Tjalling C. Koopmans Research Institute

Transcription

1 Tallg C. Koomas Researh Isttute

2 Tallg C. Koomas Researh Isttute treht Shool of Eooms treht versty Jaskerkhof 35 BL treht The Netherlads telehoe fax webste The Tallg C. Koomas Isttute s the researh sttute ad researh shool of treht Shool of Eooms. It was fouded 003, ad amed after Professor Tallg C. Koomas, Duth-bor Nobel Prze laureate eooms of 975. I the dsusso aers seres the Koomas Isttute ublshes results of ogog researh for early dssemato of researh results, ad to ehae dsusso wth olleagues. Please sed ay ommets ad suggestos o the Koomas sttute, or ths seres to.vadort@eo.uu.l otwer voorblad: WRIK treht How to reah the authors Please dret all orresodee to the frst author. Loek Groot treht versty treht Shool of Eooms Jaskerkhof 35 BL treht The Netherlads. E-mal: l.groot@eo.uu.l Ths aer a be dowloaded at: htt://

3 treht Shool of Eooms Tallg C. Koomas Researh Isttute Dsusso Paer Seres The Cotest for Olym Suess as a Publ Good Loek Groot treht Shool of Eooms treht versty November 008 Abstrat Ths study osders the erformae of outres at the Olym Games as a ubl good. Frstly, t s argued that, at the atoal level, Olym suess meets the two key odtos of a ubl good: o-rvalry ad o-exludablty. Seodly, t s demostrated that stadard ome equalty measures, suh as the Lorez urve ad the G dex, a be suessfully aled to the dstrbuto of Olym suess. The atual dstrbuto of Olym suess s omared wth alteratve hyothetal dstrbutos, amog whh aordg to oulato shares, the dstrbuto favoured by a soal laer ad the oooeratg Nash- Courot dstrbuto. By way of oluso, a deve s roosed to make the dstrbuto of Olym suess more equtable. Keywords: Olym Games, ubl goods, exteraltes, soal welfare, Nash JEL lassfato: D63, H4, H50

4 Itroduto At the Summer Olyms Games 008 Beg, more tha eleve thousad athletes from over 00 outres ometed for medals 30 dfferet sort evets. Overall, a total of 958 medals were dstrbuted. ore tha half (56%) of all medals, ad 65% of all gold medals, were olleted by the To 0 outres, whh omrse slghtly above oe thrd of the world oulato. Oly oe four artatg outres sueeded wg at least oe gold medal, whlst half of the artatg outres faled to w ay medal. At fae value, these fgures do ot show that the medal tally s (u)equally dstrbuted over outres. Whether or ot the medal tally s (u)evely dstrbuted deeds o the rtera used. Wth a few exetos, the eoom lterature o Olym erformae oetrates o exlag the erformae of outres at the Olym games by detfyg relevat fators lke oulato sze, GDP ad GDP er ata, hostg ad eghbourg outres ad soalst bakgroud. By ad large, the exlaatory ower of these models s qute hgh. For examle, Berard ad Busse (004: 47) deloy ther favourte model 3 to a out-of-samle redto for the medal tally of the Summer Olyms of 996 ad atta a R of 96%. Johso ad Al (004: 98-8) atta smlar fgures for the out-of-samle redtos for the The total medal out s more tha three tmes the umber of dsles, beause sometmes medalwg athletes ed exatly equal, whh ase a double broze, slver of golde medal s awarded (see htt://e.beg008./). Exluso of Cha from the to 0 gves that the other 9 outres, wth a world oulato share of oly 4%, ature almost half of all gold medals. For the Olyms 004 ad 000, the to te had a gold share of 60% ad 66% resetvely, agast oulato shares of 33%. I 996 t was 65% agast 34%, 99 78% agast 34%, 988 8% agast 4%. 3 Aart from the sef eoometr tehques, the ma dfferee of the model of Berard ad Busse from other ovetoal models exlag the medal tally (e.g. Ba (005), Hoffma et al. (00; 004) ad Tha (004)) s the luso of a varable reresetg the lagged medal share. Ths varable stads for the tme to buld -effet: vestmets for oe Olyms rease the wg odds subsequet Olym Games. Past suess turs out to be a strog redtor of urret suess, datg that (vestmets ) OS a be see as a kd of durable atal good bearg frut over several Olym yles.

5 umber of artats ad the gold medal out er outry at the Wter Olyms 00 Salt Lake Cty (R = 0.96 ad 0.85 resetvely) ad at the Summer Olyms 000 Sydey (R = 0.95 ad 0.85 resetvely). The redtos of Kuer ad Sterke (008) for the last olym yle atta a smlar exlaatory ower. uh more hallegg s to exla whh outres wll w whh medals. Tsha ad Persh (003) started ths roet by alyg the aalyss of omaratve advatages teratoal trade theory to the outry s erformaes eah sort, e.g. outres wth a log oastle are exeted to have a omaratve advatage salg or rh outres have a omaratve advatage the exesve equestra sort evets. I otrast to ths strad of researh, the urose of ths aer s ot to exla whh fators determe the Olym medal tally. Istead of takg a exlaatory or desrtve ersetve, I delberately adot a ormatve ersetve. There are several reasos why a ormatve ersetve may be terestg. Frstly, the dstrbuto of Olym medals s a fxed sum game. By defto, the umber of dfferet evets s lmted ad fxed ex ate, ad er evet oly three medals a be assged. Therefore, ay outry tryg to or sueedg gettg a larger share the medal out moses a egatve exteralty o all other ometg outres. From a ormatve ersetve, t a be desrable to hage the etves suh a way that relatvely (u)suessful outres beome (more) less suessful. I wll gve a examle of oe suh strumet, the auto of etry tkets, seto 5. Seodly, the former soalst outres have show that, a sese, Olym suess (herafter abbrevated as OS) a be maufatured. At the Olym Summer Games of Seoul 988, ust ror to the fall of the Wall 989, the Peole s Reubl of Germay DDR wth oly 7 mllo habtats wo more gold medals tha the SA wth a oulato of early 50 mllo. ore tha 55% of all gold medals wet

