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1 Doshsha Unversty Center for the Study of the Creatve Economy Dscusson Paper Seres No Nonlnear Effects of Superstar Collaboraton: Why the Beatles Succeeded but Broke Up Tadash Yag Dscusson Paper Seres

2 1 Nonlnear Effects of Superstar Collaboraton: Why the Beatles Succeeded but Broke Up Tadash Yag (Faculty of Economcs, Doshsha Unversty) Abstract Ths paper examnes the knowledge creaton process that takes place n a group of superstar nnovators. How does a superstar nnovator nfluence the generaton of knowledge n a team? In partcular, does the effect ncrease nonlnearly as the number of talented team members ncreases? We explore these questons by consderng the success and subsequent breakup of the Beatles, one of the most popular musc groups n hstory. Through the mathematcal analyss for explorng the fundamental mechansm of the breakup and ts mplcatons for superstar collaboratons, we show that the breakup was an nevtable consequence of the superstar collaboraton. Correspondng Author: Tadash Yag Faculty of Economcs, Doshsha Unversty, Kamgyo, Kyoto, , Japan Tel.: Fax: E-mal:

3 2 I. Introducton Studes on the knowledge creaton process are becomng ncreasngly mportant n regard to the creatve economy, where new marketable knowledge and concepts are the key drvers of value creaton and nnovaton. To date, much of the research n ths feld has focused on knowledge management and ts effects on nnovaton, but the creatve process s treated largely as a black box. Levn and Stephan (1991) emprcally examne research motvatons and show that the nvestment motve model s more effectve than the consumpton motve model n explanng the pattern of lfe-cycle research actvtes. Wetzman (1998) establshes the mcro-foundatons of knowledge creaton, fndng that the process entals not so much generatng new deas, as recombnng an abundance of old deas nto a new usable form. Jones (2009) nvestgates recent trends n technologcal progress by consderng the ncreasng educatonal burden on nnovators, suggestng that ncreasng dffculty of nnovaton hnders long-run economc growth. In the framework of knowledge creaton, how are new deas created wthn a team? Wuchty, Jones, and Uzz (2007) pont out the benefts of freely sharng knowledge through collaboraton, and Mas and Morett (2009) emprcally study the strength of the peer effect wthn a group, showng that the productvty of an ndvdual worker affects the productvty of co-workers, even for low-sklled workers. Ths paper shares the smlar dea wth Azoulay, Zvn and Wang (2010) whch estmate the magntude of spllovers generated by academc superstars. Ths examnes the knowledge creaton process that takes place n a group of superstar nnovators. How does a superstar nnovator nfluence the generaton of knowledge n a team? In partcular, does the effect ncrease nonlnearly as the number of talented team members ncreases? We explore these questons by consderng the success and subsequent

4 3 breakup of the Beatles, one of the most popular musc groups n hstory. Of the four muscans n the Beatles John Lennon, Paul McCartney, George Harrson and Rngo Starr Lennon has a reputaton for beng nnovatve, socally conscous, and knowledgeable of aesthetcs; McCartney s known for hs nnovatve and joyous approach to musc; Harrson s regarded as the quet and phlosophcal Beatle wth a strong sense of aesthetcs; and Starr s known as the skllful, nnovatve, good-natured drummer of the band. Wth four dstnct and complementary personaltes brought together n a creatve and synergstc allance, the Beatles quckly found success and made musc that was dstngushed for beng nnovatve, joyful, appealng, and dverse. Other talented collaborators who contrbuted to the success of the Beatles are followng two persons. Producer George Martn played a leadng role n creatng the dstnct sound of the band by overseeng the group s muscal arrangements, and the band s manager Bryan Epsten (who ded n 1967) had a keen apttude for promoton. By examnng the way the Beatles created ther musc, we am to examne whether a nonlnear effect of superstar collaboraton s generated, and f so, how the effect comes about; moreover, we seek to elucdate the condtons for successful superstar collaboraton. In consderng the nonlnear effect of collaboraton n the Beatle, we cannot gnore the fact that the Beatles broke up only eght years after releasng ther debut record. Whle there have been many theores regardng the breakup of the band, ths paper focuses on the fundamental mechansm of the breakup and ts mplcatons for superstar collaboratons. We show that the breakup was an nevtable consequence of the superstar collaboraton. We present results of an analyss usng a mathematcal model to

