Vertical Licensing, Input Pricing, and Entry

Transcription

1 Vertical Licensing, Input Pricing, and Entry Elpiniki Bakaouka and Chrysovalantou Milliou May 2016 Preliminary Draft Abstract In this paper, we explore the incentives of an incumbent firm to license the production technology of its core input to an external firm. We find that licensing always arises in equilibrium independently of whether or not it induces the entry of the licensee into the final goods market. Interestingly, we also find that although the entry of the licensee increases the intensity of market competition faced by the licensor, it reinforces the latter s licensing incentives. Both with and without entry, licensing enhances welfare. Keywords: licensing; vertical relations, entry; two-part tariffs; outsourcing JEL classification: L22; L24; L13; L42; D45 Bakaouka: Department of International and European Economic Studies, Athens University of Economics and Business, Athens 10434, Greece, bakaoukael@aueb.gr. Chrysovalantou Milliou: Department of International and European Economic Studies, Athens University of Economics and Business, Athens 10434, Greece, cmilliou@aueb.gr. We would like to thank Maria Alipranti, Christos Constantatos, Lampros Pechlivanos, Emmanuel Petrakis, Joel Sandonis, and Spyros Vassilakis for their useful comments. This research has been co-financed by the European Union (European Social Fund - ESF) and Greek national funds through the Operational Program "Education and Lifelong Learning" of the National Strategic Reference Framework (NSRF) - Research Funding Program: Thalis - Athens University of Economics and Business - "New Methods in the Analysis of Market Competition: Oligopoly, Networks and Regulation". Full responsibility for all shortcomings is ours.

2 1 Introduction Original brand manufacturers often license the production technology of their core inputs to external firms. 1 Such licensing activities may trigger the entry of the latter - the licensees - into direct competition with their licensors. An illustration of this business practice comes from the commercial aircraft market, where, in 2003, Boeing, the US aircraft manufacturer, licensed its wing technology to Mitsubishi Heavy Industries, a Japanese engineering and electrical equipment firm, after agreeing to source the wings of its planes from the latter. Boeing, as well as its main competitor in the market, Airbus, had been already subcontracting the production of various aircraft components to external suppliers. However, never before a commercial aircraft manufacturer had subcontracted its wing production. Boeing s decision to do so, was accepted with wide spread criticism. First, because the wing technology of Boeing has been regarded as its crown jewel, and second, because the transfer of wing manufacturing and assembly expertise to Mitsubishi effectively gave to the latter total production competence with regard to commercial aircrafts. Mitsubishi is now ready to launch its own passenger jet, which is due to enter service in A similar illustration can be found in the electronic appliances market, where, Haier, a Chinese firm which was initially manufacturing electrical equipment for original brand manufacturers, acquired in 1984 the technology for producing high-quality refrigerators from Liebherr, the German manufacturer of refrigerators. A year after the licensing of Liebherr s technology, Haier introduced its own first four-star refrigerator into the market. That is, Haier transformed from an original equipment manufacturer to an original brand manufacturer. It soon became the leader refrigerator producer in China and, eventually, it also became a major competitor in the global market. The above illustrations give rise to a number of important questions regarding vertical licensing: Does a firm have incentives to license its input technology to an external supplier when the latter can turn into its competitor in the final goods market? How does the pricing of the input affect the licensing decision? Does the entry of the licensee into the 1 According to empirical evidence, technology licensing is a common practice among firms (see e.g., Caves et al., 1983, Nadiri, 1993, Anand and Khanna, 2000). Many well-known firms, such as IBM, Hitachi, Kodak, and Procter & Gamble, have licensed their technology to others, earning millions of dollars in licensing revenue (see e.g., A market for ideas, The Economist (October 20, 2005)). 2 Note that without the ability to make its own wings, Mitsubishi could never become an independent player in the passenger jet industry. For more information regarding this case, see e.g., Secret Wounds Of Globalism: Boeing Sells Its Technology Cheap To Japan, Forbes (January 2014), and Boeing Outsourcing Gives Wing to Concerns, Chicago Tribune (December 21, 2003). 1

3 licensor s market weaken the licensing incentives? What are the welfare implications of vertical licensing? Does the type of vertical contract and the commitment of the licensor influence the licensing incentives and implications? In this paper, we attempt to address these questions. To this end, we consider a framework in which two incumbent firms produce two competing final goods using an input that initially they produce in-house. The firm which is more effi cient in input production considers licensing its input technology to a potential input supplier for a fixed licensing fee. Once the licensing agreement is signed, the licensor can source the input from the licensee after bargaining with the latter over the terms of a two-part tariff contract. Moreover, once the licensing agreement is signed, the licensee can enter into the final goods market and compete with the two incumbents. We assume that competition in the final goods market takes place in quantities and examine what happens when the licensee does not enter into the final goods market (the no entry case ) as well as when it enters (the entry case ). We find that the incumbent always opts for licensing. This holds independently of whether the licensee enters into the final goods market or not. The driving force behind licensing, however, differs substantially among the entry and the no entry case. In the no entry case, licensing is mainly driven by effi ciency reasons: when the incumbent licenses its input technology, it becomes more effi cient, and thus, it enjoys a larger competitive advantage in the final goods market. The higher effi ciency of the licensor is not due to a cost advantage of the licensee. It is due, instead, to input pricing. In particular, when the licensee does not enter into the final goods market, it subsidizes the production of its customer - it charges a wholesale price which is below the input s marginal cost. It has incentives to do so because it can extract part of the resulting higher profits of the licensor through the fixed fee included in the two-part tariff contract. Interestingly, due to the higher effi ciency that the incumbent enjoys under licensing, it is willing to license its input technology even for free. This holds as long as the share of the licensor s profits that the licensee extracts is suffi ciently enough, i.e., when the bargaining power of the licensee is low enough. When the licensee enters into the final goods market, it no longer has incentives to subsidize the licensor since the latter is now both its customer and its rival. On the contrary, in order to extract higher profits from its own sales in the final goods market, the licensee now raises its rival s cost by charging a wholesale price that exceeds the input s marginal 2