6 to the soalst outres. Fve formerly soalst outres (SSR, DDR, Hugary, Bulgara ad Romaa) were the to 0, together omrsg oly 4.% of the world oulato, but wg early half of all gold medals. Although dog deftely layed a role, these outres have udoubtedly show that a oordated sort oly a breed OS. I other words, there s o suh thg as a atural dstrbuto of OS. The reset dstrbuto s strogly based towards the rh outres ad some outres whh attah a hgh oltal referee for OS. After the demse of early all the soalst outres 989, ad wth t ther sueror teratoal sort erformae, t has beome more attratve for other outres all over the world to ursue a atve oly of ther ow order to share as muh as ossble the OS. To a reasg extet, outres embark a rat rae to omete for OS by meas of govermet exedtures exlusvely alloated to stmulate rofessoal sort, whereas these sare resoures ould also be alloated to sort atvtes geeral. From a ormatve ersetve, t mght be referable to alloate more of the atoal sort budget to romote amateur sort, stead of the sgfatly hgher exedtures alloated to to sort. 4 Thrdly, as trade, some outres have omaratve advatages some sorts. Oe of the best examles s Keya, wth a oulato of oly 8 mllo, but the world leader of dstae rug. Barra (Wall Street Joural, 0 Setember 000) argues that based o oulato eretages aloe, the odds of Keya domatg these evets would be oe.6 bllo. 5 If t s deed the ase that outres have omaratve advatages some sorts, for examle due to the geet edowmets of ther oulato, the t s effet that they sealze these sorts rather tha 4 For stae, The Netherlads has set about 80 mllo, a quarter of the etre govermetal sort budget, for the last Olym yle Beg 008 to realze ts ambto of a lae amog the to 0. 5 A better examle stll s the habtats of the Nad dstrt Keya, wth 500,000 eole holdg about 0% of the world dstat reords rug 000.

7 3 others. Sealzato s more effet tha whe (too) may outres omete for suess the same dsle. atros ad Namoro (004: 5), based o the observato that the SA, SSR ad DDR shared the odum muh less tha ould be exeted from ther overall erformae, suggest that the ast they strategally ad tatly sltted the market for medals. Fourthly, the elebrato of OS s essetally a ubl good, beause the leasure reated by a athlete wg gold s truly a o-exludable ad o-rval good. The eoymet of oe assve setator seeg hs fellow outry(wo)ma w a medal does ot exlude the eoymet of aother setator from the same outry: oe s osumto does ot redue the osumto of others ad all a osume OS at the level of ts total suly. Nor s t ossble to exlude some tzes from assvely sharg the suess of ts outry. Therefore, the assve eoymet of OS meets the two key odtos of a ure ubl good. Se t s o-exludable, rvate markets may ot geerate the otmal amout of OS. As far as I kow, the ubl good ature of OS, beause of the o-exluso ad o-rvalry attrbutes, has ever bee addressed the eoom lterature. 6 As wth other ubl goods, there s a rma fae ase for the govermet to tervee the rovso of ths good. 7 Fally, the Olyms are advertsed as a feast of brotherhood of makd. Aordg to Coubert, the fouder of the moder Olyms, the Olym rgs symbolzes the uo betwee me. Also the arade of athletes at the oeg eremoy of the Games suggests that the Olyms are really global. However, 6 oosa ad Smth (004: 88) refer to the Coe reort of 985, where argumets are gve why govermets are about OS ad why OS resembles a ubl good: Frst, suess makes eole roud of ther atoal detty ad ve versa. Seod, suess the Olyms mroves the outry s mage abroad, helg to sell atoal roduts. Thrd, t boosts artato sort ad rereato, leadg to a geeral mrovemet the health of the average tze. These three argumets do ot refer to o-exludablty or o-rvalry. 7 Ths mght exla why may outres do have tax-fuded to sort oles ad heavly subsdze to sorters (e.g. by gvg them obs the army or the ole).

8 4 deste ths rhetor, rh outres ad some other outres that strve for OS for maly oltal reasos, are far more suessful tha other outres. The ormatve ssue here s whether the Olym movemet to lve u aordg to ts ow fudametal rles of Olymsm should ot take (more) ato to eourage ad suort the develomet of sort for all (Olym Charter,. 5), that s, to establsh more of a level layg feld. There are also good reasos to evaluate the remse of ths study, that s to arrve at a dstrbuto of OS that s more ust or results hgher soal welfare, as hghly questoable. Frst of all, the urose of the Games s to sgle out the wers; that s to say that the best must w, rresetve whether the overall dstrbuto of OS s (ds)agreemet wth some kd of atter based o uste or soal welfare. Seodly, there are huge dfferees betwee outres, ot oly the geet edowmets of ts oulato ad atural evromet, but also ulture ad referees. 8 These dfferees fluee eah outry s haes for OS, but also mge o the value attahed to OS. aybe suessful outres are more about OS tha relatvely usuessful outres. If so, the a soal welfare futo should take these dfferees to aout. Admttedly, these obetos, as well as others, to aly stadard soal welfare futos to sort otests may make ths aalyss a o-starter. I rle, however, the aalyss may be terestg ts ow rght: t a be read as a vestgato to the fores determg alteratve dstrbutos of absolutely sare goods at the global level, e.g. atgs of old masters, whh s rval osumto aross atos but a ubl good wth atos. 8 Ida s a otorous udererformer at the Olyms, but t s very strog rket, whh s ot a Olym sort. The same goes for Lat Amera outres, where soer s by far the most oular sort, for whh oly oe Olym medal a be wo.

