Vertical Integration and Differentiation in an Oligopoly with Process Innovating R&D

Lambertini, Luca; Rossini, Gianpaolo Working Paper Vertical Integration and Differentiation in an Oligopoly with Process Innovating R&D Quaderni - Working Paper DSE, No. 468 Provided in Cooperation with: University of Bologna, Department of Economics Suggested Citation: Lambertini, Luca; Rossini, Gianpaolo (2003) : Vertical Integration and Differentiation in an Oligopoly with Process Innovating R&D, Quaderni - Working Paper DSE, No. 468, Alma Mater Studiorum - Università di Bologna, Dipartimento di Scienze Economiche (DSE), Bologna, https://doi.org/10.6092/unibo/amsacta/4826 This Version is available at: https://hdl.handle.net/10419/159309 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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ThL|t Lu |i ?|i}h@|i_ @?_ |i ?L? ?|i}h@|i_ U@ti . 2e Ai @t)44i|hU U@tit 5L u@h i @i @tt4i_ |@| h4t Mi@i ? @ t)44i|hU @) OLiihc i tL*_ @*tL UL?t_ih |i U@ti ? U |i _LTL*) t 4@_i M) L?i ?|i}h@|i_ h4 UL4Ti|?} | @ ?L? ?|i}h@|i_ L?i 5TTLti |@| h4  ?|i}h@|it *i 2 _Lit ?L| AihiuLhi Mi|ii? h4 2 N @?_ h4 2 #` |ihi @htit @ M*@|ih@* 4L?LTL*) L?t_ih |i? ThL|t Lu h4 G DV\  LQW  'E s   f  }  t  Eb *i ThL|t Lu |i |L ?L? ?|i}h@|i_ h4t @hiG DV\  GZ 2 ' E s 2  f  j 2  t 2 E 2f DV\  XS 2 ' E j 2  }  t 2 = E 2 `i U@? ?_ |i |L i^*Mh4 ^@?||it Lu ?@* }LL_t ThL_Ui_c t H  @?_ t H 2 M) }L?} |hL} |i uL**L?} 6tG ; A A ? A A = C DV\  LQW  Ct  'f C DV\  GZ 2 Ct 2 'f E 22 @?_ tL*?} |i4 t4*|@?iLt*)c LM|@??}G t H  '2 } nE d  f E v  2  j 2 v v 2  eE2 t H 2 '2 j 2 n E d  f  E v  2  v} v 2  e = E 2e Ai? t?} t H 2 i }i| DV\  H XS 2 = A@!?} |i 6 L? DV\  H XS 2 | hitTiU| |L j 2 i }i|G j W 2 ' E d  f  E 2  v n E 2n v  } e = E 2D u|ih tMt|||L? Lu j W 2 >t H  >t H 2 i }i| hi_Ui_ uLh4t LT|4@* ThL|t uLh |i  h4t LTih@|?} ? |i @t)44i|hU U@tiG H AihiuLhi i U@? h|iG H E  L  '  L>L n  E     L>QL ED. H E  QL  'E     E  XS QL>L n  GZ QL>L nE   E     QL>QL > ihi  @?_  @hi |i i?_L}i?Lt ThLM@M*|it Lu |i ?|i}h@|L? t|h@|i}) Lu |i |L t_it Lu |i ?_t|h) hitTiU|i*)c *i |ih UL4T*i4i?|t |L  @hi |i ThLM@M*|it Lu |i ?L? ?|i}h@|L? t|h@|i}) H t |i i TiU|@|L? LTih@|Lh W4TLt?} H E  L  ' H E  QL   > @?