Technology Licensing, International Outsourcing and Home-bias E ect

Technology Licensing, International Outsourcing and Home-bias E ect Tai-Liang Chen Wenlan School of Business, Zhongnan University of Economics and Law, China Zuyi Huang y Wenlan School of Business, Zhongnan University of Economics and Law, China February 23, 206 Abstract Outsourcing might lower consumers perceptions of product quality due to the home bias. This paper constructs a vertically di erentiated Cournot duopoly to examine the impacts of the home bias and the cost di erentials associated with a patent holder s optimal choices of outsourcing, licensing, or both. Under certain conditions, the cost di erential gap between outsourcing and domestic production may be large enough for a patent holder to set a two-part tari -licensing contract when outsourcing inputs. Alternatively, the patent holder conducts manufacturing processes domestically and simply charges a licensee royalty licensing. occur when the patent holder outsources inputs. However, welfare-reducing licensing can Corresponding author. T.-L. Chen, Wenlan School of Business, Zhongnan University of Economics and Law, 82 Nanhu Avenue, East Lake High-tech Development Zone, Wuhan, Hubei 430073, China. E-mail: tailiang.znuel@gmail.com. y Email: jjcmshzy@63.com

Keywords: Patent Licensing, Outsourcing, Vertical Product Di erentiation, Home Bias, Cost Asymmetry JEL Classi cation: D2, D43, F23, L3, L24

Introduction Licensing is a voluntary form of innovation dissemination whereby licensors can enjoy some of the gains from trade by disseminating the use of their technologies to potential licensees. In the business world, inventors can pro t from licensing their creations to manufacturers or distributors for commercial use. 2 Although licensing provides inventors with opportunities to realize pro ts on their initial investments in research and development, it can create tight competition when competitors obtain the new technology. Earlier work on this subject can be traced back to Arrow (962) who argued that a perfectly competitive industry provides a higher incentive to innovate than a monopoly. Kamien and Schwartz (982) extended Arrow s analysis to licensing within an oligopolistic industry by means of both a xed fee and a royalty. In recent decades, there has been a profusion of theories relating to patent licensing. 3 However, few studies have examined the licensing of a vertical product. This study develops a duopoly model of vertical product di erentiation in which two domestic competing rms of di ering quality incur various costs other than production costs. These include iceberg trade costs resulting from outsourcing production inputs, xed costs from creating production lines for the inputs, and licensing fees associated with the transfer of superior technology from a high-quality rm to a lower-quality rm. This paper de nes outsourcing as the purchase of an input by a rm instead of producing it within its own facility, which is endowed with costly technologies. The patent holder or the rm with a superior technology can, therefore, choose either option for acquiring production inputs. An important recommendation of the WTO is to strengthen patent protection in developing countries to provide proper returns to rms in developed countries from their innovations. 2 The World Intellectual Property Organization s 203 report indicates that the growth rates of worldwide patent lings have been accelerating in recent years, from 7.6% in 200, to 8.% in 20, and 9.2% in 202. 3 The existing literature has focused either on optimal licensing contracts (e.g., Katz and Shapiro, 985; Kamien and Tauman, 984, 986; Rockett, 990a; Kamien et al., 992; Wang, 998; Poddar and Sinda, 2004; Sen, 2005; Sen and Tauman, 2007; Stamatopoulos and Tauman, 2009), or on welfare implications (e.g., Rockett, 990b; Fauli-Oller and Sandonis, 2002; Marjit and Mukherjee, 2008 ). 3