9 5 The equalty the atual dstrbuto of Olym suess I what follows t s heurstally assumed that () the Olym Games are truly global ( the sese that tzes all outres have detal utlty futos for OS); () the dstrbuto of OS s ot a kd of atural dstrbuto but rather already maufatured to a osderable extet by to sort oles adoted by atoal govermets ad teratoal goverg bodes; () all dsles are equally mortat (so, a gold medal obsure sorts as feg, arhery or skeet shootg s as mortat as oe trak ad feld) ad (v) for smlty, we oetrate o the dstrbuto of gold medals oly. I Table, the outres are raked desedg order aordg to oulato shares (olum ). Colum 3 gves the atual gold medal tally of Beg 008, ad olum 4 the gold medal share. If gold medals were dstrbuted roorto to oulato shares, as olum 5, the Cha would reeve eve eleve medals more; Ida would w 5 stead of oe gold medal; whlst the SA oly retas 4 gold medals. Comarg olums 4 ad 5, t are maly the rh outres (SA, Germay, K, Frae, Italy ad Jaa) whh ature a muh larger share of medals tha would follow f medals were dstrbuted aordg to oulato shares. These sx rh outres omrse oly 0.9% of the world oulato, but hold almost three of every te gold medals (3.5%), ad so aturg a exessve share of 0.6%. Due to the fxed sum game of Olym medals, the hgher tha roortoal share of some outres has as mrror mage that other outres reeve less tha ther roortoal share. The lower tha roortoal shares of oulous Ida (wth o gold ad oly a slver medal 004 ad oly oe gold 008),

10 6 together wth Cha, more or less omesate the hgher tha roortoal share of gold medals of the above metoed sx outres. Table. Dfferet dstrbutos of Olym suess Coutry m y N SP I Cha 0,7% 5 6,9% 6,4 4,4,0 60, Ida 6,9% 0,3% 5, 8,6,9 07,4 SA 4,7% 36,9% 4, 6,8 9,0 8, Idoesa 3,4% 0,3% 0,3 4, 4,7 4,4 Brazl,8% 3,0% 8,5 7,7 7, 3,0 Paksta,3% 0 0,0% 7,,8,7,0 Russa,3% 3 7,6% 7,0 8,0 7,4,0 Bagladesh,% 0 0,0% 6,6,5,4,8 Ngera,% 0 0,0% 6,5 0,7,4,7 Jaa,% 9 3,0% 6, 0, 3,6,6 exo,6% 0,7% 4,9 5,3 5,6,0 Germay,3% 6 5,3% 4,0,8 0,0 0,7 Vetam,3% 0 0,0% 3,9,3, 0,6 Phles,3% 0 0,0% 3,9, 3,0 0,6 Turkey,% 0,3% 3,4,9 3,7 0,5 Ethoa,% 4,3% 3,3 0,3 0,8 0,4 Egyt,% 0 0,0% 3,,5,4 0,4 Ira,% 0,3% 3,,8 3,6 0,4 Thalad,0% 0,7% 3,0,7 3,5 0,4 Frae,0% 7,3%,9 9,3 8, 0,3 K,0% 9 6,3%,9 9,5 8,3 0,3 Italy 0,9% 8,6%,8 8,5 7,7 0,3 Cogo (DR) 0,8% 0 0,0%,5 0, 0,7 0,3 Burma 0,8% 0 0,0%,4 0,5, 0, krae 0,8% 7,3%,4,7,6 0, Other outres 4,3% 36,8% 73,5 74,0 35,4 3, Total 00% 30 00% Poulato data from htt:// ome data from the World Bak, World Develomet Idators. These dstrbutos a be ely llustrated by meas of the Lorez urve (see Fgure, Pael A-D). To vsualze the equalty the ome dstrbuto usg the Lorez urve, dvduals are raked aordg to ome from lowest to hghest. Treatg OS as a ubl good, the strt arallel of the ome-based Lorez urve aled to OS requres that we rak outres aordg to ther gold medal sore: eah tze a outry osumes the medal sore of ts outry. If we rak the outres

11 7 aordg to gold medal sore, the outres wth zero medals are stuated at the left of the Lorez urve ad those wth the hghest sores (Russa, SA ad Cha) at the rght. ovg from left to rght, the horzotal axs regsters the umulatve share of the world oulato, whle the vertal axs regsters the umulatve share the world gold medal sore. Fgure. Lorez urves for the dstrbuto of Olym gold medals 008. Pael A: Cumulatve gold medal share (% g) versus umulatve oulato share (% ), outres raked by G. 00% 80% 60% % g 40% SA RS K CHN 0% IND 0% 0% 0% 40% 60% 80% 00% % 00% Pael B: Cumulatve gold medal share (% g) versus umulatve oulato share (% ), outres raked by g/. % g 80% 60% 40% K RS SA 0% CHN IND 0% 0% 0% 40% 60% 80% 00% %

12 8 00% Pael C: Cumulatve gold medal share (% g) versus umulatve world GDP share (% y), outres raked by g/y. % g 80% 60% 40% K CHN RS 0% SA IND 0% 0% 0% 40% 60% 80% 00% % y Pael D. Cumulatve oulato share (%) versus umulatve oulato weghted medal sore (%G), raked by G. 00% CHN 80% %G 60% 40% 0% SA IND K RS 0% 0,0% 0,0% 40,0% 60,0% 80,0% 00,0% % As Pael A shows, ths rakg results a awkwardly shaed Lorez urve. The sloe of the Lorez urve does ot rease mootoously. Comare Russa wth Cha. Russa aouts for oly.3 eret of the world oulato, but holds 3 gold medals, orresodg to 8 eret of the world gold medal sore. Cha aouts for more tha 0 eret of the world oulato, but holds 5 gold medals, whh s oly 7 eret of all gold medals. Beause outres are raked aordg to gold medal sore, Cha s loated at the rght of Russa. Se the sloe of the Lorez urve s

13 9 the rato of the gold medal share ad oulato share, for Russa ths rato s 3.3, agast 0.8 for Cha, whh mles that the Lorez urve flattes whe Cha s eterg the see after Russa. The same heomeo exlas the stee art the mddle, whh otas all moderately oulated but rh outres wth medal shares muh hgher tha ther world oulato shares. Therefore, to get a roerly shaed Lorez urve, we have to rak outres aordg to rato of medal share ad oulato share, as doe Pael B. Now we see that Cha s stuated more at the left sde of the Lorez urve, se ts medal share s less tha ts oulato share, whle Russa ad the K move further to the rght. The Lorez urve shows that almost half of the world oulato has a zero medal share ad that 80% of the world oulato has a medal share oly of 0%. The dagoal Pael B orresods to the stuato where eah outry s gold medal share s equal to ts world oulato share, so alog ths 45º le every world tze has the same hae of suess, rresetve of oltal regme, ome er ata, rae or relgo. At the left sde Pael B - as log as the sloe of the urve s less tha the sloe of the dagoal (whh has a sloe of ) - are all outres whh have a lower tha roortoal medal sore (alteratvely, these are the outres for whh the rato betwee the medal share ad oulato share s less tha ). O ths segmet, besdes all outres wthout ay medals, Ida ad Cha are loated. Predomatly, these outres are Seod or Thrd World outres (wth the exetos of Hog Kog, Tawa, Irelad ad Swede wth o gold medals). Argeta (wth a rato of.09) s the outry stuated most early left to the ot where the Lorez urve s eredular to the dagoal. To the rght of ths ot, where the sloe of the urve s hgher tha of the dagoal, outres are loated wth hgher tha roortoal medal sores. O ths segmet we frst all rh outres,

