Transcript Uncertainty and Licensing in a Vertical Structure

Uncertainty and Licensing in a
Vertical Structure
Fang-yueh Chen
National Chung Cheng University
Tsai-chen Shen
Tatung 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.
22th April, 2011
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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
Firm A
Country T
Licensing
Firm C
input market
Firm B
Country E
Figure 1: The basic model
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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: P 1  Q
The derived demand for the input, r  1 2Q
The input monopolist’s expected profit function without licensing
E AN   (r  0)Q  (1   )( r  k )Q
 rQ  (1   )kQ
The input monopolist’s expected profit function with licensing
E AL   (r  0) x A  (1   )( r  k ) x A  xC
The profit function of a licensee (firm C) E CL  (r  k0   ) xC
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VI. The intuition of licensing and
the finding (Cont.)
dE AL d  (E A x A )( dx A d )  (E A xC )( dxC d )  xC   (dxC d )
Lemma 1: In the licensing regime, both firm A and C have positive output
production if and only if the condition k0  (1   )k  (5  2k0 ) 7 holds.
Equilibrium figures in the licensing contract:
 *  [5  (1   )k  4k0 ] 10 , r  [5  2k0  3(1   )k ] 10,
x A*  [5  7(1   )k  2k0 ] 20 , xC*  [(1   )k  k0 ] 5,
Q L  x A*  xC*  [5  2k0  3(1   )k ] 20 ,
E AL  (5  4k02  10 M  8k0 M  9M 2 ) 40
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VI. The intuition of licensing and
the finding
Equilibrium without licensing
E AN  2(Q A ) 2  [1  (1   )k ]2 8
E AL  E AN  [k0  (1   )k ]2 10  0 if and only if
k0  (1   )k  M
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.)
E ALC  QC vs. E CL  (r  k0   )QC
E AL  E ALC  (5  3k02  20 M  18 M 2  2k0 (8M  5) 80
M low  10  8k0  10 1  k0  18 ,
M high  10  8k0  10 1  k0  18
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VII. Equilibrium with licensing and
entry mode of an outsider
Proposition 2: In the licensing regime if and only if M  M low, firm A will
choose to be an insider and produce the input. Otherwise,
firm A will choose to be an outsider.
Assume k0  0.88
E A
No licensing
0.0009
insider
outsider
M
0.88 0.925 0.965 1
Figure 3: The choices of insider and outsider
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VIII. The extended model
Country J
Firm A
Country T
Licensing
Input Market, M1
Firm B
Firm C
Input Market, M2
Firm D
Country E
Figure 4: The extended model
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IX. Main equations
The profits functions of firm B and firm D (downstream firms)
 B  ( P  r1) x B
 D  ( P  r2 ) x D
The inverse derived demands for input in market M i
r1  1  2( x A  xC1 )  xC 2 ,
r2  1  ( x A  xC1 )  2 xC 2
The expected profit of firm A and the profit of firm C
E AL   (r1  0) x A  (1   )( r1  k ) x A   ( xC1  xC 2 )
 CL  (r1  k0   ) xC1  (r2  k0   ) xC 2
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X. The intuition of licensing and the
finding
dE AL d  (E A xC1)( dxC1 d )  ( xC1  xC 2 )   (d ( xC1  xC 2 ) d )
x A*  0 if and only if M  (13  5k0 ) 18  M max ,
xC1*  0 if and only if M  (13  45k0 ) 58  M min ,
xC 2*  0 if and only if M  (15k0  13) 2 M cc .
Lemma 2: In the licensing regime, it is necessary that the condition M  M cc holds.
If k0  13 / 15, then firm C produces a positive quantity of input.
Also, if
and only if M cc  M  M min , then firm A alone produces the input in the
M1 market, firm C provides the input in the M 2 market and does not sell
the input in market M1 .
If and only if the condition M min  M  M max
holds, both firm A and C sell inputs in the M1 market and firm C provides
the input in the M 2 market.
If the condition M max  M occurs, firm A
will not produce any input at all.
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XI. The equilibrium in the extended
model (Cont.)
 *  [13  2(1   )k  11k0 ] 26 , x A*  [13  18(1   )k  5k0 ] 52 ,
xC1*  [58(1   )k  13  45k0 ] 312 , xC 2*  [13  2(1   )k  15k0 ] 156 .
E AL  E AN  {13  75k02  62 M 2  2[13  62 M ]k0} 624  0
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 M1 and M 2 market and where firm C only produces in
M 2 market.
M   [312  1174 k0  754 (1  k0 )] / 1480
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 M1 and M 2 markets and where firm A is an
outsider in the market.
M   [39  31k0  2 39 (1  k0 )] / 70 .
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XI. The equilibrium in the extended
model (Cont.)
Proposition 2: If k0  13 / 15 or M  M cc , then firm A will definitely license the input production
technology to firm C.
When M cc  M  M min , then firm A will license the input
production technology to firm C, and firm C will not sell the input in input market
M1 but provides the input in market M 2 .
When M min  M  M  , firm C
chooses only to supply the input in market M 2 . When M   M  M  firm C
sells the input both in input markets M1 and M 2 .
firm A chooses to be an outsider to maximize its profits.
When M   M  M max ,
Finally, firm A will quit
from input market in input market M1 if firm A is disadvantageous in input
production such that M  M max holds.
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XI. The equilibrium in the extended
model
Assume k0  0.88
E A
E31 , E32 , E33
insider
outsider
0.0012
Firm C only produces for Firm D
0.1
No licensing
0.906 0.925 0.967
1
0.968
0.902 0.907
M
902
Figure 6: The equilibrium in the extend model
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Thank for your listening
and
comments are very welcome.
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