通し組／２．論説：大橋克成

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1 Brander and Spencer, 1983 ; Fudenberg and Tirole, 1984 ; Bulow et al., 1985 d Aspremont and Jacquemin R&D R&D R&D R&D R&D R&D R&D R&D R&D R&D Kamien et al.suzumuraleahy and Neary Salant and Shaffer R&D R&D R&D R&D

2 R&D R&D Steurs R&D R&D R&D Clark and Fujimoto R&D Bernstein R&D Steurs R&D R&D R&D R&D Steurs R&D R&D R&D R&D R&D R&D R&D

3 R&D R&D Fudenberg and Tirole Bulow et al. p R&D R&D R&D R&D R&D R&D R&D Steurs R&D R&D R&D R&D R&D A R&D B R&D C i j"1 i"j kl"34 k"l R&D c 0"c"1

4 p i 1&1x i u i "u p k &1y k v k "v x j i y l k u j i%j&1% i&$j v l k%l&3%4 k&$l " x i u i i y k v k k i u i j R&D R i R j k l R&D S k S l 1&4%R u i&$[r i j 1&4%#(S k 1&4%S 1&4 l )] $'0 Symeonidis$ u i R&D #(0%1) ##(0%1) "0(#"0) R&D Jones R&D k v k l R&D S k S l i j R&D R i R j 1&4%S v k&$[s k l 1&4%#(R i 1&4%R j 1&4 )] $'0 " "#(0%) ""0 "" u i&u j v k&v l p i 1 i p k k " SteursSuttonSymeonidis " j i u i (1p i 1 x i&u )"u (1p j 1 ) i%j&1% i&$j (%")(") l k v k (1p k y k&v )"v (1p l ) k%l&3%4 k&$l (%")(") i k # $ # $ Sutton Symeonidis Steurs Symeonidis Jones Romer R&D u i R&D R& D R&D v k

5 " " R&D R&D j ( i 1c )u i u i (1p i 1 i 1$p ( i 1c )x i$p )"u (#")(") k c k $p ( k c )y k$p l ( )v k v k (1p k )"v (#")(") (1p j 1 ) (1p l ) " R&D R&D A R&D B R&D C i u i (1p i $p i 1$u 1#c)"u " k v k (1p k $p k $v #c)"v $i 1 j (1p j 1 ) $0 i#j$1# i$"j # (#")(") $k l (1p l ) $0 k#l$3#4 k$"l $ (#")(") # $ i k 1$"u j p i 4u i p k $"v j 4u i p j 1#u i (1#c)"u l 4v k p l #v k (1#c)"v l 4v k # $

6 " p i 1$c#(1c) (8# )u i#u j # (4##)(4#)u i p k $c#(1c) (8# )v k#v l $ (4##)(4#)v k " " " # $ i k i 1$(1c) (8# )u i#u j (##)(#)(4##) (4#) k $(1c) (8# )v k#v l (##)(#)(4##) (4#) % & )(# i&j$1& #(8# )(# k&l$3&4 p i 1 p k i 1 k i 1R i k S k R&D #(8# )'u i(u j'(8# *i 1 *R i$*i *k *S k$*k 1 i *u i*u i#*i 1 *R )'v k(v l'(8# j ' *u j*u *R i$1 i$"j k *v k*v k#*k l *S *v l*v )#" (1c) 4 (8# " (1#"#$) (##) (4##) (4#) *S k$1 k$"l ( ' ( R&D "(4# u i v k R&D R A$S A$%4 ) ) $'(4##)(#)4#" R&D $)(4##)(#)4#" "(4# R&D R&D Brander and Spencer B C

7 "1' )#" A A, u A#v A#% (1c) (8# (1"""$) 3' ("#) 1' (4"#) 1' (4#) % & ( ) * +, x A#y A#%4 (1c) )#" )#" 3 "(1"""$) (8# 3 " ("#) (4"#)(4#) 3 A#%4 (1c) 4 "(1"""$) 1 A# (#) (8# 3 # ("#) )#" (4"#)(4#) 4," # A#4%4 (1c) 4 "(1"""$) (8# ) WE $ ("#) (4"#) (4#) 4 R&D R&D " "(1# )"4$(4"#)(3#)"(16## A ' + R&D R&D )i #% 1 (1c) )R i )i 1 )R i )j 1 )R j )i 1 )R j)r i [(8# )#"]["(44#3# )"6$(4"#)(#)"(83## )] )j 1 j#%4 (1c) 4 (1"") )R i)r 4("#)(#)(4"#) (4#) ["(44#3# )"6$(4"#)(#)"(84## R3' &0 ["(44#3# )"6$(4"#)(#)"(48#3# )] )] R3'("#) (#) (4"#) 4 )#" (4#) )#" "(1"""$) 3'("#) ""(8## "(1"""$) )"4$(4"#)(#)"(84## ) ("#) (4"#) (4#) 4(0 CS PS CS A#8%4 (1c) 4 (8# PS A#4%4 (1c) 4 (8# (4"#)(4#) 4 4.