14 0 alog wth outres wth a strog sort ulture (Russa ad former soalst outres) or defte omaratve advatages artular sorts (otably some Afra outres suh as Keya ad Etha). At the far rght, there are two outlers: ogola ( gold, wth a rato of 3) ad Jamaa (6 gold, a rato of 66). The further the urve lays from the dagoal, the greater the degree of dsroortoalty betwee medals shares ad oulato shares. From Table ad the Lorez urve Pael B we already oted that wth oly a few exetos the medals shares of the rh outres are hgher tha ther oulato shares. Istead of usg the umulatve oulato shares, we may also ut the umulatve world ome share o the horzotal axs. To get a smooth Lorez urve ad a meagful G-dex, outres must be raked aordg to the rato of world share gold medals ad share world ome (g /y ). I Pael C, the horzotal axs ow measures the umulatve share of the world ome ad the vertal axs aga the umulatve share of gold medals. The dagoal obtas whe medals are dstrbuted roortoal to world GDP shares (see olum 6 of Table ). Cotrary to Paels A ad B, the SA s ow stuated more to the left: ts GDP aouts for more tha 0 eret of world outut, agast a gold medal share of oly.9 eret. Iterestgly, omarg Paels B ad C shows that OS s muh less uequally dstrbuted f thed agast umulatve world ome shares rather tha umulatve oulato shares. The degree of equalty deted by the Lorez urve a be exressed as the G oeffet. The G oeffet s grahally the rato of the area betwee the dagoal ad the urve ad the tragle below the dagoal. The G-oeffet for the former s 55. eret (5.7 for 004), agast 7.7 eret (74.7) for the latter.

15 Summarzg, to get a roerly shaed Lorez urve, outres have to be raked aordg to the rato of the varable whose umulatve frato s measured o the vertal axs ad the varable whose umulatve frato s measured o the horzotal axs. I Pael A, the rakg aordg to absolute gold medal sore s ot the same as the rakg aordg to the rato of gold medal share ad oulato share, whose umulatve fratos are o the axes. However, a roerly shaed Lorez urve a be draw usg the rakg of outres aordg to the absolute gold medal sore f we draw a geeralzed Lorez urve, wth world oulato share o the horzotal axs ad the umulatve share the oulato weghted gold medal sore o the vertal axs. I drawg the geeralzed Lorez urve of Pael D, wth the same rakg of outres as Pael A, for eah outry the rodut of the medal sore ad world oulato share s alulated, whh s used to obta the umulatve fratos, whh adds u to a oulato weghted average medal sore of 4.3. To llustrate, the oulato share of the SA s 4.6 eret ad ts medal sore s 36, so ts otrbuto to the oulato weghted average medal sore s.66; for Cha, wth a oulato share of eret ad a medal sore of 5, the otrbuto s The vertal axs of Pael D smly gves the umulatve otrbutos, dvded by the oulato weghted average medal sore. 9 The G-oeffet for ths urve s 69.3 eret ( ). 9 The dagoal rereset the state of affars where the rato of the otrbuto of eah outry to the oulato weghted gold medal sore ad ts oulato share s equalzed, whh mles a equal medal sore for eah outry.

16 Fgure. Lorez urves ,0 0,8 % g 0,6 0,4 0, 0,0 0,0 0, 0,4 0,6 0,8,0 % Fally, Fgure gves a overvew of the Lorez urve for the last fve Olym Games. For every Olym yle, outres are raked aordg to the rato of medal ad oulato share, as Pael B of Fgure. Clearly, there s a modest but steady ward shft of the Lorez urve over tme, whh suggests that the dstrbuto of medal shares beomes more le wth the dstrbuto of oulato shares over tme. 3 The Nash-Courot dstrbuto of Olym suess I ths seto the dstrbuto of OS s derved whe all outres follow Nash- Courot strateges: they maxmze the utlty futo of a reresetatve tze wth reset to ubl vestmets OS, takg the vestmets of other outres as gve. Cosder the world wth outres dexed by =,,,, wth P the oulato outry ad = P /N the world oulato share of outry, where

17 3 N s the world oulato. The reresetatve tze a outry has a twe otuously dfferetable utlty futo that s reasg er ata ome for osumto Y ad the medal sore : () = Y, ) ( Eah outry faes a budget ostrat where er ata ome avalable for osumto s er ata ome roduto as a ubl good: b Y mus the er ata ost C ( ) / P of medal b () Y = Y C( ) / P Aordg to Eq. (), the roduto of OS s osdered as a ubl good o the outry level, so the ost of medal roduto s shared over the etre oulato P of the outry, where C ( ) / P exresses the er ata ost of medal roduto. Equato (3) sefes a stadard otest futo, also kow as the roortoate share rule (see e.g. Cogleto 984: 03-4), where eah outry s share OS s roortoal to ts share world wde vestmet OS: C (3) = t C = where deotes the total umber of medals ( deotes the umber of medals t hold by all other outres tha ). Eq. (3) esures that the sum of all medals wo s equal to the total umber of medals avalable. Se we osder oulato shares

18 4 ad er ata omes as gve, er ata osumto deeds oly o the hose vestmet levels or ost of medal roduto, so Eq. () a also be wrtte as = ( Y ( C ), ( C )). Dret substtuto of the budget ostrat () ad the overall medal alloato ostrat mled by the otest futo (3) the utlty futo gves: b C C (4) ( Y, ) = ( Y, t ) P C = The oooeratve Nash-Courot strategy followed by eah outry maxmzato of wth reset to the amout of vestmet OS (C ) takg the vestmets of other outres (C - ) as gve a be derved by dfferetato of (4) wth reset to C : Y C (5) + = 0 t P ( C + C ) Note that rewrtg Eq. (3) as C = C ) /( ) ad dfferetato wth ( t reset to gves that the margal ost of medal roduto ( C / ) s equal to ( C + C ) /( C ). Substtuto of ths exresso Eq. (5) results the t Samuelso rule P ( / ) = C / for the otmal rovso of the ubl good Y at the outry level. I other words, eah outry vest OS u to the ot where the margal osts are equal to the rvate margal beefts. Iseto of the Samuelso rule lears us that gve the (world) margal ost of medal roduto 0, 0 sg Eq. (3), the margal ost a also be wrtte as Ct /, whh mles that the margal ost of medal roduto for all outres wth a low medal sore (so ) s aroxmately equal to the world average ost of medal roduto. t

