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Vertical licensing, input pricing, and entry
Accepted Manuscript
Vertical Licensing, Input Pricing, and Entry Elpiniki Bakaouka, Chrysovalantou Milliou PII: DOI: Reference:
S0167-7187(17)30298-9 10.1016/j.ijindorg.2018.03.007 INDOR 2438
To appear in:
International Journal of Industrial Organization
Received date: Revised date: Accepted date:
12 May 2017 16 February 2018 11 March 2018
Please cite this article as: Elpiniki Bakaouka, Chrysovalantou Milliou, Vertical Licensing, Input Pricing, and Entry, International Journal of Industrial Organization (2018), doi: 10.1016/j.ijindorg.2018.03.007
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Highlights • We explore a vertically integrated firms incentives to license its input production technology.
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• Licensing arises even when the licensee becomes a rival of the licensor in the downstream market.
• The entry of the licensee in the downstream market reinforces the licensing incentives.
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• The incentives for vertical licensing can be stronger than those for horizontal licensing.
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Vertical Licensing, Input Pricing, and Entry Elpiniki Bakaouka and Chrysovalantou Milliou∗ February 2018
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Abstract
We explore the incentives of a vertically integrated incumbent to license the production technology of its core input to an external firm, transforming the licensee into its input supplier. We find that the incumbent opts for licensing even when licensing also transforms the licensee into one of its direct competitors in the final products market. In fact, the licensee’s entry into the final products market, although it increases
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the competition and the cost that the licensor faces, reinforces the licensing incentives. Furthermore, the licensee’s entry augments the positive welfare implications of vertical
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licensing.
Keywords: licensing; vertical relations, entry; two-part tariffs; outsourcing
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JEL classification: L22; L24; L13; L42; D45
Bakaouka: Department of International and European Economic Studies, Athens University of Eco-
nomics and Business, Athens 10434, Greece, e-mail: [email protected]; Milliou: Department of Interna-
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tional and European Economic Studies, Athens University of Economics and Business, Athens 10434, Greece, e-mail: [email protected]. We are grateful to Marie-Laure Allain and to Lambros Pechlivanos for their valuable suggestions. We would like to thank the Editor and three anonymous referees, Maria Alipranti, Christos Constantatos, Tony Ke, Emmanuel Petrakis, Patrick Rey, Joel Sandonis, Spyros Vassilakis as well as the conference participants at the Workshop on Competition and Bargaining in Vertical Chains in Toulouse, the CRETE 2016 in Tinos, the EARIE 2016 in Lisbon, the ASSET 2016 in Thessaloniki, and the IIOC 2017 in Boston 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.
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Introduction
Original brand manufacturers often license the production technology of their core inputs to external firms.1 Such a practice transforms the licensees into the licensors’ input sup-
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pliers and potentially also into their direct competitors in the final products market. An illustration comes from the commercial aircraft market, where, in 2003, the US aircraft manufacturer Boeing licensed its wing production technology to Mitsubishi Heavy Industries, the Japanese engineering and electrical equipment producer. Boeing, as well as its main competitor, Airbus, had already been subcontracting the production of various air-
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craft components to external suppliers. However, never before had a commercial aircraft manufacturer subcontracted its wing production. Boeing’s decision met with widespread criticism: first, because Boeing’s wing technology has been regarded as its crown jewel, and second, because the transfer of wing manufacturing effectively gave to Mitsubishi ‘total production competence’ with regard to commercial aircraft. Mitsubishi is now ready to launch its own passenger jet, which is due to enter service in 2020.2
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A similar illustration can be found in the electronic appliances market, where, in 1984, a Chinese firm, Haier, which at the time was operating as a producer of electrical equip-
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ment for original brand manufacturers, acquired the technology for producing high-quality refrigerators from a German original brand manufacturer, Liebherr. A year after the li-
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censing of Liebherr’s technology, Haier introduced its own first four-star refrigerator in the market, evolving into an original brand manufacturer too. Haier soon became the leading refrigerator producer in China and, eventually, a major competitor in the global market.3 According to empirical evidence, technology licensing is a common practice among firms (e.g., Caves et
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al., 1983, Nadiri, 1993, Anand and Khanna, 2000). Many well-known firms, such as IBM, Hitachi, Kodak, and Procter & Gamble, have licensed their technologies, earning millions of dollars in licensing revenue. For
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more on this, see e.g., A Market for Ideas, The Economist (October 20, 2005). 2 Without the ability to manufacture wings, Mitsubishi could not become an independent player in the passenger jet market. For more on this, see e.g., Secret Wounds Of Globalism: Boeing Sells Its Technology – Cheap – To Japan, Forbes (January 5, 2014), and Boeing Outsourcing Gives Wing to Concerns, Chicago Tribune (December 21, 2003). 3 Samsung and Foxconn, after becoming Apple’s component suppliers, also became its competitors in the mobile phone and the smartwatch market, respectively. Similarly, after Dell outsourced its product’s parts to Asus, the latter started producing its own computers. For more on this, see e.g., How Apple’s Outsourcing Strategy Created Two Giant Competitors, CIO (June 1, 2015), and Has Apple Created Its Own Threat in Samsung?, Forbes (December 9, 2012).
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The above illustrations give rise to a number of interesting questions regarding vertical licensing, such as: Does a firm license its input production technology to an external firm when licensing can cause the licensee’s entry into its final product market? How does the transformation of the licensee into a rival affect the licensing incentives? What is the role
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of input pricing? Is vertical licensing welfare-improving? In this paper, we address these questions.
To this end, we consider a framework in which two competing incumbents produce two final goods using an input that they initially produce in-house. One incumbent considers licensing its input production technology to an external firm for a fixed licensing fee. When
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licensing takes place, the licensee produces the input for the licensor and the two firms trade through a two-part tariff contract whose terms are determined through bargaining. We consider what happens both when the licensee enters into the final goods market and competes with the incumbents in quantities - the ‘entry case’ - and when it does not enter - the ‘no entry case’.
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We find that independently of whether the licensee enters into the final goods market or not, the incumbent always opts for licensing. The key drivers of licensing, however, differ
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substantially among the entry and the no entry case. In the no entry case, licensing is driven by input pricing. Specifically, just as under strategic delegation, the input producer - the licensee - subsidizes the licensor by setting the wholesale price below the input’s marginal
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cost. We refer to this as the input pricing effect of licensing. The licensee does so because it can extract part of the resulting higher profits of the licensor through the fixed fee of
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the two-part tariff. Clearly then, in the no entry case, the licensor enjoys a cost-advantage relative to the other incumbent. In fact, due to this cost-advantage, it is willing to license its input production technology even for free when its bargaining power is sufficiently high.4
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In contrast, in the entry case, the licensee sets the wholesale price above the input’s
marginal cost, increasing the licensor’s cost. In addition, the number of downstream competitors increases and, thus, competition is intensified. We refer to this as the competition intensification effect of licensing. Furthermore, in this case, licensing results in the market 4
The free sharing of technology is observed in various markets, including the market for open source
software. For instance, in January 2015, Toyota announced that it would make more than 5,600 patents on fuel-cell technologies available for use for free to a wide array of firms 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).
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expansion effect and the business stealing effect. The market expansion effect refers to the fact that the licensee’s entry causes an increase of product variety, and thus, an expansion of the demand in the final products market. The business stealing effect refers instead to the fact that the licensee, by entering into the final products market, ‘steals’ part of
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the sales and market share of the licensor’s rival. Capturing the licensee’s profits, through the licensing fee, the licensor takes full advantage of both the market expansion effect and the business stealing effect, which work in favor of licensing and lead to its emergence in equilibrium.
Importantly, the entry of the licensee into the final goods market, although it intensifies
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competition and increases the licensor’s cost, strengthens the licensing incentives. Why is that? In the entry case, due to the market expansion effect and the business stealing effect, the licensor enjoys both a larger pie and a larger share of the pie. At the same time, the licensor does not suffer severely from the competition intensification effect, since the wholesale price is set in such a way as to reduce the negative impact of the increased
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downstream competition. Actually, the licensee and the licensor use their vertical trading contract as an instrument that allows them to behave in a pro-collusive way. This is a
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feature of vertical licensing which is absent in horizontal licensing and can alleviate the potential negative implications of the licensee’s entry. Vertical licensing is desirable not only for the licensor, but also for the consumers and
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the economy as a whole. This holds both with and without the licensee’s entry. Intuitively, licensing results in lower final prices, and thus in higher consumer surplus, either because
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it enhances the efficiency of the licensor in the no entry case or because it intensifies competition in the entry case. In fact, in the entry case, licensing is even more desirable due to the enhanced product variety and the increased competition.
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Extending our main model, we demonstrate that the licensee’s entry into the final goods
market can reinforce the licensing incentives in other instances too, such as, when the rival incumbent can also opt for licensing or when competition is in prices. Interestingly, there are instances in which the emergence of vertical licensing in equilibrium would be impossible without the licensee’s entry. This occurs when the licensor is initially the only incumbent in the market or when input trading is through a wholesale price contract. In contrast, when licensing is through royalties, the licensee’s entry can discourage licensing. Our work is related to the vast theoretical literature on technology licensing, where similarly to our paper, an owner of a technology sells the rights of its use to another firm. 3
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This literature analyzes various aspects of licensing, such as the choice among royalties and licensing fee (e.g., Kamien and Tauman, 1986, Muto, 1993, Wang, 1998), 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.,
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Fauli-Oller and Sandonis, 2003), and the possible anticompetitive effects of licensing (FauliOller and Sandonis, 2002). Most papers in this literature assume that the licensor and the licensee(s) are in different markets or in a one-tier market. Exceptions include the papers by Mukherjee (2003), Arya and Mittendorf (2006), Mukherjee and Ray (2007), and Rey and Salant (2012), which, similar to our paper, examine licensing in vertically related markets.
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In contrast to our paper, they focus on settings in which the licensor and the licensee do not have a seller-buyer relationship.5 Moreover, when they consider entry, triggered by licensing, they do not allow for the licensee’s entry into the licensor’s final goods market. Our paper is also related to the literature on outsourcing. A number of papers in this literature (e.g., Pack and Saggi, 2001, Shy and Stenbacka, 2003, Sappington, 2005, Buehler
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and Haucap, 2006, Arya et al., 2008a and 2008b, Lim and Tan, 2010) analyze a final product manufacturer’s ‘make-or-buy’ decision. That is, its choice among input production
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in-house and input sourcing from an external firm - outsourcing.6 Some of these papers assume that input production is outsourced to an already existing vertically integrated rival. Others, instead, assume that it is outsourced to an independent upstream firm. In
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particular, Pack and Saggi (2001) and Goh (2005) examine a buyer’s incentives to outsource its technology to a supplier when technology diffusion can result in the entry of another
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firm in the downstream and the upstream market, respectively. Both papers find that entry, by driving the input price to marginal cost, can be beneficial for the incumbents engaged in technology transfer. In contrast, we consider the entry of the firm to which the input
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production is outsourced and we show that it is beneficial even when it causes an increase in the input price. Lim and Tan (2010), similarly to our paper, consider a setting in which the supplier becomes a direct competitor of the buyer after outsourcing. However, they focus on the role of the buyer’s rate of learning and brand equity, while we focus on the role of input pricing. In our paper, vertical licensing without a licensing fee coincides with vertical separation. 5 6
An exception in this respect is the paper by Rey and Salant (2012) which considers vertical licensing. The practice of outsourcing is obviously quite similar to the practice of licensing, especially when licensing
does not involve fees or royalties.
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Clearly then, our paper is also related to the literature on vertical separation versus vertical integration (e.g., Vickers, 1985, Grossman and Hart, 1986, Bonanno and Vickers, 1988, Lin, 1988, Gal-Or, 1990, Jansen, 2003, Rey and Tirole, 2007). This literature provides the same strategic rationale for vertical separation (vertical licensing) as our paper in the no
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entry case. Our paper complements this literature by demonstrating that licensing can be used as a way through which the downstream firms, and not the upstream firms, can take advantage of the additional profits generated by vertical separation. And importantly, we consider the entry case. That is, we explore the incentives and the implications of vertical separation when it is accompanied by the entry of the vertically disintegrated upstream
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firm into the downstream market, and in turn we provide an additional argument in favor of vertical separation.7
A number of papers consider markets with multiple vertically integrated incumbents and, as we do in the entry case, examine their incentives to supply the input to a nonintegrated downstream entrant (e.g., Ordover and Shaffer, 2007, H¨offler and Schmidt, 2008,
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Brito and Pereira, 2010, Bourreau et al., 2011, Atiyas et al., 2012). They show that an incumbent does not foreclose the entrant unless the latter’s product is a closer substitute
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to its own product than to its rival’s (Ordover and Shaffer, 2007), it is asymmetrically located (Brito and Pereira, 2010), or contracts are unobservable (Atiyas et al., 2012). In these papers, all the vertically integrated firms, and not just one of them as in our paper
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and in H¨ offler and Schmidt (2008), can supply the entrant. Importantly, in these papers, the input suppliers are always integrated and thus the incentives for vertical licensing or
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vertical separation and the impact of entry on them are not examined. The remainder of the paper is organized as follows. In Section 2, we describe our main model. In Section 3, we determine the licensing incentives in both the no entry case and
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the entry case, and characterize the impact of entry on them. In Section 4, we evaluate the welfare implications of vertical licensing. In Section 5, we examine the robustness of our main findings when the licensee can serve as a common supplier and when both incumbents 7
One could also think of vertical licensing as vertical divestiture or as a spin-off of a firm’s upstream
division. Hence, our paper also relates to the literature on vertical divestiture and spin-offs (e.g., Chen, 2005, Lin, 2006, Sappington, 2006). Its main difference from this literature too is the consideration of the entry of the spin-off firm in the downstream market. Moreover, the analysis of the incentives for vertical licensing in the entry case shares some common features with the literature that analyses the incentives for horizontal divisionalization (e.g., Baye et al., 1996, Ziss, 1998).
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can opt for licensing. In Section 6, we discuss a number of further extensions of our main model. Finally, in Section 7, we conclude. All the proofs are included in the Appendix.
The Model
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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 at marginal cost c.
Both firms hold a patent for their input production technologies. One of them, without
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loss of generality firm 1, considers licensing its input production technology to an external firm, firm S, for a fixed licensing fee, F ≥ 0.8 When licensing takes place, the licensee (firm
S) is in the position to produce the licensor’s (firm 1’s) input at marginal cost c.9
The knowledge that firm S acquires through licensing regarding the production of the final good’s core input could also allow it to produce the final good. Thus, licensing could cause firm S’s entry into the final goods market too. In what follows, we consider the ‘entry
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case’ in which firm S enters into the final goods market and the ‘no entry case’ in which it does not enter.10 We assume that when the licensing agreement is signed, firm 1 commits to
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sourcing the input from firm S.11 The input sourcing terms include the terms of a two-part tariff: a fixed fee, T , and a wholesale price per unit of input, w, that firm 1 pays to firm
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S. These terms are determined through Nash bargaining between firm S and firm 1. The bargaining power of firm S and firm 1 is given by β and 1 − β, respectively, with 0 < β < 1.
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The (inverse) demand function for firm i’s final good is: pi (qi , Q−i ) = a − qi − γQ−i , 0 < γ < 1, a > c > 0,
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where pi and qi are the price and the quantity of firm i’s final good, respectively, and Q−i
is the quantity of its rival(s)’ final good(s). Specifically, Q−i = qj , with i, j = 1, 2 and i 6= j, 8 9
As we demonstrate in Section 6, the licensor prefers using a fixed licensing fee to a variable royalty. We abstract from assuming that firm S is more efficient in input production than firm 1. Clearly,
otherwise, the higher efficiency of the licensee would work in favor of vertical licensing. 10 This could be so because, for instance, the cost of entry in the final goods market is prohibitively high and, thus entry is blocked, or because the ability to produce the core input does not suffice for the production of the final good. 11 For instance, firm 1 shuts down its input production facility. Examining, in Section 6, what happens when firm 1 continues to have the option of producing the input in-house under licensing too, we conclude that our main results are qualitatively robust.
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in the no entry case, while Q−i = qj + qk , with i, j, k = 1, 2, S and i 6= j 6= k, in the entry case. The parameter γ measures the degree of product differentiation; namely, the higher γ is, the closer substitutes the final goods are. The timing of moves is as follows. First, firm 1 decides whether to license its input
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technology to firm S. In case of licensing, it sets the licensing fee F and, in turn, firm S signs or not the licensing agreement. If the agreement is signed, 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 the case of licensing and entry, choose their quantities simultaneously and separately.12 We solve for the subgame perfect Nash equilibrium of this game.
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We make the following assumption throughout in order to guarantee that all the firms face a non-negative marginal cost in all the cases under consideration: Assumption 1: a ≤ 5c
We start our analysis with the benchmark case in which there is no licensing. Firm 1 and firm 2 compete then in the standard Cournot way. Specifically, each firm i chooses qi
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to maximize its profits: π i (qi , qj ) = (a − qi − γqj )qi − cqi , with i, j = 1, 2 and i 6= j. Solving the resulting system of first order conditions, we obtain the Cournot-Nash equilibrium
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B quantities, q1B and q2B , and the equilibrium profits, π B 1 and π 2 , included in Table 1 of the
Appendix.
Licensing Incentives
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In this section, we first determine the licensing incentives with and without the licensee’s entry into the final goods market and then we examine how they are influenced by entry.
Licensing and No Entry
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3.1
When the licensing agreement has been signed and firm S has stayed out of the final goods market, in the last stage, firm 2 faces the same maximization problem as in the benchmark case. Firm 1 maximizes instead the following (gross from T and F ) profits: 12
In Section 6, we also examine what happens when firms compete in prices, when firm 2 does not observe
(w, T ) before choosing its quantity, when (w, T ) are determined before the licensing decision is made, and when firms bargain over F too.
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π 1 (q1 , q2 , w) = (a − q1 − γq2 )q1 − wq1 . The resulting equilibrium quantities are: q1 (w) =
a(2 − γ) + γc − 2w a(2 − γ) − 2c + γw and q2 (w) = . 4 − γ2 4 − γ2
(1)
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In stage two, firm S and firm 1 solve the following generalized Nash bargaining problem: max [π S (w) + T ]β [π 1 (w) − T ]1−β , w,T
(2)
where π S (w) = (w − c)q1 (w) are firm S’s profits and π 1 (w) = π 1 (q1 (w), q2 (w), w). Their disagreement payoffs are equal to zero since neither firm has an outside option. Maximizing (2) with respect to T , we find: T (w) = βπ 1 (w) − (1 − β)π S (w). Thus, we can rewrite the
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(gross from F ) profits of firm S and firm 1 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)).
(3)
¿From (2) and (3), it follows that the equilibrium wholesale price maximizes the joint profits wLN =
8c − 2(a + c)γ 2 + (a − c)γ 3 . 4(2 − γ 2 )
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of firm S and firm 1:
(4)
Note that wLN < c, i.e., firm S subsidizes, through the wholesale price, the production of its
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customer, firm 1. As the literature on strategic delegation (e.g., Vickers, 1985, Fershtman and Judd, 1987, Sklivas, 1987) and on vertical separation (e.g., Jansen, 2003) has explained,
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the upstream firm has incentives to enhance the output of its customer at the rival’s expense in order to increase its customer’s profits that it (partially) captures through T . Firm 1 knows that firm S will reject the licensing agreement if and only if its profits
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without the agreement exceed its profits with the agreement. Since the former are equal to 0, firm 1 optimally sets: F LN = π S (wLN ) + T LN , where T LN = T (wLN ). Its net equilibrium
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profits (included in Table 1 of the Appendix) are: π LN = π 1 (wLN ) − T LN + F LN = 1
π 1 (wLN ) + π S (wLN ). Therefore, firm 1 captures all of its joint profits with firm S.
Proposition 1 When firm S does not enter into the final products market, firm 1 always licenses its input technology. Firm 1 licenses its input technology even when licensing is for free (F = 0) as long as β is sufficiently low. According to Proposition 1, firm 1 always opts for licensing when the licensee does not enter into the final goods market. Firm 1 would opt for licensing even if licensing was for free, as long as its bargaining power was sufficiently high. A similar finding and reasoning 8
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exists in the literature demonstrating the preference of vertical separation over vertical integration (e.g., Vickers, 1985, Jansen, 2003). Intuitively, firm 1 faces lower marginal cost with licensing than with in-house production, wLN < c. We refer to this as the input pricing effect of licensing. As a result, licensing leads to higher (gross from T LN ) profits for firm
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1 in the final goods market. When β is small, firm S obtains a small share of these profits through T LN ; hence, firm 1 is willing to license its input technology even for free.