5 4 examne when collaboraton becomes no longer benefcal for ndvdual members of the Beatles, and show that the breakup of a superstar collaboraton s a logcal consequence of the knowledge creaton process. Ths paper s organzed as follows. Secton II descrbes the knowledge creaton process of the Beatles, llustratng the nonlnear effects of superstar collaboraton. Secton III presents a mathematcal model for capturng the breakup mechansm of superstar collaboratons. Secton IV dscusses the mplcatons of the fndngs for the knowledge creaton process n general. II. Knowledge Creaton Process of the Beatles Ths secton descrbes the knowledge creaton process of the Beatles and llustrates the nonlnear effects of collaboraton between talented musc artsts. For ths purpose, we focus on cases of co-creaton documented n journals, books, and vdeos. A. Defnton of Nonlnearty The qualty of musc created by the Beatles s descrbed by several factors (denoted by e ) such as aesthetcs, socal conscousness, nnovatveness, joyfulness, phlosophcal degree, harmonousness, and varety. The lnear characterstc equaton of the co-creaton process s defned as Q( λe, λe, λe,..., λe) = λqe (, e, e,..., e), (1) n n where Q s the qualty of musc created. If the qualty functon s specfed by the lnear combnaton of elements Q( e, e, e,..., e ) = a + ae + ae + ae,..., ae, (2) n n n the qualty of musc wll ncrease lnearly as the number of talented artsts n the group

6 5 ncreases. On the other hand, the nonlnear characterstc equaton of co-creaton process s defned as Q( λe, λe, λe,..., λe) = λ Qe (, e, e,..., e), t> 1. (3) t n n One example of a specfcaton that exhbts nonlnear characterstcs s multple combnaton of qualty elements: Q( e, e, e,..., e ) = ae. (4) n n = 1 The analyss ams to ascertan whether the qualty of musc ncreases nonlnearly as the number of talented artsts n the group ncreases. B. Understandng Nonlnearty Before examnng the knowledge creaton process, t s mportant to have an ntutve understandng of nonlnearty. Connolly and Krueger (2006) and Strobl and Tucker (2000) argue that there s a skewed dstrbuton of revenue from album sales. Ths s n lne wth the superstar effect proposed by Rosen (1981). In other words, the sales revenue dffers drastcally among musc groups; a lnear correlaton between album sales and album qualty mples that the qualty of albums dffers drastcally among recordng artsts. Notably, there s strong evdence showng that nonlnear effects arse from the collaboraton of superstar nnovators as seen from the sales revenue generated by the Beatles as a group and generated by ndvdual Beatles members after the band splt. Accordng to the webste Statstc Bran, as of Aprl 16, 2013, the estmated total number of albums sold by the Beatles s 2.3 bllon. Onlne encyclopeda Wkpeda

7 6 estmates the total number of albums sold by McCartney and Lennon as solo artsts to be around 100 mllon and 14 mllon, respectvely. These fgures suggest strong nonlnear effects arsng from superstar collaboraton n the band. Table 1 ALBUM SALES OF THE BEATLES Data Total album sales statstcs Total albums sold 2,303,500,000 Total albums sold on Tunes 585,000 Total sngles sold on Tunes 2.8 mllon Bllboard chart statstcs Total weeks on chart 1,278 weeks Total number ones 15 Total weeks at number one Album wth longest tme spent at number one 175 weeks 30 weeks (Please Please Me) Source: Note: As of Aprl 16, 2013.Statstcs are from the Recordng Industry Assocaton of Amerca, Apple Records, EMI. Date verfed s July 23, The nonlnear qualty mprovement n the qualty of the Beatles musc can be attrbuted to several factors. Foremost, the appeal of the band les n the evoluton of the