19 5 the larger the oulato of a outry ad the lower ts margal utlty of er ata ome, the lower the margal utlty of OS must be, whh mles that the more rh ad/or oulous a outry, the hgher ts level of OS. Solvg Eq. (5) for C gves the followg equato for the Nash reato urve: (6) C = C + SC wth S = P t a measure for the sum of margal utlty of OS at the outry Y level exressed terms of margal utlty of er ata osumto. Aordg to Eq. (6), how muh oe outry vests deeds o how muh other outres vest ad the welfare beefts of OS for that outry. From Eq. (6) t also follows that C wll oly be ostve f S = P ( ) > C. Ths mles that for may small Y t ad/or oor outres t s otmal ot to vest OS: they wll vest oly f S s at least as hgh as the total vestmets made by all other outres the world. The tuto behd ths result s that () for a small outry the vestmet ost a oly be shared amog relatvely few eole, () the total beefts, se OS s a ubl good at the outry level, are modest beause oulato sze s small ad () for a oor outry, the oortuty ost of vestmet OS s hgh, beause the margal utlty of ome s hgh, whh lowers the value of S. Lkewse, the rh ad/or oulous outres wll have a strog etve to vest OS, the former beause the margal utlty of er ata osumto s low, the latter beause P s hgh, both whh make the value of S hgh. I addto, outres that attah a hgher The same result a be obtaed by maxmzg the Lagrage futo: C L( Y,, C, µ, λ) = ( Y, ) µ [ t ] λ[ Y ( C + C ) b Y C ] P

20 6 relatve mortae to OS wll also vest more. Ths result of a threshold value for the beefts of OS s a dret osequee of the otest futo, where eah outry s share OS s roortoal to ts share world vestmets OS ad o sealzato (see Box ) s yet aouted for. I other words, by usg Eq. (3), outres a oly omete for a share OS take as a fxed stok ( t ), where ths stok s dstrbuted aordg to the roortoate share rule. Gve the otest futo of Eq. (3) ad the Nash reato futo of Eq. (6), the resultg Nash-Courot dstrbuto of OS s determed by the followg set of equatos: (7) P = y = = t P y Assumg a addtvely searable utlty futo ad the Atkso sefato for margal utltes, so beomes: = / ad ε = /, the oeratoalsato of Eq. (7) y y (8) y P ε = = P y y P ε P y (+ ε ) Together wth the overall medal ostrat, Eq. (8) stulates that the Nash equlbrum medal shares are determed by relatve world GDP shares. The Nash dstrbuto of OS for ε = 0 odes wth the dstrbuto strtly aordg to GDP shares, gve olum 6 of Table. The dstrbuto for ε = ½ s gve olum 7

21 7 of Table. Ida s always udererformg, whle for Cha ad Russa the atual medal sores are hgher tha the Nash medal sores. Box : Sealzato At the oeg eremoy of the Olyms we see that almost all outres are sedg athletes. Aaretly, all outres, however small or oor, vest OS. Ths a be exlaed by the fat that the aalyss so far has gored the effets of sealzato ad omaratve advatages. By sealsato, a outry hooses a subset of t, say *, for whh t wats to omete for a medal. I the lmt, * ludes oly oe evet. All the vestmets doe by other outres outsde the subset of * are ot relevat. For smlty, suose oly two outres omete for the hegemoy oe sort evet, so the otest futo a be exressed as: (B) Pr rc = ( r C C * + ) wth Pr the robablty for outry to w the medal * ad r > a measure of the relatve omaratve advatage of outry wg ths evet. The Nash reato futos beome: (B) C = ( C + r SC ) / r C + = rc r S C ad the Nash equlbrum s gve by:

22 8 * r S S (B3) C = ( r S + S ) C * r SS = ( r S + S ) Surrsgly, a omaratve advatage of oe outry affets the vestmets of both outres the same way. However, seto of Eq. (B) lears that the threshold value to vest hages more favourably for the outry wth the atural advatage: (B4) C > 0 S > C / r C > > 0 S rc If outry has amog ts talets a towerg favourte for a artular evet, so r s far above, the t s ot lkely that the other outry wll omete ths evet, uless ts sum of margal utlty of OS ths evet s very hgh. I geeral, the hgher the omaratve advatage, the lower the threshold to vest. If both outres value OS ths evet equally (S = S = S), the C = C = rs/(+r). For r =, C = C = S/4 ad total vestmets are S/, a well-kow result the ret-seekg lterature. 4 Soal laer: Zero ost futos It s terestg to see whether the oooeratg Nash outome dffers from the oe mosed by a hyothetal soal laer. ay dfferet tyes of soal

23 9 laers a be maged, deedg o the owers bestowed uo them (e.g. the ower of lum sum taxato, or the ower to fore outres to take egatve exteraltes mosed o other outres to aout). I wll osder oly oe tye, wth the ower to assg dfferet felds of sort to dfferet outres, e.g. based o omaratve advatages: sort evets of say swmmg are assged to Australa, trak ad feld to SA ad log dstae rug to Afra outres, etetera. I the lmt, ths bols dow to makg the ost futos zero. To fd the otmum for the soal laer, world welfare s smly set equal to the sum of welfare over all = = outres, W = W = P ( Y, ) ad the otmum odto s: W W (9) = = µ Aordg to (9), the otmum alloato, the margal otrbuto to world welfare must be equalzed aross outres ad equal to the fxed medal ostrat multler (see Box below). I a two outry world, due to the fxed medal ostrat =, so Eq. (9) a be rewrtte as: The dstrbuto of OS of a soal laer wth oly the ower to revet that outres sed more or less tha s otmal for them s the same as the Nash dstrbuto beause eah outry faes the same overall medal ostrat as the soal laer does. Also the budget ostrats do ot dffer: uder Nash behavour, eah outry has ts ow budget ostrat, whle the soal laer ludes all budget ostrats searately to ts Lagraga futo. It a also be show that the resultg dstrbuto of OS of a soal laer wth the ower to forbd vestmets OS beyod the ot where the et welfare beeft of oe outry s hgher tha the egatve exteraltes mosed o the other outres uder the assumto of the zero Nash oeture ( C C = 0) s detal to the soal laer the ma text, beause the otmum s that o ost are made. Startg from a stuato of zero ost, a small outry vestg OS wll ature all medals, so deftely mosg egatve exteraltes o all others. But eve the et welfare ga for the largest outry of vestg OS s less tha the total welfare of the o ost dstrbuto.