Many countries are liberalizing their economies to create more competition within their domestic markets. Outsourcing has been growing in popularity as a method for rms to achieve lower costs and increase their market competitiveness. 4 However, anecdotal evidence suggests that outsourcing leads to problems in the quality of goods or services. Lu et al. (202) constructed a simple model to illustrate how outsourcing leads to lower product quality. Their theoretical predictions were con rmed by the results of a survey of 2,400 rms in China conducted by the World Bank in 2003. They suggested that imperfect contract enforcement would lead to lower product quality after outsourcing. Furthermore, consumers tend to have a home bias, resulting in the perception that the nal good of a rm that outsources its inputs is inferior to that of a rm that produces its inputs domestically. Their perceptions of a particular good are, therefore, independent of the actual physical quality of the nal good produced. This concept of a home bias is not without foundation. Armington (969) demonstrated how a home bias in consumption improved the t of the Heckscher- Ohlin-Vanek model. Therefore, this scenario of a home bias of a good is called the Armington e ect in this paper. Furthermore, Lewis (999) provided evidence to suggest that equity and consumption home biases are linked, which is reasonable given that the equity growth of a rm and the consumption of that rm s products are fundamentally related. It is common for a rm to face with the decision of whether or not to license a particular technology while outsourcing leads to lower quality either through consumer bias or in relation to the production line. Until recently, the connection between outsourcing and licensing was rarely mentioned in the literature. 5 In the comparison of incentives for outsourcing and R&D licensing for a monopolist input supplier, Mukherjee and Ray (2007) have shown 4 According to the CNN report Exporting America, there are hundreds of companies outsourcing at least some of their manufacturing processes to areas with lower production costs. http://www.cnn.com/cnn/programs/lou.dobbs.tonight/popups/exporting.america/content.html. 5 In the context of an open economy, Saggi (999) studied a two-period model of technology transfer, wherein FDI and licensing werethe two respective modes of entry for foreign rms. Mukherjee and Pennings (2006) further examined trade policies and optimal licensing rates. Sinha (200) has analyzed the modes of entry of a foreign rm into a host country. See, 4

that outsourcing occurs if it increases competition within a downstream market, and if the number of incumbent downstream rms is very low. Furthermore, in the case of xed fee licensing, input monopolist generally outsources its technology. Dinda and Mukherjee (20) expressed concern about patent policies in the presence of outsourcing. They suggested that during the process of designing patent policies in developing countries, their e ects must be considered in conjunction with other government policies such as taxation. The recent literature on outsourcing and licensing is based on a homogeneous nal goods market. Since di erent technologies bring not only cost di erentials but also quality gaps, some studies have examined vertical product di erentiation models as well as technology licensing within an open economy (e.g., Li and Song, 2009; Li and Wang, 200; Nguyen et al., 203, 204). However, none of these studies have discussed a connection between outsourcing and licensing. As mentioned earlier, outsourcing lowers quality but provides cost advantages for a rm. The purpose of this article is to explore how a patent holder makes decisions regarding whether to outsource, license, or engage in both options. In the context of vertical product innovation, the use of a Cournot framework is common. 6 De Fraja (996) and Avenel and Caprice (2006) have supported the assumption of quantity competition, indicating that Bertrand competition eliminates head-to-head competition. 7 Thereby, this paper considers a vertically di erentiated Cournot duopoly wherein a patent holder, that is, a rm with a high-quality product, could choose to license its superior technology, outsource its production inputs, or do both. Once a rm outsources its production inputs for cost-saving purposes, consumers perceptions of the product quality may induce the Armington e ect, which reduces the perceived quality of the product in the market. Depending on cost and quality di erentials between two varieties of a good, the following outcomes may occur: head-to-head competition, complete di erentiation, or 6 For studies on Bertrand-price competition in a vertically-di erentiated market, refer to Musa and Rosen (978), Gabszewicz and Thisse (979), Shaked and Sutton (982, 983), Chang and Kim (989), Ronnen (99), Motta (993), Aoki and Prusa (997), Lehmann-Grube (997), and Aoki (2003). 7 See also Moorthy (985), Motta (993), Valletti (2000), Jinji (2004), Li and Song (2009),and Li and Wang, (200). 5

partial di erentiation. Put simply, after licensing, either both rms will sell the high quality product, or only one of them will sell the high quality product. This study presents a comprehensive discussion of the strategic e ects at work in the model. In other words, our choice of Cournot competition can be justi ed on two grounds. On the one hand, licensing leads low-quality rm to upgrade its quality. After licensing, rms may supply product lines containing homogenous products. On the other hand, the study of Cournot competition between heterogeneous goods is often used as a proxy device for situations in which oligopolistic competition is less severe than price competition with perfect substitutes. We show that both the Armington e ect and the cost di erential between outsourcing and in-house production are in relation to the patent holder s decision regarding outsourcing and licensing. Certainly, licensing raises the patent holder s pro t and creates more incentive to license and transfer the advanced technology. We further show that under certain conditions if the cost of input-outsourcing is su ciently smaller than the cost of domestic production, the patent holder may set up a two-part tari -licensing contract and outsource inputs. Alternatively, the patent holder conducts all manufacturing processes domestically and only charges the licensee royalty licensing. Moreover, we address the preference of the licensee and of the government for the licensor s manufacturing process to be conducted domestically. This is because outsourcing generates home bias and then leads to a reduction in the licensee s pro t and social welfare. In other words, if the patent holder chooses to outsource inputs, this results in welfare-reducing licensing. This paper is organized as follows. In section 2, we depict the model s framework and assumptions. In section 3, we analyze the four strategies available to a patent holder: inhouse production with licensing, in-house production without licensing, outsourcing with licensing, and outsourcing without licensing. In section 4, we compare and characterize the results obtained in section 3 to explore whether a patent holder will opt for outsourcing or licensing. In the nal section, we o er concluding remarks. 6

