopolistic Competition. 研究生：蘇志榮撰指導教授：王鳳生. 中華民國九十五年六月. i.

(2) 雙占競爭下管理授權與技術移轉之研究指導教授：王鳳生教授國立高雄大學應用經濟學系學生：蘇志榮國立高雄大學經濟管理研究所. 摘要本研究主要討論在雙占市場競爭模型下，廠商間技術移轉的發生可能性、技術授權費用的收取方式、以及最適授權費的決定等策略行為，在廠商考量進行管理者授權的誘因設計後會有何改變。研究結果發現，在標準的 Cournot、Stackelberg 和 Bertrand 模型下，擁有技術的廠商，相對於採用固定授權費用(fixed fee)的方式，其會較傾向於採用權利金授權(royalty rate)的方式來向欲購買專利的廠商收取費用。當雙占市場上的廠商選擇將管理者授權放入廠商的策略考量後，我們發現此一結果仍然不變。此外，在 Cournot 和 Stackelberg 模型中，當廠商皆採取管理者授權的誘因設計後，技術移轉發生的可能性會比標準模型、無管理者授權下來的小。但在 Bertrand 模型中此一結果會受產品差異程度的大小而有所改變。當產品差異程度小時，廠商若皆採取管理者授權，則技術移轉發生的可能性會比標準模型來的小；但當產品差異程度變大時，廠商採取管理者授權下之技術移轉發生的可能性，反而會比標準模型來的大。. 關鍵字：管理授權、技術移轉、固定費用授權、權利金授權、雙占競爭. ii.

(3) Studies on Managerial Delegation and Technology Transfer under Duopolistic Competition Advisor: Professor Leonard F.S. WANG Department of Applied Economics National University of Kaohsiung Student: Chih-Jung Su Institute of Economics and Management National University of Kaohsiung. ABSTRACT In our studies, we studies and compared the different licensing fee policies of a cost-reducing innovation which a patent-holding firm could charge the paten-buyer, and find that: in the basic Cournot, Stackelberg and Bertrand model, if technology transfer occurs, then for the patent-holding firm, it would prefer royalty-fee licensing to fixed-fee licensing. And we also find that in the Cournot, Stackelberg and Bertrand model with delegation, patent-holder would still prefer royalty-fee licensing to fixed-fee licensing. Besides, in the Cournot and Stackelberg model, patent-holder would license less likely than they do in the basic Stackelberg model without delegation. In the Bertrand model, if the product differentiated level is low, patent-holding firm would license less under strategic delegation than under standard price competition, but the product differentiated level is high, patent-holding firm would license more under strategic delegation than under standard price competition.. Keywords: Managerial delegation, Technology transfer, Fee licensing, Royalty licensing, Duopolistic competition iii.

(4) 謝. 辭. 從上大學到唸研究所以來，轉眼間已經在高雄大學渡過六個年頭，如今終於要從高大畢業，心中的感受是千言萬語也難以道盡。我想，在這個學校發生的點點滴滴，都將是我人生旅途中無法忘懷的美麗回憶，也將帶領著我繼續往人生的下個階段繼續邁進。此刻回想起這六年求學過程所受到的關心與幫助，心中的的感動與感謝無法言喻。首先最要感謝的是我的恩師及指導教授－王鳳生老師。大學時代便深受老師的言行風采影響，讓我的大學生活不只從老師身上獲得了許多專業領域的學問，也堅定了許多在人生路途上應秉持的正確信念與價值觀。研究所兩年間，老師除不厭其煩地從旁協助與指導我們建構論文外，也不時給予我們課業與生活上的關心與提攜，讓我的研究所生涯走的既溫暖又踏實，再多的言語也無法表達對老師深深的謝意。家人的支持與鼓勵，也是我碩士班生活屢次度過瓶頸的最大動力，感謝每逢我低潮時，願意傾聽、支持我的老媽，讓我能順利堅持完這兩年的生活。另外也要感謝眾多同門學長學姊的關心，特別要感謝雅津學姊和珮瑜姐在我碩士生活中的協助與指點。此外，一直以來不斷給我鼓勵與建議的鄭義暉老師及蔡宗秀老師，以及兩年同窗好友的陪伴與關懷，都是我這一路走來格外珍惜與感謝的緣分。論文的完成要感謝的人有太多太多，難以用短短的篇幅道盡。謹將這篇論文獻給所有幫助過、指導過我的師長、朋友及家人們，感謝你們的鼓勵與支持，讓我能順利完成碩士班學業，繼續往人生的下個階段前進。. 蘇志榮. 謹誌于. 高雄大學經管所民國九十五年七月 iv.

(5) Table Contents Chapter 1 Introduction……………………………………………………………….... 2 1.1 Managerial Delegation …………………………………………………… ………….... 3 1.2 Technology Transfer………………………………………………………………........ ..4. Chapter 2 Technology Licensing under Cournot Duopoly…………………......8 2.1 Technology Licensing………………………………………………………………........8 2.2 Technology Licensing with Delegation………………………………………………....13. Chapter 3 Technology Licensing in a Stackelberg Duopoly ……………….....18 3.1 Technology Licensing………………………………………………………………......18 3.2 Technology Licensing with Delegation………………………………………………....25. Chapter 4 Technology Licensing under Bertrand Duopoly……………….......37 4.1 Technology Licensing………………………………………………………………......37 4.2 Technology Licensing with Delegation………………………………………………....41. Chapter 5 Conclusion………………………………………………………………......48. Reference……………………………………………………………….............................50. Appendix………………………………………………………………..............................53. 1.

(6) Studies on Managerial Delegation and Technology Transfer under Duopolistic Competition. Chapter 1 Introduction Under the oligopolistic competition, the uses of strategic instruments among firms are widely discussed in previous literatures. For example, in the private sector, the relevant strategic instruments are the firms’ managerial decisions; and in the public sector, the ones may be the industrial and trade policies. The purposes of these literatures are mainly discussing how the different choices or combination of these strategic instruments would mutually affect the competition relationships and the interactions which are among the oligopolistic firms or not. As more and more modern firms separate the role of owners and managers to maximize their profits, how to make an optimal monitor way or incentive system for the firm’s owner to ensure their agents, the manager, can do the most efforts to create the best performance for the company has been discussed more and more. Besides, as more and more modern firms emphasize in investing on R&D or innovation activities, the technology transfer issues has also been investigated more and more. So in our studies, we will discuss two strategic instruments which are about the issues we talk about in the above that firms can use to compete in market: Managerial delegation decisions and technology transfer decisions.. 2.

(7) 1.1 Managerial Delegation Modern firms often separate the owners and managers to maximize profits. Based on the “opportunism”, managers may have the incentives to do the non-profit-maximizing behaviors under the asymmetric information. If a firm’s owner wants to avoid this manager’s “Moral Hazard” problem and assure that the manager would work as hard as possible for the firm’s profits, in general, he can take two correction ways: one is to monitor the manager’s working behaviors carefully and pay the manager rewards according to these behaviors; the other is to design an incentive scheme which can encourage the manager to work hard and efficiently. The managerial delegation is a strategic instrument about the incentive scheme designation. Owners increase the managers’ incentives and rewards throughout the “Profit-shifting” system, then the managers would not only try their best to reduce the production costs and raise the firms’ profits but also decrease the possibilities of efficiency loss due to the moral hazard. Vickers (1985), Fershtman and Judd (1987), and Sklivas (1987) explained the key strategic meanings of managerial delegation system under oligopolistic competition model. They doubted the profit-maximization assumption in the traditional market theories and pointed out that a firm may not only care about maximizing its profits, but also take account of its sales volume and market power. So they suggested that when a firm’s owner and manager are separated, the incentive scheme designation used for motivating the manager to work hard should be based on a performance indicator consists of profits and the market power measurement factor which is like the sales volume. During the duopoly competition, they found that this incentive system, managerial delegation, would significantly affect the competition behaviors of each firm. And they also found that if a firm’s owner sets the incentive scheme for the manager according to a performance indicator which is the combination of profits and sales volume, then no matter the competition is under Cournot or Bertrand model, the firm would gain the advantages of cost reducing and profit increasing. 3.

