uncertainty and licensing in a vertical structure
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Uncertainty and Licensing in a Vertical Structure. Fang-yueh Chen National Chung Cheng University Tsai-chen Shen Tatung Institute of Commerce and Technology. - PowerPoint PPT PresentationTRANSCRIPT
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.
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I. Motivations
Licensing in a vertical structure
Licensing with risk sharing
Endogenizing insider and outsider models
Licensing and vertical externality
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II. Purposes
Investigate how an input monopolist shares risks through international licensing and its consequences
Examine the impact of entry in the downstream market
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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)
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IV. The basic model
Country J Country T
Figure 1: The basic model
Firm A
Firm B
Firm C
Country E
input market
Licensing
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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
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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
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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
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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.
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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
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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
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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
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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
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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.
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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 .
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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.
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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
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Thank for your listening and
comments are very welcome.