3.2
Licensing and Entry
We turn now to the examination of the case in which the licensing agreement has been
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signed and firm S has entered into the final products market.
In the last stage, firms 1, 2, and S choose their outputs in order to maximize their respective profits:
(5)
π 2 (q1 , q2 , qS , w) = (a − q2 − γq1 − γqS )q2 − cq2 ;
(6)
π S (q1 , q2 , qS , w) = (a − qS − γq1 − γq2 )qS − c(q1 + qS ) + wq1 .
(7)
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π 1 (q1 , q2 , qS , w) = (a − q1 − γq2 − γqS )q1 − wq1 ;
Solving the system of the first order conditions, we obtain:
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q1 (w) =
a(2 − γ) + 2cγ − (2 + γ)w ; 2(2 − γ)(1 + γ) 2(a − c) − γ(a − w) . 4 + 2γ − 2γ 2
(9)
max [π S (w) − dS + T ]β [π 1 (w) − T ]1−β ,
(10)
q2 (w) = qS (w) =
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(8)
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In the second stage, firm S and firm 1 solve the following maximization problem:
w,T
where π 1 (w) and π S (w) are found after substituting (8) and (9) into (5) and (7), respectively. It is important to note that while the disagreement payoff of firm 1 continues to be null, the same no longer holds for firm S’s disagreement payoff. Firm S now has an outside option in its bargaining with firm 1: in case of disagreement, firm S has profits from its own sales in
the final goods market given by dS = (a − qSD − γq2B )qSD − cqSD , where qSD = q1B . Maximizing (10) with respect to T , we obtain: T = βπ 1 (w) − (1 − β)[π S (w) − dS ]. 9
(11)
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Using the above expression, we find: (12)
π 1 (w) − T = (1 − β)[π S (w) + π 1 (w) − dS ].
(13)
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π S (w) − dS + T = β[π S (w) + π 1 (w) − dS ];
Substituting (12) and (13) into (10), 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: wLE =
a(2 − γ)(1 − γ)γ + c(4 + γ(2 − γ − 3γ 2 )) . 2(2 + 2γ − 2γ 2 − γ 3 )
(14)
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It can be confirmed that wLE > c. In other words, in contrast to the no entry case, when firm S enters into the final products market, the wholesale price exceeds the input’s marginal cost; there is an inverse input pricing effect in place. Why is that? Initially, one might think that this result is driven by firm S’s incentive to ‘raise rival’s cost’ in order to increase its own market share in the final goods market. However, this is not
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so here. As we saw above, the wholesale price is chosen in order to maximize the joint profits of firm S and firm 1 and not the profits of firm S alone. The two firms manage to
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behave as a multi-product firm through the setting of the wholesale price. But why are their joint profits higher when the wholesale price exceeds the marginal cost? Firm S’s entry into the final goods market intensifies downstream competition. We refer to this as
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the competition intensification effect of licensing. Firm S and firm 1 alleviate the negative impact of the competition intensification effect on their joint profits through the setting of
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a higher wholesale price that leads them to produce lower joint output. In other words, the licensor and the licensee set the wholesale price in a pro-collusive way.
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It remains to determine the presence or absence of licensing incentives in the first stage of the game. We can obtain the equilibrium fixed fee T LE after substituting (14) into (11).
In turn, substituting T LE and wLE into (12) and (13), we can also obtain the gross from
F equilibrium profits of firm 1 and firm S. For the reasons explained in subsection 3.1, firm 1 fully extracts, through F , firm S’s profits: F LE = π S (wLE ) + T LE . Therefore, firm 1’s net equilibrium profits (included in Table 2 of the Appendix) in the licensing and entry case are: π LE = π 1 (wLE ) + π S (wLE ). Comparing π LE with π B 1 1 1 , we find that firm 1 has incentives to license its input technology even though licensing reinforces competition.13 13
If firm 2 could also offer a licensing agreement to firm S and the latter could sign only one licensing
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Proposition 2 When firm S enters into the final products market, firm 1 always licenses its input technology. The intuition is as follows. As mentioned above, licensing, when it is accompanied by entry,
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gives rise to the competition intensification effect and the inverse input pricing effect. These effects clearly decrease the profits that firm 1 obtains from its own sales in the final products market. Thus, in the absence of a licensing fee, firm 1 would never opt for licensing in the entry case. However, in addition to the competition intensification effect and the inverse input pricing effect, licensing, when it triggers entry, also brings about a business stealing
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effect and a market expansion effect. The former refers to the fact that firm 2’s output falls as the number of firms in the market increases. In other words, when firm S enters into the final goods market, it ‘steals’ part of the sales and market share of firm 1’s rival. The market expansion effect refers to the fact that firm S’s entry results in an increase in the number of differentiated final products and, thus, in an increase in product variety that in turn expands the demand in the final products market.14 Both of these effects augment the
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joint profits of firm S and firm 1 that the licensor enjoys, making licensing profitable. The main reasoning of the above finding resembles the reverse of the ‘merger paradox’
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found in the merger literature. In their seminal paper, Salant et al. (1983) demonstrated that Cournot competitors do not want to merge because their non-merged rival(s) will react
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to the merger-induced decrease in competition by increasing their output. Accordingly, licensing with entry can be seen as a situation where one of the firms splits profitably into two firms - a reverse merger. However, the firms in our setting, unlike in Salant et al.
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agreement, competition between firm 1 and firm 2 would drive the licensing fee down. This means that the licensor would not be able then to fully extract its joint profits with the licensee and, in turn, that the incentives for licensing, both with and without entry, would be weaker. The analysis is available from the
AC
authors upon request. 14 The market expansion effect appears to be present in the Boeing/Mitsubishi case. Mitsubishi is about to
introduce the Mitsubishi Regional Jet (MRJ) - a new and differentiated product in the market for short-haul passenger aircrafts known as ‘regional jets’. In particular, the MRJ will come in versions seating roughly 70-90 passengers, while Boeing and Airbus’ aircrafts seat over 100 passengers. Demand for regional jets has picked up after the MRJ made its maiden flight in November 2015. In fact, Mitsubishi already has 243 orders and 204 options for these jets. According to a newspaper article (Mitsubishi Aims for the Sky After Jet Takes Off, The Wall Street Journal, (November 11, 2015)), “a consulting firm estimates that carriers will order 4,360 regional jets through 2034 and it is predicted that Mitsubishi will capture 27% of that market.” For more on this see e.g., Can Mitsubishi Heavy Industries’ MRJ Regional Jet Lift It To A ‘Buy’ ?, Forbes (October 20, 2014), Japanese Planemaker in Talks for Major Deal, Financial Tribune (July 13, 2016).
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(1983), have differentiated products and, importantly, they are affected by input pricing. In fact, input pricing works in such a way that the licensing incentives are stronger when the licensor and the licensee are also vertically related (vertical licensing) than when they are only horizontally related (horizontal licensing). Intuitively, horizontal licensing - a reverse
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merger in a one-tier market - results in the competition intensification effect, the business stealing effect and the market expansion effect.15 It does not, however, result in the inverse input pricing effect. Thus, it does not allow the licensor and the licensee to alleviate the negative competition intensification effect and to behave in a pro-collusive way. It follows that input pricing - the vertical contract - is an instrument that can allow the firms involved
3.3
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in vertical licensing to behave in a pro-collusive way, strengthening the licensing incentives.
The Impact of Entry
Having explored the licensing incentives both with and without entry, we are now able to
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characterize the impact that entry has on them.
Proposition 3 The entry of firm S into the final products market reinforces firm 1’s li-
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censing incentives.
Interestingly, when the licensee enters into direct competition with the licensor, there are more incentives for licensing. Why is that? The entry of the licensee increases the intensity
PT
of competition faced by the licensor. This - the competition intensification effect - is clearly a negative effect for the licensor. At the same time though, the entry allows the licensor
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to steal away market share from its rival (firm 2) as well as to enjoy a larger market size. These effects - the business stealing effect and the market expansion effect - augment firm 1’s
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profits and, along with the entry’s inverse input pricing effect, which mitigates the negative competition intensification effect, render entry desirable.16 As Proposition 4 states below, entry also alters the impact that product differentiation
has on the licensing incentives. 15 16
For a detailed analysis of entry in a one-tier market, see e.g., Mankiw and Whinston (1986). Tyagi (1999) and Mukherjee and Zhao (2017) also demonstrate that entry can raise the profits of the
incumbent(s). However, they do not focus on licensing, they consider different settings (in Tyagi, 1999, the downstream entrant is not present in the upstream market, while in Mukherjee and Zhao, 2017, there are no vertical relations), and the driving forces of this result differ substantially from ours.
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Proposition 4 An increase in product differentiation has a negative impact on the licensing incentives when firm S does not enter into the final products market and a positive one when it enters.
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In the no entry case, the higher product differentiation is, the higher is the wholesale price; hence, the smaller is firm S’s subsidy to firm 1. In other words, the weaker market competition is, the lower are firm S’s incentives to enhance the competitive position of its customer by decreasing the latter’s variable cost and, thus, the smaller is firm 1’s efficiency enhancement. Therefore, in the no entry case, due to the intensity of the input pricing effect, licensing incentives exist even in markets with products that tend to be homogeneous and
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in fact are stronger in such markets than in markets with differentiated products.
In the entry case on the other hand, a decrease in product differentiation has two negative implications for the licensor: it enhances the competition intensification effect and it weakens the market expansion effect. In particular the relationship between the equilibrium wholesale price and product differentiation is U-shaped: ∂wLE /∂γ < 0 if and only if
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γ ≥ 0.438. Intuitively, an increase in wLE decreases the negative competition intensification
effect. When, however, competition is already too fierce, a (further) increase in wLE is not
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pursued since it can lead to firm 1’s foreclosure. The latter is not desirable in the presence of firm 2 in the market because while it will not allow firm S to achieve the monopoly profits, it will allow firm 2 to take advantage of it, by increasing its market share.17 As a consequence,
PT
when licensing is accompanied by entry, licensing incentives are stronger in markets with more differentiated products. Still, licensing arises even in markets with products that tend
CE
to be homogeneous. In fact, in the latter case, wLE equals c, firm 1 is not foreclosed, and licensing with entry coincides with a reverse merger in a one-tier market, which as we know
AC
(Salant et al., 1983) is more profitable than no licensing (merger). Firm 1’s preference of entry over no entry however does not hold when products tend to be homogeneous; firm 1 is indifferent then between entry and no entry. This is so because the input pricing effect makes licensing without entry preferable to no licensing and is stronger when γ tends to 1. Since under licensing with entry, firm 1 and firm S use the same input technology, one might think that their final products differ less between them than they differ from firm 2’s final product. We can capture this possibility in our model, simply by assuming that 17
For a review of the market foreclosure issues that arise in the presence of vertical integration, see e.g.,
Rey and Tirole (2007). Note that, as we explain in Section 6, if firm 2 was not in the market, firm 1 would be foreclosed but only when products tend to be homogeneous.
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while the degree of interbrand differentiation among firm 2’s product and the products of firm 1 and S is γ, the degree of intrabrand differentiation among the products of firm 1 and firm S is given by δ, with 0 < γ < δ < 1. In such a case, as expected, the competition intensification effect is stronger and the market expansion effect is weaker.
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The business stealing effect is also weaker since the fact that the entrant competes more fiercely with its licensor induces firm S to produce less than firm 2. It follows that the licensing incentives are weaker when intrabrand differentiation is smaller than interbrand differentiation. Importantly though, they are again always present, due almost exclusively now to the presence of the business stealing effect. In the extreme case in which the final
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products of firm 1 and firm S tend to be homogeneous (δ tends to 1), the market expansion effect disappears and the competition intensification effect is even stronger. At the same time though, the inverse input pricing effect is also stronger; firm 1 and firm S use the wholesale price to soften the more intense competition among them. Still, even then firm 1 is not foreclosed because, as explained above, through foreclosure, firm S will not make
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monopoly profits and firm 2 will increase its market share. This contrasts with Ordover and Shaffer (2007) who find that foreclosure arises when interbrand differentiation exceeds
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intrabrand differentiation. This is so mainly because in their setting, the wholesale price cannot sufficiently soften the increased competition; the non-integrated downstream firm is not already in the market and, for foreclosure not to occur, the incumbent should charge a
PT
sufficiently low wholesale price so that the entrant covers its fixed entry cost. Summing up, in the absence of intrabrand differentiation, the stronger competition intensification effect
CE
is mitigated by the stronger also inverse input pricing effect, and the business stealing effect again renders licensing desirable for firm 1. Furthermore, when intrabrand differentiation is lower than interbrand differentiation,
AC
the licensing incentives continue to be stronger with than without entry because of the business stealing effect and the market expansion effect which, although they are weaker, still exist. In fact, even when there is no intrabrand differentiation and the market expansion effect is absent, firm 1 has no strict preference for no entry; just as when γ tends to 1, the business stealing effect makes firm 1 indifferent between entry and no entry.
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4
Welfare Implications
We have already seen that vertical licensing is desirable from firm 1’s viewpoint. Next, we
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examine whether it is also desirable from a welfare viewpoint. Proposition 5 Vertical licensing both with and without the entry of firm S into the final products market always has a positive impact on consumer surplus and on total welfare. Its impact is larger with entry than without entry.
Vertical licensing is beneficial both for the consumers and for the economy as a whole.
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Intuitively, the licensing’s positive impact on consumer surplus is due to firm 1’s subsidization in the no entry case and to the increase in product variety and competition intensity in the entry case. In turn, licensing enhances total welfare through its positive impact on consumers and on the licensor’s profits that outweigh its negative impact on firm 2’s profits. As we demonstrate in Section 6, licensing’s positive welfare impact can be present
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even when the licensor has a dominant position in the market and, in particular, when it is the only incumbent in the market and/or it has a cost advantage relative to the other incumbent. Moreover, licensing with entry can have a positive impact on consumer and
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total welfare also when intrabrand differentiation is smaller than interbrand differentiation, although the magnitude of its impact is smaller then due to the weaker market expansion
PT
effect.
As Proposition 5 informs us, vertical licensing is even more desirable from a welfare
CE
viewpoint when it triggers entry into the final goods market. Intuitively, in the entry case, although firm 1 faces higher cost, competition is fiercer and the market is larger. This also holds when intrabrand differentiation is smaller than interbrand differentiation. In fact, as
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we show in Section 6, there are cases (e.g., when competition is in prices or when a wholesale price contract is used), in which licensing increases welfare in the entry case and decreases it in the no entry case. Therefore, the licensee’s entry into multiple production stages of a market can even be the main driving force of the positive welfare implications of licensing. Recently, the EU and the US both revised their rules for the assessment of technology licensing agreements under the EU competition law and the US antitrust law, respectively. The new regulations continue to reflect the view that licensing, by facilitating technology diffusion, is in most cases pro-competitive. Based on this view, a block exemption applies
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to all the licensing agreements among firms with limited market shares.18 Our analysis puts forward an additional and novel channel through which licensing can be pro-competitive even in cases in which the firms involved in licensing have large market shares. It demonstrates that vertical licensing, by triggering entry into more than one stage of a market, can
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generate more intense market competition and thus can (further) increase welfare.
5
Common Supplier and Common Licensee
So far, we have assumed that only firm 1 can opt for licensing, and that when it does, firm
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2 cannot source the input from the licensee - firm S. These assumptions could make one wonder what would happen if, alternatively, firm S could become the common supplier of the two incumbents, through licensing by just one of them, or their common licensee.19 Next, we explore these possibilities.
Common Supplier
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5.1
We examine now what happens when, after the licensing agreement between firm 1 and firm S is signed and before the contracting stage, firm 2 decides whether it will source
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the input from firm S and commits to its decision. A consequence of this is that in the subgame in which firm 2 decides to trade with firm S, the latter bargains in stage 2 with
PT
two downstream firms. To model this multilateral bargaining game, we invoke the Nash equilibrium of simultaneous generalized Nash bargaining games; we assume that firm S
18
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bargains with each firm i, with i = 1, 2, simultaneously and separately over (wi , Ti ).20 To According to the new EU regulation, Regulation N. 316/2014, in the case of licensing agreements between
non-competitors, the block exemption applies when the individual market share of each party does not exceed
AC
30%. According to the US Antitrust Guidelines for the Licensing of Intellectual Property (updated on August 12, 2016 by the US Department of Justice and the Federal Trade Commission), the US Agencies will not challenge an agreement if the licensor and the licensee collectively account for no more than 20% of each relevant market significantly affected by the licensing restraint. 19 If the inputs of the two firms do not differ significantly, firm S could produce both of them once it
obtains firm 1’s input production technology through licensing. If instead they differ significantly (e.g., they have different technical specifications), their production technologies could also differ and firm S might be unable to produce firm 2’s input unless firm 2 also licenses its own input production technology to it. 20 This assumption is standard in situations with multilateral contracting (e.g., Cremer and Riordan, 1987, Horn and Wolinsky, 1988, Hart and Tirole, 1990, O’Brien and Shaffer, 1992, McAfee and Schwartz, 1994 and 1995, Rey and Verg´e, 2004, Milliou and Petrakis, 2007, Alipranti et al., 2014).
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avoid the multiple equilibria that can arise due to the multiplicity of the beliefs that the downstream firms can form when they receive out-of-equilibrium offers, we impose pairwise proofness on the equilibrium contracts.21 Moreover, in order to ensure that all the firms face a non-negative marginal cost in all the cases under consideration, we assume that a ≤ 3c.
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We find that firm 2 always produces the input in-house and in turn that the licensing incentives and implications are exactly the same as in the main analysis.22 In particular, in the no entry case, when firm S acts as a common supplier, it subsidizes both firms, wiCN < wLN < c, because it suffers from the ‘commitment problem’ (e.g., Milliou and Petrakis, 2007, Rey and Tirole, 2007): when it trades with firm i, it cannot commit to not
when β < β(γ) ≡
γ3 ; 4−2γ−2γ 2 +γ 3
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offering better trading terms to firm j. In fact, because of this, firm S’s profits are negative hence, when β < β(γ), it trades only with firm 1. The same
holds when β > β(γ), but for a different reason: firm 2 decides then to produce in-house since otherwise firm S would extract a large share of its profits through T2 . In the entry case, when firm S acts as a common supplier, the wholesale prices are higher than in the
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main analysis, wiCE > wLE > c, because when they are set all the firms in the market, and not only firm 1 and firm S, behave as a multi-product monopolist. Still, firm 2 always
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decides to produce the input in-house in order to have a cost-advantage relative to firm 1 and to fully enjoy its own profits - firm S does not partially extract them through T2 . If firm 2 did not commit to sourcing the input from firm S, it would have to be compen-
PT
sated through T2 for its outside option to produce in-house. Although this would increase its incentives to source the input from firm S, firm 1’s licensing incentives would always be
CE
present. In fact, in the entry case, firm 1’s licensing incentives would be higher than in our main analysis because firm 2 would then source the input from firm S and thus the inverse input pricing effect would be stronger. However, the stronger inverse input pricing effect
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would restrict the downstream efficiency and the market expansion effect and, in turn, the extent of licensing’s positive welfare implications with entry. 21
That is, we require that a contract between firm S and firm i be immune to a bilateral deviation of firm
S with firm j, with i, j = 1, 2 and i 6= j. For more information on this, see e.g., O’Brien and Shaffer (1992), McAfee and Schwartz (1994 and 1995), Milliou and Petrakis (2007). 22 The detailed equilibrium analysis is included in the Appendix.