(8) In recent years, the relevant studies about the use of strategic managerial delegation under oligopolistic competition have been applied into many different topics and areas. For example, compared to those strategic instruments that firms can take to reduce the production costs and raise market competition abilities like the managerial delegation system, Lambertini and Primavera (2000) found that if firms make the R&D activities, then the cost-reducing and profit-increasing effects of these firms may be better than those who use the delegation system. Besides, Bárcena-Ruiz (2004) suggested that when the cost structures are distinct in different firms under oligopolistic market, then if they all choose the delegation strategies, they will have more incentives to engage in the R&D or innovation activities to reduce the production costs. Lambertini (2004), Zhang and Zhang (1997), Krakel (2004) found another interesting issue, compared to a managerial firm which takes the delegation system and an entrepreneur firm which is only cares about the profit-maximization, when the R&D spillover effects are lower, then the managerial firm will take more advantages from R&D and invest more in R&D activities than the entrepreneur firm.. 1.2 Technology Transfer In addition to the widely discussions of a firm’s strategic instrument about managerial delegation system, the topic of technology transfer strategy is also a popular issue in recently. Except for the R&D and technology innovation activities, in order to reduce production costs and increase profits, firms may choose to buy the production technology patent from the patent-holder. The patent licensing literatures can be classified to two forms: Inside & Outside. The outside technology transfer case is the one that the patentee is outside the market of operation, i.e. the patentee is not a competitor in the product market, like an outside independent research lab. The reward of the outside patent- holder may be realized through licensing its innovation to the producing firms, so the outside patent- holder is only interested in its total licensing revenue. The inside technology transfer case is the one that the patentee 4.

(9) is inside the market of operation and is a competitor in the product market. For an inside patent-holding firm, it may keep its innovation for its own use and gains an advantage in competing with its competitors, or it may also license its innovation to the other competitors to gain the licensing revenue. Several important reasons have been advanced in the literature as to why a firm may want to license an innovation to its competitors, covering both the profit motive and the strategic incentive. For example, Gallini (1984) points out the incentive for an incumbent to license to a potential entrant so as to reduce the likelihood of the latter developing a better technology; Katz and Shapiro (1985) regard the incentive to license as an integral part of a firm’s R&D decision in evaluating the profitability of a R&D project; Eswaran (1994) explores the possibility that licensees can serve as a barrier to entry; Lin (1996) shows that licensing in the form of a fixed fee may serve as a facilitating device for collusion among competitors. When licensing a patented cost-reducing process innovation, a patentee may consider several different policies, and the most popular cases are like (1) the auction: auctioning off a limited number of licenses through a sealed bid auction; (2) the fixed fee: offering a lump-sum licensing fee; and (3) the royalty: offering a royalty payment per unit of production. In a complete information framework, if the patentee is an outsider, then fixed-fee licensing dominates royalty licensing (Kamien and Tauman, 1986; Katz and Shapiro 1986; Kamien, 1992), whereas in a leadership structure the optimal contract depends on the innovation size (Kabiraj, 2005). Muto (1993), Wang (1998, 2002), Kamien and Tauman (2002), and Wang and Yang (2004) analyze the case where the patentee is an insider and competition in the output market is Cournot. They show that royalty licensing dominates fixed fees. Saracho (2002) found a similar result when the oligopolistic industry is manager-managed. During the past time, the patent- licensing literature has still followed traditional theory and treated firms as economic agents with the sole objective of profit maximization. But 5.

(10) when economists began to consider seriously the fact that the modern corporation is characterized by a separation of ownership and management, and the analysis of the firm’s objective function began to focus on managerial objectives and the owner–manager relationship, this potentially important features should be taken consideration into the patent-licensing literature. Saracho (2002) extended the framework of Kaimen and Taumen (1986) with delegation and found that the patent-owner will still prefer royalty than fixed fee. Wang and Hsu (2004) used the inside technology transfer mode with managerial delegation to construct model and found that licensing is less likely to occur under strategic delegation compared to no delegation. But except for the articles in the above, there are still very few studies which are focusing on the relationship between the managerial delegation and technology transfer. So in our studies, we will extend the traditional technology transfer literatures, combining the managerial delegation system with the technology transfer model to discuss some interesting issues. Our studies will mainly focus on the inside technology transfer model and combine with managerial delegation. We will discuss this issue under different market competition structures. For the Cournot competition, Wang (1998) and Wang and Hsu (2004) have discussed traditional inside technology transfer model and extended it with managerial delegation. For the Cournot Stackelberg competition, Kabiraj (2005) has discussed the traditional Stackelberg model, and Wang and Yang (2004) extended it with pre-innovation model to talk about the inside technology transfer, but they haven’t applied the managerial delegation within the models, so we will extend their basic model with managerial delegation in our studies. Besides, for the Bertrand competition, Wang and Yang (1999) just discussed the traditional basic inside Bertrand technology transfer model without managerial delegation, so we will also extend their models with managerial delegation to see if their results of models will change or not.. 6.

(11) Table 1.. Model. Inside Technology Transfer Model Comparison. Basic Model. Extension Model with Managerial Delegation. Cournot. Wang (1998). Wang and Hsu (2004). Cournot Stackelberg. Kabiraj (2005) Wang and Yang (2004). Our Studies. Bertrand. Wang and Yang (1999). Our Studies. Market Structure. The rest of this study is organized as follows: Chapter 1 in the above is the introduction, which includes the research background, literature reviews and the position of our studies among the relative literatures. In Chapter 2, 3 and 4 we will consider basic technology licensing model under Cournot, Stackelberg and Bertrand duopoly market structures which are with and without the managerial delegation system designation. And we will make the conclusion in Chapter 5.. 7.

(12) Chapter 2 Technology Licensing under Cournot Duopoly. In this chapter, we will discuss about which patent-licensing policy, the fixed fee or the royalty fee, for the patent holding firm is better under Cournot and Cournot Stackelberg market competition structures. At first we will review some model settings and results in the past literatures, and then we will combine the managerial delegation into these models to see if the results will change or not.. 2.1 Technology Licensing. In this part, we will introduce the basic technology transfer model under Cournot duopolistic competition of Wang (1998), which taking a two-stage game model to discuss the technology transfer actions between the two competition firms.. Stage I. Stage II Time. Patent-holding firm sets up the license contract of license fee. Both firm’s managers choose the quantities in the market.. Figure 1 Game Stages of Technology Transfer. In the first stage, the patent-holding firm 1 sets up the license contract of license fee. In the second stage, the two firms compete in quantities in the market. The settings of Wang (1998) are as follows: the market structure is a homogeneous duopoly Cournot model, each firm’s profit function is π i = Ri − C (qi ) , i =1, 2. Revenue 8.

(13) function is Ri = pqi , and the inverse demand function is p = a − (q1 + q 2 ) , cost function is C i (q i ) = c i q i . Besides, firm 1’s marginal cost c1 = c − ε , firm 2’s marginal cost c 2 = c , if firm 1 would be likely to license its technology patent to the competitor, firm 2, then firm 2 may have the incentive to buy the cost-reducing innovation patent from firm 1 if it can earn more profit from the buying action.. 2.1.1 Fixed-fee Licensing. In the market competition stage, firm 1 and firm2 will choose q1 and q 2 to maximize π 1 and π 2 . The equilibrium quantities can be solved by taking the first order condition to solve the Cournot equilibrium for each firm,. qi * =. a − 2c i +c j. i, j = 1,2. 3. i≠ j. (2-1). and each firm’s profit is. π i* =. ( a − 2c i + c j ) 2 9. i, j = 1,2. i≠ j. (2-2). Substituting c1 = c − ε and c 2 = c into Eqs. (2-1) and (2-2) gives the firms’ Cournot equilibrium quantities (the superscript NL denotes ‘no licensing’). q1NL =. a − c + 2ε and 3. q 2NL =. 9. a−c−ε 3. (2-3).

(14) and their equilibrium profits. π 1 NL =. ( a − c + 2ε ) 2 9. and π 2 NL =. (a − c − ε ) 2 9. (2-4). Wang (1998) considered two separate cases: non-drastic and drastic innovations, depending on the magnitude of the innovation. A drastic innovation is one where the innovating firm will become a monopoly if licensing does not occur. In other words, a drastic innovation is one where the monopoly price with the new technology is equal to or less than the unit production cost of the old technology (so that the firm using the old technology is driven out of the market). It is easy to verify that the monopoly price with the new technology is less than or equal to c c if ε ≥ a − c . Hence, as ε that is greater than or equal to a − c gives a drastic innovation. If 0 < ε < ( a − c ) , then implies that firm 1 owns the producing cost advantage from a non-drastic innovation. Like the conditions that separate the patent-holding firm’s pre-innovation is drastic or non-drastic, we can use the same way to distinguish the differences of innovation in the following chapters and models. But in order to discuss the cases under duopoly competition, we will only consider the non-drastic innovation cases in the chapters in the below. Under the fixed-fee licensing method, firm1 licenses its cost-reducing technology to firm 2 at a fixed fee F which is invariant of the quantity firm 2 will produce using the new technology. The maximum license fee firm 1 can charge firm 2 is what will make firm 2 indifferent between licensing and not licensing the new technology. In the case that licensing occurs, both firms will produce at constant unit cost c − ε . So the maximum license fee firm 1 can charge firm 2 is. F = π 2L (c − ε , c − ε ) − π 2NL (c − ε , c ) =. 10. 4(a − c)ε 9. (2-5).