2 The Model Frameworks Envisage an industry in which two rms, and 2, produce vertically di erentiated products in a market. Each rm produces its nal goods using a single input that can either be produced at the rm s plant, or outsourced from an independent rm outside the country that specializes in the production of this input. As previously stated, outsourcing is de ned as the purchase of an input by a rm instead of production of the input within its own facility, which is endowed with costly technologies. We assume that the two rms produce a single vertically-di erentiated product and that the quality of the product produced by Firm is higher than that of the product produced by Firm 2. There are two alternative strategies available to Firm to raise its total income. The rst one is input outsourcing, which reduces the production cost, but also reduces the perceived quality. The second one is technology transfer licensing. Licensing the new technology enables the patent holder to earn a higher licensing income, while intensifying market competition. Speci cally, consumers are assumed to have a home bias. This means that they perceive the nal good of a rm that outsources its input production to be inferior to that of the rm that produces its inputs domestically. The consumers perceptions of a good are thus independent of the actual physical quality of the nal good. The concept of a home bias in relation to product quality is referred to as the Armington e ect. For our model, a rm produces a single product of a certain quality, s i, i = H; M; L. Note that s H > s M > s L, where s H, s M and s L denotes high quality, median quality and low quality, respectively. Initially, the quality of the product produced by Firm is s H. If Firm outsources its input out of country, the perceived quality is s M. In this model, s M = s H, where 2 (0; ) denotes the perceived quality parameter or the Armington e ect parameter. If the rm conducts all of its production processes domestically, the Armington e ect does not occur and =. Furthermore, Firm 2 is assumed to possess the lowest quality product that consumers will accept in the market, s L. Let s L = s M = s H, where the parameter 2 (0; ) captures the degree of vertical product di erentiation. A larger value of implies 7

a higher level of substitutability between the two products, while a lower value of indicates a greater di erence in quality. To save notation without the loss of generalization, we normalize s H =. Thus s M = and s L =. In addition to reducing its production cost by outsourcing the input, Firm can acquire licensing revenue by licensing its superior technology to Firm 2. If Firm has an incentive to license its technology, it will provide Firm 2 with a take-it-or-leave-it o er by setting a xed fee, a royalty rate, or both. The decision to license is subsequently examined in relation to three possible regimes. As Firm 2 successfully obtains the superior technology, the quality of its product is upgraded from s L to s H. Note that patent protection is assumed to be particularly strong such that imitation is impossible. Furthermore, we apply non-drastic innovation in this study to rule out the monopoly case. 8 2. Households There is a continuum of consumers. Each consumer buys, at most, one unit of the verticallydi erentiated product. The utility function is U = f s i 0 p i ; if one buys a good with quality s i if one does not buy ; () where i = H; M; L. 2 [0; ] is a taste parameter with uniform distribution, whose density function is one; and p i is the price. The population is normalized to one. It should be noted that a higher preference for quality s increases the consumers willingness to pay for any given quality of goods. In a scenario that disregards outsourcing and licensing, the marginal consumer indi erent between Good (with quality s H ) and Good 2 (with quality s L ) has a taste parameter of such that s H p = s L p 2 or, equivalently, = (p p 2 ) = (s H s L ). On the other hand, the marginal consumer indi erent between buying the low-quality good and not 8 Following Arrow s (962) de nition, a drastic innovation gives the innovator a monopoly, whereby the price is below the competitor s marginal cost. On the contrary, a non-drastic innovation results in the monopoly price being above the competitor s marginal cost. 8