24 0 (0) N W N W = + = = = Aordg to Eq. (0), a soal laer wll alloate more medals to the more oulous outres. What the soal laer s dog s to mmze the sum of egatve exteraltes mosed by outres aturg oe more medal o all other outres. Startg from srath ad assume oe outry s small ad the other large, f a small outry ws oe the frst medal, t moses a large egatve exteralty (welfare loss) o the large outry, but f the large outres ws, t moses oly a small egatve exteralty o the small outry. Itally, most medals wll therefore go to the large outry, utl the ot s reahed where the ga welfare of eve more medals for the large outry, due to a delg margal utlty of OS, beomes equal to the egatve exteralty mosed o the small outry, whh of ourse s equal to the ga welfare for the small outry to w a frst medal, et. I a -outry world, the effet of a hage the umber of medals of oe outry o the medal tally of other outres s more omlated. If all other - outres are equally affeted, so ) / ( =, the Eq. (0) stll holds, beause: () ) /( ) /(, = + = N W k k k k k k ) /( ) /(, = + = N W k k k k k k

25 ad usg (9) aga gves =. However, t s more robable that outres wth a hgh medal tally wll be affeted more. The exeted hage the umber of medals of outry beause of a margal hage the umber of medals of outry a be exressed as = ( /( )), whh ase the t otmum odto beomes: () = [ + [ + /( /( t t )] )] Althoug Eq. () s theoretally to be referred, for the smulato, we wll use the more smle exresso of Eq. (0) or () that =. sg aga the Atkso sefato of ε ε =, t follows that = ( / ). Summg both sdes over =,,, gves: (3) SP I / ε = = t / ε The otmal dstrbuto of medals for ε = ½ s gve the fal olum of Table. Note that for ε =, the dstrbuto aordg to oulato shares of olum 5 results, whh a be see as the otmal dstrbuto f govermets do ot sed aythg to rase ts level of OS beyod what arses sotaeously a stuato where Olym talet s radomly dstrbuted. As sad, these welfare otmal dstrbutos of medals abstrats from roduto osts of OS ad s more based towards the more oulous outres, the lower the dele margal utlty of OS as measured by ε. For ε = 0.5, Cha ad Ida would ature more tha half of all medals. The SA, urretly

26 holdg 36 gold medals, qualfes for 4 medals aordg to ts oulato share (see olum 5 of Table ). Now that the delg margal utlty of OS s take to aout, favourg Cha ad Ida at the exese of all other outres, ths umber further dereases to oly 8 medals. Jaa retas oly of ts atual 6 gold medals. Eve more dramat are Germay, Frae, the K ad Italy. Ther atual umbers of gold medals vary betwee 9 ad 4, they qualfy for at most 5 medals eah aordg to oulato shares ad f the delg margal utlty s aouted for, they qualfy for less tha half a medal eah. 3 Box. The meag of the fxed medal ostrat multler I Eq. (9), the otmum odto states that the margal otrbutos of world welfare must be equalzed aross outres ad the margal otrbuto of eah outry s equal to µ. To areate where µ stads for, the maxmzato roblem for soal laer I has to be gve the Lagraga form: = = L (..., ) = (, ) [( µ Y µ ) ] t where the Lagrage multler µ measures the hage the otmal value of the obetve futo (dw) wth reset to a ut or ftesmal rease the ostrat (d t ), so µ = dw/d t. The frst order odtos are: L = µ = 0 =,,..., gvg the same result as Eqs. (9) ad (0), so the otmal dstrbuto s the oe haraterzed by = µ. I a way, µ s a summary statst whh measures the 3 For ε = ½, margal utlty of OS deles rather slowly. Gve the assumto of OS as a ubl good, the soal laer wll alloate most medals to the most oulous outres, wth the result that small outres wll have early zero medal sores.

27 3 global equlbrum value of OS, or the world shadow re of OS. 4 If ths global value s hgh, eah outry wll exeree that rodug OS s more dffult tha whe ths value s low. Se µ s gve for a dvdual outry, the more oulous, the lower the margal utlty of OS, so the hgher the medal tally for that outry. The fxed sum medal ostrat ( t ) a evetually be relaxed by trodug more Olym evets. However, the more the ostrat s relaxed that s, the hgher the total umber of medals the stroger the flatoary ressure o the value of ay medal. Ths may exla why the IOC s rather reserved wth elstg ew sorts evets. The otmum for the IOC, harge of exadg or otratg the lst of Olym sort evets that s varyg the umber of gold medals - s to rease the umber of evets u to the ot where the ga welfare by gratg oe more medal (oe more sort evet o the rogramme) s equal to the welfare loss of flato the value of the other medals. 5 Oe must kee md that the medal ostrat s dfferet ature tha a stadard resoure ostrat a otmzato roblem. To fully areate ths fat requres a slghtly dfferet model, where both the value ad the ost of OS s also deedet o the total umber of medals. I the utlty ad ost futo t was mltly assumed that a medal s a medal. The utlty derved from or the ost urred to aheve a artular medal sore was deedet of the total umber of medals. However, f gold medals are dsbursed to ayoe who takes the trouble to show u at the Olyms, the both the value ad the ost of medals dwdles to zero. 5 The auto of etry tkets So far, we have see four dfferet medal talles ths aer, whh a roughly be dvded to two ar: oe ar, the atual medal tally ad the Nash equlbrum medal 4 If there would be a trasfer market, lke football, for alber athletes by hagg atoalty, ths arameter would be a good redtor of the trasfer re for a athlete wth a ear 00 eret hae of wg a gold medal. 5 At the Paralyms, the umber of medals s muh hgher tha for the regular Olyms, maly beause for eah sort evet there are searate omettos for dfferet hadas, whh reases the umber of medals er sort evet to about a fator fve. Deste the lmted umber of dfferet sort evets, at the Paralyms of Beg, 47 gold medals a be wo.