4 cost. Therefore, in the entry case, in contrast to the no entry case, licensing deteriorates the effi ciency of the licensor, leading to a decrease in the licensor s profits from its own sales in the final goods market. Moreover, in the entry case, licensing results in an increase in the number of downstream competitors, and thus, in an increase in the intensity of competition in the final goods market. This contributes to the further decrease in the licensor s profits from its own sales in the final goods market. Why then does the licensor opt for licensing in the entry case? There are two effects that both are profit increasing for the licensor. First, the entry of the licensee into the final goods market, gives rise to a market expansion eff ect. That is, it expands the demand for the final goods. Second, the wholesale price that exceeds the input s marginal cost gives rise to a strategic eff ect. Although, the greater wholesale price decreases the licensor s profits, it increases the licensee s profits. Thus, this tradeoff results to a greater profit margin for the licensor under licensing with entry than under no licensing. In equilibrium, the licensor manages to extract, through the licensing fee, not only all of the profits that are generated by its own sales, but also all the profits that the licensee generates in the final goods market. In other words, in equilibrium, the licensor takes full advantage of both the market expansion effect and the strategic effect. As long as a licensing fee can be used, the latter effects outweigh the decreased effi ciency and the increased competition intensity and leads to the emergence of licensing in equilibrium. Importantly, the entry of the licensee into the final goods market, although it intensifies the market competition and reduces the effi ciency of the licensor, it strengthens instead of weakens the licensing incentives. Even the fact that the licensor s wholesale price is greater than its rival s cost, it turns to be an advantage for the licensor instead of a drawback. Stated in different words, the incumbent has stronger licensing incentives when the licensee becomes its competitor and faces a greater marginal cost. The intuition for this somewhat surprising result lies again on the market expansion eff ect and the strategic eff ect of licensing. Vertical licensing turns out to be desirable not only for the licensor, but also for the consumers and the society as a whole. This holds both with entry and without entry of the licensee in the final goods market. In fact, in the former case, licensing is even more desirable. Intuitively, licensing results in lower final prices, and thus, in higher consumers surplus, either because it enhances the effi ciency of the licensor (in the no entry case) or because it intensifies the market competition (in the entry case). The positive impact of licensing on consumers surplus and on the licensor s profits dominate its negative impact on the profits of the other incumbent, rendering vertical licensing to a welfare-enhancing 3

5 practice. We demonstrate that our main findings are robust when we relax the assumption that the effi cient incumbent commits to not producing the input in-house after licensing. Moreover, examining what happens when the licensor and the licensee trade through a wholesale price contract, we find that licensing incentives exist if and only if the licensee enters into the final goods market. This occurs because double marginalization is present both in the entry and in the no entry case; hence, the licensor does not enjoy higher effi ciency under licensing in either case. In the entry case though, the licensor benefits again from the market expansion eff ect which is in place. Finally, considering what happens when licensing takes place through a per-unit of output royalty, we find that, in contrast to the fixed licensing fee case, the firm has incentives to license its input technology only for free and only in the no entry case. 3 Our work is related to the vast theoretical literature on technology licensing. This literature has analyzed various aspects of licensing such as, the choice among royalties and licensing fees (e.g., Wang, 1998, Kamien and Tauman, 1986, Muto, 1993), the impact of licensing on innovation (e.g., Gallini and Winter, 1985), the role of information asymmetries (e.g., Gallini and Wright, 1990, Beggs, 1992), the choice among merger and licensing (e.g., Fauli-Oller and Sandonis, 2003). The majority of this literature has done so assuming that the licensor and the licensee(s) operate in the same one-tier market or that the licensor is not active in the market (an outsider). Some recent exceptions include the papers of Mukherjee (2003), Arya and Mittendorf (2006), Mukherjee and Ray (2007), Rey and Salant (2012), which, similarly to ours, have examined licensing within a vertically related market. The latter papers, however, differ from ours in three important aspects. First, most of them have considered licensing either among downstream firms or among upstream firms, and not among vertically related firms. 4 Second, they have analyzed settings in which, after the signing of the licensing agreement, the licensor is not a customer of the licensee. Third, they have examined the possibility that the licensing triggers the entry of a new firm into the market, but not the entry of the licensee into the licensor s market. It follows from 3 It should be noted that free licensing is observed quite often. It is observed not only in the open source software market, but also in other markets. For instance, in January 2015, Toyota announced that it would make more than 5,600 patents on fuel-cell technologies available for use, free of royalty payments, to a wide array of companies in the transportation sector. For more on this, see e.g. Toyota Offers To License Hydrogen Fuel-Cell Patents, For Free, Green Car Reports (January 5, 2015), and Toyota To Share Hydrogen Fuel Cell Patents, Forbes (January 5, 2015). 4 An exception in this respect is the paper of Rey and Salant (2012) which does consider vertical licensing. 4

