1 M&A Keywords:,. Address: 742-1, Higashinakano, Hachioji-shi, Tokyo 192-09,Japan fax:+81 426 74 425 E-mail: yangc@tamacc.chuo-u.ac.jp ; yasuokaw@tamacc.chuo-u.ac.jp 1 Yang and Kawashima(2008)
1 2 ( MVI ) 4 5 M&A MVI 2 100, Richardson(2009) (1997) 1 2 (1997)22 225, (1999) (1999)4 (tying good) (tied good) 4 (2009)15 5 (2008) (2008)281 1
6 Whinston(2006) (exclusionary vertical contracts) (exclusionary contracts) (vertical contracts) tied sales) Whinston(1990) 2 Whinston(1990) MVI Tirole(1988) Rey and Tirole (2007) MVI (foreclosure) 7 DeGraba (200) ( VBM ) Salinger (1988) VBM Westfield (1981) Westfield (1981) (pure monopoly) Tirole(1988) Rey and Tirole(2007) 6 (1998)69 7 Tirole(1988) Tirole(1988)19-198 2
Rey and Tirole(2007) M&A Tirole(1988) MVI 8 9 10 8 (2005) 62 9 10 (1998)176 192
11 Whinston(1990) 2 tied sales) MVI tied sales) 12 11 2009 4 12 (2009) 4
2 ( ) 1 2 2 1 2 P = a x = a (x 1 + x 2 ), (1) P x i i, i =1, 2 α i i α i 1 y i 1 2 x i = 1 α i y i, i =1, 2 (2) 2 1 α = α 1 /α 2 > 1. () 2 1 (, ) (2) 1 α i i 1 Economides(1998) 5
c i c i = α i p b, i =1, 2, (4) p b 2 2 (1) (4) i π i =(P c i )x i =(a α i p b (x 1 + x 2 ))x i, i =1, 2, x i π 1 x 1 = a α 1 p b 2x 1 x 2 =0 π 2 x 2 = a α 2 p b x 1 2x 2 =0. x 1 = a (2α 1 α 2 )p b, x 2 = a +(α 1 2α 2 )p b, X X = x 1 + x 2 = 2a (α 1 + α 2 )p b. MC 0 <MC= β, (5) a 4α 1 β. (6) (6) 1 6
p b p b 1 2 x 1 P B x 2 P B 1: 1. p b = a(α 1 + α 2 )+2(α 2 1 α 1 α 2 + α 2 2)β 4(α 2 1 α 1α 2 + α 2 2 ) >β, (7) P B = a(5α2 1 2α 1 α 2 +5α 2 2)+2(α 1 + α 2)β 12(α 2 1 α 1α 2 + α 2 2 ) >α 1 p b, (8) x 1 = a (2α 1 α 2 )p b x 2 = a +(α 1 2α 2 )p b > 0, > 0.. (2) x 1,x 2 y b y b = α 1 x 1 + α 2 x a +( 2α 1 + α 2 )p b 2 = α 1 = a(α 1 + α 2 ) 2(α 2 1 α 1 α 2 + α 2 2)p b. 7 + α 2 a +(α 1 2α 2 )p b
π b =(p b β)y b =(p b β) a(α 1 + α 2 ) 2(α 2 1 α 1α 2 + α 2 2 )p b. π b p b p b p b p b = a(α 1 + α 2 )+2(α 2 1 α 1α 2 + α 2 2 )β 4(α 2 1 α 1α 2 + α 2 2 ). X p b (1) P B P B = a(5α2 1 2α 1α 2 +5α 2 2 )+2(α 1 + α 2 )β 12(α 2 1 α 1α 2 + α 2 2 ). p b β p b β p b β = a(α 1 + α 2 )+2(α 2 1 α 1α 2 + α 2 2 )β 4(α 2 1 α 1α 2 + α 2 2 ) β = a(α 1 + α 2 ) 2(α 2 1 α 1α 2 + α 2 2 )β 4(α 2 1 α 1α 2 + α 2 2 ). α 1 >α 2 p b β, (6) a(α 1 + α 2 ) 2(α 2 1 α 1α 2 + α 2 2 )β 4α 1β(α 1 + α 2 ) 2(α 2 1 α 1α 2 + α 2 2 )β =2β(α2 1 +α 1α 2 α 2 2 ) =2α 2 2 β(α2 +α 1) > 0, (), i.e., α>1 p b β P B α 1 p b α 1 p b 1 P B α 1 p b = a(5α2 1 2α 1 α 2 +5α 2 2)+2(α 1 + α 2)β a(α 1 + α 2 )+2(α 2 1 α 1 α 2 + α 