_ |t UL*4? UL?|ihT@h|c )i*_tG  W '  W '  QL>QL   L>QL  L>L   L>QL   XS QL>L   GZ QL>L n  QL>QL = E DH `i _L ?L| UL?t_ih |i U@ti v '  MiU@ti Lu |i _tUL?|?|) ThLM*i4t @ht?} L| |i L4L}i?iLt ih|h@?_ 4L_i* t @ T@h|@* UL?U*tL? 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L|ih Lh_tc |i ?i}@|i i |ih?@*|) @ttLU@|i_ | |i ?L? ?|i}h@|L? t|h@|i}) LUUht ? @ hi_Ui_ T@h@4i|ih @hi@ e W?|i}h@|L? @?_ +:# W| tii4t Lh|*i |L i |i?_ |i ThiLt 4L_i* |L UL?t_ih tL4i uLh4 Lu U@T|@* UL44|4i?| |L +:# AL |t ThTLti i UL?t_ih ThLUitt ??L@|L?c D i +:# _iL|i_ |L _iUhi@ti |i ULt| Lu ThL_U|L? ,i? u i UL*_ ? _gihi?|*) @?@*)3i +:# ? N Lh #` ThL_U|L?c i UL??i |i ??L@|i @U||) |L |i tTT*) Lu |i ?|ih4i_@|i }LL_ , |i?tL?t @hi i@t*) @@* @M*i L? |i M@tt Lu |i t@4i @TThL@U Ai @?@*)tt t ?L| i?|hi*) }i?ih@* t?Ui | t t| 4i@?| |L thi) U@tit ? U |i _t?|i}h@|i_ T@h| Lu @? ?_t|h) 4@) Mi 4Lhi iUi?| ii? ? |i Thiti?Ui Lu L*}LTL*t|U 4@h!i|t Ai tUi?@hL i ?it|}@|i ? L?i ? U |i 4@h!i| uLh |i #` ?@* }LL_ t ULihi_ M) q n  h4tc L?i Lu U t ih|U@**) ?|i}h@|i_c *i |i hi4@??} q #` h4t M) |i ?|ih4i_@|i }LL_ uhL4 @ t?}*i N h4 Ai 4@h!i| uLh |i ?@* }LL_ t _gihi?|@|i_ Ai ?ihti _i4@?_ u?U|L? uLh |i ?|i}h@|i_ h4 tG s LQW ' d  t LQW  v # t l n [ m  ' l t m $ E Db ihi t l n S m  ' l t m t |i |L|@* L|T| Lu |i q #` h4t Ai ?ihti _i4@?_ u?U|L? Lu i@U #` h4 tG s l>GZ ' d  t l  v # t LQW n [ m  ' l t m $ = E Sf Ai ThL_U|L? Lu |i ?@* }LL_ |@!it T*@Ui @| UL?t|@?| hi|h?t |L tU@*ic @t ? |i ThiLt tiU|L? `i @tt4i |@| ThLUitt ??L@|?} +:# |@!it T*@Ui ? |i N h4 @?_ ? |i N _tL? Lu |i ?|i}h@|i_ h4c @UULh_?} |L |i uL**L?} t4T*i |iU?L*L})G } k ' }  n k >k ' LQW>XS ES ?L*?} @ ^@_h@|U ULt|G f E n k ' n 2 k = E S2 t |L |i ?|i}h@|i_ h4c |i ?T| |h@?tuih |@!it T*@Ui @| |i 4@h}?@* ULt| Lu ThL_U|L?c *i ?L??|i}h@|i_ h4t M) | uhL4 |i N h4 @| |i 4@h!i| ThUi j= Ai?c i @hi @M*i |L h|i |i ThL| u?U|L? Lu |i ?|i}h@|i_ h4G  LQW ' E s LQW  } LQW  t LQW  n 2 LQW E S *i L? |i ?L??|i}h@|i_ t_i Lu |i ?_t|h) ThL| u?U|L?t @hiG  XS ' E j XS  } XS  # t l n [ m  ' l t m $  n 2 XS E Se S  l 'E s l  j XS  t l = ESD Ai uLh4 Lu  XS hiuiht |L |i U@ti ihi |i ?|ih4i_@|i }LL_ t L4L }i?iLt A@| tc i @hi ?|ihit|i_ ? ?it|}@|?} |i TihuLh4@?Ui Lu @? ?_t|h) ihi ?@* }LL_t i4ML_) |i t@4i M@tU |iU?L*L}) @?