(15) and the equilibrium profits. π1. F. (a − c + 2ε ) 2 4(a − c)ε (a − c − ε ) 2 F = + and π 2 = 9 9 9. (2-6). Besides, combining (2-4) and (2-6), the condition that firm 1 may have the incentive to license to firm 2, π 1F ≥ π 1NL , would be supported if and only if 0 < ε ≤. 2(a − c) . 3. 2.1.2 Royalty-fee Licensing Follow the basic settings of 2.1.1, and firm 1 will license its technology to firm 2 at a fixed royalty rate r, and the amount of royalty firm 2 pays will depend on the quantity firm 2 will produce by using the technology patent. In this case, firm 1’s unit production cost is c − ε , firm 2’s unit production cost is c − ε + r if it licenses from firm 1 and c if it does not license. Note that the maximum royalty rate firm 1 can charge obviously cannot exceed ε (i.e., 0 ≤ r ≤ ε ). In the market competition stage, firm 1 and firm 2 will choose q1 and q 2 to maximize π 1 + rq 2 and π 2 − rq 2 . And in the licensing stage, firm 1 will choose r to maximize π 1 + rq 2 . If the innovation is non-drastic, the optimal royalty rate r = ε (see Appendix), and the. equilibrium quantities. q1R =. a − c + 2ε and 3. q 2R =. 11. a −c −ε 3. (2-7).

(16) and their equilibrium profits. π1. R. (a − c + 2ε ) 2 ε (a − c − ε ) (a − c − ε ) 2 R = + and π 2 = 9 3 9. (2-8). 2.1.3 Comparison: Fixed fee versus royalty fee Evaluate the superiority of a fixed fee licensing versus a royalty licensing,. π 1F − π 1R < 0. (2-9). Hence, for firm 1, licensing by means of a royalty is superior to licensing by means of a fee in this case.. 12.

(17) 2.2 Technology Licensing with Delegation In this part, we will introduce the technology transfer model under Cournot duopolistic competition with delegation of Hsu and Wang (2004), which taking a three-stage game model to discuss the technology transfer actions between the two competition firms. Besides, because the timing arrangement of Wang and Hsu (2004) seems not to be appropriate, so we make some modifications to reintroduce the results of this paper. Consider a three-stage game model to discuss the technology transfer actions between the two competition firms under delegation.. Stage I. Stage II. Stage III. Time. Patent-holder chooses the license fee to sell,. Firm’s owner chooses the incentive parameter.. Firm’s manager chooses the quantity in the market.. Figure 2 Delegating Game Stages of Technology Transfer.. In the first stage, the patent-holding firm chooses the licensing fee to sell to the patent-buyer. In the second stage, each firm’s owner chooses the incentive parameter to encourage their managers to compete harder in the market. In the third stage, the two firms compete in quantities in the market. The settings of managerial delegation system of Wang (2004) is following Sklivas (1987) and Fershtman and Judd (1987). To attain the profits and market power, owner will measure his manager’s performance according to a function g i , which combines firm’s profits ( π i ) and revenues ( Ri ). The higher is g i , the higher is manager i ’s bonus or the lower is the. 13.

(18) likelihood that he will be fired, so g i could represent manager i ’s incentives. For simplicity, it sets g i as a linear combination of profits and revenues, and the marginal costs are constant.. Max g i = λi π i (q1 , q 2 ) + (1 − λi )Ri (q 1 , q 2 ) = Ri (q1 , q 2 ) − λi C i (qi ) , i =1, 2. 2.2.1 Fixed-fee licensing Using the backward-induction to solve this licensing game. In the third stage, the two firms’ managers compete in market according to the performance indicator g i , so take the first order condition to solve the Cournot equilibrium for each firm, and just discuss the interior solution case; we can derive the equilibrium quantities. q i (λ i , λ j ) =. a − 2λi c i +λ j c j 3. i, j = 1,2. i≠ j. (2-10). And substituting Eq. (2-10) to the profit function of delegation stage and taking the first order condition, we can obtain each firm’s optimal incentive parameter is. λi =. (8ci − 2c j − a). i, j = 1,2. 5ci. i≠ j. (2-11). each firm’s equilibrium quantities is. qi. **. =. 2( a + 2c j − 3c i ). i, j = 1,2. 5. 14. i≠ j. (2-12).

(19) and each firm’s equilibrium profits is. π. ** i. =. 2(a − 3ci + 2c j ) 2 25. i, j = 1,2. i≠ j. (2-13). Substituting c1 = c − ε and c 2 = c into Eqs. (2-12) and (2-13) to give the firms’ Cournot equilibrium quantities and profits (the superscript NL denotes ‘no licensing’). q1NL* =. π 1NL* =. 2 ( a − c + 3ε ) 5. 2 5. and q 2NL* = ( a − c − 2ε ). 2 2 (a − c + 3ε ) 2 and π 2NL* = (a − c − 2ε ) 2 25 25. (2-14). (2-15). The maximum license fee firm 1 can charge firm 2 is what will make firm 2 indifferent between licensing and not licensing the new technology. In the case that licensing occurs, both firms will produce at constant unit cost c − ε . The maximum fixed license fee firm 1 can charge firm 2 is. F * = π 2L* (c − ε , c − ε ) − π 2NL* (c − ε , c ) =. 6 [2(a − c) − ε ]ε 25. (2-16). and the equilibrium profits are. π 1F =. 2 6 2 (a − c + 3ε ) 2 + [ 2( a − c) − ε ]ε and π 2F = ( a − c − 2ε ) 2 25 25 25. 15. (2-17).

(20) Combining Eqs. (2-15) and (2-17), the condition that firm 1 may have the incentive to license to firm 2, π 1F ≥ π 1NL , would be supported if and only if 0 < ε ≤. ( a − c) . 2. 2.2.2 Royalty-fee licensing. Follow the basic settings in the above, and firm 1 will license its technology to firm 2 at a fixed royalty rate r, and the amount of royalty firm 2 pays will depend on the quantity firm 2 will produce by using the technology patent. In this case, firm 1’s unit production cost is c − ε , firm 2’s unit production cost is c − ε + r if it licenses from firm 1 and c if it does not license. Note that the maximum royalty rate firm 1 can charge obviously cannot exceed ε (i.e., 0 ≤ r ≤ ε ). In the market competition stage, firm 1 and firm 2 will choose q1 and q 2 to maximize π 1 + rq 2 and π 2 − rq 2 . In the managerial delegation stage, each firm’s owner chooses incentive parameter λi to maximize firms’ profits. And in the licensing stage, firm 1 will choose r to maximize π 1 + rq 2 . If the innovation is non-drastic, the optimal royalty rate r = ε , and the equilibrium. quantities are q1R =. π 1R =. 2 ( a − c + 3ε ) 5. 2 5. and q 2R = ( a − c − 2ε ). 2 2r 2 (a − c + 3ε ) 2 + ( a − c − 2ε ) and π 2R = (a − c − 2ε ) 2 25 5 25. 16. (2-18). (2-19).

(21) 2.2.3 Comparison: Fixed fee versus royalty fee Evaluate the superiority of a fixed fee licensing versus a royalty licensing,. π 1F − π 1R < 0. (2-20). Hence, for firm 1, if it takes the designation of managerial delegation system, it would still prefer royalty fee to fixed fee when it chooses the best patent licensing policy.. Comparison: 2.1 and 2.2. Comparing the results of 2.1 and 2.2, we can make two simple conclusions 1. When inside technology transfer occurs in Cournot market, then either the competing firms take the managerial delegation designation or not, the patent-holding firm would prefer royalty fee licensing to fixed fee licensing. 2. Patent licensing is less likely to occur under strategic delegation than under no delegation, which means that under strategic delegation, firms (managers) will behave more aggressively than under standard quantity competition, so it will reduce the incentive for the patent-holding firm to license its innovation to the other firm.. 17.

