Pattern Bargaining as an Equilibrium Outcome. Anthony Creane * and Carl Davidson *,+

Transcription

1 Pern Brgnng s n Equlrum Ouome Anhony Crene * nd Crl Dvdson *, * Deprmen of Eonoms, Mhgn Se Unversy GEP, Unversy of Nonghm Asr: Pern rgnng s negong sregy h s ofen employed y ndusry-de unons n olgopols ndusres o se ges. The onvenonl sdom s h pern rgnng kes lor ou of ompeon nd herefore sofens rgnng eeen he unon nd frms, resulng n hgher ndusry de ges. Hoever, hs does no expln hy frms gree o pern rgnng. We nlyze model n hh he gens negoe over he rgnng mehnsm, he order of he negoons nd he ges hen fed h unerny. We sho h heher pern rgnng rses n equlrum depends on he soure of he unerny. Fnlly, e sho h hen equlrum s hrerzed y pern rgnng, my hrm onsumers. Ths provdes n explnon s o ho pern rgnng n rse n equlrum nd hy here s ofen srong poll opposon o. We hve enefed from dsussons nd/or orrespondene h Jeff Bddle, John Budd, Wlly Mulln, João Monez, Dnel Sedmnn, Pul Voos nd semnr prpns Emory Unversy, Georg Teh nd IIOC 007. Eml Addresses: Crl Dvdson, dvdso4@msu.edu; Anhony Crene, rene@msu.edu Correspondng Auhor: Crl Dvdson; Deprmen of Eonoms; Mhgn Se Unversy; Es Lnsng, MI 4884.

2 Pern rgnng s dely-used, somemes onroversl negong sregy h s ofen employed y ndusry-de unons o se ges. If mplemened perfely, he unon pks one frm o rgn h frs (he rge nd negoes ge. I hen uses hs ouome s preeden, nd mkes ke-or-leve- demnds o he remnng frms for smlr onessons. 1 Assumng h he frms gree, nd hey usully do, hs pre resuls n unform ge re ross frms. Convenonl sdom s h hs pre, ofen rued n he Uned Ses o he Uned Auo Workers nd he Temsers, provdes he unon h ounervlng poer n s relonshp h he poerful frms h employ her memers. I s rgued h y kng lor ou of ompeon pern rgnng helps he unon seure hgher ges hn hey ould on oherse. Conroversy over s mp on ges reenly led he Hord Governmen n Ausrl o oul hs pre under he WorkChoes legslon (hh eme effeve on Mrh 7, 006. I s he onenon of unon leders h he governmen s oeve n dong so s o rrevoly shf rgnng poer n ndusrl relons o employers. 3 Explnons of hy pern rgnng orks nd ho omes o e doped re rre. Ths s surprsng gven h hs sregy lerly plys n mporn role n ge deermnon n mos OECD ounres, ofen n mporn ndusres. The kng lor ou of ompeon explnon s he one mos ommonly gven, lhough, s fr s e kno, hs never een formlzed. The s de s smple. Ordnrly, unonzed olgopols frms hve n nenve o rgn ough sne ny ge onessons h hey n pry from he unon ll provde hem h ompeve edge over her produ 1 Wh e hve n mnd s n ndusry n hh severl unonzed olgopols frms negoe ges h he sme ndusry-de unon nd hen ompee h eh oher n he produ mrke. Thus, he ges h re eng negoed re pd o orkers h smlr sklls n smlr oupons. The U.S. uomole ndusry n hh he Uned Auo Workers negoes ges h Ford, Chrysler nd Generl Moors or he U.S. rlnes ndusry n hh he Ar Lnes Plo Assoon (ALPA negoes erms h he mor rlnes oh f no hs frmeork nely. Pern rgnng s lso used n oher sengs y employers o e-don he ges of orkers h dfferen skll ses nd oupons. For exmple, n he U.S. Arlne ndusry pern rgnng lnks he ges of plos, mnenne orkers, nd orkers n oher rfs. Pern rgnng s lso used dely n se nd lol governmen negoons h pul seor employees h dfferen skll ses (e.g., frefghers nd pole. In hs pper, e resr enon o pern rgnng of he former ype. Reled o pern rgnng s he me oo greemen n hh some frms gree o ep he erms negoed y oher frms. For exmple, orkers employed y Ls Vegs snos hve her ges se hrough negoons eeen her unon nd mul-employer rgnng group. Csnos h re no memers of he mul-employer group ofen sgn me oo greemens h nd hem o ep hose erms hou ddonl negoons. 3 See he dsusson of pern rgnng nd he reen hnges n Ausrln Lor L on he Consruon Foresry Mnng Energy Unon e se:.fmeu.sn.u/onsruon/reserh/seondve/pern.hml. 1