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5.2
Common Licensee
Next, we explore what happens when firm 2 can also opt for licensing to firm S, assuming that otherwise it cannot source its input from firm S.23
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When firm 2 decides, after observing if firm 1 has signed a licensing agreement with firm S, whether to license its input technology to firm S, we find that at least one incumbent always opts for licensing. We also find that both of them do so only when β is sufficiently high and firm S enters into the final goods market. Intuitively, both with and without entry, firm 2 does not opt for licensing when its rival does and firm S’s bargaining power is sufficiently low because it is foreclosed from the market then - firm S optimally trades with
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one licensor to avoid the ‘commitment problem’. However, firm 2 does not opt for licensing in the no entry case even when it is not foreclosed, because it then has to compensate firm S for the lower profits that it makes due to the ‘commitment problem’. In the entry case instead, when firm 2 is not foreclosed, it opts for licensing similarly to its rival mainly because firm S’s profits, part of which firm 2 extracts, are then larger.24 We should note
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however that the licensing incentives are weaker under licensing by both incumbents than under licensing by just firm 1, since in the former case firm 1 is unable to fully extract
ED
the licensee’s profits. Moreover, the positive welfare implications of licensing are weaker under licensing by both incumbents due to the stronger inverse input pricing effect. Still, entry continues to have a positive impact on the licensing incentives even when it results in
23
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licensing by both incumbents.25
In the toys market, Mattel has been both a common licensee of Walt Disney and Warner Bros and a
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competitor. In 2000, Walt Disney and Warner Bros licensed to Mattel the production of the Princess dolls (e.g., Snow White, Cinderella, Rapunzel) and of the Harry Potter branded dolls respectively. A few years later, Mattel launched its own goth-themed dolls, Monster High, and its princess-themed dolls, Ever After
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High, based upon characters from fairy tales and fantasy stories, as well as created its own film production studio. For more information, see e.g., The Media Business Advertising: Dragons and Flying Brooms, New
York Times (March 1, 2001), and The $500 Million Battle Over Disney’s Princesses, Bloomberg (December 17, 2015). In the smartphone manufacturing market also, for a number of years Samsung has been a licensee and a rival of both Nokia and Apple. For more information, see e.g., Nokia Expands Licensing Agreement with Samsung, Reuters (July 13, 2016). 24 Details are available in the Appendix. Note that if firm S committed to trading with its licensor(s) (e.g., if it had to pay a high enough penalty in case of violation of the licensing agreement), in the no entry case the outcome would be the same, while in the entry case both firms would always opt for licensing. 25 As mentioned in Section 2, we abstract from explanations for licensing which are based on the licensee’s efficiency. We should note though that licensing by both incumbents to the same licensee would be more
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When, instead, the two firms decide simultaneously and separately whether they will opt for licensing and make their (unobservable) offers at the same stage, in the no entry case, there are two asymmetric equilibria in pure strategies with licensing by just one of them (firm 1 or 2) and with the same licensing fee as in our main analysis. Intuitively, the
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firm that does not opt for licensing does not want to deviate to licensing because if it does, it will be foreclosed or it will be unable to extract sufficiently high profits. The same holds in the entry case, unless β is sufficiently high. There is an equilibrium then, not necessarily unique, in which both firms opt for licensing.
If, alternatively, the two incumbents could license their input technologies to two dif-
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ferent licensees, then both of them would opt for licensing in the no entry case. This is so because both would be subsidized (e.g., Jansen, 2003). In the entry case, in contrast, if both firms opted for licensing, then one of the licensors would foreclose its licensee when products were too close substitutes; otherwise, there would be four firms in the market and the competition intensification effect would be quite strong. Thus, in such a case, entry
Extensions - Discussion
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6
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could reinforce firm 1’s licensing incentives by deterring licensing by its rival.
In this section, we discuss briefly a number of further extensions of our main model to
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extract some additional insights. (i) Wholesale Price Contract
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We consider here what happens if input trading occurs through a wholesale price contract that includes only w. For simplification reasons, we assume that firm S makes a take-it-orleave-it offer to firm 1 regarding w.
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Due to the absence of T , firm S is not able to extract part of firm 1’s profits and double
marginalization and, in turn, the inverse input pricing effect, emerge under licensing with
and without entry, w bLN > c and w bLE > c.
Proposition 6 When vertical trading takes place through a wholesale price contract, firm 1 licenses its input technology if and only if firm S enters into the final products market. likely if it led to an increase in the latter’s efficiency, due e.g., to complementarities in know-how. This is so mainly because the increased efficiency would have a positive impact on input pricing and in turn on industry profits.
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When trading is through a wholesale price contract, licensing does not arise in equilibrium unless it is accompanied by entry. Intuitively, due to the inverse input pricing effect, the licensor faces higher cost under licensing. This in turn means that it also faces lower profits. The licensing incentives are restored when entry occurs mainly because of the
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market expansion effect, which is again in place. Note that if there was bargaining over w, the licensing incentives would be even stronger in the entry case, while they would continue to be absent in the no entry case since the equilibrium wholesale prices would be lower due to the licensor’s bargaining power. A straightforward implication of the inverse input pricing effect is that licensing would result in lower consumer and total welfare in the no
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entry case. In the entry case on the other hand, the positive impact of the market expansion effect dominates and licensing is again beneficial for consumers and the economy as a whole. In light of the above, we can draw two conclusions. First, that the contract type used in input trading can be crucial for the licensing incentives and implications. And second, that when input trading takes place through a wholesale price contract, the licensee’s entry
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not only does not discourage licensing, but, in fact, it constitutes its driving force. (ii) Ex-ante Monopoly
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We have assumed in our analysis that there are initially two vertically integrated incumbents in the market. We consider here the alternative case in which initially firm 1 is a monopolist. In the no entry case, since downstream competition is absent, firm S does not have
PT
incentives to increase the aggressiveness of its downstream customer. Instead, as it is well established in the literature, firm 1 and firm S set wM N = c and they achieve the profits of
CE
a monopolist just as in the benchmark case of no licensing. In the entry case, there is a single vertically integrated firm, firm S, trading with the non-integrated downstream firm 1. Maximization of their excess joint profits leads to a(2−γ)2 γ+c(8−γ(4+γ(2+γ))) 8−6γ 2
AC wM E =
> c, with
∂wM E ∂γ
> 0. If their products were homoge-
neous, as Reisinger and Tarantino (2015) also note, wM E would be such that firm 1 would be foreclosed from the market but would obtain, through F , the monopoly profits just as in the benchmark case of no licensing. When instead products are differentiated, even slightly, foreclosure is not profitable (Reisinger and Tarantino, 2015). This holds even though now, the negative competition intensification effect is stronger than in our main analysis; firm S’s entry transforms the final goods market from a monopoly to a duopoly. In other words, the reasoning of the reverse merger does not apply here and in turn the presence of licensing
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incentives is more striking. Intuitively, under no licensing, firm 1 achieves the profits of a single-product monopolist. A multi-product monopolist however makes higher profits. Under licensing and entry, firm S and firm 1 set the wholesale price in a collusive way, achieving profits that are almost equal to those of a multi-product monopolist and exceed
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the profits of a single-product monopolist.
Proposition 7 When firm 1 is initially a monopolist in the market, it licenses its input technology if firm S enters into the final products market. Otherwise, it is indifferent between licensing and no licensing.
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In terms of welfare, licensing without entry - by not altering the market outcomes leaves both consumer and total welfare unaffected. In contrast, licensing with entry, just as in our main analysis, by increasing firms’ profits and enhancing downstream competition, improves consumer and total welfare. (iii) Unobservability of Contract Terms
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The vertical contracting literature has stressed the importance of the observability of the contract terms in order for the contract used by a vertical chain to serve as a form of binding
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precommitment resulting in advantages relative to rivals. In fact, it has shown that when the terms of two-part tariffs are unobserved, then in settings with competing vertical chains (e.g., Arya and Mittendorf, 2011) or with a common supplier (e.g., O’Brien and Shaffer,
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1992, McAfee and Schwartz, 1994), contracts play no role; the wholesale prices are set equal to the input’s marginal cost and the vertically integrated outcome is reproduced.
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In our setting, under licensing without entry, just as in Katz (1991), there is a vertical chain and a vertically integrated firm, and one contract: (w, T ) between firm S and firm 1. Given this, we can have only full observability of the contract terms as in our main model or
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asymmetric unobservability in which only firm 2 cannot observe w. In the latter case, in the last stage, profit maximization leads to the following best responses: q1 (q2 , w) =
and q2 (q1 ) =
a−c−γq1 . 2
a−w−γq2 2
Since however firm 2 does not observe w, it forms beliefs regarding
w and in turn q1 , denoted by w and q 1 , respectively. Given this, we substitute firm 1’s best a(2−γ)−2c+γw . In turn, substituting q2 (w) into 4−γ 2 2 2 2a(2−γ)−w(4−γ )+2γc−γ w . In the previous stage, the bargaining 2(4−γ 2 )
response into q2 (q 1 ), and we obtain: q2 (w) = q1 (q2 , w), we get: q1 (w, w) =
problem is given again by (5), with the difference that now instead of q1 (w) and q2 (w), we have q1 (w, w) and q2 (w). Solving for w, we obtain wU N = c.26 In equilibrium, firm 26
The same result can also be found in Pagnozzi and Piccolo (2012) under unobservability of contract
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2’s expectations must be fulfilled, wU N = w. Therefore, under licensing without entry and unobservability of the contract terms, the equilibrium quantities coincide with the ones in the benchmark case without licensing, q1B and q2B . Since firm 1 extracts through F firm S’s profits, it follows that its profits also coincide with those in the no licensing case π B 1 and
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thus that it is indifferent between licensing without entry and no licensing.
Following a similar procedure in the licensing with entry case under asymmetric unobservability, we find the equilibrium wholesale price: wU E = that
wU E
>
wLE
aγ(2−γ)2 +2c(4−γ 2 (2+γ)) . 8+γ(4−γ(8+γ))
Note
> c. This is so because firms 1 and S, even when their rival cannot
observe w, set w to maximize their joint profits; they have incentives to set the wholesale
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price above the input’s variable production cost to alleviate the competition between them the competition intensification effect. In other words, in the entry case, the licensor and the licensee can use the vertical contract, even when it is unobserved by the other incumbent, in their favor. It follows that just as in the main analysis, licensing incentives are always present in the entry case. In fact, under asymmetric unobservability of the contract terms,
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entry can constitute licensing’s driving force. (iv) Reverse Timing
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In our main model, the input trading terms (w, T ) are determined after the licensing agreement has been signed. In the opposite case in which (w, T ) are determined in stage 1, while the licensing decision along with the determination of the licensing fee takes place in stage
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2, our results remain exactly the same. To see the above, consider the no entry case with the reverse timing. In stage 2, firm
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1 optimally offers F (w, T ) = π S (w) + T = (w − c)q1 (w) + T , with q1 (w) given by (1), and firm S accepts the offer. In the same stage, firm 1 decides to make such an offer if and
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only if π 1 (w) − T + F (w, T ) > π B 1 . Taking this into account, in stage 1, firm 1 and firm
S end up maximizing their joint profits, subject to the constraint (w − c)q1 (w) + T ≥ 0. The constraint is necessary since otherwise firm S will not supply the input to firm 1 in the
continuation of the game. The wholesale price that maximizes the joint profits of firm 1 and firm S is again wLN and in turn firm 1’s profits are π LN 1 . This logic also applies in the entry case resulting again in the equilibrium values of the main analysis. Note that we would also have obtained the same results in the case in which F and (w, T ) were determined in the
same stage. terms in various market structures including ours.
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(v) Cost Asymmetry One might wonder what would happen if the two incumbents were asymmetric. To examine this, we assume that firm 1 and firm 2 face initially marginal cost c and c2 , respectively, with c < c2 , and we find that the results of our main model are qualitatively robust. Moreover,
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we find that the licensing incentives are stronger when the licensor enjoys a cost-advantage than when it does not and that the positive impact of licensing on consumer and total welfare is larger under entry. This occurs mainly because when the licensor enjoys a cost advantage, both the input pricing effect and the market expansion effect are stronger. (vi) Bargaining over the Licensing Fee
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We consider here what happens if the licensor bargains with the licensee, in a Nash bargaining fashion, in stage 1 over the licensing fee with the same bargaining powers as in the bargaining over the input’s trading terms in stage 2. When the bargaining power of firm S is positive, firm 1 is not able to fully extract firm S’s profits through F . Still, even then, firm 1 always opts for licensing both with and without entry. This holds because during
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the negotiations over F , firm S has to compensate firm 1 for the profits that it would make without licensing. Because of this, in the extreme case in which firm 1 has no bargaining
ED
power, it is indifferent among licensing and no licensing. In all other cases, it prefers licensing to no licensing, and the higher its bargaining power is, the more it prefers licensing. Since the allocation of the licensing fee does not affect consumer and total welfare, our
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conclusions regarding the welfare implications of licensing remain unchanged. (vii) Licensing through Royalty
CE
One might wonder what happens if licensing takes place through a per-unit of output royalty, r ≥ 0, instead of through a fixed licensing fee. When a royalty is used, firm 1 is unable to
AC
fully extract firm S’s profits. Moreover, firm S’s marginal cost is then r + c instead of c. The higher marginal cost of firm S can translate into worse input sourcing terms for firm 1 and, thus, into lower profits for firm 1 from its own sales in the final goods market. Not surprisingly thus, in the no entry case, firm 1 always optimally sets rN = 0. Given this, does it have incentives to license its technology? The answer is already provided in our main analysis: when F = 0, firm 1 opts for licensing if and only if its bargaining power is sufficiently high and the licensee does not enter into the final goods market. In the entry case, when the royalty is imposed only on firm 1’s output, then again rE = 0. But when it is imposed either only on firm S’s output or on both firm S’s and firm
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1’s output, rE > 0. When the latter occurs, in contrast to what happens when licensing is through a fixed fee, licensing does not arise in equilibrium. This occurs, first, because the market expansion effect is weaker when rE > 0, and second, because firm 1, by not extracting firm S’s profits, it cannot take full advantage of the market expansion effect.
CR IP T
It follows that the form of the licensing contract, whether it is a fixed licensing fee or a variable royalty, can affect the licensing incentives. It also follows that when licensing is through a royalty, entry can discourage licensing. This is in sharp contrast to our main conclusion. Nevertheless, if firm 1 was in the position to choose the licensing contract type, it would choose a fixed licensing fee contract over a royalty contract. This choice would be
AN US
aligned with the interest of consumers and the economy as a whole since the positive impact of licensing on consumer and total welfare is larger when licensing takes place through a fixed licensing fee. Stated differently, both from the licensor’s viewpoint and from a welfare viewpoint, vertical licensing is preferable when it occurs through a fixed licensing fee. (viii) Downstream Price Competition
M
Next, we discuss what happens when firms compete in prices in the final products market. As is well known from the literature, prices, in contrast to quantities, are strategic
ED
complements. Because of this, under price competition, in the no entry case, firm S does not wish its downstream partner to behave aggressively in the final market - it charges a wholesale price that exceeds its marginal cost. Still, similarly to our main analysis, firm 1
PT
always licenses its input technology. In fact, it licenses its technology even for free if firm S’s bargaining power is low enough. Why is that? As the literature on vertical separation (e.g.,
CE
Bonanno and Vickers, 1988, Lin, 1988, Gal-Or, 1990, Cyrenne, 1994) has demonstrated, vertical separation (vertical licensing in our case) dampens downstream competition, lead-
AC
ing to higher downstream profits that the upstream firm (the downstream firm in our case) extracts through the fixed fee. In the entry case, firm 1 licenses its input technology, but only if the final products are
not very close substitutes (γ < 0.979). Its licensing incentives are driven now by the market expansion effect alone; the business stealing effect is absent. Competition in the market is fiercer under price competition than under quantity competition. Hence, the competition intensification effect of licensing is stronger in the former case and dominates its market expansion effect when products are close substitutes and competition is already quite fierce. This implies that in markets in which firms’ products are quite similar, vertical licensing,
24
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when it is accompanied by entry, is more likely to be observed when firms compete in quantities than when they compete in prices. It follows that under downstream price competition, the impact of entry on the licensing incentives is again positive unless the final products are too close substitutes. Moreover,
CR IP T
licensing continues to be welfare-enhancing but only when it triggers entry and, in fact, it enhances welfare then more under price competition than under quantity competition.27 In the no entry case, licensing is welfare-detrimental due to the increase that it causes through the input price in the licensor’s cost. (ix) Licensing without Commitment
AN US
In our main model, after the signing of the licensing agreement, firm 1 commits to sourcing the input from the licensee. We relax this assumption now and examine what happens when firm 1 continues to have the option of producing the input in-house under licensing. In such a case, firm 1 has an outside option during the negotiations with firm S in stage 2: the profits that it would make with in-house input production. Since its outside
M
option does not depend on w, it does not affect the latter; it affects only T . Specifically, since firm S needs to compensate firm 1 for its outside option, T is lower now than in the
ED
commitment case both with and without entry. Recall that firm 1 manages to extract all of firm S’s profits through the licensing fee. Hence, the change in T does not affect our main conclusions. The only difference is that in the no entry case now, when licensing is for free,
PT
firm 1 always opts for licensing and not only when β is sufficiently low, since firm S always
CE
has to compensate firm 1 for its outside option.28
7
Concluding Remarks
AC
We have examined the incentives of a vertically integrated incumbent to license its input technology to an external firm. We have done so in a setting in which, after the signing of the licensing agreement, the licensor sources the input from the licensee and the licensee 27
H¨ offler and Schmidt (2008) also find that entry has a positive impact on total welfare under downstream
price competition, both spatial and non-spatial, even in the absence of the market expansion effect, but they point out that under spatial price competition, entry can decrease consumer surplus. 28 We have also examined whether, in the case of licensing and entry, firm 1 is better off when it produces the input in-house or when it does not commit and thus it has both the option of in-house production and of sourcing it from S. We have found that, due to the inverse input pricing effect, it prefers the latter. The detailed analysis of this as well as of the rest of the extensions is available from the authors upon request.
25
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can enter into the final goods market and compete with the licensor. We have shown that licensing emerges in equilibrium not only when the licensee does not enter into direct competition with the licensor, but also when it enters. In fact, we have shown that when the licensee enters into the final products market, although competition
CR IP T
becomes more intense, the licensing incentives are stronger. Intuitively, in the absence of entry, vertical licensing is motivated by the low input price at which the licensor sources the input from the licensee. The low input price translates into a cost advantage and, in turn, into larger market share and profits for the licensor. When, instead, the licensee enters into the final goods market, first, the licensor competes with more firms than without licensing,
AN US
and second, it faces a higher cost - it pays an input price that exceeds the input’s marginal cost but alleviates the increased competition. The licensor opts for licensing because the entry of the licensee results in the expansion of the final goods market and in business stealing from the rival incumbent firm.
Our welfare analysis has revealed, first, that vertical licensing is always beneficial both
M
for the consumers and for the economy as a whole, and second, that it is even more beneficial when it is accompanied by downstream entry. Importantly, it has indicated that vertical
ED
licensing can enhance welfare even more than horizontal licensing, by triggering entry into more than one market stages, and thus, by generating more intense competition in multiple production stages. Since vertical licensing can also be interpreted as vertical separation, it
PT
follows that our analysis offers arguments in favor of vertical separation and against vertical integration: vertical separation can be pro-competitive by enhancing the downstream effi-
CE
ciency through input pricing or by triggering the downstream expansion of the disintegrated input supplier, and thus, by increasing product variety and market competition. Extending our main analysis in various directions, we have shown that the entry of the
AC
licensee into the final products market can also reinforce the licensing incentives in the case in which all the incumbents, and not only the licensor, source the input from the licensee, as well as in the case in which downstream competition is in prices. Importantly, we have shown that there are instances in which vertical licensing would not emerge without the entry of the licensee into the final goods market. This holds when the licensor and the licensee trade via a wholesale price contract, when the contract terms are unobservable, or when the licensor is initially a monopolist. Summing up, we have provided an explanation for the commonly observed practice of vertical licensing in markets where licensing can transform the licensee not only into 26
ACCEPTED MANUSCRIPT
an input supplier but also into a direct competitor of the licensor in the final products market. Our explanation lies in strategic considerations and not in exogenously assumed efficiencies. Clearly, if we had assumed that the incumbent produces the input at a lower cost than the potential licensee (e.g., due to complementary skills), in-house production
CR IP T
could also arise in equilibrium (Arya et al., 2008a). In-house production could also arise if we had incorporated into our analysis factors such as unobservability of the input’s quality and production cost, costly investments in input improvement and the use of incomplete contracts (e.g., Williamson, 1971, Grossman and Hart, 1986). The joint consideration of
8
Appendix q1B = q2B =
a−c 2+γ ;
(a−c)2 ; q1LN = (a−c)(2−γ) ; q2LN = (a−c)(4−γ(2+γ)) (2+γ)2 2(2−γ 2 ) 4(2−γ 2 ) (a−c)(4−γ(2+γ))2 (1−β)(a−c)2 (2−γ)2 LN LN ; π2 = −T = 8(2−γ 2 ) 16(2−γ 2 )2 2 2 β(a−c) (2−γ) (a−c)2 (2−γ)2 LN LN F = ; π 1 = 8(2−γ 2 ) 8(2−γ 2 )
B πB 1 = π2 =
π 1 (q1LN )
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these factors is left for future research.