(22) Chapter 3 Technology Licensing in a Stackelberg Duopoly. 3.1 Technology Licensing In part 3.1 and 3.2, we will consider the technology transfer model under Stackelberg market structure without and with managerial delegation. In part 3.1, we will introduce the basic technology transfer model under Stackelberg duopolistic competition of Kabiraj (2005), which taking a two-stage game model to discuss the technology transfer actions between the two competition firms, and then we will try to combine the managerial delegation system designation with this model to see the results would change or not in part 3.2. Kabiraj (2005) considered a basic technology transfer model under Stackelberg duopolistic competition, taking a two-stage game model to discuss the technology transfer actions between the two competition firms.. Stage I. Stage II Time. Patent-holding firm sets up the license contract of license fee.. Firm’s manager chooses the quantity under Stackelberg competition.. Figure 3 Game Stages of Technology Transfer. In the first stage, the patent-holding firm sets up the license contract of license fee, and the other firm’s manager decides to accept the contract or not. In the second stage, the two firms compete in quantities under the Stackelberg competition market.. 18.

(23) Suppose firm 1 is the leading firm, and firm 2 is the following firm, and consider a homogeneous duopoly Stackelberg model, each firm’s profit function is π i = Ri − C (qi ) , i =1, 2. Revenue function is Ri = pqi , and the inverse demand function is p = a − (q1 + q 2 ) , cost function is C i (q i ) = c i q i . Solving the first order condition to derive firm 2’s reaction function.. q 2 (q1 ) =. 1 (a − q1 − c 2 ) 2. (3-1). Because firm 1 is the leading firm, so it can substitute firm 2’s reaction function (3-1) into its profit function, then under the first order condition, we can have the Stackelberg equilibrium quantities are. q1 = *. 1 (a − 2c1 + c 2 ) 2. and. q2 = *. 1 (a + 2c1 − 3c 2 ) 4. (3-2). and the equilibrium profits are. 1 1 π 1* = (a − 2c1 + c 2 ) 2 and π 2* = (a + 2c1 − 3c 2 ) 2 8 16. (3-3). Kabiraj (2005) considered two cases as follows,. 3.1.1 Leading firm is the patent-holder. 3.1.1.1 Fixed fee Assume firm 1’s marginal cost c1 = c − ε , firm 2’s marginal cost c 2 = c , 0 < ε < ( a − c ) , which implies that firm 1 owns the producing cost advantage from a non-drastic innovation. Substituting c1 = c − ε and c 2 = c into Eqs. (3-2) and (3-3) to give the firms’ Stackelberg 19.

(24) equilibrium quantities and profits (the superscript NL denotes ‘no licensing’), we can have q1 NL =. (a − c + 2ε ) 2. π 1NL =. ( a − c + 2ε ) 2 ( a − c − 2ε ) 2 and π 2NL = 8 16. and. q 2 NL =. ( a − c − 2ε ) 4. (3-4). (3-5). The maximum license fee firm 1 can charge firm 2 is what will make firm 2 indifferent between licensing and not licensing the new technology. In the case that licensing occurs, both firms will produce at constant unit cost c − ε . So the maximum license fee firm 1 can charge firm 2 is. F = π 2L (c − ε , c − ε ) − π 2NL (c − ε , c ) =. 3 [2(a − c) − ε ]ε 16. (3-6). So the equilibrium quantities and profits of each firm under fixed-fee licensing are. q1 F =. π 1F =. 1 (a − c + ε ) 2. q2 F =. and. 1 (a − c + ε ) 4. 3 1 1 ( a − c + ε ) 2 − ( a − c − 2ε ) 2 and π 2F = (a − c − 2ε ) 2 16 16 16. (3-7). (3-8). Besides, combining (3-5) and (3-8) can obtain that π 1F ≥ π 1NL if and only if 0 < ε ≤ (a − c) .. 20.

(25) 3.1.1.2 Royalty fee Following the basic settings and results in the above, if firm 1 license its technology to firm 2 at a fixed royalty rate r , and the amount of royalty firm 2 pays will depend on the quantity firm 2 will produce by using the technology patent. In this case, firm 1’s unit production cost is c − ε , firm 2’s unit production cost is c − ε + r if it licenses from firm 1 and c if it does not license. Note that the maximum royalty rate firm 1 can charge obviously cannot exceed ε (i.e., 0 ≤ r ≤ ε ). In the market competition stage, firm 1 and firm 2 will choose q1 and q 2 to maximize π 1 + rq 2 and π 2 . And in the licensing stage, firm 1 will choose r to maximize π 1 + rq 2 . If the innovation is non-drastic, the optimal royalty rate r = ε , and the equilibrium. quantities q1R =. a − c + 2ε and 2. q 2R =. a − c − 2ε 4. (3-9). and their equilibrium profits π1R =. ( a − c + 2ε ) 2 r (a − c − 2ε ) ( a − c − 2ε ) 2 + and π 2 R = 8 4 16. (3-10). 3.1.1.3 Comparison: Fixed fee versus royalty fee Evaluate the superiority of a fixed fee licensing versus a royalty licensing in the Stackelberg model, if the leading firm is the patent-holder,. π 1F − π 1R < 0. (3-11). Hence, the patent-holding firm would prefer royalty fee to fixed fee when it chooses the best patent licensing policy.. 21.

(26) 3.1.2 Following firm is the patent-holder. 3.1.2.1 Fixed fee Assume firm 1’s marginal cost c1 = c , firm 2’s marginal cost c 2 = c − ε , 0 < ε < ( a − c ) , which implies that firm 2 owns the producing cost advantage from a non-drastic innovation. Substituting c1 = c and c 2 = c − ε into Eqs. (3-2) and (3-3) to give the firms’ Stackelberg equilibrium quantities and profits (the superscript NL denotes ‘no licensing’), we can have. q1 NL =. (a − c − ε ) 2. q 2 NL =. and. ( a − c + 3ε ) 4. 1 1 π 1NL* = (a − c − ε ) 2 and π 2NL* = (a − c + 3ε ) 2 8 16. (3-12). (3-13). The technology transfer occurs when π 2NL* ≥ π 1NL* , and we can have the condition that 3 (a − c ) ≤ ε ≤ 5(a − c ) .The maximum license fee firm 2 can charge firm 1 is what will make 7 firm 1 indifferent between licensing and not licensing the new technology. In the case that licensing occurs, both firms will produce at constant unit cost c − ε . So the maximum license fee firm 2 can charge firm 1 is. F = π 1L* (c − ε , c − ε ) − π 1NL* (c − ε , c ) =. ( a − c )ε 2. (3-14). So the equilibrium quantities and profits of each firm under fixed-fee licensing are. q1 = F. 1 (a − c + ε ) 2. q2 = F. and. 22. 1 (a − c + ε ) 4. (3-15).

(27) 1 1 (a − c)ε π 1F = (a − c − ε ) 2 and π 2F = ( a − c − 2ε ) 2 + 8 16 2. (3-16). Combining (3-33) and (3-36) can obtain that π 1F ≥ π 1NL if and only if 0 < ε ≤ (a − c) .. 3.1.2.2 Royalty fee Following the basic settings and results in the above, if firm 2 license its technology to firm 1 at a fixed royalty rate r , and the amount of royalty firm 1 pays will depend on the quantity firm 1 will produce by using the technology patent. In this case, firm 2’s unit production cost is c − ε , firm 1’s unit production cost is c − ε + r if it licenses from firm 2 and c if it does not license. Note that the maximum royalty rate firm 2 can charge obviously cannot exceed ε (i.e., 0 ≤ r ≤ ε ). In the market competition stage, firm 1 and firm 2 will choose q1 and q 2 to maximize π 1 and π 2 + rq1 . And in the licensing stage, firm 2 will choose r to maximize π 2 + rq1 . If the innovation is non-drastic, the optimal royalty rate r = ε , and the equilibrium. quantities. q1R =. a −c −ε and 2. q 2R =. a − c + 3ε 4. (3-17). and their equilibrium profits. π1R =. (a − c − ε ) 2 ( a − c + 3ε ) 2 r ( a − c − ε ) and π 2 R = + 8 16 2. 23. (3-18).

(28) 3.1.2.3 Comparison: Fixed fee versus royalty fee Evaluate the superiority of a fixed fee licensing versus a royalty licensing in the Stackelberg model, if the following firm is the patent-holder,. π 2F − π 2R < 0. (3-19). Hence, whether the patent-holding firm is Stackelberg leader or follower, it would prefer royalty fee to fixed fee when it chooses the best patent licensing policy.. 24.