6 this, that our paper complements the existing literature on technology licensing. It also follows that our paper, in contrast to the existing ones, is more appropriate for the analysis of situations such as the ones that we described in the beginning of this section (see e.g., Boeing case). Our paper is also related to the literature on outsourcing. A number of papers within this literature (e.g., Pack and Saggi, 2001, Shy and Stenbacka, 2003, Sappington 2005, Arya et al., 2008a and 2008b) have analyzed a final product manufacturer s make-or-buy decision. That is, its choice among the production of an input in-house and the sourcing of the input from an external firm - outsourcing. 5 Some of these papers have assumed that the input production is outsourced to a vertically integrated rival (i.e., to a firm which is already in the downstream market). Others, instead, have assumed that it is outsourced to an independent upstream firm. One of the latter, the paper of Pack and Saggi (2001), similar to ours, has taken into account the possibility that outsourcing can result in downstream entry and examined that implications of entry. However, Pack and Saggi (2001) have allowed for the downstream entry of an external independent firm, and not of the upstream firm to which the input production is outsourced. We, instead, have considered the entry of the input supplier into the downstream market - that is, in our setting, the entrant is both a downstream rival and an upstream supplier of the incumbent firm and not just a downstream rival. The remainder of the paper is organized as follows. In Section 2, we describe our main model. In Sections 3, we examine the licensing incentives in both the no entry case and the entry case, and we characterize the impact of entry on these incentives. In the following Section, we evaluate the welfare implications of vertical licensing. In Section 5, we examine the robustness of our main findings when vertical trading takes place through a wholesale price contract. In Section 6, we discuss a number of other extensions of our main model. Finally, in Section 7, we conclude. All the proofs are included in the Appendix. 5 The practice of outsourcing is obviously quite similar to the practice of licensing. In fact, the only distinction among them is the fact that outsourcing takes place for free (i.e., there are no fees or royalties involved). 5

7 2 The Model We consider a market consisting initially of two firms, firm 1 and firm 2. Each firm i, with i = 1, 2, produces a differentiated final good using, in a one-to-one proportion, a core input that it produces in-house. 6 We assume that both firms have patented their input productions technologies and that the marginal cost that they face is equal to c. Firm 1 considers licensing its input technology to a potential input supplier, firm S. We assume that licensing takes place through a fixed licensing fee, F 0, that firm S has to pay to firm 1. 7 After the licensing agreement is signed, the licensee (firm S) is in the position to produce the licensor s (firm 1 s) patented input, facing the same cost with the licensor, i.e., at marginal cost c. 8 The signing of the licensing agreement gives rise to the possibility that the licensee also produces the final good. That is, it allows firm S to enter into the final goods market and become a competitor of firms 1 and 2. In what follows, we consider the case in which firm S enters into the final goods market as well as the case in which it does not enter. In both cases, we assume that firm 1 stops producing the input in-house and commits to sourcing it from firm S We also assume that firm S and firm 1 negotiate over the terms of a two-part tariff contract, that is, over a fixed fee, T, and a wholesale price per unit of input, w, in a Nash bargaining fashion. The bargaining power of firm S and firm 1 is given, respectively, by β and 1 β, with 0 < β < 1. The (inverse) demand function for firm i s final good is: p i (q i, Q i ) = a q i γq i, a > c > 0, 0 γ < 1, where p i and q i are, respectively, the price and the quantity of firm i s final good, and Q i is the quantity of its rival(s) final goods. In particular, Q i = q j, with i, j = 1, 2 and i j, in the no entry case, while Q i = q j + q k, with i, j.k = 1, 2, S and i j k, in the entry case. The parameter γ measures the degree of product differentiation; namely, the higher is γ, the closer substitutes the final goods are. 6 The production of the final good is impossible without the use of this input. 7 In Section 6, we discuss what happens when licensing takes place through a variable royalty instead. 8 We abstract from assuming that the input supplier will be more effi cient in input production than firm 1 since then the incentives for vertical licensing would be straightforward. 9 It can commit, for instance, by shutting-down its input producing facilities. 10 In Section 6, we examine the robustness of our main findings in the alternative scenario in which firm 1 does not commit to souring the input from its licensee and it keeps instead open the option of producing the input in-house. 6

