FACULTY OF APPLIED ECONOMICS DEPARTMENT OF ECONOMICS Reveue sharg ad ower profs professoal eam spors Sefa Késee RESEARCH PAPER 005-08 November 005 Uversy of Awerp, Prssraa 13, B-000 ANTWERP, Belgum Research Admsrao room B.13 phoe: (3) 3 0 40 3 e-mal: oer.ys@ua.ac.be The papers ca be also foud a our webse: www.ua.ac.be/ew (research > workg papers) D/005/1169/08
Reveue Sharg ad Ower Profs I Professoal Team Spors Prof. dr. Sefa Kesee Deparme of Ecoomcs Uversy of Awerp (UA) Deparme of Spors ad Moveme Sceces Caholc Uversy of Leuve (KUL) 1. Iroduco I he spors ecoomcs leraure, may auhors have aalysed ad dscussed he mpac of reveue sharg amog clubs o he compeve balace a spors league. Wha ca be cocluded, so far, s ha he mpac depeds, amog oher varables, o he club obecves, he specaor prefereces, he varables affecg club reveue, he ale supply codos, he eralzao of he exeral effecs, he specfcs of he sharg arragemes, ec. For a overvew of he ma resuls, see For ad Qurk (1995), Marburger (1997), Kesee (000, 005), Szymask (003), Szymask ad Kesee (004). Comparably, lle aeo has bee pad o he mpac of reveue sharg o ower profs. I seems obvous ha reveue sharg creases he profs of he low-budge clubs a league, as well as oal league profs, bu s uclear
how he profs of he large-budge clubs are affeced (For ad Qurk, 1995). Largebudge clubs see her seaso reveue reduced by mos sharg arragemes bu, a he same me, he player labour cos s expeced o come dow. Prof maxmzg clubs lower her demad for ale f hey have o share he margal reveue of ale wh her oppoes he league. Wh a gve supply of ale, hs wll reduce he marke clearg salary level a compeve player marke. Neverheless, mos large-budge clubs do' lke o share, hey expec boh her playg sregh ad her profs o come dow, because sharg lowers her reveue, bu hey cao be sure f, whe, ad by how much he sharg arrageme wll lower he player cos. Moreover, may Europea spors, he bes eams have o compee o wo levels: he ow aoal champoshp ad he Europea Champoshps. The bes clubs he small Europea coures are ofe oo srog for her aoal league ad oo weak for he Europea league. The am of hs paper s o vesgae how reveue sharg affecs ower profs heory ad o compare hese resuls for he wo basc models he leraure: he Walrasa-equlbrum approach, beer kow as he Roeberg (1956) or Qurk ad For (199) model, leadg o he well-kow varace proposo, ad he Nash- Couro equlbrum model as Szymask ad Kesee (004), whch challeges he varace proposo ad shows ha reveue sharg ca worse he compeve balace. Seco preses he smples possble model specfcao for he professoal eam spors dusry. I seco 3, he mpac of reveue sharg o profs s aalysed a Walrasa-equlbrum approach. Seco 4 cosders he mpac o profs f reveues are shared a Nash-Couro equlbrum approach. Seco 5 cocludes.. The model The model we sar from descrbes a -club league wh seaso reveue fucos ha are creasg, bu cocave he eam s ow wg perceage. A club's seaso reveue s also affeced by s marke sze (or he drawg poeal of he eam) ad he oal umber of ales playg he league. We assume ha he sze of he marke creases club reveue, bu hs varable cao be corolled by club maageme. The oal umber of ales employed deermes he absolue playg 3