2 12(α 2 1 α 1α 2 + α 2 2 ) α 2)β 1 4(α 2 1 α 1α 2 + α 2 2 ) = 1 12(α 2 1 α 1α 2 + α 2 2 )(a(2α2 1 5α 1 α 2 +5α 2 2)+2β( 2α 1 +α 2 1α 2 α 1 α 2 2 + α 2)) 1 12(α 2 1 α 1α 2 + α 2 2 )(4α 1β(2α 2 1 5α 1α 2 +5α 2 2 )+2β( 2α 1 +α2 1 α 2 α 1 α 2 2 + α 2 )) = β 6(α 2 1 α 1α 2 + α 2 2 )(2α 1 7α 2 1α 2 +7α 1 α 2 2 + α 2) = α 2 β 6(α 2 α +1) (2α 7α 2 +7α +1)> 0, α = α 1 /α 2 () (6) x 1 x 2 1 2 8
1 x 1 p b (7) (6) x 1 x 1 = a (2α 1 α 2 )p b 4α 1 β (2α 1 α 2 ) a(α 1+α 2 )+2(α 2 1 α 1α 2 +α 2 2 )β 4(α 2 1 α 1α 2 +α 2 2 ) = 2α 1 7α2 1 α 2 +7α 1 α 2 2 + α 2 6(α 2 1 α1α2+α22 ) = (2α 7α 2 +7α +1)α 2 6(α 2 α +1) 1 h(α) () α 2 2 h(α) h(α) =2α 7α 2 +7α +1 α>1 h(α) (1, ) α =1 h(1) = α >1 k(α) > 0 x 1 0 h(α) 2 α x 1 h 100 80 Out[2]= 60 40 20 1.5 2.0 2.5.0.5 4.0 Α 2: h(α) 2 x 2 2 x 2 p b (7) (6) x 2 x 2 = a +(α 1 2α 2 )p b 9
4α 1 β +(α 1 2α 2 ) a(α 1+α 2 )+2(α 2 1 α 1α 2 +α 2 2 )β 4(α 2 1 α 1α 2 +α 2 2 ) = (11α 1 1α2 1 α 2 +7α 1 α 2 2 2α 2 )β 6(α 2 1 α 1α 2 + α 2 2 ) = (11α 1α 2 +7α 2)α 2 β 6(α 2 α +1) 1 k(α) k(α) = (11α 1α 2 +7α 2) α>1 k(α) (1, ) α =1 k(1) = α >1 k(α) > 0 k(α) α x 2 k 140 120 100 Out[19]= 80 60 40 20 1.5 2.0 2.5.0 Α : k(α) x 1 x 2 X = x 1 + x 2 > 0 14 14 10
a 4α 1 β α>1 11
p i β p i 1 2 x 1 P I x 2 P I 4: VBM 1 2 Yang and Kawashima(2008) I VBM VBM MVI VBM VBM 4 12
VBM MVI 1 2, Westfield (1981) Westfield (1981) 1 β p i MVI β VBM MVI I 2 x I MVI x 2 π I = π d + π u =(P α 1 β)x I + α 2 (p i β)x 2 =(a α 1 β (x I + x 2 ))x I + α 2 (p i β)x 2, π 2 = (P α 2 p i )x 2 =(a α 2 p i (x I + x 2 ))x 2, π d π u MVI p i 2 ( ), π I x I = π d x I = a α 1 β 2x I x 2 =0, 1
π 2 x 2 = a α 2 p i x I 2x 2 =0, x I = a 2α 1β + α 2 p i, (9) x 2 = a + α 1β 2α 2 p i. (10) 2 MVI x 2 2 2 α 2 x 2 = Y = α 2(a + α 1 β 2α 2 p i ). (11) VBM 2. p i = 5a α 1β +6α 2 β 10α 2, (12) P I = 5a + β(α 1 +2α 2 ). (1) 10 P I α 1 p i x 2 Y x 2 = 2(α 1 α 2 )β > 0, 5 Y = 2(α 1 α 2 )α 2 β > 0. 5. MVI (11) (9) (11) MVI π I = π d + π u =(P α 1 β)x I +(p i β)y =(a α 1 β x I x 2)x I +(p i β)y = ( a α 1 β a 2α 1β + α 2 p i a + α 1β 2α 2 p ) i a 2α1 β + α 2 p i +(p i β) α 2(a + α 1 β 2α 2 p i ) ( a 2α1 β + α 2 p ) i 2 α 2 (p i β)(a + α 1 β 2α 2 p i ) = +. π I dπ I =2 (a 2α 1β + α 2 p) α 2 dp i + α 2 ((a + α 1β 2α 2 p)+(p i β)( 2α 2 ))=0. 14
p i p i = 5a α 1β +6α 2 β 10α 2. p i (9) (10) VBM P I (1) P I = a x I x 2 = a a 2α 1β + α 2 p i a + α 1β 2α 2 p i = 5a + β(α 1 +2α 2 ). 10 (10) 2 x 2 x 2 = a + α 1β 2α 2 p i = 2(α 1 α 2 )β 5 > 0, () 2 x 2 MVI P I α 2 p i = 2β(α 1 α 2 ) 5 > 0. () MVI MVI p i 2 p i β p i β = 5a α 1β +6α 2 β 10α 2 β = 5a α 1β 4α 2 β 10α 2 > 0, () (6) p i β MVI 2 MVI MVI () α 1 15