8 The timing of moves is as follows. First, firm 1 decides whether or not to license its input technology to S. In case of licensing, it sets the licensing fee F and, in turn, firm S decides to sign or not the licensing agreement. If the agreement is signed, then in the following stage, firm 1 and firm S negotiate over (w, T ). Finally, in the last stage, firm 1 and firm 2 (as well as firm S in case of licensing and entry) choose their quantities simultaneously and separately. We solve for the subgame perfect Nash equilibrium of this game. We start our analysis by considering the benchmark case of no licensing, in which, firm 1 and firm 2, compete among them in the standard Cournot way. In particular, each firm i chooses its output in order to maximize its profits: π i (q i, q j ) = (a q i γq j )q i cq i, with i, j = 1, 2 and i j. Solving the resulting system of first order conditions, we obtain the Cournot-Nash equilibrium quantities, q1 B and qb 2 and the respective equilibrium profits, πb 1 and π B 2, included in Table 1 of Appendix. 3 Entry and Licensing Incentives In this Section, first, we analyze the licensing incentives both in the no entry case and in the entry case, and then we examine how entry affects the licensing incentives. 3.1 Licensing and No Entry We examine here the case in which the licensing agreement has been signed and firm S has stayed out of the final goods market. 11 In the last stage, firm 2 faces the same maximization problem as in the benchmark case, while firm 1 chooses q 1 in order to maximize the following (gross from the fixed fee and the licensing fee) profits: π 1 (q 1, q 2, w) = (a q 1 γq 2 )q 1 wq 1. Solving the system of the two first order conditions, we derive the equilibrium quantities in terms of w: q 1 (w) = a(2 γ) + γc 2w a(2 γ) 2c + γw 4 γ 2 and q 2 (w) = 4 γ 2. (1) Obviously, a decrease in the wholesale price results in a higher output for firm 1 and a lower output for its rival. In the following stage, firm S and firm 1 negotiate over (w, T ). In particular, they solve 11 This could be so because, for instance, the entry costs are prohibitive high, and thus, entry is blocked. 7

9 the following generalized Nash bargaining problem: max w,t [π S(w) + T ] β [π 1 (w) T ] 1 β, (2) where π S (w) = (w c)q 1 (w) are the profits of firm S, and π 1 (w) = π 1 (q 1 (w), q 2 (w), w). Note that the disagreement payoffs of both firms are equal to zero since neither firm has an outside option. Maximizing (2) with respect to T we get: T = βπ 1 (w) (1 β)π S (w). (3) Using (3), the gross (from the licensing fee) profits of firm S and firm 1 can be rewritten as: π S (w) + T = β(π S (w) + π 1 (w)) and π 1 (w) T = (1 β)(π S (w) + π 1 (w)). (4) Substituting the above expressions into (2), we obtain an expression which is proportional to the joint profits of firm S and firm 1. It follows that w is chosen to maximize these profits: max w π S (w) + π 1 (w) = (a q 1 (w) γq 2 (w))q 1 (w) cq 1 (w). (5) From the first order condition of (5), we find the equilibrium wholesale price and, after substituting the latter into (3), we also find the equilibrium fixed fee: w LN = 8c 2(a + c)γ2 + (a c)γ 3 4(2 γ 2 ) and T LN = (a c)2 (2 γ) 2 (2β + (1 β)γ 2 ) 8(2 γ 2 ) 2. (6) One can easily check that w LN < c. That is, firm S subsidizes, through the wholesale price, the production of its customer, firm As we saw above, by charging a lower wholesale price, firm S increases the aggressiveness of firm 1 in the final goods market and enhances its output at the expense of firm 2 s output. Firm S has incentives to do so because it can use, in turn, the fixed fee T in order to capture part of the resulting higher firm 1 s profits. 13 Clearly, the higher is firm S s bargaining power, the larger is the share of firm 1 s profits 12 The subsidization of the downstream production arises also in settings in which an upstream monopolist faces a commitment problem, i.e., in settings in which, in contrast to here, it trades with more than one downstream firms and cannot commit to any of them that it will not offer better trading terms to the other(s). For more on this, see e.g., Milliou and Petrakis (2007), Alipranti et al. (2014). 13 A similar rationale exists in the delegation literature (e.g., Vickers, 1985, Sklivas, 1987, Fershtmam and Judd, 1987). 8

10 that it captures through T. 14 Furthermore, one can also easily check that the higher is product differentiation, the higher is the equilibrium wholesale price (i.e., ϑw LN ϑγ < 0), and thus, the smaller is the subsidy that firm S offers to firm 1. In fact, in the extreme case in which firm 1 and firm 2 do not compete in the market (i.e., γ = 0), we have that w LN = c. In other words, the weaker is the competition in the final goods market, the weaker are the incentives of firm S to enhance the competitive position of its customer by decreasing the latter s variable cost (i.e., the wholesale price). In the first stage of the game, firm 1 chooses between licensing and no licensing. Substituting (6) into π S (w) + T and π 1 (w) T from above, we obtain the gross (from the licensing fee) equilibrium profits of the licensor and the licensee. Firm 1 knows that firm S will reject the licensing agreement if and only if its profits without the agreement exceed its profits with the agreement. Since the former profits are equal to 0, it follows that firm 1 will optimally set F LN = π S (w LN ) + T LN. As a result, firm 1 s net equilibrium profits under licensing and no entry are: π LN 1 = π 1 (w LN ) T LN + F LN = π 1 (w LN ) + π S (w LN ). It is obvious that firm 1 ends up obtaining, through the licensing fee, not only the profits from its own sales in the final goods market but also the profits of firm S from the input sales, i.e., it obtains all of its joint profits with firm S. Comparing the equilibrium profits of firm 1 in the case of licensing and no entry (included in Table 1 of the Appendix) with its respective profits in the benchmark case, we reach the following conclusion. Proposition 1 When the input supplier (the licensee) does not enter into the final goods market, firm 1 always has incentives to license its input technology. As Proposition 1 informs us, firm 1 always licenses its input technology to firm S when the latter does not enter into the final goods market. It is important to note that this holds not only when firm 1 charges a positive fixed fee for the licensing agreement, but also when it offers the licensing agreement for free (F = 0) as long as its bargaining power is suffi ciently high (i.e., if β is suffi ciently low). The latter is stated formally in the following Corollary. Corollary 1 When the input supplier (the licensee) does not enter into the final goods market and there is no licensing fee (F = 0), firm 1 has incentives to license its input technology if and only if β is suffi ciently low. 14 The wholesale price, as we saw above, is chosen in order to maximize the joint profits of firm S and firm 1; hence, the equilibrium wholesale price is independent of the bargaining power distribution. 9