28 4 tally, based towards the rh outres ad the other ar, the medal tally roortoal to oulato shares ad the oe evsaged by a hyothetal soal laer, based towards the oulous (ad mostly oor) outres. The bottom le of the story outled seto by meas of Lorez urves s that the atual dstrbuto of OS s hghly uequal, based heavly towards rh outres ad redomatly former soalst outres. Ths stads shar otrast wth the dea behd the Olym movemet, that all world tzes really have the oortuty to artate. I The Olym Charter oe a fd statemets as: The rate of sort s a huma rght. Every dvdual must have the ossblty of ratsg sort, wthout dsrmato of ay kd ad the Olym srt, whh requres mutual uderstadg wth a srt of fredsh, soldarty ad far lay (4 th fudametal rle of Olymsm,. ); to ooerate wth the ometet ubl or rvate orgasatos ad authortes the edeavour to lae sort at the serve of humaty ad thereby to romote eae (4 th role the msso of the IOC,. 4); to eourage ad suort the develomet of sort for all ( th role the msso of the IOC,. 5). 6 We have to akowledge that the dea of a soal laer mltly or exltly assgg medals, based o alleged omaratve advatages, to outres s rather awkward ad ot very helful trasformg the Games to a more equtable evet. However, the IOC, emboded wth suraatoal authortes, sometmes eve suersedg oly referees by dvdual NOCs, s aable of regulatg teratoal sort affars a more equtable way. I wll show that rle t a devse a oly to softe the most grdg dsadvatages for some outres to obta OS. 6 oreover, the hater Olym Soldarty oe a fd statemets as The am of Olym Soldarty s to orgase assstae to NOCs, artular those whh have the greatest eed of t (. 8) ad To urge govermets ad teratoal orgasatos to lude sort offal develomet assstae (0 th obetve of Olym Soldarty,. 9).

29 5 Just as a thought exermet, osder the oly to auto the lmted umber of etres avalable at the Olyms. 7 Although other redstrbuto mehasms are thkable suh as redstrbuto of sosor, merhadzg ad TV reveues of the Olyms towards oor outres, ths oe has the advatage that t s smle ts dea ad ratally feasble f oly the oltal wll would be there ad t reflets the oto of a level layg feld. As oted the troduto, aroxmately eleve thousad athletes artated the last Games. Suose the IOC dstrbuted these eleve thousad etres aordg to oulato shares; thus Cha would reeve aroxmately 66 etry rghts, Ida 859, SA 506 ad Germay 43, ad so o. Ida, wth few albre athletes, would be wllg to sell a large share of ther etry rghts at the auto, whereas SA ad Germay would be eager to buy addtoal etry rghts. If the auto works well, a uform equlbrum re wll result. Ida, ad other outres wth a relatvely low sort rofle, would ear reveues, ad for by outres wth a relatvely hgh sort rofle. Although for all outres the oortuty ost of sedg athletes to the Olyms s reased by the equlbrum re of etres at the auto, the et effet s roughly a redstrbuto of moey from outres wth a rato of medal share ad oulato share hgher tha oe towards outres wth a rato of medal share ad oulato share lower tha oe. Reall the Lorez urve draw Fgure, Pael B of seto : the more a outry s stuated at the far left (lke Ida ad may other oor outres), the more t beefts from suh a sheme, whle the more a outry s stuated at the far rght (almost all rh outres, as well as some former soalst outres), the more t s a et otrbutor to the sheme. 7 Although the umber of etres a be reased further, as well as the umber of dsles, there s a lmt, beyod whh too may qualfato rouds have to be orgazed to arrve at the fal, sglg out the gold, slver ad broze medal wers. Therefore, the umber of etres a be osdered as a sare good, whh a be red, bought ad sold.

30 6 Of ourse, the IOC has to motor that the earmarked reveues derved from the auto are really used to mrove the sortg frastruture of the beeftg outres. The esug auto reveues set o sort faltes oor outres wll remove the maor obstale - moey to buy sort equmet ad to sortg kowledge o the market - why these outres erform relatvely uder the mark at the Olyms. I the ed, oor outres would be equally aable of breedg albre athletes as rh outres ( whh ase few outres would have to buy or sell etres at the auto) ad the arade of athletes the stadum at the oeg eremoy would be a true refleto of the world oulato. Eve aart from the ratal feasblty, there are a few dowsdes to ths roosal. Frst, oor outres mght stll refer to ash the reveues for sellg art of ther tally alloated etres at the auto, f the moey ould be set o other uroses. However, se the moey s earmarked, they a oly sed t to romote sort. The oly way the reveues of the auto dstorts the alloato of resoures at the atoal level s that these reveues may artly or fully relae the atoal sort budget. I ay ase, se these outres are oor, rle at least the deadweght osts wll be mor, f ot egatve (ths would be the ase f beause of the flow of auto reveues the atoal sort budget moey s redreted to other, more beefal rograms for the outry). Seod, ad more serously, the sheme ould have the result that those athletes who are ot amog the very best worldwde eter the th at the Olyms. The reset qualfato regme, wth re-olym touramets whh qualfato tkets (etres) to the Olyms a be wo, s exatly geared towards moblzg a refxed umber of the very best to the Games ad the resultg dstrbuto s to be refered above oe resultg from a more equtable reresetato