8 &(1c) (8# " )u i#u %(1c) " j )u j (%#)(#)(4%#) (4#) (%#)(#)(4%#) (4#) I &k %l &(1c) (8# " )v k#v %(1c) " l )v l (%#)(#)(4%#) (4#) (%#)(#)(4%#) (4#) I 1&i 1%j 1 #u i%(8# #v k%(8# i&j&1& i&"j k&l&3&4 k&"l i k I 1R ir j I S ks l R&D )I 1 )R i&)i )I )S k&)i 1 i )u i)u i%)i 1 )R k )v k)v k%)i )S j )u j)u )R i&1 l )v l)v )S k&1 A ( R&D u i v k R&D R B&S B&%4 (1c) 4 (#) (1%") (%#) (1%"%$) (4#) 4 ) ) R&D B B ) u B&v B&% (1c)(#) 1( (1%") (%#) 1( 1( (1%"%$) (4#) 3( ( * " # $ % & ' ) * )I 1()R (1c) #(8# %#"(8# )#$#"(83## )%6$(4%#)(#)%(44#3# )$$R3( (4(%#)(#)(4%#) (4#) '0 &% i # )$ )#"$#"(44#3# )%6$(4%#)(#)%(83##

9 R&D R&D x B$y B$%4 (1c) 3 (#)(1#")(1#"#$) 3 (##) (4#) 1 B$ (1#")(1#"#$) " (##) (4#) B$4%4 (1c) 4 (#)(1#")(1#"#$) WE (##) (4#) B$%4 (1c) 4 (#) # $ % & 4 % & (4#)(1#")#4$(3#) ' A " R&D R&D " " ik$i 1#k $(1c) (8# )u i#u #(1c) (8# j ) v k#v l (##)(#)(4##) (4#) (##)(#)(4##) (4#) i&j&k&l$1&&3&4 i$"j$"k$"l i k ikr is k R&D (ik i$(ik i (R (u i(u i#(ik j (R (u j(u i#(ik k (R (v k(v i#(ik l ( (R (v l(v (R i$1 (ik k$(ik i (S (u i(u k#(ik j (S (u j(u k#(ik k (S (v k(v k#(ik l ) (S (v l(v (S k$1 ( ) R&D u i v k R&D CS B$8%4 (1c) 4 (#)(1#")(1#"#$) 3'(##) (4#) 4 PS B$4%4 (1c) 4 (#) (1#")(1#"#4$)(1#"#$) '(##) (4#) 4.

10 " R C%S C%%4 (1c) 4 ["(8# )#"#$$(4$#)(#)] (1$"$$) ' ($#) (4$#) (4#) 4 ' $&(() (4$#)(#)4#" '4#(4$#)(#)" R&D R&D C C ' u C%v C%% (1c)["(8# )#"#$$(4$#)(#)] ($#) 1' (4$#) 1' (1$"$$) 3' 1' (4#) " # $ % & ' ( x C%y C%%4 (1c) 3 ["(8# )#"#$$(4$#)(#)] (1$"$$) 3 ($#) (1c) 4 (#)["(8# 1 C% )#"#$$(4$#)(#)] (1$"$$) 3 ($#) C%%4 ' ( ) * (4$#)(4#) 3 ) (4$#)(4#) 4 * ( WE C%4%4 (1c) 4 ["(8# )#"#$$(4$#)(#)] (1$"$$) )]'($#) (4$#) ["(1# )$$(40#3# )$(16## (4#) 4 + %% (1c) ["(8# )#"#""(44#3# )$6$(4$#)(#)$(83## )#$$(#) (4$#) )R i )ik 4($#)(#)(4$#) (4#) (3$3"$5$)] &0 CS C%8%4 (1c) 4 ["(8# )#"#$$(4$#)(#)] (1$"$$) 3'($#) (4$#)(4#) 4 C%4%4 (1c) 4 ["(8# )#"#$$(4$#)(#)] ["(8## )$3$(4$#)(#)$(84## )] (1$"$$) PS ($#) (4$#) (4#) 4.