M
Table 1: Equilibrium Values under No Licensing and under Licensing without Entry (a−c)(4−3γ 2 ) (a−c)(4−2γ−γ 2 ) ; q2LE = qSLE = 4(2+2γ−2γ 2 −γ 3 ) 4(2+2γ−2γ 2 −γ 3 ) (a−c)2 (4−3γ 2 )2 (1−β)(a−c)2 (4−2γ−γ 2 )2 LE LE LE π 1 (q1 ) − T = 8(2+γ)2 (2+2γ−2γ 2 −γ 3 ) ; π 2 = 16(2+2γ−2γ 2 −γ 3 )2 2 2 (2+γ)+β(4−2γ−γ 2 )2 ) (a−c)2 (8−8γ+γ 2 ) ; π LE F LE = (a−c) (16(1+γ)−8γ 1 = 8(2+2γ−2γ 2 −γ 3 ) 8(2+γ)2 (2+2γ−2γ 2 −γ 3 )
ED
q1LE =
PT
Table 2: Equilibrium Values under Licensing with Entry
2 (2−γ) 2 (4+γ)2 2 (6−γ 2 ) (a−c)(4+γ) bLN = (a−c) ; FbLN = (a−c) bLN = (a−c) 2 1 4(2+γ) ; π 8(2+γ) ; π 16(2+γ)2 8(2+γ)2 2) (a−c)(4−2γ−γ 2 ) (a−c)2 (4−2γ−γ 2 )2 qb1LE = 2(8+8γ−3γ b2LE = qbSLE = (a−c)(2−γ)(4+3γ ; π 1 (b q1LE ) = 4(8+8γ−3γ 2 −2γ 3 ) ; q 2 −2γ 3 )2 2(8+8γ−3γ 2 −2γ 3 ) 2 (6−γ)(2−γ) 2 (56+8γ+48γ 2 −6γ 3 −7γ 4 +γ 5 ) (a−c)2 (2−γ)2 (4+3γ 2 )2 (a−c) (a−c) LE LE LE π b2 = 4(8+8γ−3γ 2 −2γ 3 )2 ; Fb = 4(8+8γ−3γ 2 −2γ 3 ) ; π b1 = 2(8+8γ−3γ 2 −2γ 3 )2
a−c 4+2γ ;
qb2LN =
AC
CE
qb1LN =
Table 3: Equilibrium Values with a Wholesale Price Contract
q1M E =
2 2 (a−c)2 M N ) − T M N = (1−β)(a−c) ; F M N = β(a−c) 4 ; π 1 (q1 4 4 2) 2 (1−γ)2 qSM E = (a−c)(4−2γ−γ ; π 1 (q1M E ) − T M E = (1−β)(a−c) 8−6γ 2 4−3γ 2 2 2 −3γ 2 ) 2 2 E = (a−c) (8−8γ+γ ) F M E = (a−c) (4+4β(1−γ) ; πM 1 4(4−3γ 2 ) 4(4−3γ 2 )
a−c MB 2 ; π1 2(a−c)(1−γ) ; 4−3γ 2
q1M B = q1M N =
N = = πM 1
Table 4: Equilibrium Values with Ex-ante Monopoly Common Supplier and Common Licensee (a) Common Supplier
27
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In the no entry case, in the last stage, each firm i chooses its quantity to maximize: π i (qi , qj , wi ) = (a − qi − γqj )qi − wi qi . This results in: qi (wi , wj ) =
a(2−γ)−2wi +γwj . 4−γ 2
Letting wjCN denote the equilibrium outcome of the negotiations of firm S and firm j,
CR IP T
wi is chosen to maximize: max [π S (wi , wjCN ) + Ti + Tj − dS1 (wjCN , TjCN )]β [π i (wi , wjCN ) − Ti ]1−β , wi ,Ti
(15)
where π S (wi , wjCN ) = (wi − c)qi (wi , wjCN ) + (wjCN − c)qj (wi , wjCN ) and π i (wi , wjCN ) = π i (qi (wi , wjCN ), qj (wi , wjCN ), wi , wjCN ). Firm S’s disagreement payoff is dS1 (wjCN , TjCN ) =
(wjCN − c)qjmon (wjCN ) + TjCN , where qjmon (wjCN ) = (α − wjCN )/2. From the first order γ 2 (a−c) , where wiCN < wLN 2(2−γ 2 ) (a−c)(2−γ) . In turn, the equilibrium 2(2−γ 2 )
equilibrium quantities are: qiCN = π 1 (q1CN ) − T1CN
< c. The respective
net profits are:
(1 − β)(a − c)2 (2 − γ)2 ; 8(2 − γ 2 ) (a − c)2 (2 − γ)(−γ 3 + β(2 − γ)(2 − γ 2 )) . 4(2 − γ 2 )2
= π CN = 2
(16)
=
(17)
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π CN S
AN US
conditions of (15), we obtain: wiCN = c −
< 0 if and only if β < β(γ) ≡ Note that π CN S
γ3 . 4−2γ−2γ 2 +γ 3
Given this, when β < β(γ), firm
S does not supply the input to firm 2.
ED
In stage 1(b), firm 2 decides whether it will source the input from firm S: π CN − 2
(a−c)2 ((4−3γ)γ 3 −2β(2−γ)2 (2−γ 2 )) . The difference is positive 16(2−γ 2 ) γ 3 (4−3γ) . However, β 1 (γ) > β(γ); hence, there is no region 2(2−γ)2 (2−γ 2 )
PT
π LN = 2
if and only if β < β 1 (γ) ≡ in which firm 2 decides to
source the input from firm S and the latter does supply it. Thus, under licensing without
CE
entry, our main analysis continues to hold. In the entry case, each firm i, with i, j = 1, 2 and i 6= j, chooses its quantity to maximize: π i (qi , qj , qS , wi , wj ) = (a − qi − γqj − γqS )qi − wi qi . Firm S also chooses its quantity to
AC
maximize: π S (qi , qj , qS , wi , wj ) = (a − qS − γqi − γqj )qS − c(qi + qj + qS ) + wi qi + wj qj . This results in: qi (wi , wj ) =
a(2−γ)−(2+γ)wi +γ(c+wj ) 2(2−γ)(1+γ)
and qS (wi , wj ) =
a(2−γ)−(2+γ)c+γ(wi +wj ) . 2(2−γ)(1+γ)
Letting wjCE denote the equilibrium outcome of the negotiations among firm S and firm
j, wi is chosen to maximize: max [π S (wi , wjCE ) + Ti + Tj − dS2 (wjCE , TjCE )]β [π i (wi , wjCE ) − Ti ]1−β , wi ,Ti
(18)
where π S (wi , wjCE ) and π i (wi , wjCE ) are found after substituting qS (wi , wj ) and qi (wi , wj ) into π S (qi , qj , qS , wi , wj ) and π i (qi , qj , qS , wi , wj ). Firm S’s disagreement payoff is given by dS2 (wjCE , TjCE ) = (a − qSD (wjCE ) − γqjD (wjCE ) − c)qSD + (wjCE − c)qjD (wjCE ) + TjCE , where 28
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qSD (wjCE ) =
a(2−γ)−2c+γwjCE 4−γ 2
and qjD (wjCE ) =
a(2−γ)+cγ−2wjCE 4−γ 2
are the quantities expected to
be produced by firm S and firm j, respectively, when they face wjCE . From the first order a(2−γ)γ+c(2+γ)2 , where wCE > wLE > c. This results 4+6γ (a−c)(2+γ) . In turn, the equilibrium net profits are: 4+6γ
in: q1CE = q2CE =
(a−c) 2+3γ
and qSCE =
CR IP T
conditions of (18), we obtain: wiCE =
2(1 − β)(a − c)2 (2 + 2γ − 2γ 2 − γ 3 ) ; (2 + γ)2 (2 + 3γ)2 (a − c)2 A , 4(2 + γ)2 (2 + 3γ)2
π 1 (q1CE ) − T1CE = π CE = 2 π CE = S
(19) (20)
where A ≡ 16 + 32β + 64γ + 32βγ + 80γ 2 − 32βγ 2 + 16γ 3 − 16βγ 3 − 3γ 4 > 0.
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LE In stage 1(b), firm 2 decides whether it will source the input from firm S: π CE 2 − π2 =
(a−c)2 B , where B ≡ −256β−256γ−768βγ−1024γ 2 −896γ 3 +1664βγ 3 + 16(2+γ 2 )(2+3γ)2 (2+2γ−2γ 2 −γ 3 )2 1056γ 4 + 768βγ 4 + 1728γ 5 − 1152βγ 5 + 128γ 6 − 704βγ 6 − 624γ 7 + 192βγ 7 − 273γ 8 + 192βγ 8 −
32γ 9 + 32βγ 9 < 0. The difference π CE − π LE is always negative; hence, firm 2 always 2 2 produces the input in-house. Thus, under licensing with entry, the main analysis holds.
M
(b) Common Licensee
We focus on the sequential licensing case, in which, we add stage 1(b) in our game, after
ED
stage 1 and before stage 2. In stage 1(b), firm 2, after observing if firm 1 has signed a licensing agreement with firm S or not in stage 1, decides whether to license its own input technology to firm S. In case of licensing, it offers a licensing fee, F2 , to firm S, and, in
PT
turn, firm S accepts or rejects the offer. In the no entry case, in stage 2, in the subgame in which both firms have opted for
CE
licensing, if firm S trades with both of them, then the firms face again (15), which leads to wiCN and qiCN . In turn, firm S’s profits are given by π CN (see (17)) and are negative if S and only if β < β(γ). Clearly, if firm S trades with none, its profits are equal to zero. If
AC
firm S trades with just one firm, then given that both firm 1 and firm 2 have committed to licensing, there will be monopoly downstream. As is known from the literature, bargaining between the upstream and the downstream monopolist will result in wCLN = c and T will
be used to split the vertically integrated monopolist’s profits according to their bargaining powers. In particular, firm S’s profits will be π CLN = S if and only if β < β 2 (γ) ≡
γ 3 (2−γ) . 2(1−γ)2 (2−γ 2 )
β(a−c)2 . 4
CLN < 0 We find that π CN S −π S
In turn, in the previous stages, when β < β 2 (γ),
the firm that expects to be foreclosed from the market will not opt for licensing and only its rival will. When instead β > β 2 (γ), in stage 1(b), in the subgame in which firm 1 has opted for licensing, firm 2 will have to offer F2N = π CN − π LN to firm S in order for S S 29
ACCEPTED MANUSCRIPT
the latter to accept the licensing agreement. In the latter case, firm 2’s profits will be CN LN LN π CLN = π CN 2 2 + π S − π S , while if it does not opt for licensing, its profits will be π 2 . We
find that π CLN − π LN = 2 2
−γ 3 (a−c)2 (4−γ) 16(2−γ 2 )2
< 0. It follows that firm 2 never opts for licensing
when firm 1 has already opted for licensing. In turn, in the previous stage, firm 1 opts for
CR IP T
licensing knowing that if it does so, firm 2 will not also opt for licensing.
In the entry case, in stage 2, in the subgame in which both firms have opted for licensing, if firm S trades with both of them, then the firms again face (18), which leads to wiCE and qiCE . In turn, firm S’s profits are given by π CE (see (20)). Clearly, if firm S trades with S none, its profits are equal to those of a vertically integrated monopolist,
(a−c)2 4 .
If instead
AN US
firm S trades with just one firm, there will be duopoly downstream, leading to wM E (see (a−c)2 (4+4β(1−γ)2 −3γ 2 ) . 4(4−3γ 2 ) γ 2 (4−3γ 2 )(2+γ(8+3γ)) . We 16−γ 2 (32−γ(24+γ(23−9γ(2+γ))))
Ex-ante Monopolist extension) and firm S’s profits will be π CLE = 2 CLE < 0 if and only if β < β (γ) ≡ We find that π CE 3 S − π2 2
(a−c) > 0 when β > β 3 (γ). Thus, when β < β 3 (γ), firm S trades with note also that π CE 2 − 4
one firm, while when β > β 3 (γ), it trades with both firms. Given this, in stage 1(b), when
M
β < β 3 (γ), firm 2 will opt for licensing only if firm 1 has not opted for licensing in stage 1 since otherwise it will be foreclosed from the market (on the ‘first come, first served’ basis).
ED
In turn, in stage 1, firm 1 knowing this, opts for licensing and obtains the same profits as in our main analysis. In contrast, when β > β 3 (γ), in stage 1(b), in the subgame in which LE firm 1 has opted for licensing, firm 2 will have to offer F2E = π CE S − π S to firm S in order
PT
for the latter to accept the licensing agreement with it. In the latter case, firm 2’s profits LE CE will be given by π CLE = π CE 2 2 + π S − π S , while if it does not opt for licensing its profits
CE
CLE − π LE > 0, hence, when β > β (γ), firm 2 will opt for will be π LE 3 2 . We find that π 2 2
licensing when firm 1 has already opted for licensing. In turn, in stage 1, firm 1 knows that when β > β 3 (γ), firm 2 will also opt for licensing if it opts for licensing. Thus, if it opts
AC
for licensing, it will optimally set F1E = π LE and its profits will be π CLE = π CE + π LE 1 1 S S , while if it does not opt for licensing, its profits will be π LE since firm 2 will always opt 2 for licensing then. We find that π CLE − π LE > 0. Thus, when β > β 3 (γ) both firms opt 1 2 for licensing, while when β < β 3 (γ) only firm 1 opts for licensing. Moreover, we find that π CLE − π LN > 0, i.e., licensing incentives are stronger with entry. 1 1 Proof of Proposition 1: Calculating the difference in firm 1’s profits in the case of licensB ing without entry and in the benchmark case, we find: π LN 1 − π1 =
(a−c)2 γ 4 8(2+γ)2 (2−γ 2 )
> 0. Thus,
firm 1 always has incentives to license its input technology in the no entry case. Calculating
30
ACCEPTED MANUSCRIPT
the difference in firm 1’s profits in the case of licensing without entry and without a licensing fee and in the benchmark case, we find: π 1 (q1LN ) − T LN − π B 1 = if and only if β <
(a−c)2 (16β−8βγ 2 −γ 4 +βγ 4 ) 8(2+γ)2 (−2+γ 2 )
>0
γ4 . 16−8γ 2 +γ 4
Proof of Proposition 2: Calculating the difference in firm 1’s profits in the case of (a−c)2 (4−2γ−γ 2 )2 8(2+γ)2 (2+2γ−2γ 2 −γ 3 )
CR IP T
B licensing with entry and in the benchmark case, we find: π LE 1 −π 1 =
>
0. Therefore, firm 1 always has incentives to license its input technology in the entry case. Proof of Proposition 3: Calculating the difference in firm 1’s profits in the case of LN = licensing with and without entry, we find: π LE 1 − π1
(a−c)2 (1−γ)(8−8γ+2γ 3 −γ 4 ) 8(2−γ 2 )(2+2γ−2γ 2 −γ 3 )
> 0. It
AN US
follows that firm 1 has stronger licensing incentives with entry than without entry.
LE B Proof of Proposition 4: We differentiate (π LN − πB 1 1 ) and (π 1 − π 1 ) in terms of γ:
∂(π LN − πB 1 1) ∂γ LE ∂(π 1 − π B 1) ∂γ
= =
(a − c)2 γ 3 (4 + γ − γ 2 ) > 0; (2 + γ)3 (−2 + γ 2 )2 (a − c)2 (−4 + 2γ + γ 2 )(48 + 16γ − 44γ 2 − 14γ 3 + 4γ 4 + γ 5 ) < 0. 8(2 + γ)3 (2 + 2γ − 2γ 2 − γ 3 )2
M
It follows that an increase in product differentiation has a negative impact on the licensing
ED
incentives in the no entry case and a positive one in the entry case. Proof of Proposition 5: In the benchmark case, consumer surplus is:
PT
(a − c)2 (1 + γ) 1 . CS B = aq1B + aq2B − [(q1B )2 + (q2B )2 + 2γq1B q2B ] − p1 q1B − p2 q2B = 2 (2 + γ)2 In the case of licensing without entry, consumer surplus is:
AC
CE
1 CS LN = aq1LN + aq2LN − [(q1LN )2 + (q2LN )2 + 2γq1LN q2LN ] − p1 q1LN − p2 q2LN = 2 (a − c)2 32(1 − γ 2 ) + γ 3 (4 + 5γ) . 32(2 − γ 2 )2
In the case of licensing with entry, consumer surplus is: 1 CS LE = aq1LE + aq2LE + aqSLE − [(q1LE )2 + (q2LE )2 + (qSLE )2 + 2 2γq1LE q2LE + 2γq1LE qSLE + 2γq2LE qSLE ] − p1 q1LE − p2 q2LE − pS qSLE = (a − c)2 48 + 80γ − 84γ 2 − 108γ 3 + 43γ 4 + 30γ 5 . 32(2 + 2γ − 2γ 2 − γ 3 )
(a−c)2 γ 2 (32+16γ−28γ 2 −8γ 3 +5γ 4 ) as well as CS LE 32(2+γ)2 (2−γ 2 )2 (a−c)2 (4−2γ−γ 2 )(16+40γ−34γ 3 −7γ 4 +2γ 5 ) , we find that they are always positive. 32(2+γ)2 (2+2γ−2γ 2 −γ 3 )2
Calculating CS LN − CS B =
31
− CS B =
ACCEPTED MANUSCRIPT
Total welfare is defined as the sum of consumer and producer surplus: W k = CS k +π k1 + π k2 +π kS , where k = B, LN and LE. Calculating W LN −W B =
(a−c)2 γ 2 (32−16γ−20γ 2 +8γ 3 +3γ 4 ) 32(2+γ)2 (2−γ 2 )2
(a−c)2 (4−2γ−γ 2 )(12+12γ−11γ 2 −6γ 3 ) , we find that 32(2+γ)2 (2+2γ−2γ 2 −γ 3 )2 2 (1−γ)Γ Moreover, calculating CS LE − CS LN = 32(2−γ(a−c) 2 )2 (2+2γ−2γ 2 −γ 3 )2 , 144γ 2 − 272γ 3 + 104γ 4 + 200γ 5 − 20γ 6 − 60γ 7 − γ 8 + 5γ 9 > (a−c)2 (1−γ)∆ , 32(2−γ 2 )2 (2+2γ−2γ 2 −γ 3 )2 17γ 8 + 3γ 9 > 0, we find
they are always positive. where Γ ≡ 64 + 128γ −
0, and W LE − W LN =
CR IP T
and W LE − W B =
where ∆ ≡ 192 − 496γ 2 + 80γ 3 + 376γ 4 − 40γ 5 − 124γ 6 − 4γ 7 + that they are always positive.
2
(a−c) (2+γ − πB Proof of Proposition 6: Calculating, we find: π bLN 1 1 = − 8(2+γ)2
< 0, π bLE 1 −
(a−c)2 (1+γ)(6−γ 2 )(4−2γ−γ 2 )2 (a−c)2 E bLN = 8(2+γ)2 (8+8γ−3γ > 0 and π bLE 2 −2γ 3 )2 > 1 −π 1 2(2+γ)2 (8+8γ−3γ 2 −2γ 3 )2 2 3 4 5 6 7 8 512 + 256γ − 448γ − 32γ + 170γ − 32γ − 35γ + 8γ + 4γ > 0. Thus, firm
AN US
πB 1 =
E=
2)
0, where 1 always
has licensing incentives with entry while it does not have without entry.
N − π M B = 0 and π M E − π M B = Proof of Proposition 7: Calculating, we find: π M 1 1 1 1 E − πM N = πM 1 1
(a−c)2 (1−γ)2 4−3γ 2
> 0. Thus, firm 1 opts for licensing under entry, while it is
References
ED
9
M
indifferent between licensing without entry and no licensing.