qualy of he league ad has a posve effec o club reveue. Ths smple model ca he be wre as: R = R[ m, w, s] (1) where R s he seaso reveue of club, m s s marke sze ad s s he sum of all ales he league,.e. s= = 1. The clubs wg perceage, or he relave qualy of a eam, depeds o s relave playg sregh, ad s assumed o equal / mes he rao of s umber of ales o he sum of all ales he league: w = = 1 () The sum of he wg perceages of all eams does o equal uy bu half he umber of eams he league. The oal cos of a eam cosss of a fxed capal cos, ad he labour cos whch s equal o he umber of he eam s ales mulpled by he u cos of ale : 0 c c C = c + c (3) 0 The specfc reveue sharg arrageme ha s cosdered hs model s he sharg of all reveue, cludg gae receps, elevso ad commercal reveue. A fxed perceage of all club reveue s colleced ad pooled by he league ad equally dsrbued amog all clubs. If a sar dcaes he afer-sharg values, ad µ s he share parameer ( 0< µ < 1), hs sharg sysem ca be wre as: R = (1 µ ) R +µr (4) 4
where R s he average club reveue he league. Noce ha hs formulao, a hgher value of µ meas more sharg. Assumg ha club maagers kow he sharg arrageme, hey wll ake o accou whe decdg o he hrg of ale. I s a well-kow resul ha reveue sharg ca affec boh he ale demad ad he u cos of ale of a club, so ha reveue ad cos are affeced. If a club s seaso prof s he dfferece bewee seaso reveue ad seaso cos, ad f reveue s wre as a fuco of he decso varables oly, he afer-sharg prof fuco s: 0 π = (1 µ ) R [, s ] + µr [, s] c c (5) where s he -vecor of ales afer sharg, s s he oal sum of ales ad c s he u cos of ale afer sharg. I order o aalyse he mpac of reveue sharg o profs, he frs paral dervave of he prof fuco wh respec o µ ca be calculaed: π R [, s ] R [, s] R[, s ] c µ = R [, s] R[, s ] + + µ ( ) c (6) A posve sg for hs equao meas ha more reveue sharg wll ehace club profs. Sarg from hs geeral expresso, he wo scearos ca ow be vesgaed o fd he mpac of reveue sharg o profs. 3. Profs he Walrasa equlbrum model. The bechmark model of a professoal eam spors league, as roduced by El- Hodr ad Qurk (1971), also commoly referred o as he Qurk ad For model (199), goes back o Roheberg's (1956) semal arcle ad he well-kow 'Ivarace Proposo', clamg ha player marke regulaos have lle or o mpac o he ale dsrbuo amog clubs. Alhough he Roheberg paper coceraed o he mpac of he Reserve Clause he US maor leagues, laer o, he varace proposo was also used o dcae he zero-mpac of reveue sharg o compeve balace. Qurk ad El-Hodr (1974) showed ha reveue 5
sharg amog clubs does o chage he compeve balace a league ha s characerzed by prof maxmzg clubs, operag a compeve player marke wh a cosa supply of playg ale. Ths model, wh a cosa s s geerally acceped as a approprae descrpo of he closed maor leagues Norh-Amerca spors. If a club s wg perceage ca be wre as he rao of s ales o he oal ales he league as (), he mpac of ale o he ow wg perceage ca be derved as: w = (1 ) + = 1 ( ) = 1 (7) If he supply of ale s cosa, oe ca argue ha oe more ale oe eam mples a equal loss of ale he oher eams, or = 1, so ha (7) smplfes o: w =. I follows ha, apar from a cosa, he wg perceage s reveue fuco (1) ca smply be replaced by he umber of ales. I follows ha a club's demad for ale s depede of he decsos made by he oppoes, so ha he Walrasa equlbrum ca be derved. However, hs hypohess also mples ha a club, calculag s margal reveue of ale fully eralze he exeraly causes o s oppoes by subsug he cosa supply of ale o he labour demad fuco (see Szymask ad Kesee, 004; Szymask, 003, 004a). I hs case, reveue sharg o oly leaves he ale dsrbuo uchaged, also lowers he compeve salary level a Walrasa equlbrum approach, as has bee show by Qurk ad El-Hodr (1974) ad ohers. So equao (6) smplfes o: π c = R[, s] Rs [, ] = Rs [, ] Rs [, ] + c (8) 6