11 Why does firm 1 have incentives to transfer its input technology to firm S even for free? Recall that when firm 1 produces the input in-house, the marginal cost that it faces is c. When, instead, it licenses its input technology to firm S, its marginal cost is lower since w LN < c. We refer to this as the input pricing effect of licensing. It follows then that licensing results in an increase in firm 1 s effi ciency, and thus, it reinforces firm 1 s cost advantage in the final goods market. A straightforward implication of this is that the gross from T LN profits of firm 1 are larger under licensing. When the bargaining power of the input supplier is not too large (i.e., when β is low enough), the latter obtains only a small share of these profits through the T LN. As a consequence, when β is low enough, firm 1 is willing to license its input technology even for free. 15 As we know from our analysis above, when licensing takes place through a licensing fee, firm 1 enjoys all of its profits in the final goods market; hence, its licensing incentives then are independent of the bargaining power distribution. 3.2 Licensing and Entry We turn now to the examination of the case in which after the signing of the licensing agreement, firm S enters into the final goods market. In the last stage of the game, three firms, instead of two, are active in the final goods market. In particular, firms 1, 2, and S choose their outputs in order to maximize their respective profits: π 1 (q 1, q 2, q S, w) = (a q 1 γq 2 γq S )q 1 wq 1 ; (7) π 2 (q 1, q 2, q S, w) = (a q 2 γq 1 γq S )q 2 cq 2 ; (8) π S (q 1, q 2, q S, w) = (a q S γq 1 γq 2 )q S c(q 1 + q S ) + wq 1. (9) Solving the system of the first order conditions, we find the equilibrium quantities as a function of w: q 1 (w) = a(2 γ) + 2cγ (2 + γ)w ; (10) 2(2 γ)(1 + γ) q 2 (w) = 2(a c) γ(a w) 4 + 2γ 2γ 2 ; (11) 15 When licensing is for free, then there is no distinction between licensing and outsouring. 10

12 2(a c) γ(a w) q S (w) = 4 + 2γ 2γ 2. (12) In the second stage, firm S and firm 1 solve the following maximization problem: max w,t [π S(w) d S + T ] β [π 1 (w) T ] 1 β, (13) where π 1 (w) and π S (w) are found after substituting (10), (11) and (12), respectively, into (7) and (9). It is important to note that while the disagreement payoff of firm 1 continues to be null, the same does not longer hold for firm S s disagreement payoff. This is so because firm S now has an outside option in its bargaining with firm 1: in case of disagreement, S can still have profits from its own sales in the final goods market. disagreement payoff is given by d S = (a q D S γqb 2 )qd S cq S, where q D S = qb 1. Maximizing (13) with respect to T, we obtain: In particular, its T = βπ 1 (w) (1 β)[π S (w) d S ]. (14) Using the above expression, we get the following: π S (w) d S + T = β[π S (w) + π 1 (w) d S ]; (15) π 1 (w) T = (1 β)[π S (w) + π 1 (w) d S ]. (16) Substituting in turn (15) and (16) into (13), we note that the latter reduces to an expression proportional to the joint profits of firm S and firm 1 minus firm S s disagreement payoff. The wholesale price that maximizes this expression is: w LE = a(2 γ)(1 γ)γ + c(4 + γ(2 γ 3γ2 )) 2(2 + 2γ 2γ 2 γ 3. (17) ) One can check that the equilibrium wholesale price exceeds the marginal cost of producing the input, w LE > c. In other words, in contrast to the no entry case, when firm S enters into the final goods market, it no longer subsidizes firm 1. The reason for the change in firm S s behavior is quite clear. In case of entry, the profits of firm S accrue not only from its sales to firm 1 but also from its own sales in the final goods market. The less effi cient are the rivals that firm S faces in the final goods market, the larger is its own market share, and in turn, the profits that it makes from its own sales in the final goods market. Because of this, 11