8 7 group s muscal compostons. Wth each new album produced n an unprecedented lyrcal and muscal style, the Beatles created musc n a way whch resembled the makng of art. A good example s the eclectc Abbey Road, a bestsellng album whch brngs together elements of rhythm and blues, pop, soul, and rock and roll. By expermentng wth new tunes and muscal arrangements, the band mproved on the sound and qualty of ts musc. Ths would not have been possble f the band were not made up of talented artsts successfully collaboratng wth one another. By contrast, durng the early years of the Beatles when Starr had yet to jon the band, the sound of the group was characterzed by a relatvely lower qualty (The Beatles Anthology, 1995). Ths was durng the perod from 1956 to 1962 when Pete Best, who was wdely thought to be less talented than Starr, was stll the drummer of the band. The mplcaton s that artsts whose sklls are not on par wth ther group members can adversely affect the qualty of the team output. Ths s also evdence revealng the nonlnear propertes of knowledge creaton. Based on (4), we can wrte the followng: n Q( e1, e2, e3,..,0,.., e ) = ae = 0. (5) n = 1 The equaton shows that wth the presence of a subpar element, the overall qualty of musc created s severely affected, even reduced to zero n the extreme case. C. Creatve Process of the Beatles Ths secton wll examne the creatve process n whch superstar nnovators engage n. There s no doubt that the Beatles were a group of extraordnarly talented muscans. Collaboraton was key to the band s success. For nstance, Lennon and McCartney were

9 8 wrtng partners and co-wrote most of the band s bestsellng hts. 1 In the recordng studo, the four band members, together wth Martn, regularly exchanged deas and worked on enhancng the qualty of ther songs. Ths s evdent based on footage n The Beatles Anthology (1995). The lner notes from the Beatles album Sgt. Pepper s Lonely Hearts Club Band (1995) also provdes revealng nsghts nto the recordng sessons of the band: The Beatles muscal deas progressed n a most tangble way wth each album they recorded. Geoff Emerck, the recordng engneer who wth George Martn formed the magnatve team whch translated the Beatles requrements onto tape, once totted up the number of hours put nto the makng of Sgt. Pepper and came up wth 700. Please Please Me, the Beatles frst album, was recorded n 585 mnutes. The Beatles nssted that everythng on Sgt. Pepper had to be dfferent, says Emerck, so everythng was ether dstorted, lmted, heavly compressed or treated wth excessve equalzaton. We had mcrophones rght down the bells of the brass nstruments and headphones turned nto mcrophones attached to volns. We plastered vast amounts of echo onto vocals, and sent them through the crcutry of the revolvng Lesle speaker nsde a Hammond organ. We used gant prmtve oscllators to vary the speed of nstruments and vocals and we had tapes chopped to peces and stuck together upsde down and the wrong way round. (Sgt. Pepper s Lonely Hearts Club Band 1995, page 1. ) 1 In ntervew footage from The Beatles Anthology (1995), McCartney sad he and Lennon composed songs together when on concert tours.

10 9 The creatve process whch went nto the makng of the Beatles songs was not wthout challenges. Accordng to Emerck, Geoff; Massey, Howard (2006) and Lewsohn (1988), more than 70 takes were requred n order to record one song. For example, n recordng Ob-la-d Ob-la-da from The Beatles (a.k.a. The Whte Album), Lennon played the song s pano countless tmes because McCartney was unsatsfed wth t. No doubt, the calber and talent of each band member has a drect bearng on the qualty of musc produced by the group. Bands made up of ndvdually talented artsts are more lkely to produce better musc as a result of the regular exchange of deas wthn the group. Former Apple CEO Steve Jobs was reportedly mpressed wth the perfectonsm of the Beatles after lstenng to a bootleg of Strawberry Felds Forever, whch recorded the seres of many number of takes of Strawberry Felds Forever (Isaacson, 2011). Indeed, talented artsts are also more lkely to spot ssues and engage n problem solvng, whch would mprove the qualty of musc created. Another factor key to successful creatve collaboraton n a team s the need for equal member status. Take for example a band wth a chef songwrter who has a domnant poston wthn the group. In such a band, the less domnant members are unlkely to comment on aspects relatng to muscal composton. Consequently, the calber of the songwrter becomes the determnng factor of the qualty of musc produced by the band. The mplcaton s that the postve collaboratve effect n the band becomes greatly weakened, and that the qualty of the musc mght not be markedly mproved durng the recordng sessons. Hence the qualty of the knowledge creaton process of a group s determned by the degree of dea exchange and competton wthn the group. Musc groups made up of