where c s he marke clearg u cos of ale before sharg. I ca be show 1 ha s value afer sharg c µ = (1 ) c c so ha = c. Because he rgh-had sde of equao (8) s clearly posve for all clubs ha have a pre-sharg budge ha s smaller or equal o he average budge he league, reveue sharg creases he prof of he small ad md-szed clubs. Oly for eams ha have budges ha are so large, compared wh he oher eams, ha Rs [, ] c= π > Rs [, ], ha s: her profs are hgher ha he average budge he league, reveue sharg wll lower profs. I follows ha, alhough s mos lkely ha mos clubs' profs crease by reveue sharg, s possble ha he profs of he relavely rch ad very profable clubs come dow. Also oce ha he sze of he share parameer µ does o affec hs resul, eve he mos modes sharg arrageme ca lower he profs of he very doma clubs. Obvously, he mpac of reveue sharg o league-wde profs s uambguously posve; oal league reveue s o alered ad he oal player cos s comg dow. From equao (5), oal profs afer sharg ca be wre as: π = = 1 = 1 = 1 0 R [, s ] ( c + c ) (9) Because sharg does o chage he ale dsrbuo ad he supply of ale s cosa, s mpac o league-wde profs ca be foud as: = 1 π c cs > 0 (10) = 1 = = A smplfed example of a -club league wh quadrac reveue fucos shows ha, whaever he value of share parameer, reveue sharg creases he poor club's 1 Sharg arrageme (1) ca also be rewre as: (1 µ ) + µ µ R = R + R, so ha he (1 µ ) + µ µ 1 margal reveue s: MR = MR + MR ( ). I he Walrasa marke 1 equlbrum MR = c for all, so ha MR =(1-µ) c = c. 7
profs ad decreases he rch club's profs f ha club's profs are large ha he average budge he league. Assume ha x s he large-budge eam wh a marke sze of 14 ad y s he low-budge eam wh a marke sze of 6, ad ha he clubs reveue fucos are: Rx 14wx wx 14x x = = ad Ry = 6wy wy = 6y y (11) wh a cosa supply of ale of 8 ad o capal cos. Table 1 shows he resuls of hs model for creasg values of he share parameer, sarg from o sharg. As ca be see, he dsrbuo of ale, or he compeve balace, before sharg (µ=0) s 6 o, ad s o chaged by reveue sharg accordace wh he varace proposo. The al budges of he large ad he small club are 48 ad 8, so ha he average budge s 8. The al u cos of ale s ad he player cos of he large club s 1. I follows ha he large-budge club's prof s 36, whch s larger ha he average budge. Table 1. Walrasa Equlbrum, umercal example --------------------------------------------------------------------------------------------- µ x / y R x R y R c C x C y π x ---------------------------------------------------------------------------------------------- 0 6/ 48 8 8 1 4 36 4 40 0.5 6/ 38 18 8 1 6 3 16 48 1 6/ 8 8 8 0 0 0 8 8 56 ----------------------------------------------------------------------------------------------- π y π As show by equao (8), reveue sharg wll lower he large club's profs. Wh a share parameer of µ=0.5, whch meas ha he large club keeps 75% of s reveue ad receves 5% of he small clubs' reveue, he large club's reveue decreases ad he small club s reveue creases, keepg oal league reveue uchaged. Because he u cos of ale decreases from o 1, boh clubs' player coss are comg dow. The large-budge club's reduco boh reveue ad cos lower s prof from 36 o 3. As expeced, he profs of he low-budge club go up from 4 o 16. Also, oal league profs are rased by reveue sharg. If µ=1, whch meas equal sharg, all 8
