Patent Licensing and Double Marginalization in Vertically Related

Markets with a Nash Bargaining Agreement

Hong-Ren DinKuo-Feng Kao

Wen-Jung LiangPresented at National Chung-Cheng University

2011, 11, 21

Overview of the Presentation

• 1. Introduction

• 2. Model Setup

2.1 The General model

2.2 Fixed fee Licensing

2.3 Royalty Licensing

• 3. The Optimal Licensing Contract

• 4. Social Welfare and Bargaining Power

• 5. Concluding Remarks

Introduction: Two Issues Discussed

• By taking into account vertically related markets with an outsider patentee,

• The cost-reducing technology is licensed to the upstream firm

• The input price is determined by a Nash bargaining agreement.

• What is the outsider patentee’s optimal licensing contract in terms of fixed-fee and royalty licensing?

• Does a larger degree of double marginalization existed in the vertically related markets always worsen the social welfare?

Related Literature

Licensing to the final product producers.

• The outsider patentee:

Kamien and Tauman (1986), Kamien et al. (1992), Muto (1993), Poddar and Sinha (2004), and Kabiraj (2004).

• The insider patentee:

Wang (1998), Faulí-Oller and Sandonís (2002, 2003), Kabiraj and Marjit (2003), Poddar and Sinha (2004), Arya and Mittendorf (2006), Mukherjee and Pennings (2006), Poddar and Sinha (2010), and Sinha (2010).

Licensing to the Upstream Producers and Real World Evidences

• The optimal licensing contract, where the innovation is licensed to the upstream producers, has not been touched upon yet.

• Licensing technology to the upstream producers is commonplace in the real world.

• For example: Qualcomm licenses wireless technologies to MediaTek

Means of Licensing Innovation

• Rostoker (1984)

• Royalty alone is 39 percent,

• Fixed fee alone is 13 percent,

• Royalty plus fixed fee is 46 percent.

A Nash Bargaining Agreement

• The input price is determined by a Nash bargaining agreement between the upstream and downstream firms.

• This is a more general setting.

• The weaker (stronger) the upstream firm’s bargaining power), the smaller (larger) the degree of double marginalization.

A Three-stage Game• In stage 1, the outsider patentee selects an optimal

contract and the optimal fee under the fee licensing or the optimal royalty rate under the royalty licensing.

• In stage 2, the input price is determined through a Nash bargaining agreement between the upstream firm and the downstream firm.

• In stage 3, the downstream firm determines the output of the final product.

Main Result 1

• The outsider patentee prefers royalty licensing as the upstream firm’s bargaining power is small, whereas prefers fixed-fee licensing, otherwise.

Intuition• As the magnitude of the upstream firm’s bargaining

power is large, the upstream firm has the ability to extract larger profit than the downstream firm.

• The outsider patentee to choose a fixed-fee licensing for enhancing the upstream firm’s competition power by reducing its marginal production cost.

• As the magnitude of the upstream firm’s bargaining power is small, the downstream firm has the ability to extract larger profit than the upstream firm so that the output of the final product is bigger.

• The outsider patentee will choose a royalty licensing due to higher royalty revenue.

Main Result 2

• The social welfare may get improved as the bargaining power of the upstream firm is large enough. This result emerges even though the degree of double marginalization gets worse.

Intuition• Note that the outsider patentee prefers royalty licensing as

the upstream firm’s bargaining power is small, whereas prefers fixed-fee licensing, otherwise. A fixed-fee licensing can improve social welfare by enhancing the firms’ production efficiency via decreasing their production costs.

• Usually, a larger bargaining power of the upstream firm denotes a larger degree of double marginalization, which will worsen social welfare.

• However, this paper derives a counter result caused from switching from a royalty licensing to a fixed-fee licensing selected by the outsider patentee.

Model Setup: Assumptions

• One outsider patentee, one upstream firm, firm 1, and one downstream firm, firm 2.

• One unit of output employs one unit of intput.• The input price w is determined by a Nash

bargaining agreement.• The upstream firm’s marginal cost is c.• The innovation size can reduce the upstream

firm’s marginal cost by ε.• The inverse demand function for the final product is

p = a - q2.