11 10 members of unequal status easly foster rvalry. On the other hand, bands wth members who have relatvely equal status form hghly creatve and productve teams. These bands thrve on a free exchange of deas, resultng n the nonlnear effects of superstar collaboraton. Ths pont s descrbed by the followng formulaton. Suppose that the qualty of musc be represented by Qe (, e, e) = Ape ( ( ; he ) ) ee, (6) α β γ where e 1 s nnovatveness, e 2 s joyfulness, e 3 s phlosophcal degree, α the weght of nnovatveness n producng qualty musc, β s the weght of joyousness, and γ s the weght of phlosophcal degree. Let pe ( 1; h ) be the probablty of success n nnovaton whch depends on the level of compettveness between members wthn the group, h. The nonlnear effects of superstar collaboraton emerge when there s mutual cooperaton n a group, ncreasng the probablty of successful nnovaton. Lennon stated n an ntervew that he strved to create fundamentally nnovatve musc durng the Sgt. Pepper s Lonely Heart Club Band recordng sesson n response to the creatve efforts of McCartney and Harrson (Dg, 2010). Especally, the use of dscord was one of hs nnovatve challenges. The success of the nnovatve masterpece I am the Walrus on the album Magcal Mystery Tour s the frut of contnuously strvng to nclude a dscord n the musc. D. The Breakup of the Beatles The Beatles had a crtcal year n 1967.Lennon met Yoko Ono, an avant-garde artst who was wdely beleved to be the catalyst leadng to the splt of the band. Whle the appearance of Ono was not the man reason that caused the breakup of the Beatles, the

12 11 reasons why Lennon needed Ono and Harrson needed Indan phlosophy were qute mportant. 2 That year also marked the tme when Lennon began to take an nterest n the avant-garde movement. 3 He would soon ncorporate elements of avant-garde nto the musc of the Beatles for the band s next album. Revoluton 9 from The Whte Album was an expermental sound collage and shows Lennon s style dvergng from that of the other Beatles. Meanwhle, behnd the scenes n the recordng studos, trouble was brewng for the Beatles. In another round of footage from The Beatles Anthology (1995), Martn noted that there was much unhappness among the band members durng the makng of the album Let It Be, and the worsenng relatonshps among the band members s evdent n the flm Let It Be. As the four muscans began to explore dfferent muscal drectons, the postve synergstc effects of collaboraton n the Beatles began to fade. 4 At the same tme, there was a change n the power dynamcs of the band. McCartney began takng on an ncreasngly domnant role n the Beatles, a factor whch also catalyzed the splt of the band, along wth Harrson s complant of unequal treatment. The followng secton explores the breakup of the Beatles by usng a mathematcal model. III. The Breakup of the Beatles as a Knowledge Creaton Model Earler n the paper, there s an analyss of the factors resultng n the nonlnear effects of superstar collaboraton. In ths secton, the breakup of the Beatles wll be analyzed 2 Lennon s Imagne and Harrson s My Sweet Road are proof that Ono and Indan phlosophy were mportant to them. 3 Lennon sad n an ntervew publshed n The Dg Specal Edton that he dd not agree wth all of the tenets of the avant-garde movement. What he had wanted to do was create somethng smlar to avant-garde art. 4 The last album recorded by the Beatles, Abbey Road, was consdered a masterpece. It was also revealed n footage from The Beatles Anthology that the band members worked wth each other n an atmosphere of postve collaboraton durng the makng of the fnal album.