clubs' reveues ad profs are equal, ad he marke clearg u cos of ale s zero; clubs are o loger wllg o pay for ale. 4. Profs he Nash-Couro equlbrum model. Sce Roeberg s (1956) arcle, he varace proposo has bee serously challeged. Several varas of he orgal model have bee cosdered, as meoed he roduco. The vara, dscussed hs seco, sars from exacly he same model as descrbed seco, bu assumes ha he supply of ale s flexble (see: Szymask ad Kesee, 004). The flexble-supply model s more approprae for professoal spors Europe wh s mulple aoal leagues, operag a Europea compeve player marke sce he Bosma verdc. Gve he creased eraoal mobly of players, he ale supply ca o loger be cosdered as a cosa each aoal league. I follows ha equao (7): = 0 so ha he mpac of ale o wg perceage ad reveue becomes: R R w R = = w w ( ) = 1 (1) Corary o he prevous model, he mpora cosequece s ha he margal reveue of ale of a eam, or s hrg sraegy, depeds o he hrg sraegy of all oher eams he league, whch urs he model o a game. I hs game, all eams are wage akers o he ope Europea labour marke, so he margal u cos of ale for every eam each aoal champoshp has o be cosdered as a cosa. I follows ha equao (6) c = c ad c = 0. Uder hese hypoheses, Szymask ad Kesee (004) ad Kesee (005) have show ha, afer reveue sharg, he o-cooperave Nash-Couro Equlbrum wll The Bosma verdc by he Europea Cour of Jusce December 1995 abolshed he rea ad rasfer sysem Europe, as well as he so-called 3+-rule, wh lmed he umber of foreg (Europea) players a eam. 9
o oly show a decrease he demad for ale of each eam, bu also a worseg of he compeve balace. Ths mples ha equao (6) c s posve for all µ R s clubs, ad ha, for a gve value of s, [, ] s posve for he large-budge clubs, bu egave for he low-budge clubs, because of he chages her wg perceages. However, hs flexble-supply model wh a gve u cos of ale, oal ale employme s s o loger a gve cosa. Because all clubs reduce her demad for ale, he absolue qualy of he league champoshp s lower whch has a egave effec o all clubs' reveue. I follows ha he sg of R s [, ] heorecally deermae for he large-budge clubs, ad eve more egave for a low-budge club. The reduco absolue qualy of he league also mples ha he s sg of R s [, ] s egave. 3 Fally, s obvous ha he sg of [, ] [, ] R s R s s egave for he largebudge clubs ad posve for he low-budge clubs. I order o derve he mpac of sharg o profs, he sg of expresso (6) has o be vesgaed. I able, he expeced sgs of he erms are gve he colums whou pareheses for he low, he average ad he hgh budge clubs. Alhough he erms equao (6) show oppose sgs for low-, average- ad he large-budge clubs, he low-budge clubs wll experece a prof crease. I s oly her lower wg perceage, combao wh a lower absolue qualy he league, ha wll reduce her seaso reveue, bu hs effec s clearly o srog eough o oubalace he oher hree favourable effecs o profs. Moreover, Kesee (005) 3 I a rece paper, Szymask (004b) have show emprcally ha reveue sharg ca possbly ehace oal league reveue because specaors seem o prefer a more uequal compeve balace ha he oe emergg from he o-cooperave equlbrum. I equao (6) hs would mply ha R[, s ] s deermae. However, hs fdg s sll coroversal. Mos emprcal research shows ha he compeve balace a league does o have a sgfca effec o aedaces (see Borlad ad Macdoald, 003). Also, he compeve balace a league ca be approached ad measured very dffere ways (see Szymask, 003). So we assume here ha specaors are more or less dffere for margal chages compeve balace. 10