11 R&D R&D R& D R&D " R B#&R. A u B#&u A x B#&x A B#&A WE B#&WE for#"(1%1%8" A R&D R&D R&D R&D R C(R A u C(u A x C(x A C(A WE C(WE A. R&D R&D R&D R&D R C#&R WE C#&WE B B u C#&u "$ if"($ B x C#&x B C#&B for##&(1$)%(1$) %8("$) if""$ R C(R B u C(u B x C(x B C(B WE C(WE B for#$(0%) "($ R &D R&D ""$ R&D R&D "($ R&D 0&#&[(1$)%(1%$) %8("$) ]'("$) R A&R C&R B u A&u C&u B

12 x A$x C$x B WE A$WE C$WE B [(1#)#(1##) #8(#) ]% R A$R B"R C u A$u B"u C x A$x B"x C WE A$WE B"WE C [1#1#8 ]%""$ R B"R A$R C u B"u A$u C x B"x A$x C ]%(#)""$[1#1#8 WE B"WE A$WE C i R&D j k R&D Kamien et al.combined profits externality i R&D j k R&D R&D R&D "&($) [1#1#8 ]% "&($)[(1#)#(1##) #8(#) ]%(#) R&D A R&D B R&D C R&D "$[1#1#8 ]% "$[(1#)#(1##) #8(#) ]%(#)

13 R&D R&D &# R&D R&D R&D "&($)[1#1#8 ]%R&D R&D R&D R&D ]%(#) R&D R&D R&D R&D R&D R&D R&D "&($) [(1#)#(1##) #8(#) R&D R&D R&D R&D R&D R&D R&D R&D R&D Steurs "# R&D 0$"$[1#1#8 ]% R A$R B$R C u A$u B$u C x A$x B$x C WE A$WE B$WE C [1#1#8 ]%""$ R B"R A$R C u B"u A$u C x B"x A$x C WE B"WE A$WE C

14 R&D R& D R&D $## " # R&D # R&D R&D R&D R&D R&D R&D R&D R&D Steurs R&D R&D R&D R&D R&D R&D R&D R&D R&D R&D R&D Steurs R&D

15 R&D R&D R&D R&D R&D R&D #" " R&D R&D R&D R&D R&D R&D R&D R&D R&D R&D R&D R&D R&D R&D R&D R&D R&D R&D R&D R&D R&D "

16 ' i j ('0 A1 *u i*u *u j*u *R i *I 1 *R i'*i *ik *R i'*i ' % (&*j 1 i&*j *R (&*k &'0 i&*i i&*i i&*k A *R *R *R 1 i *u i*u i&*i 1 j *R *u j*u i&*i 1 *R *R i i j k l *u i*u *u j*u *R i *v k*v *v l*v *R # )#" )+ i # A1 A $(1&"&$) (1c) (8# R1( *,'0A3 # "(8# $(1&"&$)R1( )#" (&#)(4&#)(4#) 1 (&#)(4&#)(4#) $(1&"&$) (1c) (8# R1( (#)(1&"&$) R1( 1 (&#)(4&#)(4#) (&#)(4#) *I 1 *R i'% *ik *R i'% )+ *,&% (1c) )+ )+ *,'0 *,&$% (1c) A4 )# i R&D A3 i R&D j A4 i R&D k )#" R&D R&D )# (1c) " ""(8# "R (8# i3(4 R j3(4 #' (&#)(#)(4&#) (4#) )#" i'%j (1c) "R (8# i3(4 S k3(4 )0 i'%k (&#)(4&#)(4#) 0 # R&D #)[1&1&8" ](" R&D )# $ A3A4 A4A3 % (1c) 1R1( (1&"&$)$(4&#)(#)"(8# (&#)(4&#)(4#) &8("$) A4A3-/.#'for##'(1$)&(1$) for#$(0&) if""$ *I 1 *R j*r i'% for#")1&1&8" *ik *S k*r i'$% "$ if")$