buying at all has a taste parameter of 2 such that 2 s L p 2 = 0 or, equivalently, 2 = p 2 =s L. Given the above scenario, the demand function for product i, denoted q i (i = ; 2), can be easily derived by noting that all the consumers for whom will buy quality s H, all those described by 2 will buy quality s L, and nally those described by 2 > will not buy at all. will not buy at all. If Firm outsources its input, then s H becomes s M, and we have a taste parameter of 3 = (p p 2 ) = (s M s L ), indicating the marginal consumer indi erent between Good (with quality s M ) and Good 2 (with quality s L ). 2.2 Potential Strategies for the High-Quality Firm 2.2. Input Outsourcing In this study, we consider the production function between the input and nal good to be of a Leontief type, in which one unit of the nal good requires one unit of the input. Because of cost saving, a high-quality rm has an incentive to outsource its input, even though such a strategy will result in quality deterioration. In other words, outsourcing represents a trade-o between gains from cost advantage and loss from quality reduction. As de ned earlier, outsourcing means that a rm buys an input instead of producing the input at its own facility. If the rm imports its production input, it incurs an iceberg trade cost,, when one unit is shipped to a particular destination. Alternatively, a rm can produce the input by itself rather than outsourcing. In this case, each rm invests a xed amount, F, in creating the production line for this input. Generally, the associated investment cost is relatively greater than the iceberg trade cost. We then assume that F >. Once this production line is created, each unit of this input can be produced at a costant marginal cost of c. Because in this paper we mainly focus on demand side aspects of product line di erentiation, we assume that each variety is produced at constant marginal cost. 9 For the sake of simplicity, we postulate that the marginal costs of both rms are zero. Under this assumption, rms de nitely have no incentives to supply low-quality products if they 9 See also, Avenel and Caprice (2006). 9

have an advanced technology. Moreover, since s L is the lowest quality that a consumer will accept, the low-quality rm has no incentive to outsource. 2.2.2 Technology Licensing It is assumed that Firm holds patents for quality-upgrading innovations, each of which allows the user to produce high quality products. If Firm has an incentive to license its technology, a take-it-or-leave-it o er is set based on a xed-fee, a royalty rate, or both. A successful licensing deal results in technology transfer from Firm to Firm 2, after which Firm 2 upgrades its quality to s H. The optimization problem that Firm is faced with when designing the contract is given as follows: max ;r + rq 2 j s=sh + j s=sh (2) s.t. () 2 j s=sh 2 j s=sl, (2) q 2 j s=sh ; ; r 0, where denotes the xed licensing fee and r is the royalty rate. The xed fee and royalty are restricted to a positive fee on the assumption that a negative xed fee or royalty could be perceived as a bribe by antitrust authorities. The xed fee is paid at the time of issuing the license. 2.2.3 Time Phase of the Game Because of the distinct quality and cost settings, we may conceive that Firms and 2 di er in their thinking regarding their market strategies. Consequently, we set up a three-stage game as follows. In the rst stage, Firm decides whether to license its technology, outsource its input, or do both. In the second stage, Firm 2 decides whether to accept the licensing o er. In the nal stage, production occurs and royalties are paid. The rms compete through a Cournot-Nash game in the nal goods market. A backward induction is applied for optimal outcomes. 0

3 Model Analysis 3. In-house production ( = ) We start with the case where outsourcing does not occur and =. In this case, the quality levels of the two rms before licensing are s H and s L, respectively. The marginal consumer indi erent between Good and Good 2 has a taste parameter of = p I p2 I = (sh s L ), where superscript I denotes the in-house production case. The marginal consumer indi erent between buying the low quality good and not buying at all has the taste parameter of 2 = p I 2=s L. Note that s H is normalized to and s L = s H. It follows, q I = Z d = p I p I Z 2 and qi 2 = d = pi p I 2 2 p I 2. (3) Subsequently, we can derive prices as, p I = q I q I 2 and p I 2 = ( q I q I 2), (4) and the pre-licensing pro ts are, I = ( q I q I 2)q I F, and (5) I 2 = ( q I q I 2)q I 2 F. From the rst-order conditions, we can solve the best response functions, q I = q I 2 =2 and q I 2 = q I =2. Since market prices must be non-negative, then q I + q I 2 is given. Therefore, the reaction functions are kinked, and we can re-write them as, q I = f q I 2 2, q I 2, when q I 2 2 ; when q2 I > 2, (6) and q I 2 = f We then have the following lemma. q I 2, 0, when q I < ; when q I =. (7)