13 firm S now has incentives to raise its rivals cost. In other words, it has incentives to charge a higher wholesale price to its customer-rival firm 1. However, an opposite force is also in action, since firm S has incentives to decrease the wholesale price in order to keep firm 1 in the market and obtain profits from the input sales. This effect softens the incentives of firm S to set a very high wholesale price. Clearly, in this case too the equilibrium wholesale price is independent of the bargaining power distribution, while the equilibrium fixed fee, T LE, which can be found after substituting (17) into (14), increases with the bargaining power of the input supplier. One can also check that the relationship between the equilibrium wholesale price and product differentiation is U-shaped in this case. In particular, ϑw LE ϑγ < 0 if and only if γ Therefore, a decrease in product differentiation leads to a decrease in the wholesale price when the final goods are initially close enough substitutes, and to an increase otherwise. Why a further intensification of competition when competition is already quite fierce results in a decrease in the rival s cost? Intuitively, firm S, by decreasing the wholesale price, on the one hand, it reduces its own market share and on the other hand, it increases its profits from its input sales to firm 1. The latter profits are quite low when the competition in the final goods market is already too fierce. Therefore, a further increase in the intensity of competition (a decrease in γ) can result in the market foreclosure of firm 1 (since w LE > c, firm 1 faces a cost-disadvantage relative to firm S) and result in the disappearance of firm S s profits from the input sales. 16 It remains to determine the presence or absence of licensing incentives in the first stage of the game. Substituting w LE and T LE into (15) and (16), we obtain the gross from the licensing fee equilibrium profits of firm 1 and firm S. For the reasons that we explained in subsection 3.1, firm 1 optimally sets F LE = π S (w LE ) + T LE. Therefore, firm 1 s net equilibrium profits (included in Table 2) under licensing and entry are: π LE 1 = π 1 (w LE ) + π S (w LE ). Comparing π LE 1 with π B 1, we find that firm 1 has incentives to license its input technology even when licensing reinforces the intensity of competition. Proposition 2. This is formally stated in Proposition 2 When the input supplier (licensee) enters into the final goods market, firm 16 For a review of the market foreclosure issues that arise in the presence of vertical integration see Rey and Tirole (2007). 12

14 1 always has incentives to license its input technology. The intuition for this surprising result is as follows. Under no licensing, firm 1 s equilibrium profits consist only of its own profits in the final goods market. Under licensing and entry instead, firm 1 s equilibrium profits consist of three parts: (i) its own profits from the final goods market, (ii) firm S s (gross) profits from its input sales to firm 1, and (iii) firm S s profits from its own sales in the final goods market. The first part of these profits is clearly lower with licensing and entry than without licensing. This is so because in the former case, the input pricing effect is negative instead of positive (since w LE > c); hence, firm 1 is less effi cient when it licenses its input technology than when it produces the input in-house. Moreover, this is so because when firm 1 licenses its technology, there are more firms in the final goods market. Since the profits of firm 1 from its own sales in the final goods market are lower under licensing, in this case, in contrast to the no entry case, firm 1 does not have incentives to license its technology when licensing is for free. When a licensing fee though is used, then, as mentioned above, firm 1 s profits under licensing and entry include two more parts ((ii) and (iii)), both of which are positive. The profits of firm S from its input sales to firm 1 alone are not in the position to compensate firm 1 for the reduction in its own profits in the final goods market. This so due to the fact that firm 1 s output does not remain constant: firm 1 s output is lower in the licensing with entry case than in the no licensing case. It follows from the above discussion that firm S s profits from the final goods market constitute the main driver of licensing in this case. In particular, the entry of firm S in the final goods market, gives rise to two effects, the market expansion effect and the strategic effect. The market expansion effect arises from the impact that the entry of firm S has on the market demand. In particular, although firm S s entry has a negative impact on the quantities of the incumbent firms, its overall impact on the total market quantity is positive (i.e., Q LE > Q B ). The strategic effect arises from the impact that the entry of firm S has on the wholesale price. Although the licensor s revenues from sales decrease due to its lower final production, the greater licensee s revenues due to the increased level of output lead the profit margin to be greater compared to the no licensing case. So, the fact that the licensee becomes more effi cient seems to be an advantage for the licensor instead of a drawback. Thus, the entry of the licensee encourages instead of discouraging the licensing incentives. Firm 1, by extracting all of the profits that accrue from the sales of firm S in the final goods 13

15 market, it takes the full advantage of both the market expansion and the strategic benefit. These effects make licensing attractive even when licensing intensifies market competition. One might wonder why the wholesale price is chosen to exceed the input s marginal cost and not to be equal to it, so as the licensor generate the same effi ciency with its rival and thus more market quantity and profits. This is due to the strategic effect, the impact of which is more pronounced in this comparison because it increases the final price of the licensee s output. Since the licensor cannot affect directly the final price of the licensee s final good, due to the nature of the final competition, it signs a contract where its wholesale price increases in order to lead indirectly the licensee to increase its final price. Although the licensor s revenues from sales decrease due to its lower final production, the greater licensee s revenues, due to the increased level of output and the increased final price, lead the profit margin to be greater compared to the case where the wholesale price was charged equal to the input s marginal cost. So, the fact that the licensee becomes more effi cient seems to be an advantage for the licensor instead of a drawback. Since, the licensor extracts all licensee s greater profits, it fully exploits the strategic benefit. Thus, the entry of the licensee which leads to the charge of a greater wholesale price, encourages instead of discouraging the licensing incentives. 3.3 The Impact of Entry Having explored the incentives for licensing both with and without entry, we are now in the position to characterize the impact of entry on these incentives. Comparing firm 1 s profits under licensing and no entry with its respective profits under licensing and entry, we find the following. Proposition 3 The entry of the input supplier (licensee) into the final goods market reinforces firm 1 s licensing incentives. Interestingly, the entry of the licensee into the market of the licensor has a positive instead of a negative impact on the latter s incentives to license its technology. Stated in different words, when licensing intensifies the competition faced by the licensor, the licensing incentives of the latter are stronger. Why is that? The drawbacks as well as the advantages that licensing with entry has relative to licensing without entry are similar to its respective drawbacks and advantage relative to no licensing. More specifically, its first drawback is the presence of more intense market competition due to the existence of three instead of two 14