Alipranti, M., C. Milliou and E. Petrakis (2014), “Price vs. Quantity Competition in a Vertically Related Market,” Economics Letters, 124, 122-126.
PT
Anand, B. and T. Khanna (2000), “The Structure of Licensing Contracts,” Journal of Industrial Economics, 48, 103-133.
CE
Arya, A. and B. Mittendorf (2006), “Enhancing Vertical Efficiency through Horizontal Licensing,” Journal of Regulatory Economics, 29, 333-342.
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Vertical Licensing, Input Pricing, and Entry Elpiniki Bakaouka, Chrysovalantou Milliou PII: DOI: Reference:
S0167-7187(17)30298-9 10.1016/j.ijindorg.2018.03.007 INDOR 2438
To appear in:
International Journal of Industrial Organization
Received date: Revised date: Accepted date:
12 May 2017 16 February 2018 11 March 2018
Please cite this article as: Elpiniki Bakaouka, Chrysovalantou Milliou, Vertical Licensing, Input Pricing, and Entry, International Journal of Industrial Organization (2018), doi: 10.1016/j.ijindorg.2018.03.007
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Highlights • We explore a vertically integrated firms incentives to license its input production technology.
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• Licensing arises even when the licensee becomes a rival of the licensor in the downstream market.
• The entry of the licensee in the downstream market reinforces the licensing incentives.
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• The incentives for vertical licensing can be stronger than those for horizontal licensing.
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Vertical Licensing, Input Pricing, and Entry Elpiniki Bakaouka and Chrysovalantou Milliou∗ February 2018
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Abstract
We explore the incentives of a vertically integrated incumbent to license the production technology of its core input to an external firm, transforming the licensee into its input supplier. We find that the incumbent opts for licensing even when licensing also transforms the licensee into one of its direct competitors in the final products market. In fact, the licensee’s entry into the final products market, although it increases
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the competition and the cost that the licensor faces, reinforces the licensing incentives. Furthermore, the licensee’s entry augments the positive welfare implications of vertical
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licensing.
Keywords: licensing; vertical relations, entry; two-part tariffs; outsourcing
∗
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JEL classification: L22; L24; L13; L42; D45
Bakaouka: Department of International and European Economic Studies, Athens University of Eco-
nomics and Business, Athens 10434, Greece, e-mail: [email protected]; Milliou: Department of Interna-
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tional and European Economic Studies, Athens University of Economics and Business, Athens 10434, Greece, e-mail: [email protected]. We are grateful to Marie-Laure Allain and to Lambros Pechlivanos for their valuable suggestions. We would like to thank the Editor and three anonymous referees, Maria Alipranti, Christos Constantatos, Tony Ke, Emmanuel Petrakis, Patrick Rey, Joel Sandonis, Spyros Vassilakis as well as the conference participants at the Workshop on Competition and Bargaining in Vertical Chains in Toulouse, the CRETE 2016 in Tinos, the EARIE 2016 in Lisbon, the ASSET 2016 in Thessaloniki, and the IIOC 2017 in Boston 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.
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Introduction
Original brand manufacturers often license the production technology of their core inputs to external firms.1 Such a practice transforms the licensees into the licensors’ input sup-
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pliers and potentially also into their direct competitors in the final products market. An illustration comes from the commercial aircraft market, where, in 2003, the US aircraft manufacturer Boeing licensed its wing production technology to Mitsubishi Heavy Industries, the Japanese engineering and electrical equipment producer. Boeing, as well as its main competitor, Airbus, had already been subcontracting the production of various air-
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craft components to external suppliers. However, never before had a commercial aircraft manufacturer subcontracted its wing production. Boeing’s decision met with widespread criticism: first, because Boeing’s wing technology has been regarded as its crown jewel, and second, because the transfer of wing manufacturing effectively gave to Mitsubishi ‘total production competence’ with regard to commercial aircraft. Mitsubishi is now ready to launch its own passenger jet, which is due to enter service in 2020.2
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A similar illustration can be found in the electronic appliances market, where, in 1984, a Chinese firm, Haier, which at the time was operating as a producer of electrical equip-
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ment for original brand manufacturers, acquired the technology for producing high-quality refrigerators from a German original brand manufacturer, Liebherr. A year after the li-
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censing of Liebherr’s technology, Haier introduced its own first four-star refrigerator in the market, evolving into an original brand manufacturer too. Haier soon became the leading refrigerator producer in China and, eventually, a major competitor in the global market.3 According to empirical evidence, technology licensing is a common practice among firms (e.g., Caves et
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al., 1983, Nadiri, 1993, Anand and Khanna, 2000). Many well-known firms, such as IBM, Hitachi, Kodak, and Procter & Gamble, have licensed their technologies, earning millions of dollars in licensing revenue. For
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more on this, see e.g., A Market for Ideas, The Economist (October 20, 2005). 2 Without the ability to manufacture wings, Mitsubishi could not become an independent player in the passenger jet market. For more on this, see e.g., Secret Wounds Of Globalism: Boeing Sells Its Technology – Cheap – To Japan, Forbes (January 5, 2014), and Boeing Outsourcing Gives Wing to Concerns, Chicago Tribune (December 21, 2003). 3 Samsung and Foxconn, after becoming Apple’s component suppliers, also became its competitors in the mobile phone and the smartwatch market, respectively. Similarly, after Dell outsourced its product’s parts to Asus, the latter started producing its own computers. For more on this, see e.g., How Apple’s Outsourcing Strategy Created Two Giant Competitors, CIO (June 1, 2015), and Has Apple Created Its Own Threat in Samsung?, Forbes (December 9, 2012).
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The above illustrations give rise to a number of interesting questions regarding vertical licensing, such as: Does a firm license its input production technology to an external firm when licensing can cause the licensee’s entry into its final product market? How does the transformation of the licensee into a rival affect the licensing incentives? What is the role
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of input pricing? Is vertical licensing welfare-improving? In this paper, we address these questions.
To this end, we consider a framework in which two competing incumbents produce two final goods using an input that they initially produce in-house. One incumbent considers licensing its input production technology to an external firm for a fixed licensing fee. When
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licensing takes place, the licensee produces the input for the licensor and the two firms trade through a two-part tariff contract whose terms are determined through bargaining. We consider what happens both when the licensee enters into the final goods market and competes with the incumbents in quantities - the ‘entry case’ - and when it does not enter - the ‘no entry case’.
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We find that independently of whether the licensee enters into the final goods market or not, the incumbent always opts for licensing. The key drivers of licensing, however, differ
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substantially among the entry and the no entry case. In the no entry case, licensing is driven by input pricing. Specifically, just as under strategic delegation, the input producer - the licensee - subsidizes the licensor by setting the wholesale price below the input’s marginal
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cost. We refer to this as the input pricing effect of licensing. The licensee does so because it can extract part of the resulting higher profits of the licensor through the fixed fee of
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the two-part tariff. Clearly then, in the no entry case, the licensor enjoys a cost-advantage relative to the other incumbent. In fact, due to this cost-advantage, it is willing to license its input production technology even for free when its bargaining power is sufficiently high.4
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In contrast, in the entry case, the licensee sets the wholesale price above the input’s
marginal cost, increasing the licensor’s cost. In addition, the number of downstream competitors increases and, thus, competition is intensified. We refer to this as the competition intensification effect of licensing. Furthermore, in this case, licensing results in the market 4
The free sharing of technology is observed in various markets, including the market for open source
software. For instance, in January 2015, Toyota announced that it would make more than 5,600 patents on fuel-cell technologies available for use for free to a wide array of firms 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).
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expansion effect and the business stealing effect. The market expansion effect refers to the fact that the licensee’s entry causes an increase of product variety, and thus, an expansion of the demand in the final products market. The business stealing effect refers instead to the fact that the licensee, by entering into the final products market, ‘steals’ part of
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the sales and market share of the licensor’s rival. Capturing the licensee’s profits, through the licensing fee, the licensor takes full advantage of both the market expansion effect and the business stealing effect, which work in favor of licensing and lead to its emergence in equilibrium.
Importantly, the entry of the licensee into the final goods market, although it intensifies
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competition and increases the licensor’s cost, strengthens the licensing incentives. Why is that? In the entry case, due to the market expansion effect and the business stealing effect, the licensor enjoys both a larger pie and a larger share of the pie. At the same time, the licensor does not suffer severely from the competition intensification effect, since the wholesale price is set in such a way as to reduce the negative impact of the increased
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downstream competition. Actually, the licensee and the licensor use their vertical trading contract as an instrument that allows them to behave in a pro-collusive way. This is a
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feature of vertical licensing which is absent in horizontal licensing and can alleviate the potential negative implications of the licensee’s entry. Vertical licensing is desirable not only for the licensor, but also for the consumers and
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the economy as a whole. This holds both with and without the licensee’s entry. Intuitively, licensing results in lower final prices, and thus in higher consumer surplus, either because
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it enhances the efficiency of the licensor in the no entry case or because it intensifies competition in the entry case. In fact, in the entry case, licensing is even more desirable due to the enhanced product variety and the increased competition.
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Extending our main model, we demonstrate that the licensee’s entry into the final goods
market can reinforce the licensing incentives in other instances too, such as, when the rival incumbent can also opt for licensing or when competition is in prices. Interestingly, there are instances in which the emergence of vertical licensing in equilibrium would be impossible without the licensee’s entry. This occurs when the licensor is initially the only incumbent in the market or when input trading is through a wholesale price contract. In contrast, when licensing is through royalties, the licensee’s entry can discourage licensing. Our work is related to the vast theoretical literature on technology licensing, where similarly to our paper, an owner of a technology sells the rights of its use to another firm. 3
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This literature analyzes various aspects of licensing, such as the choice among royalties and licensing fee (e.g., Kamien and Tauman, 1986, Muto, 1993, Wang, 1998), 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.,
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Fauli-Oller and Sandonis, 2003), and the possible anticompetitive effects of licensing (FauliOller and Sandonis, 2002). Most papers in this literature assume that the licensor and the licensee(s) are in different markets or in a one-tier market. Exceptions include the papers by Mukherjee (2003), Arya and Mittendorf (2006), Mukherjee and Ray (2007), and Rey and Salant (2012), which, similar to our paper, examine licensing in vertically related markets.
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In contrast to our paper, they focus on settings in which the licensor and the licensee do not have a seller-buyer relationship.5 Moreover, when they consider entry, triggered by licensing, they do not allow for the licensee’s entry into the licensor’s final goods market. Our paper is also related to the literature on outsourcing. A number of papers in this literature (e.g., Pack and Saggi, 2001, Shy and Stenbacka, 2003, Sappington, 2005, Buehler
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and Haucap, 2006, Arya et al., 2008a and 2008b, Lim and Tan, 2010) analyze a final product manufacturer’s ‘make-or-buy’ decision. That is, its choice among input production
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in-house and input sourcing from an external firm - outsourcing.6 Some of these papers assume that input production is outsourced to an already existing vertically integrated rival. Others, instead, assume that it is outsourced to an independent upstream firm. In
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particular, Pack and Saggi (2001) and Goh (2005) examine a buyer’s incentives to outsource its technology to a supplier when technology diffusion can result in the entry of another
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firm in the downstream and the upstream market, respectively. Both papers find that entry, by driving the input price to marginal cost, can be beneficial for the incumbents engaged in technology transfer. In contrast, we consider the entry of the firm to which the input
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production is outsourced and we show that it is beneficial even when it causes an increase in the input price. Lim and Tan (2010), similarly to our paper, consider a setting in which the supplier becomes a direct competitor of the buyer after outsourcing. However, they focus on the role of the buyer’s rate of learning and brand equity, while we focus on the role of input pricing. In our paper, vertical licensing without a licensing fee coincides with vertical separation. 5 6
An exception in this respect is the paper by Rey and Salant (2012) which considers vertical licensing. The practice of outsourcing is obviously quite similar to the practice of licensing, especially when licensing
does not involve fees or royalties.
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Clearly then, our paper is also related to the literature on vertical separation versus vertical integration (e.g., Vickers, 1985, Grossman and Hart, 1986, Bonanno and Vickers, 1988, Lin, 1988, Gal-Or, 1990, Jansen, 2003, Rey and Tirole, 2007). This literature provides the same strategic rationale for vertical separation (vertical licensing) as our paper in the no
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entry case. Our paper complements this literature by demonstrating that licensing can be used as a way through which the downstream firms, and not the upstream firms, can take advantage of the additional profits generated by vertical separation. And importantly, we consider the entry case. That is, we explore the incentives and the implications of vertical separation when it is accompanied by the entry of the vertically disintegrated upstream
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firm into the downstream market, and in turn we provide an additional argument in favor of vertical separation.7
A number of papers consider markets with multiple vertically integrated incumbents and, as we do in the entry case, examine their incentives to supply the input to a nonintegrated downstream entrant (e.g., Ordover and Shaffer, 2007, H¨offler and Schmidt, 2008,
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Brito and Pereira, 2010, Bourreau et al., 2011, Atiyas et al., 2012). They show that an incumbent does not foreclose the entrant unless the latter’s product is a closer substitute
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to its own product than to its rival’s (Ordover and Shaffer, 2007), it is asymmetrically located (Brito and Pereira, 2010), or contracts are unobservable (Atiyas et al., 2012). In these papers, all the vertically integrated firms, and not just one of them as in our paper
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and in H¨ offler and Schmidt (2008), can supply the entrant. Importantly, in these papers, the input suppliers are always integrated and thus the incentives for vertical licensing or
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vertical separation and the impact of entry on them are not examined. The remainder of the paper is organized as follows. In Section 2, we describe our main model. In Section 3, we determine the licensing incentives in both the no entry case and
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the entry case, and characterize the impact of entry on them. In Section 4, we evaluate the welfare implications of vertical licensing. In Section 5, we examine the robustness of our main findings when the licensee can serve as a common supplier and when both incumbents 7
One could also think of vertical licensing as vertical divestiture or as a spin-off of a firm’s upstream
division. Hence, our paper also relates to the literature on vertical divestiture and spin-offs (e.g., Chen, 2005, Lin, 2006, Sappington, 2006). Its main difference from this literature too is the consideration of the entry of the spin-off firm in the downstream market. Moreover, the analysis of the incentives for vertical licensing in the entry case shares some common features with the literature that analyses the incentives for horizontal divisionalization (e.g., Baye et al., 1996, Ziss, 1998).
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can opt for licensing. In Section 6, we discuss a number of further extensions of our main model. Finally, in Section 7, we conclude. All the proofs are included in the Appendix.
The Model
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2
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 at marginal cost c.
Both firms hold a patent for their input production technologies. One of them, without
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loss of generality firm 1, considers licensing its input production technology to an external firm, firm S, for a fixed licensing fee, F ≥ 0.8 When licensing takes place, the licensee (firm
S) is in the position to produce the licensor’s (firm 1’s) input at marginal cost c.9
The knowledge that firm S acquires through licensing regarding the production of the final good’s core input could also allow it to produce the final good. Thus, licensing could cause firm S’s entry into the final goods market too. In what follows, we consider the ‘entry
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case’ in which firm S enters into the final goods market and the ‘no entry case’ in which it does not enter.10 We assume that when the licensing agreement is signed, firm 1 commits to
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sourcing the input from firm S.11 The input sourcing terms include the terms of a two-part tariff: a fixed fee, T , and a wholesale price per unit of input, w, that firm 1 pays to firm
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S. These terms are determined through Nash bargaining between firm S and firm 1. The bargaining power of firm S and firm 1 is given by β and 1 − β, respectively, with 0 < β < 1.
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The (inverse) demand function for firm i’s final good is: pi (qi , Q−i ) = a − qi − γQ−i , 0 < γ < 1, a > c > 0,
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where pi and qi are the price and the quantity of firm i’s final good, respectively, and Q−i
is the quantity of its rival(s)’ final good(s). Specifically, Q−i = qj , with i, j = 1, 2 and i 6= j, 8 9
As we demonstrate in Section 6, the licensor prefers using a fixed licensing fee to a variable royalty. We abstract from assuming that firm S is more efficient in input production than firm 1. Clearly,
otherwise, the higher efficiency of the licensee would work in favor of vertical licensing. 10 This could be so because, for instance, the cost of entry in the final goods market is prohibitively high and, thus entry is blocked, or because the ability to produce the core input does not suffice for the production of the final good. 11 For instance, firm 1 shuts down its input production facility. Examining, in Section 6, what happens when firm 1 continues to have the option of producing the input in-house under licensing too, we conclude that our main results are qualitatively robust.
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in the no entry case, while Q−i = qj + qk , with i, j, k = 1, 2, S and i 6= j 6= k, in the entry case. The parameter γ measures the degree of product differentiation; namely, the higher γ is, the closer substitutes the final goods are. The timing of moves is as follows. First, firm 1 decides whether to license its input
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technology to firm S. In case of licensing, it sets the licensing fee F and, in turn, firm S signs or not the licensing agreement. If the agreement is signed, 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 the case of licensing and entry, choose their quantities simultaneously and separately.12 We solve for the subgame perfect Nash equilibrium of this game.
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We make the following assumption throughout in order to guarantee that all the firms face a non-negative marginal cost in all the cases under consideration: Assumption 1: a ≤ 5c
We start our analysis with the benchmark case in which there is no licensing. Firm 1 and firm 2 compete then in the standard Cournot way. Specifically, each firm i chooses qi
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to maximize its profits: π i (qi , qj ) = (a − qi − γqj )qi − cqi , with i, j = 1, 2 and i 6= j. Solving the resulting system of first order conditions, we obtain the Cournot-Nash equilibrium
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B quantities, q1B and q2B , and the equilibrium profits, π B 1 and π 2 , included in Table 1 of the
Appendix.
Licensing Incentives
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3
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In this section, we first determine the licensing incentives with and without the licensee’s entry into the final goods market and then we examine how they are influenced by entry.
Licensing and No Entry
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3.1
When the licensing agreement has been signed and firm S has stayed out of the final goods market, in the last stage, firm 2 faces the same maximization problem as in the benchmark case. Firm 1 maximizes instead the following (gross from T and F ) profits: 12
In Section 6, we also examine what happens when firms compete in prices, when firm 2 does not observe
(w, T ) before choosing its quantity, when (w, T ) are determined before the licensing decision is made, and when firms bargain over F too.
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π 1 (q1 , q2 , w) = (a − q1 − γq2 )q1 − wq1 . The resulting equilibrium quantities are: q1 (w) =
a(2 − γ) + γc − 2w a(2 − γ) − 2c + γw and q2 (w) = . 4 − γ2 4 − γ2
(1)
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In stage two, firm S and firm 1 solve the following generalized Nash bargaining problem: max [π S (w) + T ]β [π 1 (w) − T ]1−β , w,T
(2)
where π S (w) = (w − c)q1 (w) are firm S’s profits and π 1 (w) = π 1 (q1 (w), q2 (w), w). Their disagreement payoffs are equal to zero since neither firm has an outside option. Maximizing (2) with respect to T , we find: T (w) = βπ 1 (w) − (1 − β)π S (w). Thus, we can rewrite the
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(gross from F ) profits of firm S and firm 1 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)).
(3)
¿From (2) and (3), it follows that the equilibrium wholesale price maximizes the joint profits wLN =
8c − 2(a + c)γ 2 + (a − c)γ 3 . 4(2 − γ 2 )
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of firm S and firm 1:
(4)
Note that wLN < c, i.e., firm S subsidizes, through the wholesale price, the production of its
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customer, firm 1. As the literature on strategic delegation (e.g., Vickers, 1985, Fershtman and Judd, 1987, Sklivas, 1987) and on vertical separation (e.g., Jansen, 2003) has explained,
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the upstream firm has incentives to enhance the output of its customer at the rival’s expense in order to increase its customer’s profits that it (partially) captures through T . Firm 1 knows that firm S will reject the licensing agreement if and only if its profits
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without the agreement exceed its profits with the agreement. Since the former are equal to 0, firm 1 optimally sets: F LN = π S (wLN ) + T LN , where T LN = T (wLN ). Its net equilibrium
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profits (included in Table 1 of the Appendix) are: π LN = π 1 (wLN ) − T LN + F LN = 1
π 1 (wLN ) + π S (wLN ). Therefore, firm 1 captures all of its joint profits with firm S.