Lemma Consider both high-quality and low-quality rms conduct all manufacturing processes domestically. The pre-licensing optimal outputs, prices and pro ts are, q I = 2, 4 qi 2 = p I = 2, 4 pi 2 =, 4 I = ( 2 4 )2 F, and I 2 = F, respectively. (4 ) 2 An increase in shortens the quality gap and makes two goods much more substitutable, and then lowers Firm s comparative advantage as well as its pro tability; Firm 2 s outcomes increase as rises. Furthermore, consumer surplus is, CS I = and then social welfare is, Z ( p I )d + Z 4, ( p I 2)d = 4 + 2 2(4 ), (8) 2 W I = CS I + I + I 2 + 2F = 2 5 + 2, (9) 2(4 ) 2 where I + I 2 + 2F represents rms producer surplus. 2 3.. Technology Licensing in the Case of No-Input-Outsourcing Firm maximizes Eq. (2) with respect to constraints () and (2) in order to decide the optimal licensing rates. After Firm transfers its technology to Firm 2, the quality of Firm 2 s product is upgraded and then =. In other words, two goods become perfect substitutes and there is no di erentiation within the market. Firm enjoys an additional revenue coming from the licensing fees in this Cournot game, and the pro ts of two rms now are I = ( q q 2 )q F + + rq 2 and I 2 = ( q q 2 r)q 2 F, respectively, where I denotes the scenario of two-part tari licensing and in-house production. From the constraint (), we have = 2 (r)j s=sh 2 j s=sl = ( 2r) 2 =9 =(4 ) 2. Solving the optimization problem, we can obtain the optimal rates, I = 0 and (0) r I = 2 ( 3 p 4 ). 2

Figure : Licensor s constrained maximization problem Since Eq. (2) shows that the @=@r of iso-pro t contour and the @=@r of constraint () are negative, the solution only locates at the downward-sloping segments of the curves. Furthermore, the @=@r of iso-pro t contour is steeper than the @=@r of constraint () when r < =2. Hence, the optimum is a corner solution of feasible set as shown in Figure. As a result, Firm does not charge a xed fee but charges only royalty rate for the technology transfer. Speci cally, although both xed-fee licensing and royalty rate can bene t licensor, only royalty rate really weakens the competition and increases rival s cost. A royalty contract permits the licensor to transform its strategic advantage from quality to cost, and to achieve maximal pro t. Therefore, under a royalty licensing, Firm always has an incentive to transfer its technology. Furthermore, since @ I =@r > 0 in Eq. (2), Firm earns a higher pro t in the case of licensing than in the non-licensing case. The current nding remains consistent with the result of Rockett (990a) and Li and Song (2009). They showed that, in the absence of imitation, the optimal licensing contract is a royalty alone. 3

Utilizing the rates in (0), we can obtain optimal outcomes and thus have the following lemma. Lemma 2 Consider a royalty licensing.. The optimal pro ts, consumer surplus, and welfare are I = 6 3+2 4(4 ) 2 F > I, I 2 = (4 ) 2 F, CS I = (4+p ) 2 8(4 ) 2, and W I = (4+p )(2 p 3) 8(4 ) 2, respectively. 2. An increase in the level of substitutability between two goods decreases the royalty rate set by the patent holder. Proof. () I I = 6 3+2 4(4 ) 2 ( 2 4 )2 = 3( ) > 0; (2) CS I = R 4(4 ) 2 p 2 [ ]( p)d = 4 (4+ p ) 2 8(4 ) 2 ; (3) W I = CS I + I + I 2 +2F = (4+p )(2 p 3) 8(4 ) 2. (4) @ri @ = 3(4+) 4(4 ) 2p < 0. 3.2 Input Outsourcing (0 < < ) In this case, Firm outsources the production input, and reduces its quality as s M = s H, where 2 (0; ). The marginal consumer indi erent between Good and Good 2 has a taste parameter of 3 = p O p O 2 = (sm s L ), where superscript O denotes the outsourcing case. The marginal consumer indi erent between buying the low quality good and not buying at all has the taste parameter of 4 = p O 2 =s L. It follows, q O = Z 3 d = p O p O Z 3 2 ( ) and qo 2 = d = po p O 2 4 ( ) p O 2. () Thus, prices are, p O = ( q O q O 2 ) and p O 2 = ( q O q O 2 ), (2) and the pre-licensing pro ts are, O = ( q O q O 2 )q O, and O 2 = ( q O q O 2 )q O 2 F. (3) 4