31 7 of the world oulato or oe whh maxmzes world welfare. der the auto sheme, t mght be exeted that rh outres, se margal utlty of er ata ome s muh lower, would be more eager to take the bet, buy a addtoal etry at the auto, ad sed a athlete wth oly a small medal-wg hae. Thus, rh outres would always kee ther omettve edge smly beause they are rh. They a easly afford the osts of buyg addtoal etry tkets, eve f ther athletes are of lower rak tha athletes from oor outres for whom o etry tket s avalable, deste assg the qualfato hurdle. The oor outres would have the etve to lmt the umber of athletes as far as ossble, oly sedg the oes wth a reasoably hgh hae of wg a medal. True, but ths would be a temorary heomeo, beause sooer or later the sorts vestmets, faed by the reveues of the auto, wll bear frut. oreover, se may Olym dsles are atal tesve, there s already a huge bult- bas favour of the redomatly rh outres that a afford the eessary exedtures ad frastruture to oursh these sorts (suh as equestra sorts, yahtg, salg). Cross-subsdzato mght outerat ths bas. Thrd, oe may be led to thk that OS s a good that s ot for sale. Ths argumet would have a bte f medals, ot etres, would be for sale. A etry s o guaratee for a medal, oly a lese to omete for the medal. 8 It mght be feasble to ombe the best of both systems. The reset re-olym qualfato touramet system a be made less strt, wth the result that more, say twe as may, qualfato tkets are ssued tha etres avalable at the fal Olyms. If tradable etry tkets are alloated roortoally to oulato shares, rh outres wth a dsroortoal hgh rato of qualfato tkets ad etry tkets a oly 8 y estmate s that eve the oorest outry the world wll sed those athletes wth a real hae of wg a medal to the Games, eve f they have to forego the reveues of sellg the etry tket at the auto.

32 8 effetuate the former by buyg addtoal etry tkets from the outres wth a dsroortoal low rato of qualfato ad etry tkets. 9 Fourth, rh outres ay the lo share of the reveues of the Olyms terms of broadast ad sosor fees. Oe may led to thk that se they are ayg more, they are also ettled to ature a larger share of OS. I thk ths argumet s a ostarter. As soo as other outres beome more suessful, ther home markets wll also be reared to ay more to broadast the Olyms. oreover, t goes strogly agast the dea of the Olyms, the brotherhood of makd. Ths system, or ay more ratal alteratve, mght hel to kee the Olym Games truly a feast of brotherhood of (wo)makd aroud the world, always leavg oe the ossblty that the dstat future the Games are really global, dsrmate to sex, rae, relgo ad ome. 0 Let me fsh wth a sugesto for a (hoefully) wg strategy for the bd of Amsterdam to orgaze the Games 08. Fedderse et al. (007) show that the rato of already exstg sort veues to sort veues requred ad the hotel aomodato aaty are muh hgher for the suessful tha for the usuessful bds. O a global sale, Amsterdam s a small ty ad t wll be hard to omete wth the bg metrooles the world, whh also have a terest to host the Games. To be suessful, Amsterdam therefore eed to do somethg seal, whh moreover a 9 I the roosed sheme, the ome effet works the rght dreto (udererformg outres reeves earmarked reveues from the auto to stmulate tosort), but the substtuto effet works the wrog dreto (deste the reveues, for oor outres the oortuty re to sed a athlete to the Olyms rses). Suggestos for a modfed sheme where both effets work tamdem are welome. 0 Suose, for oveee, that by adotg ths system the ed all world tzes have aess to the same faltes to breed ther sort talets. The medal tally that results wll reflet whh outres have omaratve advatages or strog referees to exel artular sorts, e.g. Keya dstae rug ad Australa swmmg (my rough guess s that we hardly kow whh outres have omaratve advatages artular sorts - maybe Tazaas are great surfers, see Tha ad Persh (003) for some lues). Ths dstrbuto wll be dfferet from the oe whh maxmzes world welfare; at best t strkes some sort of balae betwee the welfare otmal ad the default ust dstrbuto. Stll, t has the mert that t reveals who s really the best ts dsle worldwde, whereas the reset state the dstrbuto s heavly based towards the rh outres ad outres wth a strog oltal referee for OS.

33 9 ot be ostlessly oed by rval tes. y suggesto s that Amsterdam ad the Netherlads wll start tomorrow to lude sort ts offal develomet ad rograms. oreover, a large huk of the reserved exedtures for the bd amag, ad f suessful of the extra exedtures to atta more medals tha ormal 08 by Duth sorters, a better be vested the sort frastruture of thrd world outres. Ths strategy wll ot oly reate muh goodwll the world ad hel to make the Olyms more global, but s also squarely the srt of the Olym movemet. Referees Atkso, A.B. (983), The Eooms of Iequalty, Oxford, OP. Bambrdge,. (998), Outome ertaty Sortg Cometto: The Olym Games , Aled Eooms Letters, 5(3): Ba, X. (005), Predtg Olym edal Couts: the Effets of Eoom Develomet o Olym Performae, Park Plae Eoomst, Vol. XIII, Berard, A.B. ad. R. Busse (004), Who Ws the Olym Games: Eoom Resoures ad edal Totals, Revew of Eooms ad Statsts, 86(): Cogleto, R.D. (984), Commttees ad Ret-Seekg Effort, Joural of Publ Eooms 5, Fedderse, A., W. aeg ad Ph. Zmmerma (007), How to W the Olym Games The emrs of Key Suess Fators of Olym Bds, IASE workg aer o Hoffma, R., L. C. Gg ad B. Ramasamy (00), Publ Poly ad Olym Suess, Aled Eooms Letters, 9(8): Hoffma, R., L. C. Gg ad B. Ramasamy (004), Olym Suess ad ASEAN Coutres: Eoom Aalyss ad Poly Imlatos, Joural of Sorts Eooms, 5(3): Johso, D.K.N. ad A. Al (004), A Tale of Two Seasos: Partato ad edal Couts at the Summer ad Wter Olym Games, Soal See Quarterly, 85(4): Kuer, G. ad E. Sterke (008), De waars va Beg, Eoomsh Statstshe Berhte 93 (4540), atros, A. ad S.D. Namoro (004), Eoom Ietves of the Olym Games, Workg aer versty of Pttsburgh. oosa, I.A. ad L. Smth (004), Eoom Develomet Idators as Determats of edal Wg at the Sydey Olyms: A Extreme Bouds Aalyss, Australa Eoom Paers, 43(3): Tha,. (004), The Color of edals: A Eoom Aalyss of the Easter ad Wester Blos' Performae the Olyms, Joural of Sorts Eooms, 5(4): 3-8. Tha,. ad V. Persh (003), Reosderg Performae at the Summer Olyms ad Revealed Comaratve Advatage, Joural of Sorts Eooms, 4(3): 6-39.