17 % #'[1'1'8" ](" R&D R&D R&D R&D *ik *S k*r i*i 1 *R j*r i(% (1c) [(8# )#"][$(4'#)(#)%"(8# # *ik *S k*r i*i 1 *R j*r i$#$" % "$ if")$ )#&]R3( ('#)(#)(4'#) (4#) 'for##'(1$)'(1$)'8("$) )0 for#$(0&) if""$ Bernstein, Jeffrey I., 1988, Cost of Production, Intra and Interindustry R&D Spillovers : Canadian Evidence, Canadian Journal of Economics 1, Bernstein, Jeffrey I. and M. Ishaq Nadiri, 1988, Interindustry R&D Spillovers, Rates of Return and Production in High Tech Industries, American Economic Review 78, Papers and Proceedings, Bernstein, Jeffrey I. and M. Ishaq Nadiri, 1989, Research and Development and Intra Industry Spillovers : An Empirical Application of Dynamic Duality, Review of Economic Studies 56, Brander, James A. and Barbara J. Spencer, 1983, Strategic Commitment with R&D : The Symmetric Case, Bell Journal of Economics 14, Bulow, Jeremy I., John D. Geanakoplos and Paul D. Klemperer, 1985, Multimarket Oligopoly : Strategic Substitutes and Complements, Journal of Political Economy 93, Clark, Kim B. and Takahiro Fujimoto, 1991, Product Development Performance : Strategy, Organization, and Management in the World Auto Industry, Boston : Harvard Business School Press. d Aspremont, Claude and Alexis Jacquemin, 1988, Cooperative and Noncooperative R&D in Duopoly with Spillovers, American Economic Review 78, d Aspremont, Claude and Alexis Jacquemin, 1990, Cooperative and Noncooperative R&D in Duopoly with Spillovers : Erratum, American Economic Review 80, Fudenberg, Drew and Jean Tirole, 1984, The Fat Cat Effect, the Puppy Dog Ploy, and the Lean and Hungry Look, American Economic Review 74, Papers and Proceedings, Häckner, Jonas, 000, A Note on Price and Quantity Competition in Differentiated Oligopolies, Journal of Economic Theory 93, Henriques, Irene, 1990, Cooperative and Noncooperative R&D in Duopoly with Spillovers : Comment, American Economic Review 80, Jones, Charles I., 1995, R&D Based Models of Economic Growth, Journal of Political Economy 103, Kamien, Morton I., Eitan Muller and Israel Zang, 199, Research Joint Venture and R&D Cartels, American Economic Review 8, Leahy, Dermot and J. Peter Neary, 1997, Public Policy towards R&D in Oligopolistic Industries, American Economic Review 87, Motta, Massimo, 199, Cooperative R&D and Vertical Product Differentiation, International Journal of Industrial Organization 10,

18 Qiu, Larry D., 1997, On the Dynamic Efficiency of Bertrand and Cournot Equilibria, Journal of Economic Theory 75, Romer, David, 001, Advanced Macroeconomics, d ed. New York : McGraw Hill. Salant, Stephen W. and Greg Shaffer, 1998, Optimal Asymmetric Strategies in Research Joint Ventures, International Journal of Industrial Organization 16, Singh, Nirvikar and Xavier Vives, 1984, Price and Quantity Competition in a Differentiated Duopoly, RAND Journal of Economics 15, Steurs, Geert, 1995, Inter Industry R&D Spillovers : What Difference Do They Make?, International Journal of Industrial Organization 13, Sutton, John, 1997, One Smart Agent, RAND Journal of Economics 8, Sutton, John, 001, Technology and Market Structure : Theory and History, Cambridge, MA : MIT Press. Suzumura, Kotaro, 199, Cooperative and Noncooperative R&D in an Oligopoly with Spillovers, American Economic Review 8, Symeonidis, George, 003, Comparing Cournot and Bertrand Equilibria in a Differentiated Duopoly with Product R&D, International Journal of Industrial Organization 1, II

19 R&D R&D Quality Improving R&D and R&D Policy in Differentiated Oligopoly : Bertrand Price Competition Katsunari Ohashi This paper considers whether the results of Steurs (1995) hold under differentiated oligopoly with quality improving R&D when firms play the role of Bertrand player, focusing on the choice of optimal R&D policy. When making comparisons of market performances among three cases (e.g. R&D competition, intra industry R &D cooperation and inter industry R&D cooperation), we show that the optimal R&D policy depends on the relationship between intra and inter industry spillovers as well as the level of spillovers and product differentiation. Therefore, the government must coordinate the policy according to the level of spillovers and product differentiation after the government has probed the relationship thoroughly.

濱田弘潤 : 多角化企業の利潤分析 77 多角化企業の利潤分析多角化ディスカウントの寡占理論による説明 * 濱田弘潤 (diversification discount) Keywords: JEL classifications: D43, L13, L22, G

濱田弘潤 : 多角化企業の利潤分析 77 多角化企業の利潤分析多角化ディスカウントの寡占理論による説明 * 濱田弘潤 (diversification discount) Keywords: JEL classifications: D43, L13, L22, G34 950-2181 2 8050 Tel. and fax: 025-262-6538 E-mail: [email protected]