3 mrke rvls. Pern rgnng ssures suh frms h f hey gve n o he unon s ge demnds, hey ll no hve o orry h her ll rvls ll gn n dvnge y eng ougher durng negoons fer ll, ll frms nd up pyng he sme ge re. Thus, pern rgnng s veed s one y o sofen negoons h olgopols frms. The prolem h hs ronle s h s does no expln hy he frms re llng o ep suh n rrngemen. In reen ork, Mrshll nd Merlo (004 provde forml resoluon o he frs pee of hs puzzle y shong n model h heerogeneous unonzed frms h n ndusry-de unon prefers pern rgnng. In her model, he o frms produe susue produs nd negoe ges h he unon. The frms fe onsn oss, u dffer n lor produvy. Four dfferen rgnng mehnsms re onsdered, h he Nsh Brgnng Soluon ppled n eh se. The unon n rgn smulneously over ges h oh frms; hey n rgn sequenlly; hey n use pern rgnng h resuls n oh frms pyng he sme ge; or hey n use pern rgnng n lor oss hh resuls n ge res h equlze mrgnl oss ross he frms. In he ler hree ses, he order of rgnng s mporn, so oh possle orderngs re onsdered. Mrshll nd Merlo derve o mor resuls. Frs, hey fnd h hen frm-heerogeney s ek, he unon prefers pern rgnng n ges; heres hen frm-heerogeney s srong, he unon prefers pern rgnng n lor oss hus, he unon lys prefers some ype of pern rgnng. Seond, he unon lys hooses o use he effen frm s he rge. The frs resul s onssen h he pereved sdom h pern rgnng enefs unon memers. Mrshll nd Merlo rgue h he seond resul s onssen h sylzed f h unons lmos never sele he relvely unproduve frm s he rge. Though Mrshll nd Merlo sho formlly h he unon prefers pern rgnng, n her seng he frms lys prefer n lernve rgnng mehnsm. Ths s prulrly rue of he nonrge frm. Ths frm should surely ve he unon s ke--or-leve ge demnd s non-redle. If he frm rees he unon s ge demnd, ll lys e n he unon s neres o reopen negoons, effevely resulng n he sme ouome h ould e genered y sequenl rgnng. Thus, s

4 hrd o undersnd hy he frms ould ever gree o pern rgnng. 4 In hs pper, e rgue h he rgnng mehnsm nno smply e mposed upon he frms nd h for pern rgnng o survve s long-run feure of he negoon proess mus e greed upon y ll gens on oh sdes of he lor mrke. I follos h f e re o ruly undersnd pern rgnng, e mus exmne ondons under hh emerges endogenously from seng n hh he gens negoe no only over he ge res u he rgnng mehnsm s ell. In order o do so, e develop model h pures mny of he essenl feures of he mrkes n hh pern rgnng hs een so mporn (he US uo mrke serves s our prmry movor. In prulr, e ssume h he mrke s hrerzed y olgopols frms h produe susue goods nd h he frms produon oss re sue o rndom shoks so h her relve ompeve posons my hnge over me. 5 One he rgnng mehnsm hs een deermned nd produvy relzed, our model hen follos Mrshll nd Merlo (004 n h here re o frms h fe lner demnd urve, oss re onsn, he frms dffer n erms of lor produvy, he unon s gol s o mxmze he ge ll nd ges re deermned y he Nsh Brgnng Soluon. Hoever, our model dffers from hers n hree key ys. Frs, he dynm nure of he model nd exsene of he rndom shoks mples h he frms ll prefer he rgnng mehnsm h mxmzes her expeed profs over me. Ths mples h hey ll prefer mehnsm h rerds hem hen hey re relvely effen hou penlzng 4 Mrshll nd Merlo do reognze hs ssue nd exmne n one of he ler seons of he pper. Buldng on n nsgh orgnlly due o Wllmson 968, hey exend her nlyss o llo for poenl enrn h mus use unon lor f eners he mrke. They hen sho h n suh seng here re enry oss suh h he hrd frm ould ener under sequenl rgnng u sy ou under pern rgnng. Consequenly, hey rgue h oh he frms nd he unon my prefer pern rgnng euse serves s rrer o enry. To mke hs pon, hey sho h here exss ge h ould resul n hgher pyoffs for oh he unon nd he frms under duopoly hn hey ould ern h sequenl rgnng under ropoloy. Hoever, s unler heher or no hs ge s n equlrum ge h pern rgnng sne he unon gnores he effe on enry deerrene.. We oneure h s no nd h f e resr enon o equlrum ges s lkely o e he se h he frms prefer pern rgnng hle he unon prefers some oher rgnng mehnsm. We reurn o hs ssue nd dsuss furher n foonoe 3. 5 The ssumpon h oss re sue o rndom shoks h ler he ompeve posons of frms s eomng nresngly ommon n mny ppled res. For exmple, hs ssumpon s rul omponen of he Morensen nd Pssrdes 994 model of serh genered unemploymen n mroeonoms, he Hopenhyn 99 model of ndusry dynms n ndusrl orgnzon nd he Melz (003 model of monopols ompeon n nernonl eonoms. 3