Proposition 1 When firm S does not enter into the final products market, firm 1 always licenses its input technology. Firm 1 licenses its input technology even when licensing is for free (F = 0) as long as β is sufficiently low. According to Proposition 1, firm 1 always opts for licensing when the licensee does not enter into the final goods market. Firm 1 would opt for licensing even if licensing was for free, as long as its bargaining power was sufficiently high. A similar finding and reasoning 8
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exists in the literature demonstrating the preference of vertical separation over vertical integration (e.g., Vickers, 1985, Jansen, 2003). Intuitively, firm 1 faces lower marginal cost with licensing than with in-house production, wLN < c. We refer to this as the input pricing effect of licensing. As a result, licensing leads to higher (gross from T LN ) profits for firm
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1 in the final goods market. When β is small, firm S obtains a small share of these profits through T LN ; hence, firm 1 is willing to license its input technology even for free.
3.2
Licensing and Entry
We turn now to the examination of the case in which the licensing agreement has been
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signed and firm S has entered into the final products market.
In the last stage, firms 1, 2, and S choose their outputs in order to maximize their respective profits:
(5)
π 2 (q1 , q2 , qS , w) = (a − q2 − γq1 − γqS )q2 − cq2 ;
(6)
π S (q1 , q2 , qS , w) = (a − qS − γq1 − γq2 )qS − c(q1 + qS ) + wq1 .
(7)
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π 1 (q1 , q2 , qS , w) = (a − q1 − γq2 − γqS )q1 − wq1 ;
Solving the system of the first order conditions, we obtain:
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q1 (w) =
a(2 − γ) + 2cγ − (2 + γ)w ; 2(2 − γ)(1 + γ) 2(a − c) − γ(a − w) . 4 + 2γ − 2γ 2
(9)
max [π S (w) − dS + T ]β [π 1 (w) − T ]1−β ,
(10)
q2 (w) = qS (w) =
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(8)
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In the second stage, firm S and firm 1 solve the following maximization problem:
w,T
where π 1 (w) and π S (w) are found after substituting (8) and (9) into (5) and (7), respectively. It is important to note that while the disagreement payoff of firm 1 continues to be null, the same no longer holds for firm S’s disagreement payoff. Firm S now has an outside option in its bargaining with firm 1: in case of disagreement, firm S has profits from its own sales in
the final goods market given by dS = (a − qSD − γq2B )qSD − cqSD , where qSD = q1B . Maximizing (10) with respect to T , we obtain: T = βπ 1 (w) − (1 − β)[π S (w) − dS ]. 9
(11)
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Using the above expression, we find: (12)
π 1 (w) − T = (1 − β)[π S (w) + π 1 (w) − dS ].
(13)
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π S (w) − dS + T = β[π S (w) + π 1 (w) − dS ];
Substituting (12) and (13) into (10), 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: wLE =
a(2 − γ)(1 − γ)γ + c(4 + γ(2 − γ − 3γ 2 )) . 2(2 + 2γ − 2γ 2 − γ 3 )
(14)
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It can be confirmed that wLE > c. In other words, in contrast to the no entry case, when firm S enters into the final products market, the wholesale price exceeds the input’s marginal cost; there is an inverse input pricing effect in place. Why is that? Initially, one might think that this result is driven by firm S’s incentive to ‘raise rival’s cost’ in order to increase its own market share in the final goods market. However, this is not
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so here. As we saw above, the wholesale price is chosen in order to maximize the joint profits of firm S and firm 1 and not the profits of firm S alone. The two firms manage to
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behave as a multi-product firm through the setting of the wholesale price. But why are their joint profits higher when the wholesale price exceeds the marginal cost? Firm S’s entry into the final goods market intensifies downstream competition. We refer to this as
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the competition intensification effect of licensing. Firm S and firm 1 alleviate the negative impact of the competition intensification effect on their joint profits through the setting of
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a higher wholesale price that leads them to produce lower joint output. In other words, the licensor and the licensee set the wholesale price in a pro-collusive way.
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It remains to determine the presence or absence of licensing incentives in the first stage of the game. We can obtain the equilibrium fixed fee T LE after substituting (14) into (11).
In turn, substituting T LE and wLE into (12) and (13), we can also obtain the gross from
F equilibrium profits of firm 1 and firm S. For the reasons explained in subsection 3.1, firm 1 fully extracts, through F , firm S’s profits: F LE = π S (wLE ) + T LE . Therefore, firm 1’s net equilibrium profits (included in Table 2 of the Appendix) in the licensing and entry case are: π LE = π 1 (wLE ) + π S (wLE ). Comparing π LE with π B 1 1 1 , we find that firm 1 has incentives to license its input technology even though licensing reinforces competition.13 13
If firm 2 could also offer a licensing agreement to firm S and the latter could sign only one licensing
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Proposition 2 When firm S enters into the final products market, firm 1 always licenses its input technology. The intuition is as follows. As mentioned above, licensing, when it is accompanied by entry,
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gives rise to the competition intensification effect and the inverse input pricing effect. These effects clearly decrease the profits that firm 1 obtains from its own sales in the final products market. Thus, in the absence of a licensing fee, firm 1 would never opt for licensing in the entry case. However, in addition to the competition intensification effect and the inverse input pricing effect, licensing, when it triggers entry, also brings about a business stealing
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effect and a market expansion effect. The former refers to the fact that firm 2’s output falls as the number of firms in the market increases. In other words, when firm S enters into the final goods market, it ‘steals’ part of the sales and market share of firm 1’s rival. The market expansion effect refers to the fact that firm S’s entry results in an increase in the number of differentiated final products and, thus, in an increase in product variety that in turn expands the demand in the final products market.14 Both of these effects augment the
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joint profits of firm S and firm 1 that the licensor enjoys, making licensing profitable. The main reasoning of the above finding resembles the reverse of the ‘merger paradox’
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found in the merger literature. In their seminal paper, Salant et al. (1983) demonstrated that Cournot competitors do not want to merge because their non-merged rival(s) will react
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to the merger-induced decrease in competition by increasing their output. Accordingly, licensing with entry can be seen as a situation where one of the firms splits profitably into two firms - a reverse merger. However, the firms in our setting, unlike in Salant et al.
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agreement, competition between firm 1 and firm 2 would drive the licensing fee down. This means that the licensor would not be able then to fully extract its joint profits with the licensee and, in turn, that the incentives for licensing, both with and without entry, would be weaker. The analysis is available from the
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authors upon request. 14 The market expansion effect appears to be present in the Boeing/Mitsubishi case. Mitsubishi is about to
introduce the Mitsubishi Regional Jet (MRJ) - a new and differentiated product in the market for short-haul passenger aircrafts known as ‘regional jets’. In particular, the MRJ will come in versions seating roughly 70-90 passengers, while Boeing and Airbus’ aircrafts seat over 100 passengers. Demand for regional jets has picked up after the MRJ made its maiden flight in November 2015. In fact, Mitsubishi already has 243 orders and 204 options for these jets. According to a newspaper article (Mitsubishi Aims for the Sky After Jet Takes Off, The Wall Street Journal, (November 11, 2015)), “a consulting firm estimates that carriers will order 4,360 regional jets through 2034 and it is predicted that Mitsubishi will capture 27% of that market.” For more on this see e.g., Can Mitsubishi Heavy Industries’ MRJ Regional Jet Lift It To A ‘Buy’ ?, Forbes (October 20, 2014), Japanese Planemaker in Talks for Major Deal, Financial Tribune (July 13, 2016).
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(1983), have differentiated products and, importantly, they are affected by input pricing. In fact, input pricing works in such a way that the licensing incentives are stronger when the licensor and the licensee are also vertically related (vertical licensing) than when they are only horizontally related (horizontal licensing). Intuitively, horizontal licensing - a reverse
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merger in a one-tier market - results in the competition intensification effect, the business stealing effect and the market expansion effect.15 It does not, however, result in the inverse input pricing effect. Thus, it does not allow the licensor and the licensee to alleviate the negative competition intensification effect and to behave in a pro-collusive way. It follows that input pricing - the vertical contract - is an instrument that can allow the firms involved
3.3
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in vertical licensing to behave in a pro-collusive way, strengthening the licensing incentives.
The Impact of Entry
Having explored the licensing incentives both with and without entry, we are now able to
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characterize the impact that entry has on them.
Proposition 3 The entry of firm S into the final products market reinforces firm 1’s li-
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censing incentives.
Interestingly, when the licensee enters into direct competition with the licensor, there are more incentives for licensing. Why is that? The entry of the licensee increases the intensity
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of competition faced by the licensor. This - the competition intensification effect - is clearly a negative effect for the licensor. At the same time though, the entry allows the licensor
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to steal away market share from its rival (firm 2) as well as to enjoy a larger market size. These effects - the business stealing effect and the market expansion effect - augment firm 1’s
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profits and, along with the entry’s inverse input pricing effect, which mitigates the negative competition intensification effect, render entry desirable.16 As Proposition 4 states below, entry also alters the impact that product differentiation
has on the licensing incentives. 15 16
For a detailed analysis of entry in a one-tier market, see e.g., Mankiw and Whinston (1986). Tyagi (1999) and Mukherjee and Zhao (2017) also demonstrate that entry can raise the profits of the
incumbent(s). However, they do not focus on licensing, they consider different settings (in Tyagi, 1999, the downstream entrant is not present in the upstream market, while in Mukherjee and Zhao, 2017, there are no vertical relations), and the driving forces of this result differ substantially from ours.
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Proposition 4 An increase in product differentiation has a negative impact on the licensing incentives when firm S does not enter into the final products market and a positive one when it enters.
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In the no entry case, the higher product differentiation is, the higher is the wholesale price; hence, the smaller is firm S’s subsidy to firm 1. In other words, the weaker market competition is, the lower are firm S’s incentives to enhance the competitive position of its customer by decreasing the latter’s variable cost and, thus, the smaller is firm 1’s efficiency enhancement. Therefore, in the no entry case, due to the intensity of the input pricing effect, licensing incentives exist even in markets with products that tend to be homogeneous and
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in fact are stronger in such markets than in markets with differentiated products.
In the entry case on the other hand, a decrease in product differentiation has two negative implications for the licensor: it enhances the competition intensification effect and it weakens the market expansion effect. In particular the relationship between the equilibrium wholesale price and product differentiation is U-shaped: ∂wLE /∂γ < 0 if and only if
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γ ≥ 0.438. Intuitively, an increase in wLE decreases the negative competition intensification
effect. When, however, competition is already too fierce, a (further) increase in wLE is not
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pursued since it can lead to firm 1’s foreclosure. The latter is not desirable in the presence of firm 2 in the market because while it will not allow firm S to achieve the monopoly profits, it will allow firm 2 to take advantage of it, by increasing its market share.17 As a consequence,
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when licensing is accompanied by entry, licensing incentives are stronger in markets with more differentiated products. Still, licensing arises even in markets with products that tend
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to be homogeneous. In fact, in the latter case, wLE equals c, firm 1 is not foreclosed, and licensing with entry coincides with a reverse merger in a one-tier market, which as we know
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(Salant et al., 1983) is more profitable than no licensing (merger). Firm 1’s preference of entry over no entry however does not hold when products tend to be homogeneous; firm 1 is indifferent then between entry and no entry. This is so because the input pricing effect makes licensing without entry preferable to no licensing and is stronger when γ tends to 1. Since under licensing with entry, firm 1 and firm S use the same input technology, one might think that their final products differ less between them than they differ from firm 2’s final product. We can capture this possibility in our model, simply by assuming that 17
For a review of the market foreclosure issues that arise in the presence of vertical integration, see e.g.,
Rey and Tirole (2007). Note that, as we explain in Section 6, if firm 2 was not in the market, firm 1 would be foreclosed but only when products tend to be homogeneous.
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while the degree of interbrand differentiation among firm 2’s product and the products of firm 1 and S is γ, the degree of intrabrand differentiation among the products of firm 1 and firm S is given by δ, with 0 < γ < δ < 1. In such a case, as expected, the competition intensification effect is stronger and the market expansion effect is weaker.
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The business stealing effect is also weaker since the fact that the entrant competes more fiercely with its licensor induces firm S to produce less than firm 2. It follows that the licensing incentives are weaker when intrabrand differentiation is smaller than interbrand differentiation. Importantly though, they are again always present, due almost exclusively now to the presence of the business stealing effect. In the extreme case in which the final
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products of firm 1 and firm S tend to be homogeneous (δ tends to 1), the market expansion effect disappears and the competition intensification effect is even stronger. At the same time though, the inverse input pricing effect is also stronger; firm 1 and firm S use the wholesale price to soften the more intense competition among them. Still, even then firm 1 is not foreclosed because, as explained above, through foreclosure, firm S will not make
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monopoly profits and firm 2 will increase its market share. This contrasts with Ordover and Shaffer (2007) who find that foreclosure arises when interbrand differentiation exceeds
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intrabrand differentiation. This is so mainly because in their setting, the wholesale price cannot sufficiently soften the increased competition; the non-integrated downstream firm is not already in the market and, for foreclosure not to occur, the incumbent should charge a
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sufficiently low wholesale price so that the entrant covers its fixed entry cost. Summing up, in the absence of intrabrand differentiation, the stronger competition intensification effect
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is mitigated by the stronger also inverse input pricing effect, and the business stealing effect again renders licensing desirable for firm 1. Furthermore, when intrabrand differentiation is lower than interbrand differentiation,
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the licensing incentives continue to be stronger with than without entry because of the business stealing effect and the market expansion effect which, although they are weaker, still exist. In fact, even when there is no intrabrand differentiation and the market expansion effect is absent, firm 1 has no strict preference for no entry; just as when γ tends to 1, the business stealing effect makes firm 1 indifferent between entry and no entry.
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4
Welfare Implications
We have already seen that vertical licensing is desirable from firm 1’s viewpoint. Next, we
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examine whether it is also desirable from a welfare viewpoint. Proposition 5 Vertical licensing both with and without the entry of firm S into the final products market always has a positive impact on consumer surplus and on total welfare. Its impact is larger with entry than without entry.
Vertical licensing is beneficial both for the consumers and for the economy as a whole.
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Intuitively, the licensing’s positive impact on consumer surplus is due to firm 1’s subsidization in the no entry case and to the increase in product variety and competition intensity in the entry case. In turn, licensing enhances total welfare through its positive impact on consumers and on the licensor’s profits that outweigh its negative impact on firm 2’s profits. As we demonstrate in Section 6, licensing’s positive welfare impact can be present
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even when the licensor has a dominant position in the market and, in particular, when it is the only incumbent in the market and/or it has a cost advantage relative to the other incumbent. Moreover, licensing with entry can have a positive impact on consumer and
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total welfare also when intrabrand differentiation is smaller than interbrand differentiation, although the magnitude of its impact is smaller then due to the weaker market expansion
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effect.
As Proposition 5 informs us, vertical licensing is even more desirable from a welfare
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viewpoint when it triggers entry into the final goods market. Intuitively, in the entry case, although firm 1 faces higher cost, competition is fiercer and the market is larger. This also holds when intrabrand differentiation is smaller than interbrand differentiation. In fact, as
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we show in Section 6, there are cases (e.g., when competition is in prices or when a wholesale price contract is used), in which licensing increases welfare in the entry case and decreases it in the no entry case. Therefore, the licensee’s entry into multiple production stages of a market can even be the main driving force of the positive welfare implications of licensing. Recently, the EU and the US both revised their rules for the assessment of technology licensing agreements under the EU competition law and the US antitrust law, respectively. The new regulations continue to reflect the view that licensing, by facilitating technology diffusion, is in most cases pro-competitive. Based on this view, a block exemption applies
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to all the licensing agreements among firms with limited market shares.18 Our analysis puts forward an additional and novel channel through which licensing can be pro-competitive even in cases in which the firms involved in licensing have large market shares. It demonstrates that vertical licensing, by triggering entry into more than one stage of a market, can
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generate more intense market competition and thus can (further) increase welfare.
5
Common Supplier and Common Licensee
So far, we have assumed that only firm 1 can opt for licensing, and that when it does, firm
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2 cannot source the input from the licensee - firm S. These assumptions could make one wonder what would happen if, alternatively, firm S could become the common supplier of the two incumbents, through licensing by just one of them, or their common licensee.19 Next, we explore these possibilities.
Common Supplier
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5.1
We examine now what happens when, after the licensing agreement between firm 1 and firm S is signed and before the contracting stage, firm 2 decides whether it will source
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the input from firm S and commits to its decision. A consequence of this is that in the subgame in which firm 2 decides to trade with firm S, the latter bargains in stage 2 with
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two downstream firms. To model this multilateral bargaining game, we invoke the Nash equilibrium of simultaneous generalized Nash bargaining games; we assume that firm S
18
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bargains with each firm i, with i = 1, 2, simultaneously and separately over (wi , Ti ).20 To According to the new EU regulation, Regulation N. 316/2014, in the case of licensing agreements between
non-competitors, the block exemption applies when the individual market share of each party does not exceed
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30%. According to the US Antitrust Guidelines for the Licensing of Intellectual Property (updated on August 12, 2016 by the US Department of Justice and the Federal Trade Commission), the US Agencies will not challenge an agreement if the licensor and the licensee collectively account for no more than 20% of each relevant market significantly affected by the licensing restraint. 19 If the inputs of the two firms do not differ significantly, firm S could produce both of them once it
obtains firm 1’s input production technology through licensing. If instead they differ significantly (e.g., they have different technical specifications), their production technologies could also differ and firm S might be unable to produce firm 2’s input unless firm 2 also licenses its own input production technology to it. 20 This assumption is standard in situations with multilateral contracting (e.g., Cremer and Riordan, 1987, Horn and Wolinsky, 1988, Hart and Tirole, 1990, O’Brien and Shaffer, 1992, McAfee and Schwartz, 1994 and 1995, Rey and Verg´e, 2004, Milliou and Petrakis, 2007, Alipranti et al., 2014).
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avoid the multiple equilibria that can arise due to the multiplicity of the beliefs that the downstream firms can form when they receive out-of-equilibrium offers, we impose pairwise proofness on the equilibrium contracts.21 Moreover, in order to ensure that all the firms face a non-negative marginal cost in all the cases under consideration, we assume that a ≤ 3c.
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We find that firm 2 always produces the input in-house and in turn that the licensing incentives and implications are exactly the same as in the main analysis.22 In particular, in the no entry case, when firm S acts as a common supplier, it subsidizes both firms, wiCN < wLN < c, because it suffers from the ‘commitment problem’ (e.g., Milliou and Petrakis, 2007, Rey and Tirole, 2007): when it trades with firm i, it cannot commit to not
when β < β(γ) ≡
γ3 ; 4−2γ−2γ 2 +γ 3
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offering better trading terms to firm j. In fact, because of this, firm S’s profits are negative hence, when β < β(γ), it trades only with firm 1. The same
holds when β > β(γ), but for a different reason: firm 2 decides then to produce in-house since otherwise firm S would extract a large share of its profits through T2 . In the entry case, when firm S acts as a common supplier, the wholesale prices are higher than in the
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main analysis, wiCE > wLE > c, because when they are set all the firms in the market, and not only firm 1 and firm S, behave as a multi-product monopolist. Still, firm 2 always
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decides to produce the input in-house in order to have a cost-advantage relative to firm 1 and to fully enjoy its own profits - firm S does not partially extract them through T2 . If firm 2 did not commit to sourcing the input from firm S, it would have to be compen-
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sated through T2 for its outside option to produce in-house. Although this would increase its incentives to source the input from firm S, firm 1’s licensing incentives would always be
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present. In fact, in the entry case, firm 1’s licensing incentives would be higher than in our main analysis because firm 2 would then source the input from firm S and thus the inverse input pricing effect would be stronger. However, the stronger inverse input pricing effect
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would restrict the downstream efficiency and the market expansion effect and, in turn, the extent of licensing’s positive welfare implications with entry. 21
That is, we require that a contract between firm S and firm i be immune to a bilateral deviation of firm
S with firm j, with i, j = 1, 2 and i 6= j. For more information on this, see e.g., O’Brien and Shaffer (1992), McAfee and Schwartz (1994 and 1995), Milliou and Petrakis (2007). 22 The detailed equilibrium analysis is included in the Appendix.