(29) 3.2 Technology Licensing with Delegation In this part, we will extend the basic Stackelberg technology transfer model of Kabiraj (2005) which we introduce in part 3.1, taking a three-stage game model to discuss the technology transfer actions between the two competing firms with managerial delegation designation.. Stage I. Stage II. Stage III. Time. Patent-holder chooses the license fee to sell,. Firm’s owner chooses the incentive parameter.. Firm’s manager chooses the quantity in the Stackelberg market. Figure 4 Delegating Game Stages of Technology Transfer.. In the first stage, the patent-holding firm chooses the licensing fee to sell to the patent-buyer. In the second stage, each firm’s owner chooses the incentive parameter to encourage their managers to compete harder in the market. In the third stage, the two firms compete in quantities under the Stackelberg competition market. We follow the settings of managerial delegation of Sklivas (1987) and Fershtman and Judd (1987). To attain the profits and market power, owner will measure his manager’s performance according to a function g i , which combines firm’s profits ( π i ) and revenues ( Ri ). The higher is g i , the higher is manager i ’s bonus or the lower is the likelihood that he will be fired, so g i could represent manager i ’s incentives. For simplicity, we make g i as a linear combination of profits and revenues, and the marginal costs are constant.. 25.

(30) Max g i = λi π ' (q1 , q 2 ) + (1 − λi )Ri (q 1 , q 2 ) = Ri (q1 , q 2 ) − λi C i (qi ) , i =1, 2. And we also consider two cases: Leading firm is the patent-holder or following firm is the patent-holder.. 3.2.1 Leading firm is the patent holder. 3.2.1.1 Fixed fee Using backward-induction to solve this licensing game. In the third stage, the two firms’ managers compete in market according to the performance indicator g i .Suppose firm 1 is the leading firm, and firm 2 is the follower, and consider a homogeneous duopoly Stackelberg model. Solving the first order condition under profit-maximization condition, we can derive firm 2’s reaction function.. q 2 (q1 ) =. 1 (a − q1 − λ 2 c 2 ) 2. (3-20). Because firm 1 is the leading firm, so it can substitute firm 2’s reaction function (3-20) into its profit function, then under the first order condition, we can have the Stackelberg equilibrium quantities are. q1 (λ1 , λ 2 ) =. 1 (a − 2λ1c1 + λ 2 c 2 ) 2. and. 26. q 2 (λ1 , λ 2 ) =. 1 (a + 2λ1c1 − 3λ 2 c 2 ) 4. (3-21).

(31) And substituting Eq. (3-21) to the profit function of delegation stage and taking the first order condition, we can obtain each firm’s optimal incentive parameter is. λ1 = 1 and λ 2 = 2 −. a + 2c1 3c 2. (3-22). the equilibrium quantities are. 1 * q1 = (a − 4c1 + 3c 2 ) 3. and. q2 = *. 1 (a + 2c1 − 3c 2 ) 2. (3-23). and the equilibrium profits are. π 1* =. 1 1 (a − 4c1 + 3c 2 ) 2 and π 2* = (a + 2c1 − 3c 2 ) 2 18 12. Assume firm 1’s marginal cost c1 = c − ε , firm 2’s marginal cost c 2 = c , 0 < ε <. (3-24). (a − c) , 2. which implies that firm 1 owns the producing cost advantage from a non-drastic innovation. Substituting c1 = c − ε and c 2 = c into Eqs. (3-23) to give the firms’ Stackelberg equilibrium quantities and profits in the delegation stage (the superscript NL denotes ‘no licensing’), we can have. 1 q1** = ( a − c + 4ε ) 3. π 1NL =. and. q 2 ** =. 1 (a − c − 2ε ) 2. 1 1 (a − c + 4ε ) 2 and π 2NL = (a − c − 2ε ) 2 18 12. 27. (3-25). (3-26).

(32) The technology transfer may occur when π 1NL ≥ π 2NL , so we can have the condition that 5 13 (a − c ) ≤ ε ≤ (a − c) . If the technology transfer occurs, the maximum license fee firm 1 34 2 can charge firm 2 is what will make firm 2 indifferent between licensing and not licensing the new technology. In the case that licensing occurs, both firms will produce at constant unit cost c − ε , and we can derive the maximum fixed license fee firm 1 can charge firm 2 in the licensing stage,. 1 F = π 2L (c − ε , c − ε ) − π 2NL (c − ε , c) = [2(a − c) − ε ]ε 4. (3-27). So the equilibrium quantities and profits of each firm under fixed-fee licensing are. 1 q1 F = (a − c + ε ) 3. π 1F =. q2 F =. and. 1 (a − c + ε ) 2. 1 1 1 (a − c − ε ) 2 + [2( a − c ) − ε ]ε and π 2F = (a − c − 2ε ) 2 18 4 12. (3-28). (3-29). Combining (3-26) and (3-29) can obtain that π 1F ≥ π 1NL if and only if 0 < ε ≤ (a − c) .. 3.2.1.2 Royalty fee We use backward-induction to solve this licensing game. Suppose firm 2 has bought the patent from firm 1, so their marginal costs is the same, c1 = c 2 = c − ε , and the royalty licensing fee firm 1 charge firm 2 is r per unit. In the third stage, the two firms’ managers compete in market according to the performance indicator g i .Suppose firm 1 is the leading firm, and firm 2 is the follower, and. 28.

(33) consider a homogeneous duopoly Stackelberg model. The objective function for each firms’ manager is. g1 = λ1π 1 + (1 − λ1 ) R1 = R1 − λ1 (c − ε )q1 + λ1 rq 2. (3-30). g 2 = λ 2 π 2 + (1 − λ 2 ) R2 = R2 − λ 2 (c − ε )q 2 − λ 2 rq 2. (3-31). Solving the first order condition under profit-maximization condition, we can derive firm 2’s reaction function.. q 2 (q1 ) =. 1 [a − q1 − λ 2 (c − ε + r )] 2. (3-32). Because firm 1 is the leading firm, so it can substitute firm 2’s reaction function (3-32) into its profit function, then under the first order condition, we can have the Stackelberg equilibrium quantities in the market competition stage are. 1 q1 (λ1 , λ 2 ) = [a − (2c + r − 2ε )λ1 + (c + r − ε )λ 2 ] 2. q 2 (λ1 , λ 2 ) =. 1 [a + (2c + r − 2ε )λ1 − 3(c + r − ε )λ 2 ] 4. (3-33). (3-34). Substituting Eq. (3-23) and (3-34) to the profit function of delegation stage and taking the first order condition, we can obtain each firm’s optimal incentive parameter is λ1 = 1 and λ 2 (r ) = the equilibrium quantities are. 29. 4 a−r − 3 3(c − ε + r ). (3-35).

(34) 1 q1 (r ) = (a − c + r + ε ) 3. and. q 2 (r ) =. 1 ( a − c − 2r + ε ) 2. (3-36). Substituting Eqs. (3-35) and (3-36) into firm 1’s profit function to solve the optimal royalty rate in the licensing stage, and we can derive the optimal royalty rate r = ε . Then we can have the equilibrium quantities and profits of each firm,. 1 q1 R = ( a − c + 2ε ) 3. π 1R =. and. q2 R =. 1 (a − c − ε ) 2. (a − c − ε ) 2 + 12( a − c )ε 1 and π 2R = ( a − c − ε ) 2 18 12. (3-37). (3-38). 3.2.1.3 Comparison: Fixed fee versus royalty fee Evaluate the superiority of a fixed fee licensing versus a royalty licensing,. π 1F − π 1R < 0. (3-39). Hence, if the leading firm owns the patent and takes the designation of managerial delegation system, it would still prefer royalty fee to fixed fee when it chooses the best patent licensing policy.. 30.

(35) 3.2.2 Following firm is the patent-holder Considering a homogeneous duopoly Stackelberg model, supposing firm 1 is the leading firm, and firm 2 is the follower, and firm 2 owns the patent.. 3.2.2.1 Fixed fee The same with the cases of 3.2.1(Leading firm is the patent holder), we use the backward-induction to solve this licensing game. In the third stage, the two firms’ managers compete in market according to the performance indicator g i . Solving the first order condition under profit-maximization condition, we can derive firm 2’s reaction function.. q 2 (q1 ) =. 1 (a − q1 − λ 2 c 2 ) 2. (3-40). Because firm 1 is the leading firm, so it can substitute firm 2’s reaction function (3-40) into its profit function, then under the first order condition, we can have the Stackelberg equilibrium quantities are. q1 (λ1 , λ 2 ) =. 1 1 (a − 2λ1c1 + λ 2 c 2 ) and q 2 (λ1 , λ 2 ) = (a + 2λ1c1 − 3λ 2 c 2 ) 2 4. (3-41). And substituting Eq. (3-41) to the profit function of delegation stage and taking the first order condition, we can obtain each firm’s optimal incentive parameter is. λ1 = 1 and λ 2 = 2 −. 31. a + 2c1 3c 2. (3-42).