has show ha he Nash-Couro equlbrum approaches he Walrasa compeve equlbrum f he umber of clubs a league creases, so ha, wh 18 or 0 clubs a league, he mpac of reveue sharg o he dsrbuo of ale s relavely small. I follows ha he oly egave effec of reveue sharg o he small clubs' profs comes from he lower absolue qualy he league. Table. Expeced sgs of he erms of equao (6) Budge Low Average Hgh ------------------------------------------------------------------------------------------- R s R s + (+) 0 (0) - (-) [, ] [, ] R s [, ] R [, s] R [, s ] µ ( ) c - (-) - (0)? (+) + (+) 0 (0) - (-) + (+) + (0) + (-) c 0 (+) 0 (+) 0 (+) µ --------------------------------------------------------------------------------------------- For he md-szed clubs, wh a budge close o he league average, able shows ha equao (6) smplfes o: π R [, ] s = c (13) Because her wg perceage wll o be affeced by reveue sharg, eve a league wh a lmed umber of eams, he egavy of he frs erm (13) s oly caused by he loss of absolue qualy he league. So, alhough heorecally deermae, expresso (13) ca be expeced o be posve, because hese clubs prof from he reduco ale hrg a a fxed u cos of ale. 11
Also he hgh budge clubs prof from a reduco player labour cos, bu he mpac of reveue sharg o her profs ca be egave depedg o he relave sze of her budge ad o he sze of he share parameer µ. Also he reduco absolue qualy he league ca be expeced o have a sroger egave effec o he large clubs' budge, oubalacg he expeced small posve effec of a hgher wg perceage, so ha he heorecally udeermed erm able ca also be egave. Remark A mpora remark s ha he fxed-supply model of seco 3, was assumed ha a club compleely eralzes he exerales causes o her oppoes by sregheg s eam. However, oe ca also cosder a fxed-supply markeclearg model whou he eralzao of he exerales, or, oher words, a Nash-Couro equlbrum model wh a cosa ale supply. Wh a cosa supply of ale equal o s, equao (1) ca be wre as: R R w R R ( s ) (14) w w s w s = = = Compared wh he flexble-supply scearo hs seco, reveue sharg wll ow lower he u cos of ale, gve he dowward shf of he marke demad for ale ad he fxed supply of ale. I follows ha equao (6), he las erm: c o loger equal o zero. Because of hs adusme o a ew marke equlbrum, large-budge clubs wll have creased ad low-budge clubs wll have reduced her hrg of ale, compared wh he pre-sharg suao (see Szymask, 004a). The compeve balace has worseed ad he absolue playg qualy he league s he same as before ( s = s). I able, he expeced sgs of he erms of expresso (6) are ow gve bewee pareheses. For he low-budge clubs, profs wll go up eve furher ow because of he lower u cos of ale. Somewha surprsg s ha he oucome for he mdszed clubs s ow uambguously posve. O he reveue sde, o oly he absolue qualy of he league s he same as before, also hese clubs' relave qualy, or her s 1
wg perceage says more or less he same. O he cos sde, hey o loger reduce her ale hrg, bu hey prof from he lower u cos of ale. For he large-budge clubs, he mpac of reveue sharg o profs s sll heorecally deermae. Compared wh he flexble-supply case, he secod erm able s ow clearly posve because of he mproved wg perceage ad he uchaged absolue qualy he league, bu hrg more playg ale creases he labour cos he fourh erm, bu he labour cos s reduced by he lower u cos of ale he las erm able. Reurg o he umercal example (11) of seco 3, he Nash-Couro equlbrum, wh a fxed supply of ale, ca be foud by solvg he followg reaco fucos: R x Rx wx = = w = w s x x x R R w w s y y (14 x) (14 / 4) x 64 y y y x = = (6 wy) = (6 / 4) x y y y y 64 = c = c (15) The compeve balace urs ou o be smply he rao of he marke szes of he wo clubs or: x wx mx 14 = = = =.33 wh x = 5.6 ad y =.4. The marke clearg w m 6 y y y u cos of ale s ow 0.475. So, we fd a more equal dsrbuo of ale ad a lower average player salary level compared wh he Walrasa equlbrum seco (3) where he exerales were fully eralzed. Ths does o come as a surprse because he egave exeral effecs ha small clubs cause o large clubs are sroger he he egave effecs ha large clubs cause o small clubs, because large clubs have hgher margal reveues ad, cosequely, more o loose. Cosequely, small clubs ves oo much ale whch leads o a more equal dsrbuo of ale (see Szymask, 004b). Because reveue sharg worses he compeve balace, we ca derve ha he case of equal sharg, he compeve balace s he same as he Walrasa 13