From the rst-order conditions derived by (3), we have the best reaction functions, q O = q2 O =2 and q O 2 = q O =2. Again, the restriction, q O + q2 O, is given for the non-negative prices. We then have the following lemma. Lemma 3 If the high-quality rm outsources its input and low-quality rms conducts all manufacturing processes domestically, the pre-licensing optimal outputs, prices and pro ts are derived as, q O = 2 4, qo 2 = 4, po = O 2 = (4 ) 2 F, respectively; (2 ) 4, po 2 = 4, O = ( 2 4 )2, and Analogously, Firm s outcomes decrease in while rm 2 s outcomes increase in. Furthermore, consumer surplus is, CS O = and then social welfare is Z Z 3 ( p O )d + ( p O 2 )d = 3 4 (4 )(3 ) 2(2 )2 2(4 ) 2, (4) W O = CS O + O + O 2 + + F = 2 (7 2 ) 2(4 ) 2. (5) We can observe that an increase in reduces consumer surplus but raises social welfare. If the Armington e ect is weak, prices increase and then consumer surplus decreases. Alternatively, a weakness of the e ect improves rms pro ts and also social welfare. 3.2. Technology Licensing in the Case of Input-Outsourcing Under licensing, Firm 2 s quality upgrades from s L to s H. In addition, because of outsourcing, Firm saves cost spending but loses quality advantage from s H to s M. Subsequently, the marginal consumer indi erent between Good 2 and Good has a taste parameter of 5 = p O 2 p O = (sh s M ), where superscript O denotes the outsourcing case in the presence of licensing. The marginal consumer indi erent between buying the median quality good and not buying at all has the taste parameter of 6 = p O =s M. Hence, the demand functions are, respectively, q O = Z 5 6 d = p O 2 p O p O Z, and qo 2 = d = 5 5 p O 2 p O. (6)

Solving (6), prices are derived as, It follows, p O = ( q O q O 2 ), and p O 2 = q O q O 2. (7) O = ( q O q O 2 )q O + rq O 2 +, and (8) O 2 = ( q O q O 2 r)q O 2 F. Simultaneously solving the rst-order conditions derived from (8), we obtain the outputs, prices, and pro ts, respectively: q O = + r 4, qo 2 = 2 2r 4, po O = = ( + r) 4, po 2 = ( + r)(2 ), 4 + r(8 (4 ) r(8 3)) (4 ) 2 + and O 2 = ( 2 2r 4 )2 F. Turning to licensor s optimization equation (2), We solve the royalty and xed fee, r = (8 (4 )) = (6 6) and = (4( ) 2 (4 ) 2 (8 3) 2 ) =(8 3) 2 (4 ) 2, respectively. As a result, Firm o ers a two-part tari licensing to licensee under the condition, 2 p (4 )= > p (8 3)= ( ). Figure 2 shows that, if = (complete substitutes between two goods) and = 0 (a representative consumer abominates outsourcing), Firm charges Firm 2 the highest xed fee and the lowest royalty rate. Moreover, an increase in increases r but decreases. Intuitively, since an increase in monotonically increases O, i.e. @ O =@ = ( + r)(4 + r(4 3))=(4 ) 3 > 0, then we can know that = 0 induces the minimal pro t of Firm. Thus Firm will charge Firm 2 xed fee as high as possible instead of the royalty rate. Since high royalty rate weakens the competition and increases rival s cost, the licensing restrains licensee s incentive for expansion of market share. However, in the case of 2 p (4 )= p (8 3)= ( ), Firm sets = 0 and only charges Firm 2 royalty rate, i.e. O = 0, and (9) r O = p (4 ) 2 (2 ). (4 ) 6

Figure 2: Fixed-fee licensing when licensor outsources In what follows, under such conditions, the optimal market prices, pro ts, consumer surplus and social welfare are illustrated in Table, Table. Optimal Outcomes in the Case of the Combination of Outsourcing and Licensing p O p O 2 O O 2 if 2p (4 ) p (8 3) if 2p (4 ) > p (8 3) (4 p ) 2(4 ) (2 )(4 p ) 2(4 ) 3 2 +4(4 ) p +( 4(4 p )+6( p )) 4(4 ) 2 (4 ) 2 F (6 ) 6 6 (6 )(2 ) 6 6 (6 )(8 3(2 )) 4(8 3) 2 (4 ) 2 (4 ) 2 F CS O [8(2+ p ) (3 +2(2 p ))] 6+(52 (52 9)) 8(4 ) 2 8(8 3) 2 W O 3 2 +8(4 ) p +(24(2 p ) (28 3 6 p )) (4+)(28 (6 3)). 8(4 ) 2 8(8 3) 2 Notice that consumer surplus is CS O = R 5 ( p O 2 )d + R 5 6 ( p O )d and social welfare is CS O + O + O 2 + + F. 7