(36) the equilibrium quantities are. 1 * q1 = (a − 4c1 + 3c 2 ) 3. q2 = *. and. 1 (a + 2c1 − 3c 2 ) 2. (3-43). and the equilibrium profits are. π 1* =. 1 1 (a − 4c1 + 3c 2 ) 2 and π 2* = (a + 2c1 − 3c 2 ) 2 18 12. (3-44). Assume firm 1’s marginal cost c1 = c , firm 2’s marginal cost c 2 = c − ε , 0 < ε <. ( a − c) , 3. which implies that firm 2 owns the producing cost advantage from a non-drastic innovation. Substituting c1 = c and c 2 = c − ε into Eqs. (3-43) and (3-44) to give the firms’ Stackelberg equilibrium profits (the superscript NL denotes ‘no licensing’), we can have. 1 * q1 = (a − c − 3ε ) 3. π 1NL =. 1 (a − c + 3ε ) 2. (3-45). 1 1 (a − c − 3ε ) 2 and π 2NL = (a − c + 3ε ) 2 18 12. (3-46). and. q2 = *. Because π 2NL ≥ π 1NL , so the technology transfer may occur. If the technology transfer occurs, the maximum fixed license fee firm 2 can charge firm 1 is what will make firm 1 indifferent between licensing and not licensing the new technology. In the case that licensing occurs, both firms will produce at constant unit cost c − ε . And we can derive the maximum license fee firm 2 can charge firm 1 in the licensing stage, 4 F = π 1L (c − ε , c − ε ) − π 1NL (c − ε , c) = [(a − c ) − ε ]ε 9 32. (3-47).

(37) So the equilibrium quantities and profits of each firm under fixed-fee licensing are. 1 q1 F = (a − c + ε ) 3. π 1F =. and. q2 F =. 1 (a − c + ε ) 2. 1 1 4 (a − c − 3ε ) 2 and π 2F = (a − c + 3ε ) 2 + [(a − c) − ε ]ε 18 12 9. Combining (3-46) and (3-49) can obtain that π 2F ≥ π 2NL if and only if 0 < ε ≤. (3-48). (3-49). ( a − c) . 3. 3.2.2.2 Royalty fee In the royalty fee licensing case, we also use the backward-induction to solve this licensing game. Suppose firm 1 has bought the patent from firm 2, so their marginal costs is the same, c1 = c 2 = c − ε , and the royalty licensing fee firm 2 charge firm 1 is r per unit. In the third stage, the two firms’ managers compete in market according to the performance indicator g i .Suppose firm 1 is the leading firm, and firm 2 is the follower, and consider a homogeneous duopoly Stackelberg model. The objective function for each firms’ manager is. g1 = λ1π 1 + (1 − λ1 ) R1 = R1 − λ1 (c − ε )q1 − λ1 rg 1. (3-50). g 2 = λ 2π 2 + (1 − λ 2 ) R2 = R2 − λ 2 (c − ε )q 2 + λ1 rg 1. (3-51). Solving the first order condition under profit-maximization condition, we can derive firm 1’s reaction function. 1 q 2 (q1 ) = [a − q1 − λ 2 (c − ε )] 2 33. (3-52).

(38) Because firm 1 is the leading firm, so it can substitute firm 2’s reaction function (3-52) into its profit function, then under the first order condition, we can have the Stackelberg equilibrium quantities in the market competition stage are. 1 q1 (λ1 , λ 2 ) = [a − 2(c − ε + r )λ1 + (c − ε )λ 2 ] 2. (3-53). 1 q 2 (λ1 , λ 2 ) = [a + 2(c − ε + r )λ1 − 3(c − ε )λ 2 ] 4. (3-54). Substituting Eq. (3-53) and (3-54) to the profit function of delegation stage and taking the first order condition, we can obtain each firm’s optimal incentive parameter is. λ1 = 1 and λ 2 (r ) =. 4 a − 2r − 3 3(c − ε ). (3-55). the equilibrium quantities are. 1 q1 (r ) = (a − c − 2r + ε ) 3. and. q2 =. 1 (a − c + ε ) 2. (3-56). Substituting Eqs. (3-55) and (3-56) into firm 2’s profit function to solve the optimal royalty rate in the licensing stage, and we can derive the optimal royalty rate r = ε . Then we can have the equilibrium quantities and profits of each firm,. 1 R q1 = (a − c − ε ) 3. and. 34. q2 = R. 1 (a − c + ε ) 2. (3-57).

(39) π 1R =. (a − c − ε ) 2 (a − c + ε ) 2 + 8(a − c)ε and π 2R = 18 12. Combining (3-44) and (3-54) can obtain that π 2R ≥ π 2NL if and only if 0 < ε ≤. (3-58). ( a − c) . 3. 3.2.2.3 Comparison: fixed fee versus royalty fee Evaluate the superiority of a fixed fee licensing versus a royalty licensing,. π 2F − π 2R < 0. (3-59). Hence, if the following firm owns the patent and takes the designation of managerial delegation system, it would still prefer royalty fee to fixed fee when it chooses the best patent licensing policy.. Integrate the results of 3.2.1 and 3.2.2, we have proposition 1. Proposition 1. Under Cournot Stackelberg market competition, either the leading firm owns the patent or not, it won’t take the managerial delegation decision anymore. Because the managerial delegation designation is a system that help firm to win more quantities in market, but for a Stackelberg leading firm, taking the quantity-leader actions and make the emphasis of market share is originally included in leading firm’s market competition decisions, so if the quantity-leader actions can help it win get more quantities in the market, then it may not prefer take the managerial delegation decisions.. 35.

(40) Comparing the results of 3.1 and 3.2, we can have the follow propositions,. Proposition 2. When inside technology transfer occurs in Stackelberg market, then either the competing firms take the managerial delegation designation or not, or the patent-holding firm is the leading firm or following firm in the markets, they would prefer royalty fee licensing to fixed fee licensing.. Proposition 3. In Stackelberg market, either the patent-holding firm is the leading firm or is the following firm, technology transfer will be less likely to occur under strategic delegation than under no delegation. This proposition is the same like the case in Cournot market that under strategic delegation, firms (managers) will behave more aggressively than under standard quantity competition, so it will reduce the incentive for the patent-holding firm to license its innovation to the other firm. Besides, comparing the results of Stackelberg and Cournot model, we can have the proposition.. Proposition 4. Either the patent-holder is the leading firm or the following firm, and either the patent-holder takes the managerial delegation designation or not, the licensing fee (either fixed or royalty fee) that it can gain from transferring the technology to the patent-buyer under Stackelberg competition will be less than it can get under Cournot competition.. 36.

(41) Chapter 4 Technology Licensing under Bertrand Duopoly In this chapter, we will still discuss about which patent-licensing policy, the fixed fee or the royalty fee, for the patent holding firm is better under Bertrand market competition structure. At first we will review the basic Bertrand technology transfer model settings and results of Wang and Yang (1999), and then we will combine the managerial delegation into the basic Bertrand model to see if the results will change or not.. 4.1 Technology Licensing In this part, we will introduce the basic technology transfer model under Bertrand duopolistic competition of Wang and Yang (1999), which taking a two-stage game model to discuss the technology transfer actions between the two competition firms.. 4.1.1 Fixed fee Stage I. Stage II Time. Patent-holding firm 1 sets up the license contract of license fee, and the other firm’s manager decides to accept the contract or not.. Both firm’s managers choose the prices in the market.. Figure 5 Game Stages of Technology Transfer. In the first stage, the patent-holding firm 1 sets up the license contract of license fee. In the second stage, the two firms compete in prices in the market. The model settings of Wang and Yang (1999) consider a differentiated product Bertrand model, and set each firm’s profit function is π i = Ri − C (qi ) . Revenue function is Ri = Pq i and the demand function is qi = a − pi + δp j , i, j = 1,2 and i ≠ j . Cost function is C i (q i ) = c i q i . 37.

