Discussion Papers Collana di E-papers del Dipartimento di Economia e Management Università di Pisa

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1 Dscusson Papers ollana d E-papers del Dpartmento d Economa e Management Unverstà d Psa Lucano Fant and Luca Gor Dscusson Paper n. 7

2 Dscusson Paper n. presentato: eptember 7 orrespondng Authors: L. Fant Department of Economcs and Management Unversty of Psa Va osmo Rdolf I 6 Psa (PI) Italy; e-mal: lucano.fant@unp.t L. Gor (correspondng author) Department of Poltcal cence Unversty of Genoa Va alb /9 I 66 Genoa (GE) Italy; e-mal: luca.gor@unge.t or dr.luca.gor@gmal.com Lucano Fant and Luca Gor La presente pubblcazone ottempera agl obblgh prevst dall art. del decreto legslatvo luogotenenzale agosto 9 n. 66. Please quote as follows: Lucano Fant and Luca Gor (7) A product nnovaton game wth manageral delegaton Dscusson Papers del Dpartmento d Economa e Management Unverstà d Psa n. (

3 Dscusson Paper n. Lucano Fant and Luca Gor Ths artcle revsts the works of Lambertn and Rossn (998) and ernhofen and ernhofen (999) and also extends the analyss to the effects of product nnovaton n ournot and ertrand duopoles wth sales delegaton. Keywords Duopoly; Product nnovaton; ales delegaton JEL lassfcaton D; J; L

4 . Introducton Ths work contrbutes to the strand of the ndustral organsaton lterature focused on product dfferentaton as a devce relaxng competton. As s known nvestng to reduce product substtutablty may be even more mportant than other related strateges for frms (e.g. the cost-reducng R&D) to cope wth the ncreased competton. Although there exst several artcles devoted to showng that (exogenous) product dfferentaton softens competton there were a few contrbutons on the sde of the endogenous choce of the extent of product dfferentaton (Lambertn 996; Lambertn and Rossn 998; ernhofen and ernhofen 999; Lorz and Wrede 9; Hoefele 6). The present artcle relates more closely to the works of Lambertn and Rossn (988) and ernhofen and ernhofen (999) (LR and henceforth). The man am of LR s to queston whether and how n a symmetrc duopoly wth proft maxmsng (PM) frms the shape of market competton can affect R&D efforts amed at reducng product substtutablty. The authors show that ) a prsoner s dlemma at R&D stage may arse due to externaltes affectng product nnovaton so that frms may be entrapped n a competton game wth perfect substtutes n both ournot and ertrand settngs. ) The less effectve nnovaton nvestments are the less lkely frms nvest n R&D. ) The lkelhood to nvest n product dfferentaton s larger under prce competton thus reversng the establshed wsdom on the relatve ncentves of nvestng n cost-reducng R&D. The present artcle revsts ths ssue by accountng for the separaton between ownershp and control. Industres wth dfferentated products product nnovaton and manageral delegaton are wdely observed n actual markets. nce Vckers (98) the lterature on manageral delegaton has grown rapdly. However ths stream of lterature neglects to account for the strategc use of product nnovaton. Ths work ams at fllng ths gap by consderng salesdelegated () frms. The man fndngs are the followng. ) The results of LR wth PM-frms are re-examned showng that a prsoner s dlemma wth undfferentated products cannot occur n a ertrand game. ) ales delegaton always enhances (resp. reduces) the lkelhood of nnovaton (no nnovaton) n the case of ournot (resp. ertrand) competton. The rest of the artcle proceeds as follows. ecton brefly sketches the model set up. ecton revsts the results of LR wth PM-frms. ecton studes the case of -frms. ecton concludes.. The model set-up In emprcal analyses product nnovaton s often seen as equvalent to dfferentatng products. For nstance cherer and Ross (99) suggests that three quarters of nvestment expendtures of U-based frms go nto product nnovaton and even Japanese frms whch have the lowest share n product nnovaton stll nvested one ffth.