_ ThL_U| _gihi?|@|L? t 4i@?| |L 4ii| UL?t4ih |@t|it M| _L ?L| hi^hi tTiUU ?it|4i?|t 5|h@|i}U ?|ih@U|L?t @hi _itUhMi_ M) @ |hii t|@}i }@4i W? |i ht| WA @?_ N UL4Ti|i ? +:# M) ULLt?} t4*|@?iLt*) |i LT|4@* *ii*t Lu n k = W? |i tiUL?_ t|@}i h4 N ti|t ThUi j XS ? |i 4@h!i| uLh |i ?|ih4i_@|i }LL_ W? |i |h_ t|@}i @** #`<t @?_ WA T*@) t4*|@?iLt*) @ Lh?L| i^*Mh4 ? |i 4@h!i| uLh |i ?@* }LL_ Ai }@4i t tL*i_ M) M@U!@h_ ?_U|L? e Ai U@h@U|ih3@|L? Lu |i tM}@4i TihuiU| i^ *Mh4 6t U@? Mi i@t*) _ihi_ h| t LQW @?_ t l G ; A ? A = C LQW Ct LQW 'f C l Ct l 'f E SS )i*_?} i^*Mh4 L|T|tG 2 t H LQW ' d E2  v n qvj XS  E }  n LQW d2n v E q  o E2  v E qv n2 ES. t H l ' d E 2  v n v E }  n LQW   2 j XS E 2  v  E qv n2 E SH *}}?} E SH ?|L E Sec i h|i |i hi*i@?| LMiU|i u?U|L? Lu |i N h4 @| |i tiUL?_ t|@}i t?} t)44i|h) @UhLtt #`<tG  XS ' qt H l E j XS  } n n XS ' q d d E 2  v n v E }  n LQW   2 j XS o E j XS  } n n XS  E 2  v  E qv n2 = E Sb # Lq rughu wr vroyh wkh v|vwhp + 99 , / zh lpsrvh rq GZ*v wkh v|pphwu| frqglwlrq t m @ t l iru doo m= . 6hL4 |i 6 h| j XS > i LM|@? |i i^*Mh4 ThUi uLh |i ?|ih4i _@|i }LL_G j H XS ' d E2  v n } E2 n v   2 n XS  vn LQW e = E.f Aihi hi4@?t |L Mi tL*i_ |i @t i^*Mh4 ? +:# igLh|t @| |i ht| t|@}i Ai 6t _itUhM?} |i t|h@|i}U ?|ih@U|L? Mi|ii? N @?_ WA )i*_ |i uL**L?} LT|4@* ?it|4i?| *ii*tG n W LQW 'E d  }   q 2 E v  eE  v  2 v ne q E2 v   f v 2 n v  2nSE2  v  2  q 2 E D v   DS v 2 nDD v  2 v ne q E e v   D2 v 2 nD v  SneH E 2  v  2 > E . n W XS ' q E d  }  d e qv  n v 2 E H  D q ne v E  q  .n2e o q 2 E D v   DS v 2 nDD v  2 v ne q E e v   D2 v 2 nD v  SneH E 2  v  2 = E .2 Lc t?} |i @MLi i ThittL?tc i U@? LM|@? |i LT|4@* ?@* L|T|c ULhhitTL?_?} ThUi *ii*tc @t i** @t ThL|tG t W LQW 'e d e E v  2 n q E v   2 o E v  2 E 2n qv  E d  }  eH E 2  v  2 ne q E v  2 d n2 v E . v  2 o n q 2 v i v d DD n v E D v  DS o  2 j E . t W XS 'e d e E v  2 n q E v   2 o E v  2 E 2n qv  E d  }  eH E 2  v  2 ne q E v  2 d n2 v E . v  2 o n q 2 v i v d DD n v E D v  DS o  2 j = E .e L i @hi hi@_) |L UL4T@hi |i *ii* Lu +:# UL44|4i?| Mi|ii? |i ?|i}h@|i_ h4 @?_ |i _t?