(42) Besides, firm 1’s marginal cost c1 = c − ε , firm 2’s marginal cost c 2 = c , 0 < ε < (a − c)(1 − δ ) , which implies that firm 1 owns the producing cost advantage from a non-drastic innovation, so firm 2 may have the incentive to buy the cost-reducing innovation patent from firm 1 if it can earn more profit from the buying action. In the market competition stage, the two firms compete in prices; taking the first order condition to solve the Bertrand equilibrium for each firm, the equilibrium prices are. pi = *. 2(a + ci ) + (1 − δ )(aδ − c j ) (1 − δ )(3 + 2δ − δ 2 ). i, j = 1,2. i≠ j. (4-1). and each firm’s profit is. πi = *. (a − aδ + ci − (2 − δ )c j ) 2 (1 − δ )(3 − δ ) 2. i, j = 1,2. i≠ j. (4-2). Substituting c1 = c − ε and c 2 = c into Eqs. (4-1) and (4-2) to give the firms’ Bertrand equilibrium profits (the superscript NL denotes ‘no licensing’). π1. NL. =. [(a − c )(1 − δ ) − ε ]2 [(a − c)(1 − δ ) + (2 − δ )ε ]2 NL and π = 2 (1 − δ )(3 − δ ) 2 (1 − δ )(3 − δ ) 2. (4-3). The maximum fixed license fee firm 1 can charge firm 2 is what will make firm 2 indifferent between licensing and not licensing the new technology. In the case that licensing occurs, both firms will produce at constant unit cost c − ε , so the maximum license fee firm 1 can charge firm 2 is. 38.

(43) F = π 2L (c − ε , c − ε ) − π 2NL (c − ε , c) =. ε (2 − δ )[2(a − c)(1 − δ ) − δε ] (1 − δ )(3 − δ ) 2. (4-4). So the equilibrium profits of each firm under fixed-fee licensing are. π 1F =. (1 − δ )(a − c + ε ) 2 ε (2 − δ )[2(a − c)(1 − δ ) − δε ] + (3 − δ ) 2 (1 − δ )(3 − δ ) 2. π 2F =. [(a − c)(1 − δ ) + (2 − δ )ε ]2 (1 − δ )(3 − δ ) 2. Combining (4-3) and (4-6) can obtain that π. F 1. ≥π. (4-5). (4-6). NL 1. 2(a − c )(1 − δ ) 2 if and only if 0 < ε ≤ (3 − δ ) 2. and 0 < δ < 1 .. 4.1.2 Royalty fee Follow the basic settings of 4.1.1, and firm 1 will license its technology to firm 2 at a fixed royalty rate r, and the amount of royalty firm 2 pays will depend on the quantity firm 2 will produce by using the technology patent. In this case, firm 1’s unit production cost is c − ε , firm 2’s unit production cost is c − ε + r if it licenses from firm 1 and c if it does not license. Note that the maximum royalty rate firm 1 can charge obviously cannot exceed ε (i.e., 0 ≤ r ≤ ε ). In the market competition stage, firm 1 and firm 2 will choose p1 and p 2 to maximize π 1 + rq 2 and π 2 − rq 2 . And in the licensing stage, firm 1 will choose r to maximize π 1 + rq 2 . If the innovation is non-drastic, the optimal royalty rate would be r = ε , so the equilibrium. prices are. 39.

(44) c(1 + δ ) + a (2 + δ − δ 2 ) − 2(1 − δ )ε (1 − δ )(3 − δ ). (4-7). c (1 + δ ) + a(2 + δ − δ 2 ) − (1 − δ ) 2 ε = (1 − δ )(3 + 2δ − δ 2 ). (4-8). p1 = R. p2. R. and their equilibrium profits are. π1 = R. π2. R. (1 − δ )[(a − c) 2 + ε 2 ] + (a − c )(7 − 4δ + δ 2 ) (3 − δ ) 2. (1 − δ )(a − c − ε ) 2 = (3 − δ ) 2. (4-9). (4-10). Combining (4-3) and (4-10) can obtain that π 1R ≥ π 1NL if and only if 0<ε ≤. 2(a − c )(1 − δ ) 2 and 0 < δ < 1 . (3 − δ ) 2. 4.1.3 Comparison: Fixed fee versus royalty fee Evaluate the superiority of a fixed fee licensing versus a royalty licensing,. π 2F − π 2R < 0. (4-11). Hence, in the Bertrand competition, the patent-holding firm would prefer royalty fee to fixed fee when it chooses the best patent licensing policy.. 40.

(45) 4.2 Technology Licensing with Delegation In this part, we will extend the model of Wang and Yang (1999) and consider the technology transfer model under Bertrand duopolistic competition with delegation, taking a three-stage game model to discuss the technology transfer actions between the two competition firms.. Stage I. Stage II. Stage III. Time. Patent-holder chooses the license fee to sell,. Firm’s owner chooses the incentive parameter.. Firm’s manager chooses the prices in the market.. Figure 6 Delegating Game Sages of Technology Transfer.. In the first stage, the patent-holding firm chooses the licensing fee to sell to the patent-buyer. In the second stage, each firm’s owner chooses the incentive parameter to encourage their managers to compete harder in the market. In the third stage, the two firms compete in prices in the market. The settings of managerial delegation still follow Sklivas (1987) and Fershtman and Judd (1987). To attain the profits and market power, owner will measure his manager’s performance according to a function g i , which combines firm’s profits ( π i ) and revenues ( Ri ). The higher is g i , the higher is manager i ’s bonus or the lower is the likelihood that he will be fired, so g i could represent manager i ’s incentives. For simplicity, it sets g i as a linear combination of profits and revenues, and the marginal costs are constant. Max g i = λi π i (q1 , q 2 ) + (1 − λi )Ri (q 1 , q 2 ) = Ri (q1 , q 2 ) − λi C i (qi ) , i =1, 2. 41.

(46) 4.2.1 Fixed fee We use the backward-induction to solve this licensing game. In the third stage, the two firms’ managers compete in market according to the performance indicator g i .. g i = λi π i + (1 − λi ) Ri = Ri − λi ci qi. i, j = 1,2. i≠ j. (4-12). Taking the first order condition to solve the Bertrand equilibrium for each firm, we can derive the equilibrium price is. pi (λ1 , λ 2 ) =. 2(a + λi c i ) + (1 − δ )(aδ − λ j c j ) (1 − δ )(3 + 2δ − δ 2 ). i, j = 1,2. i≠ j. (4-13). And substituting Eq. (4-11) to the profit function of delegation stage and taking the first order condition, we can obtain each firm’s optimal incentive parameter is. 2(2 − δ ) 2 c i − (1 − δ )[a(1 − δ ) + c 2 (2 − δ )] λ = (5 − 3δ )ci * i. i, j = 1,2. i≠ j. (4-14). and each firm’s equilibrium profits is. π i* =. (2 − δ )[a (1 − δ ) + ci (2 − δ ) − (3 − 2δ )c j ]2 (5 − 3δ ) 2 (1 − δ ). i, j = 1,2. i≠ j. (4-15). Substituting c1 = c − ε and c 2 = c into Eqs. (4-15) to give the firms’ Bertrand equilibrium profits (the superscript NL denotes ‘no licensing’). 42.

(47) (2 − δ )[(a − c)(1 − δ ) − ε (2 − δ )]2 (5 − 3δ ) 2 (1 − δ ). (4-16). (2 − δ )[(a − c)(1 − δ ) + ε (3 − 2δ )]2 = (5 − 3δ ) 2 (1 − δ ). (4-17). π 1NL =. π. NL 2. The maximum license fee firm 1 can charge firm 2 is what will make firm 2 indifferent between licensing and not licensing the new technology. In the case that licensing occurs, both firms will produce at constant unit cost c − ε . And we can derive the maximum license fee firm 1 can charge firm 2 in licensing stage. F = π 2L (c − ε , c − ε ) − π 2NL (c − ε , c) =. (6 − 7δ + 2δ 2 )ε [2(a − c)(1 − δ ) − ε ] 2 (5 − 3δ ) 2 (1 − δ ). (4-18). and the equilibrium profits are. π 1F =. (2 − δ )(1 − δ )(a − c + ε ) 2 (6 − 7δ + 2δ 2 )ε [2(a − c )(1 − δ ) − ε ]2 + (5 − 3δ ) 2 (5 − 3δ ) 2 (1 − δ ). π 2F =. (2 − δ )[(a − c)(1 − δ ) + ε (3 − 2δ )]2 (5 − 3δ ) 2 (1 − δ ). Combining (4-3) and (4-16), we obtain that π 1F ≥ π 1NL* if and only if 0<ε ≤. 2(a − c )(1 − δ ) 2 , 0 <δ <1 11 − 12δ + 3δ 2. 43. (4-19). (4-20).