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5.2
Common Licensee
Next, we explore what happens when firm 2 can also opt for licensing to firm S, assuming that otherwise it cannot source its input from firm S.23
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When firm 2 decides, after observing if firm 1 has signed a licensing agreement with firm S, whether to license its input technology to firm S, we find that at least one incumbent always opts for licensing. We also find that both of them do so only when β is sufficiently high and firm S enters into the final goods market. Intuitively, both with and without entry, firm 2 does not opt for licensing when its rival does and firm S’s bargaining power is sufficiently low because it is foreclosed from the market then - firm S optimally trades with
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one licensor to avoid the ‘commitment problem’. However, firm 2 does not opt for licensing in the no entry case even when it is not foreclosed, because it then has to compensate firm S for the lower profits that it makes due to the ‘commitment problem’. In the entry case instead, when firm 2 is not foreclosed, it opts for licensing similarly to its rival mainly because firm S’s profits, part of which firm 2 extracts, are then larger.24 We should note
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however that the licensing incentives are weaker under licensing by both incumbents than under licensing by just firm 1, since in the former case firm 1 is unable to fully extract
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the licensee’s profits. Moreover, the positive welfare implications of licensing are weaker under licensing by both incumbents due to the stronger inverse input pricing effect. Still, entry continues to have a positive impact on the licensing incentives even when it results in
23
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licensing by both incumbents.25
In the toys market, Mattel has been both a common licensee of Walt Disney and Warner Bros and a
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competitor. In 2000, Walt Disney and Warner Bros licensed to Mattel the production of the Princess dolls (e.g., Snow White, Cinderella, Rapunzel) and of the Harry Potter branded dolls respectively. A few years later, Mattel launched its own goth-themed dolls, Monster High, and its princess-themed dolls, Ever After
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High, based upon characters from fairy tales and fantasy stories, as well as created its own film production studio. For more information, see e.g., The Media Business Advertising: Dragons and Flying Brooms, New
York Times (March 1, 2001), and The $500 Million Battle Over Disney’s Princesses, Bloomberg (December 17, 2015). In the smartphone manufacturing market also, for a number of years Samsung has been a licensee and a rival of both Nokia and Apple. For more information, see e.g., Nokia Expands Licensing Agreement with Samsung, Reuters (July 13, 2016). 24 Details are available in the Appendix. Note that if firm S committed to trading with its licensor(s) (e.g., if it had to pay a high enough penalty in case of violation of the licensing agreement), in the no entry case the outcome would be the same, while in the entry case both firms would always opt for licensing. 25 As mentioned in Section 2, we abstract from explanations for licensing which are based on the licensee’s efficiency. We should note though that licensing by both incumbents to the same licensee would be more
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When, instead, the two firms decide simultaneously and separately whether they will opt for licensing and make their (unobservable) offers at the same stage, in the no entry case, there are two asymmetric equilibria in pure strategies with licensing by just one of them (firm 1 or 2) and with the same licensing fee as in our main analysis. Intuitively, the
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firm that does not opt for licensing does not want to deviate to licensing because if it does, it will be foreclosed or it will be unable to extract sufficiently high profits. The same holds in the entry case, unless β is sufficiently high. There is an equilibrium then, not necessarily unique, in which both firms opt for licensing.
If, alternatively, the two incumbents could license their input technologies to two dif-
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ferent licensees, then both of them would opt for licensing in the no entry case. This is so because both would be subsidized (e.g., Jansen, 2003). In the entry case, in contrast, if both firms opted for licensing, then one of the licensors would foreclose its licensee when products were too close substitutes; otherwise, there would be four firms in the market and the competition intensification effect would be quite strong. Thus, in such a case, entry
Extensions - Discussion
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6
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could reinforce firm 1’s licensing incentives by deterring licensing by its rival.
In this section, we discuss briefly a number of further extensions of our main model to
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extract some additional insights. (i) Wholesale Price Contract
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We consider here what happens if input trading occurs through a wholesale price contract that includes only w. For simplification reasons, we assume that firm S makes a take-it-orleave-it offer to firm 1 regarding w.
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Due to the absence of T , firm S is not able to extract part of firm 1’s profits and double
marginalization and, in turn, the inverse input pricing effect, emerge under licensing with
and without entry, w bLN > c and w bLE > c.
Proposition 6 When vertical trading takes place through a wholesale price contract, firm 1 licenses its input technology if and only if firm S enters into the final products market. likely if it led to an increase in the latter’s efficiency, due e.g., to complementarities in know-how. This is so mainly because the increased efficiency would have a positive impact on input pricing and in turn on industry profits.
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When trading is through a wholesale price contract, licensing does not arise in equilibrium unless it is accompanied by entry. Intuitively, due to the inverse input pricing effect, the licensor faces higher cost under licensing. This in turn means that it also faces lower profits. The licensing incentives are restored when entry occurs mainly because of the
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market expansion effect, which is again in place. Note that if there was bargaining over w, the licensing incentives would be even stronger in the entry case, while they would continue to be absent in the no entry case since the equilibrium wholesale prices would be lower due to the licensor’s bargaining power. A straightforward implication of the inverse input pricing effect is that licensing would result in lower consumer and total welfare in the no
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entry case. In the entry case on the other hand, the positive impact of the market expansion effect dominates and licensing is again beneficial for consumers and the economy as a whole. In light of the above, we can draw two conclusions. First, that the contract type used in input trading can be crucial for the licensing incentives and implications. And second, that when input trading takes place through a wholesale price contract, the licensee’s entry
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not only does not discourage licensing, but, in fact, it constitutes its driving force. (ii) Ex-ante Monopoly
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We have assumed in our analysis that there are initially two vertically integrated incumbents in the market. We consider here the alternative case in which initially firm 1 is a monopolist. In the no entry case, since downstream competition is absent, firm S does not have
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incentives to increase the aggressiveness of its downstream customer. Instead, as it is well established in the literature, firm 1 and firm S set wM N = c and they achieve the profits of
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a monopolist just as in the benchmark case of no licensing. In the entry case, there is a single vertically integrated firm, firm S, trading with the non-integrated downstream firm 1. Maximization of their excess joint profits leads to a(2−γ)2 γ+c(8−γ(4+γ(2+γ))) 8−6γ 2
AC wM E =
> c, with
∂wM E ∂γ
> 0. If their products were homoge-
neous, as Reisinger and Tarantino (2015) also note, wM E would be such that firm 1 would be foreclosed from the market but would obtain, through F , the monopoly profits just as in the benchmark case of no licensing. When instead products are differentiated, even slightly, foreclosure is not profitable (Reisinger and Tarantino, 2015). This holds even though now, the negative competition intensification effect is stronger than in our main analysis; firm S’s entry transforms the final goods market from a monopoly to a duopoly. In other words, the reasoning of the reverse merger does not apply here and in turn the presence of licensing
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incentives is more striking. Intuitively, under no licensing, firm 1 achieves the profits of a single-product monopolist. A multi-product monopolist however makes higher profits. Under licensing and entry, firm S and firm 1 set the wholesale price in a collusive way, achieving profits that are almost equal to those of a multi-product monopolist and exceed
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the profits of a single-product monopolist.
Proposition 7 When firm 1 is initially a monopolist in the market, it licenses its input technology if firm S enters into the final products market. Otherwise, it is indifferent between licensing and no licensing.
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In terms of welfare, licensing without entry - by not altering the market outcomes leaves both consumer and total welfare unaffected. In contrast, licensing with entry, just as in our main analysis, by increasing firms’ profits and enhancing downstream competition, improves consumer and total welfare. (iii) Unobservability of Contract Terms
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The vertical contracting literature has stressed the importance of the observability of the contract terms in order for the contract used by a vertical chain to serve as a form of binding
ED
precommitment resulting in advantages relative to rivals. In fact, it has shown that when the terms of two-part tariffs are unobserved, then in settings with competing vertical chains (e.g., Arya and Mittendorf, 2011) or with a common supplier (e.g., O’Brien and Shaffer,
PT
1992, McAfee and Schwartz, 1994), contracts play no role; the wholesale prices are set equal to the input’s marginal cost and the vertically integrated outcome is reproduced.
CE
In our setting, under licensing without entry, just as in Katz (1991), there is a vertical chain and a vertically integrated firm, and one contract: (w, T ) between firm S and firm 1. Given this, we can have only full observability of the contract terms as in our main model or
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asymmetric unobservability in which only firm 2 cannot observe w. In the latter case, in the last stage, profit maximization leads to the following best responses: q1 (q2 , w) =
and q2 (q1 ) =
a−c−γq1 . 2
a−w−γq2 2
Since however firm 2 does not observe w, it forms beliefs regarding
w and in turn q1 , denoted by w and q 1 , respectively. Given this, we substitute firm 1’s best a(2−γ)−2c+γw . In turn, substituting q2 (w) into 4−γ 2 2 2 2a(2−γ)−w(4−γ )+2γc−γ w . In the previous stage, the bargaining 2(4−γ 2 )
response into q2 (q 1 ), and we obtain: q2 (w) = q1 (q2 , w), we get: q1 (w, w) =
problem is given again by (5), with the difference that now instead of q1 (w) and q2 (w), we have q1 (w, w) and q2 (w). Solving for w, we obtain wU N = c.26 In equilibrium, firm 26
The same result can also be found in Pagnozzi and Piccolo (2012) under unobservability of contract
21
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2’s expectations must be fulfilled, wU N = w. Therefore, under licensing without entry and unobservability of the contract terms, the equilibrium quantities coincide with the ones in the benchmark case without licensing, q1B and q2B . Since firm 1 extracts through F firm S’s profits, it follows that its profits also coincide with those in the no licensing case π B 1 and
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thus that it is indifferent between licensing without entry and no licensing.
Following a similar procedure in the licensing with entry case under asymmetric unobservability, we find the equilibrium wholesale price: wU E = that
wU E
>
wLE
aγ(2−γ)2 +2c(4−γ 2 (2+γ)) . 8+γ(4−γ(8+γ))
Note
> c. This is so because firms 1 and S, even when their rival cannot
observe w, set w to maximize their joint profits; they have incentives to set the wholesale
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price above the input’s variable production cost to alleviate the competition between them the competition intensification effect. In other words, in the entry case, the licensor and the licensee can use the vertical contract, even when it is unobserved by the other incumbent, in their favor. It follows that just as in the main analysis, licensing incentives are always present in the entry case. In fact, under asymmetric unobservability of the contract terms,
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entry can constitute licensing’s driving force. (iv) Reverse Timing
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In our main model, the input trading terms (w, T ) are determined after the licensing agreement has been signed. In the opposite case in which (w, T ) are determined in stage 1, while the licensing decision along with the determination of the licensing fee takes place in stage
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2, our results remain exactly the same. To see the above, consider the no entry case with the reverse timing. In stage 2, firm
CE
1 optimally offers F (w, T ) = π S (w) + T = (w − c)q1 (w) + T , with q1 (w) given by (1), and firm S accepts the offer. In the same stage, firm 1 decides to make such an offer if and
AC
only if π 1 (w) − T + F (w, T ) > π B 1 . Taking this into account, in stage 1, firm 1 and firm
S end up maximizing their joint profits, subject to the constraint (w − c)q1 (w) + T ≥ 0. The constraint is necessary since otherwise firm S will not supply the input to firm 1 in the
continuation of the game. The wholesale price that maximizes the joint profits of firm 1 and firm S is again wLN and in turn firm 1’s profits are π LN 1 . This logic also applies in the entry case resulting again in the equilibrium values of the main analysis. Note that we would also have obtained the same results in the case in which F and (w, T ) were determined in the
same stage. terms in various market structures including ours.
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(v) Cost Asymmetry One might wonder what would happen if the two incumbents were asymmetric. To examine this, we assume that firm 1 and firm 2 face initially marginal cost c and c2 , respectively, with c < c2 , and we find that the results of our main model are qualitatively robust. Moreover,
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we find that the licensing incentives are stronger when the licensor enjoys a cost-advantage than when it does not and that the positive impact of licensing on consumer and total welfare is larger under entry. This occurs mainly because when the licensor enjoys a cost advantage, both the input pricing effect and the market expansion effect are stronger. (vi) Bargaining over the Licensing Fee
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We consider here what happens if the licensor bargains with the licensee, in a Nash bargaining fashion, in stage 1 over the licensing fee with the same bargaining powers as in the bargaining over the input’s trading terms in stage 2. When the bargaining power of firm S is positive, firm 1 is not able to fully extract firm S’s profits through F . Still, even then, firm 1 always opts for licensing both with and without entry. This holds because during
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the negotiations over F , firm S has to compensate firm 1 for the profits that it would make without licensing. Because of this, in the extreme case in which firm 1 has no bargaining
ED
power, it is indifferent among licensing and no licensing. In all other cases, it prefers licensing to no licensing, and the higher its bargaining power is, the more it prefers licensing. Since the allocation of the licensing fee does not affect consumer and total welfare, our
PT
conclusions regarding the welfare implications of licensing remain unchanged. (vii) Licensing through Royalty
CE
One might wonder what happens if licensing takes place through a per-unit of output royalty, r ≥ 0, instead of through a fixed licensing fee. When a royalty is used, firm 1 is unable to
AC
fully extract firm S’s profits. Moreover, firm S’s marginal cost is then r + c instead of c. The higher marginal cost of firm S can translate into worse input sourcing terms for firm 1 and, thus, into lower profits for firm 1 from its own sales in the final goods market. Not surprisingly thus, in the no entry case, firm 1 always optimally sets rN = 0. Given this, does it have incentives to license its technology? The answer is already provided in our main analysis: when F = 0, firm 1 opts for licensing if and only if its bargaining power is sufficiently high and the licensee does not enter into the final goods market. In the entry case, when the royalty is imposed only on firm 1’s output, then again rE = 0. But when it is imposed either only on firm S’s output or on both firm S’s and firm
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1’s output, rE > 0. When the latter occurs, in contrast to what happens when licensing is through a fixed fee, licensing does not arise in equilibrium. This occurs, first, because the market expansion effect is weaker when rE > 0, and second, because firm 1, by not extracting firm S’s profits, it cannot take full advantage of the market expansion effect.
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It follows that the form of the licensing contract, whether it is a fixed licensing fee or a variable royalty, can affect the licensing incentives. It also follows that when licensing is through a royalty, entry can discourage licensing. This is in sharp contrast to our main conclusion. Nevertheless, if firm 1 was in the position to choose the licensing contract type, it would choose a fixed licensing fee contract over a royalty contract. This choice would be
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aligned with the interest of consumers and the economy as a whole since the positive impact of licensing on consumer and total welfare is larger when licensing takes place through a fixed licensing fee. Stated differently, both from the licensor’s viewpoint and from a welfare viewpoint, vertical licensing is preferable when it occurs through a fixed licensing fee. (viii) Downstream Price Competition
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Next, we discuss what happens when firms compete in prices in the final products market. As is well known from the literature, prices, in contrast to quantities, are strategic
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complements. Because of this, under price competition, in the no entry case, firm S does not wish its downstream partner to behave aggressively in the final market - it charges a wholesale price that exceeds its marginal cost. Still, similarly to our main analysis, firm 1
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always licenses its input technology. In fact, it licenses its technology even for free if firm S’s bargaining power is low enough. Why is that? As the literature on vertical separation (e.g.,
CE
Bonanno and Vickers, 1988, Lin, 1988, Gal-Or, 1990, Cyrenne, 1994) has demonstrated, vertical separation (vertical licensing in our case) dampens downstream competition, lead-
AC
ing to higher downstream profits that the upstream firm (the downstream firm in our case) extracts through the fixed fee. In the entry case, firm 1 licenses its input technology, but only if the final products are
not very close substitutes (γ < 0.979). Its licensing incentives are driven now by the market expansion effect alone; the business stealing effect is absent. Competition in the market is fiercer under price competition than under quantity competition. Hence, the competition intensification effect of licensing is stronger in the former case and dominates its market expansion effect when products are close substitutes and competition is already quite fierce. This implies that in markets in which firms’ products are quite similar, vertical licensing,
24
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when it is accompanied by entry, is more likely to be observed when firms compete in quantities than when they compete in prices. It follows that under downstream price competition, the impact of entry on the licensing incentives is again positive unless the final products are too close substitutes. Moreover,
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licensing continues to be welfare-enhancing but only when it triggers entry and, in fact, it enhances welfare then more under price competition than under quantity competition.27 In the no entry case, licensing is welfare-detrimental due to the increase that it causes through the input price in the licensor’s cost. (ix) Licensing without Commitment
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In our main model, after the signing of the licensing agreement, firm 1 commits to sourcing the input from the licensee. We relax this assumption now and examine what happens when firm 1 continues to have the option of producing the input in-house under licensing. In such a case, firm 1 has an outside option during the negotiations with firm S in stage 2: the profits that it would make with in-house input production. Since its outside
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option does not depend on w, it does not affect the latter; it affects only T . Specifically, since firm S needs to compensate firm 1 for its outside option, T is lower now than in the
ED
commitment case both with and without entry. Recall that firm 1 manages to extract all of firm S’s profits through the licensing fee. Hence, the change in T does not affect our main conclusions. The only difference is that in the no entry case now, when licensing is for free,
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firm 1 always opts for licensing and not only when β is sufficiently low, since firm S always
CE
has to compensate firm 1 for its outside option.28
7
Concluding Remarks
AC
We have examined the incentives of a vertically integrated incumbent to license its input technology to an external firm. We have done so in a setting in which, after the signing of the licensing agreement, the licensor sources the input from the licensee and the licensee 27
H¨ offler and Schmidt (2008) also find that entry has a positive impact on total welfare under downstream
price competition, both spatial and non-spatial, even in the absence of the market expansion effect, but they point out that under spatial price competition, entry can decrease consumer surplus. 28 We have also examined whether, in the case of licensing and entry, firm 1 is better off when it produces the input in-house or when it does not commit and thus it has both the option of in-house production and of sourcing it from S. We have found that, due to the inverse input pricing effect, it prefers the latter. The detailed analysis of this as well as of the rest of the extensions is available from the authors upon request.
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can enter into the final goods market and compete with the licensor. We have shown that licensing emerges in equilibrium not only when the licensee does not enter into direct competition with the licensor, but also when it enters. In fact, we have shown that when the licensee enters into the final products market, although competition
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becomes more intense, the licensing incentives are stronger. Intuitively, in the absence of entry, vertical licensing is motivated by the low input price at which the licensor sources the input from the licensee. The low input price translates into a cost advantage and, in turn, into larger market share and profits for the licensor. When, instead, the licensee enters into the final goods market, first, the licensor competes with more firms than without licensing,
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and second, it faces a higher cost - it pays an input price that exceeds the input’s marginal cost but alleviates the increased competition. The licensor opts for licensing because the entry of the licensee results in the expansion of the final goods market and in business stealing from the rival incumbent firm.
Our welfare analysis has revealed, first, that vertical licensing is always beneficial both
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for the consumers and for the economy as a whole, and second, that it is even more beneficial when it is accompanied by downstream entry. Importantly, it has indicated that vertical
ED
licensing can enhance welfare even more than horizontal licensing, by triggering entry into more than one market stages, and thus, by generating more intense competition in multiple production stages. Since vertical licensing can also be interpreted as vertical separation, it
PT
follows that our analysis offers arguments in favor of vertical separation and against vertical integration: vertical separation can be pro-competitive by enhancing the downstream effi-
CE
ciency through input pricing or by triggering the downstream expansion of the disintegrated input supplier, and thus, by increasing product variety and market competition. Extending our main analysis in various directions, we have shown that the entry of the
AC
licensee into the final products market can also reinforce the licensing incentives in the case in which all the incumbents, and not only the licensor, source the input from the licensee, as well as in the case in which downstream competition is in prices. Importantly, we have shown that there are instances in which vertical licensing would not emerge without the entry of the licensee into the final goods market. This holds when the licensor and the licensee trade via a wholesale price contract, when the contract terms are unobservable, or when the licensor is initially a monopolist. Summing up, we have provided an explanation for the commonly observed practice of vertical licensing in markets where licensing can transform the licensee not only into 26
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an input supplier but also into a direct competitor of the licensor in the final products market. Our explanation lies in strategic considerations and not in exogenously assumed efficiencies. Clearly, if we had assumed that the incumbent produces the input at a lower cost than the potential licensee (e.g., due to complementary skills), in-house production
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could also arise in equilibrium (Arya et al., 2008a). In-house production could also arise if we had incorporated into our analysis factors such as unobservability of the input’s quality and production cost, costly investments in input improvement and the use of incomplete contracts (e.g., Williamson, 1971, Grossman and Hart, 1986). The joint consideration of
8
Appendix q1B = q2B =
a−c 2+γ ;
(a−c)2 ; q1LN = (a−c)(2−γ) ; q2LN = (a−c)(4−γ(2+γ)) (2+γ)2 2(2−γ 2 ) 4(2−γ 2 ) (a−c)(4−γ(2+γ))2 (1−β)(a−c)2 (2−γ)2 LN LN ; π2 = −T = 8(2−γ 2 ) 16(2−γ 2 )2 2 2 β(a−c) (2−γ) (a−c)2 (2−γ)2 LN LN F = ; π 1 = 8(2−γ 2 ) 8(2−γ 2 )
B πB 1 = π2 =
π 1 (q1LN )
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these factors is left for future research.