16 firms in the final goods market. Its second drawback is the negative input pricing eff ect, which translates into lower effi ciency for firm 1. However, this effect drives the licensee s profits to be greater than firm 1 s profits. The extraction of these profits via the licensing fee arises the strategic benefit that firm 1 has from the greater effi ciency of firm S and thus its greater profits. In fact, the inverse input pricing effect, turns to become an advantage since it increases the joint profits of firms 1 and S. Along with the greater market expansion effect which occurs in the case of licensing with entry compared to the no entry case, firm 1 has stronger incentives for licensing. As Proposition 3 reveals, the market expansion effect and the strategic effect dominate and the entry of the licensee reinforces the licensing incentives. 4 The Welfare Implications of Vertical Licensing We have seen that vertical licensing is desirable for firm 1. What we have not seen yet, and we are going to see in this section, is whether vertical licensing is also desirable from a welfare point of view. Proposition 4 Vertical licensing both with and without the entry of the licensee in the final goods market, has a positive impact on the consumers surplus and on the total welfare. Its positive impact is larger with entry than without entry. Proposition 4 informs us that vertical licensing is beneficial both for the consumers and for the society as a whole. Intuitively, in the no entry case, the positive impact of vertical licensing on the consumers surplus is due to the positive input pricing eff ect. In the entry case instead, the positive impact of vertical licensing on the consumers surplus is due to the increase in the number of competitors in the final goods market. As for the impact of licensing on the producers surplus, we know from Propositions 1 and 2 that the profits of firm 1 are higher under licensing than under no licensing. The opposite clearly holds for firm 1 s rival: firm 2 is worse off under licensing since the latter either leads to the increase in the effi ciency of its competitor or to an increase in the number of its competitors. Still, the negative impact of licensing on firm 2 s profits is dominated by its positive impact on the consumers surplus and on the licensor s profits. Proposition 4 also informs us that the positive impact of vertical licensing on consumer welfare and on total welfare is greater when the licensee enters into the final goods market. 15

17 In light of our previous findings this is not so surprising. More specifically, even though firm 1 is more effi cient under no entry than under entry, market competition is still fiercer in the latter case because there are more competitors in the market, Consequently, the consumers surplus is larger under entry than under no entry. In turn, the total welfare is also larger under entry not only because of the higher consumers surplus, but also because of the higher profits that firm 1 enjoys under entry (Proposition 3). Recently, the EU revised its rules for the assessment of technology licensing agreements under the EU competition law. The new regulation that it adopted, Regulation N. 316/2014 on the application of Article 101(3) of the Treaty on the Functioning of the European Union to categories of technology transfer agreements, facilitates licensing and continues to reflect the view that licensing is in most cases pro-competitive. Based on this view, a block exemption applies to all the licensing agreements between firms that have limited market shares. In particular, according to the regulation, in the case of licensing agreements between non-competitors, the block exemption applies when the individual market share of each party does not exceed 30%. Our analysis suggests that vertical licensing, especially in the case in which it triggers entry into more than one stages of the vertical chain, facilitates the diffusion of technology and generates more intense product market competition even when the market share of the licensor exceeds 50% Wholesale Price Contract In this Section, we consider what would happen if in the second stage of the game, the licensor and the licensee trade through a wholesale price contract instead of through a two-part tariff contract. In order to simplify our analysis, we assume here that there is no bargaining - firm S makes a take-it-or-leave-it offer regarding w. 18 Under trading through a wholesale price contract, firm S is not in the position to extract part of firm 1 s profits through the fixed fee, since the latter is not available. Because of this, both in the no entry case and in the entry case, double marginalization is present, i.e., ŵ LN > c and ŵ LE > c. Comparing ŵ LN and ŵ LE, we find that ŵ LE > ŵ LN if and only if γ > 0.5. This occurs because when products are close substitutes, the entrant faces fierce 17 As we show in Section 6, licensing can be welfare-enhancing even when the licensor is initially a monopolist and/or when it has a cost advantage relative to the other incumbent. 18 As we discuss later on the inclusion of bargaining would not affect our results. 16

18 competition, and thus, it has stronger incentives to raise its rival s cost by charging a higher wholesale price. Clearly, once again, in equilibrium, the licensor extracts fully, through the licensing fee, both the profits that arise from its own sales and the profits of the licensee. The comparison of its net equilibrium profits in the case of licensing without entry as well as of those in the case of licensing with entry (included in Table 3) with its respective profits in the case of no licensing, results in the following. Proposition 5 When vertical trading takes place through a wholesale price contract, firm 1 has incentives to license its input technology if and only if the input supplier (licensee) enters into the final goods market. When firms trade through a wholesale price contract, in contrast to when they trade through a two-part tariff, licensing does not arise in equilibrium in the no entry case. This is so because, due to double marginalization, the input pricing eff ect is negative instead of positive. In other words, the licensor is less effi cient in the presence than in the absence of licensing. Its lower effi ciency translates into a lower market share, and, in turn, into lower profits from its own sales. When the licensee does not enter into the market, and thus, the profits from firm S s sales in the final goods market are zero, the licensor has no reason to license its technology. When instead the licensee enters into the market, and as result the final market expands, the licensing incentives are restored just like in our main analysis, as long as a licensing fee can be optimally applied. 19 It follows from the above that when vertical trading takes place through a wholesale price contract, the entry of the licensee not only does not discourage firm 1 from licensing, but in fact it constitutes the driving force behind licensing. 6 Extensions - Discussion In this Section, we discuss briefly a number of further extensions of our model in order to examine the robustness of our main findings as well as in order to extract some additional insights. 19 If we included bargaining, the equilibrium wholesale prices would be lower than ŵ LN and ŵ LE. In fact they would be decreasing with the bargaining power of firm 1 (i.e., with 1 β). Clearly, this means, that the licensing incentives in the entry case would not only be present but that they would be even stronger then. Moreover, firm 1 would continue to not have licensing incentives in the no entry case. In fact, in the latter case, even if firm 1 had all the bargaining power (β = 0), it would be indifferent among no licensing and licensing. 17