Proposition If the high-quality rm (patent holder) outsources its production input and low-quality rm conducts all manufacturing processes domestically, two-part tari licensing is optimal for the patent holder if 2p (4 ) > p (8 3), where ; 2 (0; ); otherwise, royalty contract is the optimal one. 4 Comparisons and Discussions 4. Pro t Comparisons and Optimal Strategies As analyzed earlier, once Firm outsources its production input and Firm 2 upgrades its product quality via successful licensing, the quality of the product produced by Firm will be lower than that of the product produced by Firm 2. Consequently, Firm loses its quality advantage and attempts to compensate its losses from cost-saving outsourcing and licensing revenue. On the other hand, the pro t of Firm 2 (licensee) still remains unchanged because of additional licensing payments to Firm. We further compare I 2 and O 2, and then obtain O 2 = =(4 ) 2 F < I 2 = =(4 ) 2 F. Interestingly, Firm 2 prefers Firm producing all processes domestically. The reason comes from the Armington e ect. Consumers perceptions of goods in the home country spillover to both rms while Firm outsources its input. Before licensing, the e ect reduces market prices as well as the optimal quantities, and Firm 2 s pro t, in turn, decreases. After licensing, Firm 2 cannot enjoy the bene ts from quality-upgrading since the earning raise are o set by either royalty or two-part tari fees. As a result, we have the following proposition. Proposition 2 Consumers perceptions of the quality of goods in the home country in uence both licensor and licensee while the licensor outsources its production input. Therefore, licensee would prefer licensor conducting all manufacturing processes domestically to outsourcing input production outside the country. 8

Turning to Firm s choices, we rst examine the case wherein 2 p (4 )= p (8 3)=( ). In the case, Firm simply charges a licensee royalty licensing when outsourcing its input. By comparing Firm s pro ts, we have the following lemma: Lemma 4 Consider 2p (4 ) p (8 3). () If F > B, O > O > I > I ; (2) if B > F > A, O > I > O > I ; (3) if A > F 0, O > I > I O ; where A = ( )( 2 4 )2, B = (6 3+2 ) (2 ) 2 4(4 ) 2, and B > A. From Eq. (2), one can know that an increase in a licensing rate increases the pro t. Furthermore, the cost di erential gap in uences Firm s decision of outsourcing. If the outsourcing cost is low as Case () in lemma 4, outsourcing is the best strategy for Firm although it will deteriorates its product quality due to the Armington e ect. The gains from the cost-reducing e ect compensates the loss of quality advantage. Hence, if 2 p (4 )= p (8 3)=( ), the best strategy for Firm is the combination of outsourcing and royalty-licensing. We therefore have the following proposition. Proposition 3 Consider 2p (4 ) p (8 3). If the outsourcing cost is low enough, the patent holder may set up a royalty-licensing contract and outsource its input. Alternatively, if 2 p (4 )= > p (8 3)=( ), Firm sets up a two-part tari licensing contract. Similarly, we compare Firm s pro ts among four cases, and then have the following lemma: Lemma 5 Consider 2p (4 ) > p (8 3). () If F > B, O > O > I > I ; (2) if B > F > C, O > I > O > I ; (3) if C > F > A, I > O > O > I ; (4) if A > F > D, I > O > I > O ; (5) if D > F 0, I > I > O > O ; where C = (8 3)2 (6 3+ 2 +4) (6 )(8 3(2 ))(4 ) 2 4(4 ) 2 (8 3) 2, D = 4(8 3)2 (+(2 ) 2 ) (6 )(8 3(2 ))(4 ) 2 4(4 ) 2 (8 3) 2, and B > C > A > D. If rms produce inputs by themselves rather than outsourcing, they invest a xed amount of F in creating the production line for this input. If F is su ciently large, outsourcing is 9