(48) Comparing the results of 4.1.1 and 4.2.1, for the basic Bertrand model without 2(a − c )(1 − δ ) 2 delegation, fixed-fee licensing may occur when 0 < ε ≤ ; but for the Bertrand (3 − δ ) 2 model with delegation, fixed-fee licensing may occur when 0 < ε ≤ shows that if the product differentiated level is lower,. 2(a − c )(1 − δ ) 2 . It 11 − 12δ + 3δ 2. 3− 5 < δ ≤ 1 , then licensing would 2. occur less likely under strategic delegation; but if the product differentiated level is higher, 0≤δ ≤. 3− 5 , licensing would occur more likely under strategic delegation. 2. Proposition 5. Under Bertrand competition, if the patent-holding firm takes fixed-fee licensing decision, then if the product differentiated level is lower, licensing would occur less likely under strategic delegation; but if the product differentiated level is higher licensing would occur more likely under strategic delegation.. 4.2.2 Royalty fee In the royalty fee case, we also use backward-induction to solve this licensing game. Suppose firm 2 has bought the patent from firm 1, so their marginal costs is the same, c1 = c 2 = c − ε , and the royalty licensing fee firm 1 charge firm 2 is r per unit.. In the third stage, the two firms’ managers compete in market according to the performance indicator g i . Their objective function for each firms’ manager is. g1 = λ1π 1 + (1 − λ1 ) R1 = R1 − λ1 (c − ε ) q1 + λ1 rg 2. (4-21). g 2 = λ 2 π 2 + (1 − λ 2 ) R2 = R2 − λ 2 (c − ε ) q 2 − λ 2 rg 2. (4-22). Solving the first order condition under profit-maximization condition, we can derive each firm’s equilibrium price in the market competition stage,. 44.

(49) a (2 + δ − δ 2 ) + 2(c + rδ − ε )λ1 − (1 − δ )(c + r − ε )λ 2 p1 (λ1 , λ 2 ) = (1 − δ )(3 + 2δ − δ 2 ). (4-23). a(2 + δ − δ 2 ) − (1 − δ )(c + rδ − ε )λ1 + 2(c + r − ε )λ 2 (1 − δ )(3 + 2δ − δ 2 ). (4-24). p 2 (λ1 , λ 2 ) =. Substituting Eqs. (4-18) into each firm’s profit function to solve for the optimal incentive parameter in the delegation stage, then under the first order condition, we can have the equilibrium incentive parameter of each firm,. λ1 (r ) =. (2 − δ )[(3 − δ )(c − ε ) + r (1 + δ )] − a (1 − δ ) 2 (5 − 3δ )(c + rδ − ε ). (4-25). λ2 (r ) =. 7r (1 − δ ) + 2rδ 2 + (2 − δ )(3 − δ )(c − ε ) − a (1 − δ ) 2 (5 − 3δ )(c + r − ε ). (4-26). Then substituting Eqs. (4-25) and (4-26) into firm 1’s profit function in the licensing stage to solve for the optimal royalty rate, we can have the optimal royalty rate would be r = ε if the innovation is non-drastic, so the equilibrium incentive parameter prices are. (2 − δ )[(3 − δ )c − 2(1 − δ )ε ] − a(1 − δ ) 2 λ = (5 − 3δ )(c − (1 − δ )ε ) R 1. λ R2 =. (2 − δ )(3 − δ )c − (a − ε )(1 − δ ) 2 (5 − 3δ )c. 45. (4-27). (4-28).

(50) the equilibrium prices each firm,. p1 =. a(3 + δ − 2δ 2 ) + c(2 + δ − δ 2 ) − (3 − 4δ + δ 2 )ε (1 − δ 2 )(5 − 3δ ). (4-29). p2 =. a (3 + δ − 2δ 2 ) + c (2 + δ − δ 2 ) + 2(1 − δ 2 )ε (1 − δ 2 )(5 − 3δ ). (4-30). R. R. and equilibrium profits of each firm. π 1R =. (a − c) 2 (2 − 3δ + δ 2 ) + (a − c )(21 − 24δ + 7δ 2 )ε + (2 − 3δ + δ 2 )ε 2 (5 − 3δ ) 2. π 2R =. Combing. (4-3). and. (2 − 3δ + δ 2 )(a − c − ε ) 2 (5 − 3δ ) 2. (4-31),. we. obtain. (4-31). (4-32). that. π 1R ≥ π 1NL*. if. and. only. if. (a − c)(9 − 19δ + 13δ 2 − 3δ 3 ) 0<ε ≤ (2 − δ ) 2 (4 − 3δ ). Comparing the results of 4.1.2 and 4.2.2, for the basic Bertrand model without delegation, royalty-fee licensing may occur when 0 < ε ≤ model 0<ε ≤. with. delegation,. royalty-fee. (a − c)(9 − 19δ + 13δ 2 − 3δ 3 ) . (2 − δ ) 2 (4 − 3δ ). 46. 2(a − c )(1 − δ ) 2 ; for the Bertrand (3 − δ ) 2. licensing. may. occur. when.

(51) 4.2.3 Comparison: Fixed fee versus royalty fee Evaluate the superiority of a fixed fee licensing versus a royalty licensing,. π 1F − π 1R < 0. (4-33). Hence, in the Bertrand competition with managerial delegation, the patent-holding firm would still prefer royalty fee to fixed fee when it chooses the best patent licensing policy.. Comparing the results of 4.1 and 4.2, we have the follow propositions, Proposition 6. When inside technology transfer occurs in Bertrand market, then either the competing firms take the managerial delegation designation or not, the patent-holding firm would prefer royalty fee licensing to fixed fee licensing.. Proposition 7. In Bertrand market, technology transfer will be less likely to occur under strategic delegation than under no delegation. This proposition is the same like the case in Cournot market and Stackelberg market that under strategic delegation, firms (managers) will behave more aggressively than under standard quantity competition, so it will reduce the incentive for the patent-holding firm to license its innovation to the other firm.. 47.

(52) Chapter 5 Conclusion We have examined licensing of a cost-reducing innovation by a patent-holding firm to its competitor from the profit motive in the above, and find that: in the traditional Cournot, Stackelberg and Bertrand model, if technology transfer occurs, then for the patent-holding firm, it would prefer royalty-fee licensing to fixed-fee licensing. Besides, in the Cournot model, firms’ managers behave more aggressively under strategic delegation than under standard quantity competition, reducing the incentive for the patent-holding firm to license its innovation to the other firm. In the Stackelberg model without delegation, we find that if the leading firm owns the patent, then it will license its innovation to the following firm when their costs exist difference. If the following firm owns the patent, then it will license its innovation to leading firm only if their costs-differential level is high. But in the Stackelberg model with delegation, no matter the leading firm or the following firm is the patent-holder, they would license less likely than they do in the Stackelberg model without delegation. In the Bertrand model, if the product differentiated level is lower, firms’ managers behave more aggressively under strategic delegation than under standard price competition, which reduces the incentive for the patent-holding firm to license its innovation to the other firm; but if the product differentiated level is higher, then firms’ managers increases the incentive for the patent-holding firm to license its innovation to the other firm under strategic delegation than under standard price competition. The above results may implies that on the one hand, the cost-reducing innovation affords the patent-holding firm a bigger advantage over its competitor under strategic delegation than under no delegation, and on the other hand, the potential licensing revenue is smaller due to a smaller potential for profit gain from licensing by the competitor under strategic delegation than under no delegation. Both forces work to reduce the likelihood of licensing under. 48.

(53) strategic delegation relative to no delegation. There are still many issues that we can combine the technology transfer and managerial delegation to apply to in the further research. First, we didn’t make the welfare analyses in our models, and we didn’t distinguish the patent-holding firm is in private sector or in public sector. If the patent-holding firm is in public sector, which is like an government organization, then its licensing policy would not only focus on the licensing revenue it can get form the competitors, but also the social value. So we will extend this issue in the future. Besides, we didn’t discuss the different ownership structures or organization structures among the competing firms in our models, which are like the issues about partial ownership, the firm’s internal vertical integration level, or the interaction among the firm’s owner, manager, and the union. We are interested in these different issues in the above, which may also affect the patent-holding firm’s licensing policies and levels. And we will continue to construct model to analyze these issues in the future.. 49.