122th April, 2011

Uncertainty and Licensing in a Vertical Structure

Fang-yueh ChenNational Chung Cheng University

Tsai-chen ShenTatung Institute of Commerce and Technology

This paper is to be presented in 「 Corporate Governance, Foreign Entry, and Market Competition」 International Conference 2011,held in National University of Kaohsiung, R.O.C.

2

I. Motivations

Licensing in a vertical structure

Licensing with risk sharing

Endogenizing insider and outsider models

Licensing and vertical externality

3

II. Purposes

Investigate how an input monopolist shares risks through international licensing and its consequences

Examine the impact of entry in the downstream market

4

III. Literature reviews

Related to vertical structure: Mukherjee (2010a), Mukerjee and Ray (2007, MS),

Mukherjee and Pennings (2011, IJIO) Related to threat of entry:

Kabiraj and Marjit (1993, JDE), Saggi (1996, RIE), Pack and Saggi (2001, JDE), Dinda and Mukherjee (2011, JPET)

Related to uncertainty: Bousquet et al. (1998, IJIO)

5

IV. The basic model

Country J Country T

Figure 1: The basic model

Firm A

Firm B

Firm C

Country E

input market

Licensing

6

V. Sequence of moves and main equations (Cont.)

Stage 1: Licensing game

Stage 2: Input market equilibrium

Stage 3: The uncertainty resolves

Stage 4: Final goods market equilibrium

7

V. Sequence of moves and main equations

The demand function of final goods: QP 1

The derived demand for the input, Qr 21

The input monopolist’s expected profit function without licensing

QkrQrE AN ))(1()0(

kQrQ )1(

The input monopolist’s expected profit function with licensing

CAAAL xxkrxrE ))(1()0(

The profit function of a licensee (firm C) CCL xkrE )( 0

8

VI. The intuition of licensing and the finding (Cont.)

)())(())(( ddxxddxxEddxxEddE CCCCAAAAAL

Lemma 1: In the licensing regime, both firm A and C have positive output

production if and only if the condition 7)25()1( 00 kkk holds.

Equilibrium figures in the licensing contract:

10]4)1(5[ 0* kk , 10])1(325[ 0 kkr ,

20]2)1(75[ 0* kkxA , 5])1[( 0

* kkxC ,

20])1(325[ 0** kkxxQ CAL ,

40)981045( 20

20 MMkMkE AL

9

VI. The intuition of licensing and the finding

Equilibrium without licensing

8])1(1[)(2 22 kQE AAN

010])1([ 20 kkEE ANAL if and only if

Mkk )1(0

Proposition 1: If and only if firm C has a lower marginal

production cost relative to the expected marginal

production cost of firm A, firm A will license its

input production technology to firm C.

10

VII. Equilibrium with licensing and entry mode of an outsider (cont.)

CALC QE vs. CCL QkrE )( 0

ALCAL EE 80)58(2182035( 022

0 MkMMk

18110810 00 kkM low ,

18110810 00 kkMhigh

11

VII. Equilibrium with licensing and entry mode of an outsider

Proposition 2: In the licensing regime if and only if lowMM , firm A will choose to be an insider and produce the input. Otherwise, firm A will choose to be an outsider.

Assume 88.00 k

AE

0.0009

1 0.88

outsider insider

No licensing

M

0.965 0.925

Figure 3: The choices of insider and outsider

12

VIII. The extended model

Country J Country T

Firm A

Firm B

Firm C

Country E

Figure 4: The extended model

Firm D

Input Market, M1

Licensing

Input Market, M2

13

IX. Main equations

The profits functions of firm B and firm D (downstream firms)

BB xrP )( 1

DD xrP )( 2

The inverse derived demands for input in market iM

211 )(21 CCA xxxr , 21

2 2)(1 CCA xxxr

The expected profit of firm A and the profit of firm C

)())(1()0( 2111

CCAAAL xxxkrxrE

202

101 )()( CCCL xkrxkr

14

X. The intuition of licensing and the finding

))(()())(( 212111 dxxdxxddxxEddE CCCCCCAAL

0*Ax if and only if max0 18)513( MkM

,

0*1Cx if and only if min0 58)4513( MkM

,

0*2Cx if and only if ccMkM

2)1315( 0 .

Lemma 2: In the licensing regime, it is necessary that the condition ccMM holds.

If 15/130 k , then firm C produces a positive quantity of input. Also, if

and only if minMMMcc , then firm A alone produces the input in the

1M market, firm C provides the input in the 2M market and does not sell

the input in market 1M . If and only if the condition maxmin MMM

holds, both firm A and C sell inputs in the 1M market and firm C provides

the input in the 2M market. If the condition MM max occurs, firm A

will not produce any input at all.

15

XI. The equilibrium in the extended model (Cont.)

26]11)1(213[ 0* kk , 52]5)1(1813[ 0

* kkxA ,

312]4513)1(58[ 0*1 kkxC , 156]15)1(213[ 0

*2 kkxC .

0624}]6213[2627513{ 022

0 kMMkEE ANAL

Define variable M as the larger root of M such that the expected profits of firm A are equal in the

cases where firm C produces the input in 1M and 2M market and where firm C only produces in

2M market.

M 1480/)]1(7541174312[ 00 kk

Define variable M as the smaller root of M such that the expected profits of firm A are equal in

the cases where firm A and C produces the input in 1M and 2M markets and where firm A is an

outsider in the market.

M 70/)]1(3923139[ 00 kk .

16

XI. The equilibrium in the extended model (Cont.)

Proposition 2: If 15/130 k or ccMM , then firm A will definitely license the input production

technology to firm C. When minMMMcc , then firm A will license the input

production technology to firm C, and firm C will not sell the input in input market

1M but provides the input in market 2M . When MMMmin , firm C

chooses only to supply the input in market 2M . When MMM firm C

sells the input both in input markets 1M and 2M . When maxMMM ,

firm A chooses to be an outsider to maximize its profits. Finally, firm A will quit

from input market in input market 1M if firm A is disadvantageous in input

production such that maxMM holds.

17

XI. The equilibrium in the extended model

Assume 88.00 k

Figure 6: The equilibrium in the extend model

Firm C only produces for Firm D

AE

outsider insider

No licensing M 0.925

333231 ,, EEE

0.0012

1 0.902

902

0.907 0.1 0.968 0.906 0.967

18

Thank for your listening and

comments are very welcome.