. α 1 >α 2. 2 α 1 >α 2 2 Y > 0 MVI Whinston (1990) P roposition α 1 >α 2 x 2 0 α 1 MVI MVI MVI MVI 2 () 16
1980 (2001) 15 (2004) 16 α >1 α 1 α >1 M&A α 1 = α 2 =1 15 (2001) 2 16 (2004) 207 17
α 1 = α 2 =1 OS 17 Windows ( ) α 1 = α 2 =1 α 1 = α 2 =1 OS α 1 = α 2 =1 1.. α 1 = α 2 =1 17 18
2 x 2 =0 VBM 2 P I P B 2 P I P B P I P B = 5a + β(α 1 +2α 2 ) a(5α2 1 2α 1α 2 +5α 2 2 )+2(α 1 + α 2 )β 10 12(α 2 1 α 1α 2 + α 2 2 ) (14) = 5a(α2 1 4α 1α 2 + α 2 2 ) + 2(4α 1 α2 1 α 2 +α 1 α 2 2 + α 2 )β 60(α 2 1 α 1α 2 + α 2 2 ) (15) = 5a(α2 4α + 1) + 2(4α α 2 +α +1)α 2 β 60(α 2. (16) α +1) f(α) = P I P B, g(α) = 4α α 2 +α +1 α 2. 4α +1 P I P B = f(α) = = = 2α 2 β 60(α 2 α +1) { 5a 2α 2 β (α2 4α +1)+(4α α 2 +α +1)} α 2 β 0(α 2 α +1) (α2 4α +1){ 5a 2α 2 β + 4α α 2 +α +1 α 2 } 4α +1 α 2 β 0(α 2 α +1) (α2 4α +1){ 5a 2α 2 β + g(α)}, (α 2 α +1) α f(α) =0 2 19
5a + g(α) =0, 2α 2 β f(α) =0 α α () (6) 5a 2α 2 β 5 4α 1β 2α 2 β > 5 4α 2β 2α 2 β =10. 10 + g(α) = 10 + 4α α 2 + α +1 α 2 4α +1 =0. (17) α = 4.217, 0.01, 2.166 α =1 g(1) = 1.5 α>1 g(α) 1.5 (1,.72) α g(α) g 200 Out[]= 100 2 4 5 6 Α 100 200 5: g(α) α>1( ()) (17) α =2.166 g(α) 5a/(2α 2 β) > 10 (17) α 2.166.72 1 2 2. 2 VBM 20
P I P B, for 1 <α α, P I >P B, for α > α.. P I P B P I P B P I P B = α 2 β 0(α 2 α +1) (α2 4α +1){ 5a + g(α)}. (18) 2α 2 β (), α 1 α.72 α.72 g(α) 5a + g(α) =0 2α 2 β (2.166,.72) α 5a/(2α 2 β) > 10 18) 2 (α 2 4α +1) (18) α>.72 2 g(α) > 0 α>.72 2α 5a 2 β + g(α) > 0 α>.72 (18) P I >P B 1 <α<.72 (18) 2 0 α 1.72, g(α) (1,.72) (17) g(α) (17) g(α)+ 5a 2α 2 β 0, for α α, g(α)+ 5a 2α 2 β < 0, for α > α. α (1,.72) (α 2 4α +1)< 0 (18) P I P B, for 1 <α α, P I >P B, for α > α. 21
VBM 18 2 VBM MVI MVI MVI 2 2 α 1 1 <α α MVI α>α 1 <α<α α>α ) 18, Spengler (1950) 22
1 <α= α 1 /α 2 <α 2 α>α 2 1 <α α α >α 2. α <α VBM VBM 2
α>α α<α, VBM 19 MVI 1 2 VBM P I P B 4.. 1 2 α 1 = α 2 =1 P B P I P I = a + β 2 P B = 2a + β 19 http://www.jftc.go.jp/pressrelease/09.june/09061902.pdf 24
α 1 = α 2 =1 P I P B P I P B = a + β 6 < 0, for α 1 = α 2 =1 () (6) α 1 = α 2 =1 P I <P B Widows98 20 10 21 20 http://pc.watch.impress.co.jp/docs/article/980617/jftc.htm 21 (2008)287 10 25
4, 22 M&A 22 http://www.jftc.go.jp/pressrelease/09.june/09061902.pdf 4 26
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