19 (i) Licensing without Commitment Throughout our analysis, we have assumed that after the signing of the licensing agreement, firm 1 commits to sourcing the input from the licensee. We relax this assumption now. That is, we allow for the possibility that firm 1 produces the input in-house in case of disagreement with firm S during the negotiations. In the no entry without commitment case, the last stage of the game is the same as the one in the no entry with commitment case. The second stage of the game though is now different. In particular, firm 1 now has the outside option to produce the input on its own. As a result, the maximization problem that firm S and firm 1 face is the following: where d 1 = (a q B 1 γqb 2 )qb 1 cqb 1 max w,t [π S(w) + T ] β [π 1 (w) d 1 T ] 1 β, (18) is firm 1 s disagreement payoff. Maximizing (18) with respect to T, we get: T (w) = β[π 1 (w) d 1 ] (1 β)π S (w). Using the latter, we rewrite (18) and we note that w is chosen in order to maximize the joint profits of S and firm 1 minus the disagreement payoff of the latter: max w [π S (w) + π 1 (w) d 1 ]. (19) From the first order condition of (19), we obtain the equilibrium wholesale price, w LN = w LN < c. Substituting w LN into T (w), we also obtain the equilibrium fixed fee, T LN. We note that T LN < T LN. This is a straightforward implication of the positive disagreement payoff of firm 1 under no commitment. In the entry without commitment case, the last stage of the game as well as the resulting equilibrium quantities and profits in terms of w are the same as in the case of entry with commitment. In the second stage of the game now, both firm 1 and S have outside options. Firm 1 has the outside option to produce the input on its own, while S has the outside option to operate as a final product competitor without making any input sales to firm 1. In particular, firm S and firm 1 face now the following maximization problem: max w,t [π S(w) d S + T ] β [π 1 (w) d 1 T ] 1 β, (20) where d S = (a q S γq 1 γq 2 )q S cq S, is the disagreement payoff of firm S and d 1 = (a q 1 γq 2 γq S )q 1 cq 1 is firm 1 s disagreement payoff, where q 1 = q 2 = q S = (a c) (2+2γ). 18

20 We maximize (20) with respect to T and then substituting the resulting T (w) back into (20), we observe that the maximization problem reduces to an expression proportional to the joint surplus generated by firm S and firm 1, minus their disagreement payoffs: max w [π S (w) + π 1 (w) d S d 1 ]. (21) The resulting equilibrium wholesale price is: w LE = w LE. Therefore, the equilibrium wholesale price without commitment coincides again with the equilibrium wholesale price with commitment; hence, it exceeds firm S s marginal production cost. The equilibrium fixed fees though differ among the two cases. In particular, substituting w LE into T (w), we find that the resulting T LE satisfies the following T LE < 0 < T LE. Therefore, we have here subsidization of firm 1 s production via the fixed fee and not via the wholesale price. Since the wholesale prices without commitment coincide with the respective ones with commitment, it follows that the equilibrium quantities, as well as the net equilibrium profits also coincide. A straightforward implication of this is that Propositions 1, 2, 3, and 4 hold in this case too. The only thing that differs now is Corollary 1. In particular, recall that according to Corollary 1, when licensing is for free (F = 0), then in the case of no entry with commitment, firm 1 opts for licensing if and only if β was suffi ciently low. Here, instead, when licensing is for free, firm 1 always opts for licensing in the no entry case. This difference arises from the fact that now firm 1 has an outside option during the negotiations, and thus, firm S ends up compensating for it. (ii) Licensing through Royalties Throughout our analysis, we have assumed that licensing takes place via a fixed licensing fee. Now, we consider what happens when firm 1 charges instead a per-unit of output royalty, r 0, for the licensed input technology. Clearly, in the absence of the licensing fixed fee, firm 1 is not in the position to extract the potential profits of the licensee. When r is imposed on the output of firm 1 (and not only on the output of firm S as it could be the case under entry), the marginal cost of firm S increases from c to r + c. The increase in the input supplier s marginal cost can translate into worse input sourcing terms for firm 1, and thus, into less firm 1 s profits from its own sales in the final goods market. Not surprisingly then, firm 1 optimally sets r N = r E = 0 both with and without entry. Given this, does it have incentives to license its technology? The answer to this question is already provided in our main analysis. More specifically, recall that when F = 0, firm 19