13 12 usng a knowledge creaton model. Let k () t denote the knowledge stock of ndvdual at tme t. For ths case study, e e may represent joyousness, esthetcsm, socal conscousness, phlosophcal degree and nnovatveness. The talent of an artst s a functon of hs or her knowledge accumulaton. As human captal matures, knowledge creaton wthn the group decreases for two reasons: decreasng dfferences n knowledge levels among members and reduced flexblty n acceptng dfferences of knowledge creaton. The knowledge accumulaton functon can be wrtten as dk dt. = f( k) fα ( dk ( k)) + gk ( ) f((1 α) dk ( k)) j j (7) Here, f represents the degree of flexblty n acceptng dfferences of knowledge creaton and s a decreasng functon of k, and φ s an ncreasng functon. Let g be the knowledge creaton whch arses from collaboratng wth a non-member, assumng that t s an ncreasng functon of k. Let k () t denote the vector of knowledge of member at tme t and let α() t denote the porton of tme spent wth the member of the group. The members control the porton of tme they spend workng together so as to maxmze ther creatve output n terms of qualty, subject to the dynamc equaton of knowledge captal k. The objectve functon s represented by (8) and the dynamc equaton of knowledge s shown by (9). Assume the tme dscount rate s zero, wth equal weght gven to each perod of tme so as to smplfy the model: Max Q( k (): t k ()) t dt α t T j, (8) dk st.. = f( k) fα ( dk ( kj)) + gk ( ) f((1 α) dk ( kj)) dt, (9)

14 13 H= Qk ( ( t)) + λ f( k) fα ( dk ( kj)) + gk ( ) f((1 α) dk ( kj)), (10) The optmalty condtons are gven by (11) and (12), as follows: H = λ[ f( k) f'( αdk ( kj)) ( dk ( kj)) α gk ( ) f'((1 α) dk ( k)) ( dk ( k))] = 0 j j, (11) dλ H Q = = λ[ f '( k) fα ( d( k kj)) + f( k) fα ( d'( k kj)) dt k k. (12) + g'( k ) f((1 α) d( k k )) + g( k ) f((1 α) d'( k k ))] j j The transversalty condton s lm l() tkt () = 0. (13) x T As long as λ s postve, the optmalty condton (11) mples that the optmal tme share α s determned at the pont where the followng equaton s satsfed: f( k) f'( α dk ( k)) ( dk ( k)) j j = gk ( ) f'((1 α) dk ( k)) ( dk ( k)) j j (14) Snce ' f s a decreasng functon, the left-hand sde of the equaton s a decreasng functon of α whle the rght-hand sde s an ncreasng functon of α. The left-hand sde can be consdered the margnal productvty of wthn group knowledge creaton (MPI) and the rght-hand sde measures the margnal productvty of outsde group knowledge creaton (MPO). Note the relatonshp between k and the optmal level of α. To llustrate ths, we take the frst dervatve of the left- and rght-hand sdes wth respect to k. The frst dervatve of the left-hand sde s gven by

15 14 f( k) f'( α dk ( k)) ( dk ( k)) j j k + f( k ) f''( α d( k k )) α d'( k k ) ( d( k k )) j j j + f( k ) f'( α d( k k )) ( d'( k k )). j j = f'( k) f'( α dk ( k)) ( dk ( k)) j j (15) The dervatve of the rght-hand sde wth respect to k s gk ( ) φ'((1 α) dk ( k)) ( dk ( k)) j j k g'( k) φ'((1 α) dk ( k)) ( dk ( k)) j j + g( k ) φ''((1 α) d( k k )) (1 α) d'( k k ) ( d( k k )) + g( k ) φ'((1 α) d( k k )) ( d'( k k )). j j j j j = (16) Because f s a decreasng functon of k and g s an ncreasng functon of k,, the MPO and MPI curves shft as k ncreases, as shown n Fgure 1. Therefore, one can conclude that the amount of optmal tme spent collaboratng wthn the group decreases. Ths suggests that the Beatles broke up as the knowledge stock of ts members rose. MPI MPO MPO(t1) MPO(t0) MPI(t0) MPI(t1) α(t1) α(t0)