The General Model

• In the final stage, the profit function of the downstream firm is :

where the superscript of each variable, i = {N, F, R} • The equilibrium output and profit of firm 2 :

2 2( )i i ip w q

2

( )

2

ii a w

q

2

2

( )

4

ii a w

The General Model

• The profit of the upstream firm is :

• The input price is determined by maximizing the following expression:

• The input price as follows:

1

( )( )

2

i i ii w c a w

[ ( ) 2 ]

2

i ii a c c

w

(1 )2

(1 )1 2

( )( )max ( ) ( )

2 2i

i i i ii i i

w

w c a w a w

Equilibrium• The equilibrium output:

• The equilibrium profits of the upstream and downstream firm:

1 2 (2 )( ) / 4i i iq q a c

21 (2 )( ) / 8i ia c

22 [(2 )( )] /16i ia c

Licensing Is Absent

• In the case where licensing is absent, by substituting cN=c into equilibrium profits of the upstream and downstream firm, we have:

21 (2 )( ) / 8N a c

22 [(2 )( )] /16N a c

Fixed Fee Licensing• In the case of fee licensing, the marginal cost of the

upstream firm is: c-ε• By using the general model, the output and the

profit for upstream firm and downstream firm can be derived as:

1 2 (2 )( ) / 4F Fq q a c 2

1 (2 )( ) / 8F F a c F 2

2 [(2 )( )] /16F a c

The Optimal Fixed Fee

• In stage 1, the optimal license fee is:

• The larger the bargaining power of the upstream firm is, the larger will be the outside patentee’s profit.

.8/])())[(2( 2211 cacaF NF

Lemma 1

• Suppose that the outsider patentee licenses its technology to the upstream firm and the input price is determined by a Nash bargaining agreement. A rise in the upstream firm’s bargaining power increases the optimal fixed-fee.

The Royalty Licensing

• In the case of royalty licensing, the marginal cost of the upstream firm is: c-ε+r

• By using the general model, the output and the profit for upstream firm and downstream firm are:

1 2 (2 )( ) / 4R Rq q a c r 2

1 (2 )( ) / 8R a c r 2

2 [(2 )( )] /16R a c r

The Optimal Royalty Rate• In stage 1, the outsider patentee selects the optimal

royalty rate to maximize its profit.

• The optimal royalty rate is:

1

[(2 )( )]max

4R

r

r a c rR rq

, ,

( ) / 2, .

if a cr

a c if a c

The Outside Patentee’s Profit

• The outside patentee’s profit under royalty licensing is as follows:

• The larger the bargaining power of the upstream firm is, the lower will be outside patentee’s profit under royalty licensing.

2

( )(2 ) / 4, ,

( ) (2 ) /16, .

a c if a cR

a c if a c

Lemma 2

• Suppose that the outsider patentee licenses its technology to the upstream firm and the input price is determined by a Nash bargaining agreement. A rise in the upstream firm’s bargaining power decreases the outsider patentee’s profit under royalty licensing.

Optimal Licensing Contract

• When the innovation is small, i.e., ε < a- c

• When the innovation is large, that is, ε > a- c

Aca

caifFR

22

)(2)(0)(

Bca

cacaifFR

)22(2

)22()()(0)(

2

Proposition 1

• Suppose that the outsider patentee licenses its technology to the upstream firm and the input price is determined by a Nash bargaining agreement. The outsider patentee prefers fixed-fee (royalty) licensing if and only if the upstream firm’s bargaining power is large (small) regardless of the innovation size.

Social Welfare and Bargaining Power

• The social welfare is measured as the sum of consumer surplus, and the aggregate profits of the downstream firm, the upstream firm and the outside patentee.

2(2 )(6 )( ) / 32FSW a c

2

(2 )( )[(6 )( ) 8 ] / 32

(2 )(14 )( ) /128 R a c a c if a c

SWa c if a c

The Difference in Social Welfare• Given the level of bargaining power, the social

welfare under fixed-fee licensing is always higher than that under royalty licensing.

2

(2 )[6( )(2 ) (6 )] / 32 0 ,

( ) (2 )(10 3 ) /1128 0 .

F RSW SW

a c if a c

a c if a c

The Issue

•Does a larger degree of double marginalization existed in the vertically related markets always worsen the social welfare?

Since the social welfare functions under fixed-fee licensing is decreasing in the upstream firm’s

bargaining power, it follows that the levels of the social welfare under fixed-fee licensing in Figure 1

are higher than those under royalty licensing.

)28.(0)ˆ()1( ARF SWSW

Figure 1

• Figure 1. The welfare locus in various licensing contracts for the case of small innovation size.

SW

FSW

RSW

0 A

32

)(7 2 ca

8

)(3 2 ca

1

Proposition 2• Suppose that the outsider patentee licenses its

technology to the upstream firm and the input price is determined by a Nash bargaining agreement. The social welfare may get improved as the bargaining power of the upstream firm is large enough. This result emerges even though the degree of double marginalization gets worse.

Concluding Remarks• The outsider patentee prefers royalty (fixed-fee)

licensing to fixed-fee (royalty) licensing, as the bargaining power of the upstream firm is small (large) irrespective of the innovation size.

• The social welfare may get improved by switching from a royalty licensing to a fixed-fee licensing selected by the outsider patentee, as the bargaining power of the upstream firm is large enough.

Thank you for your listening.