5 The economy conssts of a duopoly where frm ( { }) produces (a horzontally dfferentated) product of varety. The lnear nverse and drect demand functons (ngh and Vves 98) of product ( { } j ) are p q d q j () and q p d d dp d j () where p ( q ) denote frm s prce (resp. quantty) and d s the extent of product substtutablty (when d products are homogeneous). Average and margnal costs are constant and equal to zero so that profts of frm are p q. y followng Vckers (98) we assume that owner hres a manager whose pay s u where s the fxed salary and s a constant that weghts the utlty of manager u whch s expressed as: u b q () where b s the ncentve parameter. When b (resp. b ) the owner provdes ncentves (resp. dsncentves) to the manager. We assume that -frms non-cooperatvely play a three-stage game. Owners choose whether to nvest or to do not nvest n product nnovaton (R&D stage) and then set the bonus for the management (contract stage). Managers compete n the product market (market stage). The soluton concept s subgame perfecton by backward nducton. The strategy set at R&D stage s common knowledge and ncludes two polar choces: nvestng a fxed monetary amount ( F ) or not nvestng at all ( F ) n product nnovaton. We denote ths bnary strategc choce as I (nvest) and NI (not nvest). Products are hghly heterogeneous ( d d ) [resp. homogeneous ( d ) f both frms nvest [resp. do not nvest n R&D. Products are scarcely dfferentated ( d d ) f only one frm nvests n R&D ( d d ).. LR s results revsted Let us frst assume PM ( b ). tandard calculatons n ournot () and ertrand () models lead to: and NI / NI I / NI d 9 ( d) NI / I F ( d) I / I ( d) F As usual owners offer a take-t-or-leave-t contract and managers are remunerated at ther reserve salary (f the latter s zero then the fxed salary component n manager s compensaton wll be negatve.e. ).

6 NI / NI d NI / I d ( d)( d) I / NI d I / I d F F. ( d)( d) ( d)( d) k I / NI NI / NI k NI / I I / I k NI / NI I / I : : : k Let be proft dfferentals and F k x x the correspondng threshold curves ( { } x {} k { } ). In partcular and Then ( d)( d) F : 9( d) ( d d)( d d) F : ( d) ( d) ( d)( d) F : 9( d) d F : ( d)( d) ( d d)[ ( d d) ( d) ( d) ( d) ( d)( d) ( d)( d) ( d) F : d F : ( d)( d). Lemma. (a) [ournot. There exst fve regmes n ( d F ) space for any I.. One (Pareto neffcent) Nash equlbrum (NINI). II.. Two Nash equlbra (NINI) and (II). I payoff domnates NI. III.. One (Pareto effcent) Nash equlbrum (II). IV.. Two (Pareto effcent) asymmetrc Nash equlbra (NII) and (INI). V.. One (Pareto effcent) Nash equlbrum (NINI). (b) [ertrand. Only regmes III ( ) and IV ( ) exst. Proof. Part a) s proved by lookng at the sgn of proft dfferentals. Part b) / holds as NI NI NI / NI and F. Then f F were crossed by F n ( d F) space t would mean that the latter curve would enter a regon where devatng from I would gve negatve profts unlaterally. Therefore (NINI) can never emerge n a ertrand game. Q.E.D. Remark. [ournot. LR dentfy wth regon I+V the lkelhood of a prsoner s dlemma. However when F s suffcently hgh (NINI) becomes Pareto d.

7 effcent (ths was already ponted out by ). In such a case n fact an ncrease n product dfferentaton does not allow to get an adequate compettve advantage (as the effectveness of the R&D nvestment s low) compared to the dsadvantage of nvestng unlaterally n product nnovaton. As LR do not account for regon V n Proposton they state The lkelhood of a prsoner s dlemma arsng n the R&D stage ncreases as the effectveness of nvestment decreases. (LR 998 p. ). However by a smple nspecton of Fgure ( d ) and Fgure ( d. ) t s clear that although the area I+V ncreases when the effectveness of R&D nvestments decreases the lkelhood of a prsoner s dlemma correspondngly reduces (regon I). Fgure. ournot (PM). Proft dfferentals n ( d F ) space ( d ). Fgure. ournot (PM). Proft dfferentals n ( d F ) space ( d. ).