x compeve equlbrum of seco 3 (.e. = 6/). The reaso s ha, by equal sharg, he effecs of he exerales are euralzed, so ha he same resuls shows up as he scearo where he exerales are fully eralzed. No surprsgly, also he marke clearg u player cos wll be zero; a prof maxmzg club s o wllg o ves ale he case of equal sharg. y 5. Cocluso Ths paper has show ha he mpac of reveue sharg o ower profs s o as sraghforward as mgh seem. Whle s obvous ha oal league profs, ad he profs of he low budge clubs, are rased by reveue sharg, s o always clear wha happes o he profs of he hgh budge clubs. I hs paper we have coceraed o wo bascally dffere models erms of he ale supply codos There are oly lle dffereces bewee he mpac of reveue sharg o profs he Walrasa fxed-supply model compared wh he Nash-Couro approach wh flexble or fxed ale supply. Small ad md-szed clubs wll see her profs go up. For he large budge clubs, he case was clear he fxed-supply Walrasa approach: f a club's pre-sharg profs are larger ha he average club budge he league, s profs wll be reduced by reveue sharg. I he Nash-Couro approach, he oucome for large-budge clubs s heorecally deermae, bu he larger he budge, compared wh he average budge he league, he hgher he chaces o experece a prof reduco. Oe dfferece wh he Walrasa approach s ha Nash-Couro approach he oucome also depeds o he sze of he share parameer. I he Walrasa model, eve a modes sharg arrageme wll reduce he profs of he very doma clubs. Wha happes o he large-budge clubs' profs he Nash- Couro approach depeds o he value of several parameers he model ad s herefore a emprcal queso. 14
Refereces Borlad J. ad Macdoald, R., (003), Demad for Spor, Oxford Revew of Ecoomc Polcy, 19 (4), 478-50 El-Hodr M. ad Qurk J., (1971), A Ecoomc Model of a Professoal Spors League, Joural of Polcal Ecoomy, 79 (6), 130-19 For R. ad Qurk J. (1995), Cross-subsdzao, Iceves ad oucomes Professoal Team Spors Leagues, Joural of Ecoomc Leraure XXXIII, (3), 165-99 Kesee S., (000), Reveue Sharg ad Compeve Balace Professoal Team Spors, Joural of Spors Ecoomcs, 1 (1), 56-65 Kesee S. (005), Reveue Sharg ad Compeve Balace, does he Ivarace Proposo hold? Joural of Spors Ecoomcs, 6(1), 98-106 Marburger D.R., (1997), Gae Reveue Sharg ad Luxury Taxes Professoal Spors, Coemporary Ecoomc Polcy, XV (), 114-13 Qurk J. ad El Hodr M., (1974), The Ecoomc Theory of a Professoal Spors League, : Noll, R., ed., (1974), Goverme ad he Spor Busess, Brookgs Isuo, Washgo DC., 33-80 Qurk J. ad For R., (199), Pay Dr, he busess of professoal eam spors, Prceo U.P, 538 p. Roeberg Smo (1956), The Baseball Players' Labor Marke, Joural of Polcal Ecoomy, LXIV (3), 4-58 Szymask S., (003), The Ecoomc Desg of Sporg Coess, Joural of Ecoomc Leraure, XLI, December, 1137-1187 Szymask S. ad Kesee S. (004), Compeve balace ad gae reveue sharg eam spors, Joural of Idusral Ecoomcs, LII (1), 165-177 Szymask S., (004a), Professoal Team Spors are oly a Game: he Walrasa Fxed-Supply Coecure model, Coes-Nash Equlbrum, ad he Ivarace Prcple, Joural of Spors Ecoomcs 5 (), 111-16 Szymask S., (004b), Tlg he Playg Feld: why a spors league plaer would choose less, o more, compeve balace, workg paper, Taaka Busess School, Imperal College, Lodo, 36 p. 15