|i}h@|i_ h4G n W LQW  n W XS ' E d  }  E v  2 d q 2 v E v E v  HnHnH qv E v E v  en2nS E v  2 o eH E 2  v  2 ne q E v  2 d n2 v E . v  2 o n q 2 v i v d DD n v E D v  DS o  2 j = E .D `i @hi |i? @M*i |L ThLi |i uL**L?}G wi44@ 2 6Lh @** v 5 d f > f = fD i @i  n W LQW An W XS uLh @** q 5 d  > h q n  @?_ uLh @** qAq n (  n W LQW ?n W XS uLh @** q 5 E h q n >q n  = 6Lh @** v 5 E f = fD >  o i @i H  n W LQW An W XS uLh @** q 5 d > h q n (  n W LQW ?n W XS uLh @** qA h q n = hLLu Ai ?4ih@|Lh E.D t i^@* |L 3ihL u G h q 'e  v Ee  v   2  s 2E2  v 2 E2  v   v EH n v E v  H = E.S Ai t4@**ih hLL| t @*@)t ?i}@|i uLh tMt|||itc *i |i *@h}ih hLL| t *@h}ih Lh i^@* |L 2 uLh @** v 5 d f >  o = Ai _i?L4?@|Lh Lu E .D t ?* @| q '2 E v  2  2 v E 2  . v 2    s bnS v e  v E D v   DS v 2 nDD v  2 E .. *tL ? |t U@ti |i t4@**ih hLL| t ?i}@|i uLh tMt|||it Ai *@h}ih hLL| t t|hU|*) TLt|i uLh v 5 d f > f = fD > *i | t ?i}@|i ? |i hi4@?_ih Lu |i tMt|||@M*|) h@?}i 6Lh @** v 5 d f > f = fD i @i q n A h q n = At wi44@ tLt |@| |ihi @hi @_4ttM*i T@h@4i|ih h@?}it @?_ ? _t|h) t|hU|hit ihi |i N h4 ?it|t 4Lhi |@? |i WA h4 t @ hit*| Lu *@h}ih +:# UL44|4i?| |i 4Lhi ?it|4i?| ThL?i h4 4@) _L Lhti |@? |i *itt ?it|4i?| ThL?i @?_ |i ?_t|h) Lh}@?3@|L? 4@) Mi *@M*i |L U@?}i Wu i ThLUii_ |L @ UL4T@h@|i @ttitt4i?| Lu |i i^*Mh4 ThL|tc i @i |L tT@?  W LQW   W XS  q W l E.H Lih |i tT@Ui v 5 d f >  o @?_ q   = W| U@? Mi @tUih|@?i_c |hL} ?4ihU@* U@*U*@|L?c |@| |ihi @hi @_4ttM*i ?|ih@*t Lu v @?_ q ihi  W LQW ?  W XS n q W l = At ?i^@*|) t @?@*)ti_ ? |i TTi?_  6Lh ?t|@?Uic u q '2G  W LQW ? W XS n q W l uLh @** v 5 d f > f = eSD = E .b W| U@? @*tL Mi ihi_ |@| q '  t ?tUi?| |L ThL_Ui  W LQW ? W XS n q W l = Aiti @h}4i?|t ThLi |i uL**L?}G hLTLt|L?  6Lh @** q  2 > |ihi i t|t tL4i @_4ttM*i _i}hii Lu tM t|||@M*|) v tU |@| |i ?L??|i}h@|i_ T@h| Lu |i 4@h!i| t TihuLh4?} Mi||ih |@? |i ?|i}h@|i_ T@h| b `i? i|ih E   q '  uLh @** _i}hiit Lu tMt|||@M*|)c Lh E   v 'fuLh @** q>  W LQW A W XS n q W l MiU@ti Lu |i t@* Thi_L4?@?Ui Lu |i ?i}@|i i |ih?@*|) E5Ti?}*ihc bDf( ihh)c bHb N?*!i ? |i @?@*)tt U@hhi_ L| ? |i ThiLt |L tiU|L?tc ihi i @hi ?L| i?_L}i?3?} 4@h!i| t|hU|hi AihiuLhic i 4@) Mhi) ?tTiU| @? @*|ih?@|i 4@h!i| tUi?@hL 5TTLti L? |i ?L??|i}h@|i_ t_i Lu |i ?_t|h) |ihi t @ TLT*@|L? 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