8 Remark. [ertrand. As only regmes III and IV exst (Fgure ) (NINI) does never emerge and no prsoner s dlemma arses. In addton the threshold curves cannot ntersect (part (b) of Lemma ) and thus Fgure n LR s work and Fgure n s work do not hold n a ertrand settng. Therefore ournot and ertrand models are not equvalent wth regard to the occurrence of a prsoner s dlemma. However the lkelhood of the good equlbrum (II) s stll larger under ertrand competton. Fgure. ertrand (PM). Proft dfferentals n ( d F ) space ( d ). Defne and Then D D ( d)[( d) ( d) ( d) d 6 9( d)( d) ( d) : F F : F F ( d d) ( d)( d)( d) ( d) ( d) ( d) 6[ d( d) ( d) d ( d) dd ( d) ( d) ( d) [ d( d) ( d) d dd 8. Proposton. Under PM the lkelhood of (II) s larger hgher under ertrand competton than ournot competton. Proof. As D and D. ales delegaton () Proft functons under are: the result follows. Q.E.D. 6

9 and NI / NI I / NI d NI / NI I / NI d [ ( d) NI / I [ ( d) d( d) F I / I d( d) d( d) NI / I ( d)[ ( d) F ( d)[ ( d) ( d) d( d) [ ( d) F ( d)[ ( d) F. ( d) d( d) ( d) d( d) Fgure (ournot) and Fgure (ertrand) show that Lemma holds also under. The threshold curves k F k x x ( x { } k { } ) are not reported to save space but are avalable on request. I / I. Fgure. ournot (). Proft dfferentals n ( d F ) space ( d ). Fgure. ertrand (). Proft dfferentals n ( d F ) space ( d ). 7

10 Lemma. Under the lkelhood of (II) s larger under ertrand competton than ournot competton. Proof. As D F F and D F F the result follows. Q.E.D. : : Let us now study the effects of (compared to PM) on product nnovaton by consderng ournot and ertrand duopoles separately. Defne Z ( d)[8 d 79( d) 78( d) 7( d) ( d) [ d( d) 7( d) : F F Z : F 6( d) ( d) 8d( d) 6( d) Z F ( d d) ( d) ( d) [ d( d) [ d( d) 9( d) ( d) 9( d) ( d) ( d) 7( d) d 7d( d) ( d) ( d) 9( d) ( d) ( d) ( d) 8( d) d 6( d) ( d) 9( d) 6( d) 6dd ( d) ( d) ( d) ( d) ( d)[8 d 79( d) 78( d) 7( d) ( d) [ d( d) 7( d) : F F Z ( d) ( d)( d) ( d)( d) [ d( d) : F F Z : F F 6 ( d) ( d) 6 ( d) ( d) 6( d) ( d) 9( d) ( d) ( d d) ( d)( d)( d) ( d) [ d( d) [ d( d) ( d) ( d) ( d) ( d) ( d) ( d) 6 6 7( d) ( d) ( d) ( d) ( d) ( d) 9( d) d 6( d) ( d) ( d) ( d) ( d) ( d) 9( d) ( d) 6( d) ( d) ( d) ( d) 9( d) 9d( d) 6( d) d 8( d) ( d) 6d( d) 9( d) 8( d) 8( d) 6( d) 6( d) 6dd 7( d) d 7d( d) and Then Z ( d) ( d)( d) ( d)( d) [ d( d) 6 6 7( d) ( d) : F F ( d) ( d) 7( d) ( d) Proposton. [ournot. reduces (resp. ncreases) the lkelhood to do not nnovate (resp. to nnovate).. 8