still the best strategy for Firm. However, if the cost di erential between and F is smaller as Cases (3), (4), and (5) in lemma 5, Firm should stay domestically. Intuitively, if gains from cost advantage can not compensate the reduction of quality, patent holder chooses to produce its input domestically. In this case, the royalty contract is optimal. Proposition 4 Consider 2p (4 ) > p (8 3). If the cost di erential gap between outsourcing and domestic production is large enough, the patent holder sets up a two-part tari licensing contract and outsources its input. However, if the gap is small, the patent holder conducts all manufacturing processes domestically and only charges the licensee royalty licensing. 4.2 Welfare Implications Fauli-Oller and Sandonis (2002) characterized situations in a horizontal di erentiated market. They showed that a two-part tari contract for licensing a cost-reducing innovation to a rival rm deteriorates social welfare. In a vertically di erentiated Cournot market, we give a di erent result from them. If patent holder conducts all manufacturing processes domestically, it enjoys quality advantage before licensing. As we discussed earlier, royalty contract will be the optimal choice for the patent holder. Royalty rate raises prices and harms consumer surplus. Nonetheless, licensing reduces the di erential gap and results in a perfect substitutability achieved by two goods. Once goods become substitutes and quality di erences are small, welfare increases (See, e.g. Singh and Vives, 984; Häckner, 2000; Zanchettin, 2006). It follows that W I > W I. 0 On the other hand, if patent holder chooses to outsource its input, welfare-reducing licensing can occur; that is, W O > W O regardless of 2 p (4 )= S p (8 3)= ( ). Intuitively, outsourcing reduces Firm s quality and would in turn impact Firm s pro t. Then, Firm sets up higher licensing rates for compensating the loss, which increases prices 0 W I W I = 8 p 5 2 3 2 2 =8 (4 ) 2 > 0, where 0 < <. 20

and deteriorates consumer surplus. Social welfare therefore reduces. Figures 3. and 3.2 graphically show the numerical results of welfare comparisons with G = W O p p j 2 (4 ) (8 3) = 8(4 ) 2 [32 + 4 (4 ) W O 3 + + 2 p + 3 2 2 6 p + 8 2 p ] and H = W O p p j 2 (4 ) (8 3) > W O = ( ) (80 (28 3)) 8 (8 3) 2 : Figure 3. W O p p j 2 (4 ) (8 3) W O ; ; 2 (0; ) Figure 3.2 W O p p j 2 (4 ) (8 3) > W O ; ; 2 (0; ) We further compare W O and W I W O W I j ;2(0;) = 8(4 ) 2 and show that 8 p (3 8) + 2 3=2 + 2 < 0: Strict consumers perceptions of the quality result in the deterioration of social welfare once Firm outsources its input. Nonetheless, if there is no Armington e ect in the market, we then certainly have W O = W I. In the present model, if the patent holder conducts all manufacturing processes domestically, the social welfare under licensing is the highest among four cases, and the ranking can be listed by W I > W I > W O > W O for ; 2 (0; ). 2

Moreover, @ W O W I =@ < 0, indicating that an increase in retrenches the di erence between W O and W I. We then have the nal proposition. Proposition 5 Consider a vertically di erentiated Cournot market.. If the patent holder conducts all manufacturing processes domestically, licensing improves social welfare; if the patent holder chooses to outsource its production input, welfare-reducing licensing can occur. 2. If the patent holder conducts all manufacturing processes domestically and licenses its superior technology, the social welfare is the highest. 5 Concluding Remarks In this paper, we considered a vertically di erentiated Cournot duopoly wherein a patent holder, that is, a rm with a high-quality product, could choose to license its superior technology, outsource its production inputs, or do both. Once a rm outsources its production input, consumers perceptions of the quality induce the Armington e ect. Such the e ect reduces the perceived quality of the product in the market. The rm thus has a trade-o between cost saving and quality sacri ce once it outsources its production input. On the other hand, the patent holder can also license its superior technology for earning licensing revenue. In this case, the rm faces the other trade-o between higher revenue and intensive competition. We have examined the impacts of the Armington e ect and the cost di erentials associated with a patent holder s optimal choices of outsourcing, licensing, or both. Certainly, a licensing raises patent holder s pro t and makes patent holder have more incentives to license and transfer its advanced technology. In the literature of an inside innovator, a royalty licensing is optimal. In the present paper, we showed that under certain conditions, if the cost of input-outsourcing is smaller enough than the cost of domestic production, then the patent holder sets up a two-part tari -licensing contract and outsources its input. Otherwise, 22

the patent holder conducts all manufacturing processes domestically and charges a licensee royalty licensing alone. Furthermore, we showed the preference of the licensee and of the government. They prefer licensor s manufacturing processes conducted domestically to licensor s input-outsourcing since the Armington e ect deteriorates licensee s pro t and social welfare. In other words, if the patent holder chooses to outsource its input, a welfare-reducing licensing can occur. 23

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