16 15 Fgure 1: Value of co-creaton wthn and outsde group Combned wth (6), the optmalty condtons mply that the qualty of musc produced by the group s as follows: α β γ Q= Q( A( p( e1( k1( α1),.., k4( α4)); h) e1( k1( α1),.., k4( α4))) e2 ( k1( α1),.., k4( α4)) e3( k1( α1),.., k4( α4)) (17) Based on ths equaton, one can fnally understand why the fnal album recorded by the Beatles, Abbey Road, s crtcally acclamed as a masterpece, even though t was recorded when the group was on the verge of breakng up: the perod durng whch the album was recorded concded wth the creatve peak of each member of the band. As opposed to the recordng of Let It Be, whch was made at a tme marked by tense relatons between the band members, the producton of Abbey Road saw the Beatles successfully work as a team. IV. Concluson Takng up the case of the Beatles, ths paper examned the knowledge creaton process of superstar nnovators and the nonlnear effects whch arose from peer collaboraton. The fndngs of ths paper may be appled to the practce of human resource management n frms. An mportant mplcaton of ths work s that the ncentves for collaboratng wthn a team tend to decrease as the knowledge of each member s shared over tme. Company executves may decde to employ the same personnel so as to mantan contnuty of the company brand and mage or ncrease the staff turnover as a way of nculcatng a more compettve sprt n employees. The paper also revealed the condtons conducve to successful nnovaton through

17 16 collaboraton. A harmonous envronment n whch team members can trade deas freely and engage n far play fosters creatvty, leadng to nnovaton. Ths fndng wll be useful to busnesses for plannng the organzatonal structure of the company s research and development dvson. In partcular, the study wll be useful for busnesses n decdng on a flat or herarchcal structure for the research team. It s mpled that overly strong ntatve on the part of an ndvdual team member n the research and development process possbly deterorates the collaboraton effect among researchers. Lastly, the analyss llustrated the mportance of dversty durng the process of knowledge creaton. The nonlnear effects of superstar collaboraton emerge n a team made up of talented ndvduals who each possesses a unque specalst knowledge or expertse. By puttng to use the dverse sets of sklls and knowledge, talented nnovators can acheve successful nnovaton n a team, and the value of the nnovaton and new knowledge ncreases nonlnearly as the talent of members of the team ncreases.

18 17 References Azoulay, Perre, Joshua S. Graff Zvn, and Jalan Wang Superstar Extncton. The Quarterly Journal of Economcs 125: Connolly, Mare, and Alan B. Krueger Rockonomcs: The Economcs of Popular Musc. In Handbook of the Economcs of Art and Culture, edted by Vctor A. Gnsburg, and Davd Throsby, Amsterdam: Elsever. Emerck, Geoff; Massey, Howard (2006). Here, There and Everywhere: My Lfe Recordng the Musc of The Beatles. New York: Pengun Books. Isaacson, Walter Steve Jobs. New York: Smon and Schuster. Jones, Benjamn F The Burden of Knowledge and the Death of the Renassance Man : Is Innovaton Gettng Harder? Revew of Economc Studes 76: Levn, Sharon G., and Paula E. Stephan Research Productvty over the Lfe Cycle: Evdence for Academc Scentsts. Amercan Economc Revew 81: Lewsohn, Mark (1988). The Beatles Recordng Sessons. New York: Harmony Books. Sgt. Pepper s Lonely Hearts Club Band. CD, lner notes. London: Captol Records, Mas, Alexandre, and Enrco Morett Peers at Work. Amercan Economc Revew 99: Rosen, Sherwn The Economcs of Superstars, The Amercan Economc Revew 71 (December): Statstc Bran, s.v. The Beatles, last modfed July 23, 2012, Strobl, Erc A., and Clve Tucker The Dynamcs of Chart Success n the U.K. Pre-Recorded Popular Musc Industry. Journal of Cultural Economcs 24:

19 18 The Beatles Anthology. DVD. Drected by Kevn Godley, Bob Smeaton, and Geoff Wonfor. London: Captol Records, THE DIG Specal Edton John Lennon (Shnko Musc Mook). [In Japanese.] Tokyo: Shnko Musc Entertanment Co., Ltd., Wetzman, Martn L Recombnant Growth. Quarterly Journal of Economcs 113:

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