11 Proof. As Z Z and knowng that the total area of feasble choces (for a gven F ) s smaller under than PM then area I+V (resp. III) s smaller (resp. larger) under. Q.E.D. orollary. [ournot. As Z then the area n whch (NINI) s Pareto neffcent s smaller under than PM. Gven Proposton the area of a prsoner s dlemma under can be smaller or larger than under PM. Result. [ertrand. ncreases the lkelhood of nvestng n product nnovaton. As Z for any d d and Z for any d d when d s * suffcently small or Z f d d d when d s suffcently large 6 then when R&D nvestments are hghly effectve what happens to the sze area III s a pror ambguous. Nevertheless even n the polar case d (maxmal effectveness) area III reduces as the upward shft n Z always exceeds the downward shft n Z (see Example and Fgure 6). Gven also that the area of feasble choces for a gven F s ncreased Result follows. Example. To evaluate the lkelhood of (II) n ( d F ) space ( d ) n a ertrand game under and PM we compute the correspondng area III as follows: and A III A III : :.67 ( F F) dd ( F F) dd ( F F) dd ( F F) dd A well-establshed result snce Vckers (98) s that profts under are smaller (resp. larger) than under PM n ournot (resp. ertrand) competton. Thus the area of feasble choces for a gven F s correspondngly reduced (resp. ncreased). nce the area of feasble choces for a gven F s ncreased under ertrand competton then the area of (II) and the area of (INI) and (NII) are enlarged by. 6 * The analytcal expresson of d s not tractable. However numercal smulatons show that d * [.86 when d correspondngly belongs to range [.87. 9

12 Fgure 6. ertrand. Area III: (red) versus PM (black) n ( d F ) space ( d ).. onclusons Ths artcle analysed a product nnovaton game n ournot and ertrand duopoles wth -frms. After revewng the case of PM-frms early analysed by LR and the work showed that ) enhances (resp. reduces) the lkelhood to nnovate (resp. to do not nnovate) n a quantty-settng context ) enhances the lkelhood to nnovate n a prce-settng context. Although n a ournot game ends up wth a pro-compettve effect at equlbrum t also causes an ant-compettve outcome as t makes frms more prone to nvest n product nnovaton. In a ertrand game s per se procollusve: t becomes even more pro-collusve to the extent that t favours nvestments n product dfferentaton (.e. n a ertrand game wth R&D s a wn-wn result for owners). onflct of Interest nterest. The authors declare that they have no conflct of References ernhofen D.M. ernhofen L.T On the lkelhood of a prsoners dlemma n a dfferentated duopoly. Economcs Letters Hoefele A. 6. Endogenous product dfferentaton and nternatonal R&D polcy. Internatonal Revew of Economcs and Fnance 6. Lambertn L hoosng roles n a duopoly for endogenously dfferentated products. Australan Economc Papers.

13 Lambertn L. Rossn G Product homogenety as a prsoner s dlemma n a duopoly wth R&D. Economcs Letters Lambertn L. Poddar. asak D.. Research jont ventures product dfferentaton and prce olluson. Internatonal Journal of Industral Organzaton Lorz O. Wrede M. 9. Trade and varety n a model of endogenous product dfferentaton..e. Journal of Economc Analyss & Polcy 9 Artcle. cherer F. Ross D. 99. Industral Market tructure and Economc Performance. Houghton Mffln. ngh N. Vves X. 98. Prce and quantty competton n a dfferentated duopoly. RAND Journal of Economcs 6. Vckers J. 98. Delegaton and the theory of the frm. Economc Journal

14 Dscusson Papers ollana del Dpartmento d Economa e Management Unverstà d Psa omtato scentfco: Lucano Fant - oordnatore responsable Area Economca Guseppe ont Lucano Fant Davde Fasch Paolo capparone Area Azendale Maracrstna ont Guseppe D'Onza Alessandro Gandolfo Elsa Gulan Enrco Gonnella Area Matematca e tatstca ara agn Laura aros Ncola alvat Emal della redazone: lfant@ec.unp.t