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Table 1: Equilibrium Values under No Licensing and under Licensing without Entry (a−c)(4−3γ 2 ) (a−c)(4−2γ−γ 2 ) ; q2LE = qSLE = 4(2+2γ−2γ 2 −γ 3 ) 4(2+2γ−2γ 2 −γ 3 ) (a−c)2 (4−3γ 2 )2 (1−β)(a−c)2 (4−2γ−γ 2 )2 LE LE LE π 1 (q1 ) − T = 8(2+γ)2 (2+2γ−2γ 2 −γ 3 ) ; π 2 = 16(2+2γ−2γ 2 −γ 3 )2 2 2 (2+γ)+β(4−2γ−γ 2 )2 ) (a−c)2 (8−8γ+γ 2 ) ; π LE F LE = (a−c) (16(1+γ)−8γ 1 = 8(2+2γ−2γ 2 −γ 3 ) 8(2+γ)2 (2+2γ−2γ 2 −γ 3 )
ED
q1LE =
PT
Table 2: Equilibrium Values under Licensing with Entry
2 (2−γ) 2 (4+γ)2 2 (6−γ 2 ) (a−c)(4+γ) bLN = (a−c) ; FbLN = (a−c) bLN = (a−c) 2 1 4(2+γ) ; π 8(2+γ) ; π 16(2+γ)2 8(2+γ)2 2) (a−c)(4−2γ−γ 2 ) (a−c)2 (4−2γ−γ 2 )2 qb1LE = 2(8+8γ−3γ b2LE = qbSLE = (a−c)(2−γ)(4+3γ ; π 1 (b q1LE ) = 4(8+8γ−3γ 2 −2γ 3 ) ; q 2 −2γ 3 )2 2(8+8γ−3γ 2 −2γ 3 ) 2 (6−γ)(2−γ) 2 (56+8γ+48γ 2 −6γ 3 −7γ 4 +γ 5 ) (a−c)2 (2−γ)2 (4+3γ 2 )2 (a−c) (a−c) LE LE LE π b2 = 4(8+8γ−3γ 2 −2γ 3 )2 ; Fb = 4(8+8γ−3γ 2 −2γ 3 ) ; π b1 = 2(8+8γ−3γ 2 −2γ 3 )2
a−c 4+2γ ;
qb2LN =
AC
CE
qb1LN =
Table 3: Equilibrium Values with a Wholesale Price Contract
q1M E =
2 2 (a−c)2 M N ) − T M N = (1−β)(a−c) ; F M N = β(a−c) 4 ; π 1 (q1 4 4 2) 2 (1−γ)2 qSM E = (a−c)(4−2γ−γ ; π 1 (q1M E ) − T M E = (1−β)(a−c) 8−6γ 2 4−3γ 2 2 2 −3γ 2 ) 2 2 E = (a−c) (8−8γ+γ ) F M E = (a−c) (4+4β(1−γ) ; πM 1 4(4−3γ 2 ) 4(4−3γ 2 )
a−c MB 2 ; π1 2(a−c)(1−γ) ; 4−3γ 2
q1M B = q1M N =
N = = πM 1
Table 4: Equilibrium Values with Ex-ante Monopoly Common Supplier and Common Licensee (a) Common Supplier
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In the no entry case, in the last stage, each firm i chooses its quantity to maximize: π i (qi , qj , wi ) = (a − qi − γqj )qi − wi qi . This results in: qi (wi , wj ) =
a(2−γ)−2wi +γwj . 4−γ 2
Letting wjCN denote the equilibrium outcome of the negotiations of firm S and firm j,
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wi is chosen to maximize: max [π S (wi , wjCN ) + Ti + Tj − dS1 (wjCN , TjCN )]β [π i (wi , wjCN ) − Ti ]1−β , wi ,Ti
(15)
where π S (wi , wjCN ) = (wi − c)qi (wi , wjCN ) + (wjCN − c)qj (wi , wjCN ) and π i (wi , wjCN ) = π i (qi (wi , wjCN ), qj (wi , wjCN ), wi , wjCN ). Firm S’s disagreement payoff is dS1 (wjCN , TjCN ) =
(wjCN − c)qjmon (wjCN ) + TjCN , where qjmon (wjCN ) = (α − wjCN )/2. From the first order γ 2 (a−c) , where wiCN < wLN 2(2−γ 2 ) (a−c)(2−γ) . In turn, the equilibrium 2(2−γ 2 )
equilibrium quantities are: qiCN = π 1 (q1CN ) − T1CN
< c. The respective
net profits are:
(1 − β)(a − c)2 (2 − γ)2 ; 8(2 − γ 2 ) (a − c)2 (2 − γ)(−γ 3 + β(2 − γ)(2 − γ 2 )) . 4(2 − γ 2 )2
= π CN = 2
(16)
=
(17)
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π CN S
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conditions of (15), we obtain: wiCN = c −
< 0 if and only if β < β(γ) ≡ Note that π CN S
γ3 . 4−2γ−2γ 2 +γ 3
Given this, when β < β(γ), firm
S does not supply the input to firm 2.
ED
In stage 1(b), firm 2 decides whether it will source the input from firm S: π CN − 2
(a−c)2 ((4−3γ)γ 3 −2β(2−γ)2 (2−γ 2 )) . The difference is positive 16(2−γ 2 ) γ 3 (4−3γ) . However, β 1 (γ) > β(γ); hence, there is no region 2(2−γ)2 (2−γ 2 )
PT
π LN = 2
if and only if β < β 1 (γ) ≡ in which firm 2 decides to
source the input from firm S and the latter does supply it. Thus, under licensing without
CE
entry, our main analysis continues to hold. In the entry case, each firm i, with i, j = 1, 2 and i 6= j, chooses its quantity to maximize: π i (qi , qj , qS , wi , wj ) = (a − qi − γqj − γqS )qi − wi qi . Firm S also chooses its quantity to
AC
maximize: π S (qi , qj , qS , wi , wj ) = (a − qS − γqi − γqj )qS − c(qi + qj + qS ) + wi qi + wj qj . This results in: qi (wi , wj ) =
a(2−γ)−(2+γ)wi +γ(c+wj ) 2(2−γ)(1+γ)
and qS (wi , wj ) =
a(2−γ)−(2+γ)c+γ(wi +wj ) . 2(2−γ)(1+γ)
Letting wjCE denote the equilibrium outcome of the negotiations among firm S and firm
j, wi is chosen to maximize: max [π S (wi , wjCE ) + Ti + Tj − dS2 (wjCE , TjCE )]β [π i (wi , wjCE ) − Ti ]1−β , wi ,Ti
(18)
where π S (wi , wjCE ) and π i (wi , wjCE ) are found after substituting qS (wi , wj ) and qi (wi , wj ) into π S (qi , qj , qS , wi , wj ) and π i (qi , qj , qS , wi , wj ). Firm S’s disagreement payoff is given by dS2 (wjCE , TjCE ) = (a − qSD (wjCE ) − γqjD (wjCE ) − c)qSD + (wjCE − c)qjD (wjCE ) + TjCE , where 28
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qSD (wjCE ) =
a(2−γ)−2c+γwjCE 4−γ 2
and qjD (wjCE ) =
a(2−γ)+cγ−2wjCE 4−γ 2
are the quantities expected to
be produced by firm S and firm j, respectively, when they face wjCE . From the first order a(2−γ)γ+c(2+γ)2 , where wCE > wLE > c. This results 4+6γ (a−c)(2+γ) . In turn, the equilibrium net profits are: 4+6γ
in: q1CE = q2CE =
(a−c) 2+3γ
and qSCE =
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conditions of (18), we obtain: wiCE =
2(1 − β)(a − c)2 (2 + 2γ − 2γ 2 − γ 3 ) ; (2 + γ)2 (2 + 3γ)2 (a − c)2 A , 4(2 + γ)2 (2 + 3γ)2
π 1 (q1CE ) − T1CE = π CE = 2 π CE = S
(19) (20)
where A ≡ 16 + 32β + 64γ + 32βγ + 80γ 2 − 32βγ 2 + 16γ 3 − 16βγ 3 − 3γ 4 > 0.
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LE In stage 1(b), firm 2 decides whether it will source the input from firm S: π CE 2 − π2 =
(a−c)2 B , where B ≡ −256β−256γ−768βγ−1024γ 2 −896γ 3 +1664βγ 3 + 16(2+γ 2 )(2+3γ)2 (2+2γ−2γ 2 −γ 3 )2 1056γ 4 + 768βγ 4 + 1728γ 5 − 1152βγ 5 + 128γ 6 − 704βγ 6 − 624γ 7 + 192βγ 7 − 273γ 8 + 192βγ 8 −
32γ 9 + 32βγ 9 < 0. The difference π CE − π LE is always negative; hence, firm 2 always 2 2 produces the input in-house. Thus, under licensing with entry, the main analysis holds.
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(b) Common Licensee
We focus on the sequential licensing case, in which, we add stage 1(b) in our game, after
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stage 1 and before stage 2. In stage 1(b), firm 2, after observing if firm 1 has signed a licensing agreement with firm S or not in stage 1, decides whether to license its own input technology to firm S. In case of licensing, it offers a licensing fee, F2 , to firm S, and, in
PT
turn, firm S accepts or rejects the offer. In the no entry case, in stage 2, in the subgame in which both firms have opted for
CE
licensing, if firm S trades with both of them, then the firms face again (15), which leads to wiCN and qiCN . In turn, firm S’s profits are given by π CN (see (17)) and are negative if S and only if β < β(γ). Clearly, if firm S trades with none, its profits are equal to zero. If
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firm S trades with just one firm, then given that both firm 1 and firm 2 have committed to licensing, there will be monopoly downstream. As is known from the literature, bargaining between the upstream and the downstream monopolist will result in wCLN = c and T will
be used to split the vertically integrated monopolist’s profits according to their bargaining powers. In particular, firm S’s profits will be π CLN = S if and only if β < β 2 (γ) ≡
γ 3 (2−γ) . 2(1−γ)2 (2−γ 2 )
β(a−c)2 . 4
CLN < 0 We find that π CN S −π S
In turn, in the previous stages, when β < β 2 (γ),
the firm that expects to be foreclosed from the market will not opt for licensing and only its rival will. When instead β > β 2 (γ), in stage 1(b), in the subgame in which firm 1 has opted for licensing, firm 2 will have to offer F2N = π CN − π LN to firm S in order for S S 29
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the latter to accept the licensing agreement. In the latter case, firm 2’s profits will be CN LN LN π CLN = π CN 2 2 + π S − π S , while if it does not opt for licensing, its profits will be π 2 . We
find that π CLN − π LN = 2 2
−γ 3 (a−c)2 (4−γ) 16(2−γ 2 )2
< 0. It follows that firm 2 never opts for licensing
when firm 1 has already opted for licensing. In turn, in the previous stage, firm 1 opts for
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licensing knowing that if it does so, firm 2 will not also opt for licensing.
In the entry case, in stage 2, in the subgame in which both firms have opted for licensing, if firm S trades with both of them, then the firms again face (18), which leads to wiCE and qiCE . In turn, firm S’s profits are given by π CE (see (20)). Clearly, if firm S trades with S none, its profits are equal to those of a vertically integrated monopolist,
(a−c)2 4 .
If instead
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firm S trades with just one firm, there will be duopoly downstream, leading to wM E (see (a−c)2 (4+4β(1−γ)2 −3γ 2 ) . 4(4−3γ 2 ) γ 2 (4−3γ 2 )(2+γ(8+3γ)) . We 16−γ 2 (32−γ(24+γ(23−9γ(2+γ))))
Ex-ante Monopolist extension) and firm S’s profits will be π CLE = 2 CLE < 0 if and only if β < β (γ) ≡ We find that π CE 3 S − π2 2
(a−c) > 0 when β > β 3 (γ). Thus, when β < β 3 (γ), firm S trades with note also that π CE 2 − 4
one firm, while when β > β 3 (γ), it trades with both firms. Given this, in stage 1(b), when
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β < β 3 (γ), firm 2 will opt for licensing only if firm 1 has not opted for licensing in stage 1 since otherwise it will be foreclosed from the market (on the ‘first come, first served’ basis).
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In turn, in stage 1, firm 1 knowing this, opts for licensing and obtains the same profits as in our main analysis. In contrast, when β > β 3 (γ), in stage 1(b), in the subgame in which LE firm 1 has opted for licensing, firm 2 will have to offer F2E = π CE S − π S to firm S in order
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for the latter to accept the licensing agreement with it. In the latter case, firm 2’s profits LE CE will be given by π CLE = π CE 2 2 + π S − π S , while if it does not opt for licensing its profits
CE
CLE − π LE > 0, hence, when β > β (γ), firm 2 will opt for will be π LE 3 2 . We find that π 2 2
licensing when firm 1 has already opted for licensing. In turn, in stage 1, firm 1 knows that when β > β 3 (γ), firm 2 will also opt for licensing if it opts for licensing. Thus, if it opts
AC
for licensing, it will optimally set F1E = π LE and its profits will be π CLE = π CE + π LE 1 1 S S , while if it does not opt for licensing, its profits will be π LE since firm 2 will always opt 2 for licensing then. We find that π CLE − π LE > 0. Thus, when β > β 3 (γ) both firms opt 1 2 for licensing, while when β < β 3 (γ) only firm 1 opts for licensing. Moreover, we find that π CLE − π LN > 0, i.e., licensing incentives are stronger with entry. 1 1 Proof of Proposition 1: Calculating the difference in firm 1’s profits in the case of licensB ing without entry and in the benchmark case, we find: π LN 1 − π1 =
(a−c)2 γ 4 8(2+γ)2 (2−γ 2 )
> 0. Thus,
firm 1 always has incentives to license its input technology in the no entry case. Calculating
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the difference in firm 1’s profits in the case of licensing without entry and without a licensing fee and in the benchmark case, we find: π 1 (q1LN ) − T LN − π B 1 = if and only if β <
(a−c)2 (16β−8βγ 2 −γ 4 +βγ 4 ) 8(2+γ)2 (−2+γ 2 )
>0
γ4 . 16−8γ 2 +γ 4
Proof of Proposition 2: Calculating the difference in firm 1’s profits in the case of (a−c)2 (4−2γ−γ 2 )2 8(2+γ)2 (2+2γ−2γ 2 −γ 3 )
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B licensing with entry and in the benchmark case, we find: π LE 1 −π 1 =
>
0. Therefore, firm 1 always has incentives to license its input technology in the entry case. Proof of Proposition 3: Calculating the difference in firm 1’s profits in the case of LN = licensing with and without entry, we find: π LE 1 − π1
(a−c)2 (1−γ)(8−8γ+2γ 3 −γ 4 ) 8(2−γ 2 )(2+2γ−2γ 2 −γ 3 )
> 0. It
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follows that firm 1 has stronger licensing incentives with entry than without entry.
LE B Proof of Proposition 4: We differentiate (π LN − πB 1 1 ) and (π 1 − π 1 ) in terms of γ:
∂(π LN − πB 1 1) ∂γ LE ∂(π 1 − π B 1) ∂γ
= =
(a − c)2 γ 3 (4 + γ − γ 2 ) > 0; (2 + γ)3 (−2 + γ 2 )2 (a − c)2 (−4 + 2γ + γ 2 )(48 + 16γ − 44γ 2 − 14γ 3 + 4γ 4 + γ 5 ) < 0. 8(2 + γ)3 (2 + 2γ − 2γ 2 − γ 3 )2
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It follows that an increase in product differentiation has a negative impact on the licensing
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incentives in the no entry case and a positive one in the entry case. Proof of Proposition 5: In the benchmark case, consumer surplus is:
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(a − c)2 (1 + γ) 1 . CS B = aq1B + aq2B − [(q1B )2 + (q2B )2 + 2γq1B q2B ] − p1 q1B − p2 q2B = 2 (2 + γ)2 In the case of licensing without entry, consumer surplus is:
AC
CE
1 CS LN = aq1LN + aq2LN − [(q1LN )2 + (q2LN )2 + 2γq1LN q2LN ] − p1 q1LN − p2 q2LN = 2 (a − c)2 32(1 − γ 2 ) + γ 3 (4 + 5γ) . 32(2 − γ 2 )2
In the case of licensing with entry, consumer surplus is: 1 CS LE = aq1LE + aq2LE + aqSLE − [(q1LE )2 + (q2LE )2 + (qSLE )2 + 2 2γq1LE q2LE + 2γq1LE qSLE + 2γq2LE qSLE ] − p1 q1LE − p2 q2LE − pS qSLE = (a − c)2 48 + 80γ − 84γ 2 − 108γ 3 + 43γ 4 + 30γ 5 . 32(2 + 2γ − 2γ 2 − γ 3 )
(a−c)2 γ 2 (32+16γ−28γ 2 −8γ 3 +5γ 4 ) as well as CS LE 32(2+γ)2 (2−γ 2 )2 (a−c)2 (4−2γ−γ 2 )(16+40γ−34γ 3 −7γ 4 +2γ 5 ) , we find that they are always positive. 32(2+γ)2 (2+2γ−2γ 2 −γ 3 )2
Calculating CS LN − CS B =
31
− CS B =
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Total welfare is defined as the sum of consumer and producer surplus: W k = CS k +π k1 + π k2 +π kS , where k = B, LN and LE. Calculating W LN −W B =
(a−c)2 γ 2 (32−16γ−20γ 2 +8γ 3 +3γ 4 ) 32(2+γ)2 (2−γ 2 )2
(a−c)2 (4−2γ−γ 2 )(12+12γ−11γ 2 −6γ 3 ) , we find that 32(2+γ)2 (2+2γ−2γ 2 −γ 3 )2 2 (1−γ)Γ Moreover, calculating CS LE − CS LN = 32(2−γ(a−c) 2 )2 (2+2γ−2γ 2 −γ 3 )2 , 144γ 2 − 272γ 3 + 104γ 4 + 200γ 5 − 20γ 6 − 60γ 7 − γ 8 + 5γ 9 > (a−c)2 (1−γ)∆ , 32(2−γ 2 )2 (2+2γ−2γ 2 −γ 3 )2 17γ 8 + 3γ 9 > 0, we find
they are always positive. where Γ ≡ 64 + 128γ −
0, and W LE − W LN =
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and W LE − W B =
where ∆ ≡ 192 − 496γ 2 + 80γ 3 + 376γ 4 − 40γ 5 − 124γ 6 − 4γ 7 + that they are always positive.
2
(a−c) (2+γ − πB Proof of Proposition 6: Calculating, we find: π bLN 1 1 = − 8(2+γ)2
< 0, π bLE 1 −
(a−c)2 (1+γ)(6−γ 2 )(4−2γ−γ 2 )2 (a−c)2 E bLN = 8(2+γ)2 (8+8γ−3γ > 0 and π bLE 2 −2γ 3 )2 > 1 −π 1 2(2+γ)2 (8+8γ−3γ 2 −2γ 3 )2 2 3 4 5 6 7 8 512 + 256γ − 448γ − 32γ + 170γ − 32γ − 35γ + 8γ + 4γ > 0. Thus, firm
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πB 1 =
E=
2)
0, where 1 always
has licensing incentives with entry while it does not have without entry.
N − π M B = 0 and π M E − π M B = Proof of Proposition 7: Calculating, we find: π M 1 1 1 1 E − πM N = πM 1 1
(a−c)2 (1−γ)2 4−3γ 2
> 0. Thus, firm 1 opts for licensing under entry, while it is
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