5 hem oo muh hen hey re ompeve dsdvnge. Seond, lhough e follo Mrshll nd Merlo n ssumng h he frms dffer n lor produvy, e lso onsder he se n hh frm heerogeney s drven y dfferenes n non-lor oss. 6 Fnlly, s noed ove, e expnd he rgnng envronmen y llong he gens o negoe over he rgnng mehnsm. Our dynm gme onsss of hree sges. In he frs sge, he gens negoe over he rgnng mehnsm; heres he deny of he rge frm s deermned n seond sge. 7 Fnlly, n he hrd sge he gens prpe n repeed gme of quny ompeon n hh eh perod s ge re s negoed fer he frms oss hve een deermned nd pully reveled. We fnd h n hs seng here re mporn nsnes n hh oh he unon nd he frms prefer pern rgnng over sequenl rgnng, u h hey lys dsgree ou he order of negoons. As resul, he exen o hh he unon n nfluene he deny of he rge frm plys rul role n deermnng ondons under hh pern rgnng rses n equlrum. Hoever, onrry o he pereved sdom, e fnd h hs s mos lkely o our hen pern rgnng s he preferred mehnsm of he frms, no he unon. We lso fnd h he soure of frm-heerogeney plys rul role n deermnng ondons under hh pern rgnng n e suppored n equlrum hou sde pymens. Fnlly, e onsder he mp of rgnng sruure on onsumers nd fnd h pern rgnng n redue onsumer surplus. Ths ls ssue, hh hs (o he es of our knoledge reeved no enon ll n he lerure, s mporn n lgh of he reen Ausrln legslon oulng pern rgnng. The remnder of he pper dvdes no fve seons. In Seon, n order o gn some nsgh no he fores drvng our resuls, e onsder, s selne model, n exreme verson of he Mrshll- 6 The f h dfferen ssumpons ou he soure of frm heerogeney yeld dfferen onlusons hs een emphszed n Crene ( We resr enon o he o rgnng mehnsms mos ommonly oserved: pern nd sequenl rgnng. Mrshll nd Merlo lso onsder smulneous rgnng nd pern rgnng n oss. As hey sho, smulneous rgnng s lys domned, so h nno emerge n equlrum. Smlrly, pern rgnng n lor oss lys resuls smller on surplus for he unon nd he frms hn oh sequenl rgnng nd pern rgnng n ges. Thus, nno rse s n equlrum ouome. We dsuss hs pon n more del n foonoe 4 elo. 4

6 Merlo model n hh he unon hs omplee ge seng poer. Th s, rher hn llo for negoons, e sr ou y ssumng h he unon seles he ge pd y eh frm nd hen he frms hoose employmen. In suh seng, pern rgnng s equvlen o he unon demndng he sme ge from eh frm; heres e nerpre deson y he unon o demnd dfferen ges s preferene for sequenl rgnng. In hs seng, onrry o oh onvenonl sdom nd Mrshll nd Merlo (004, he unon prefers frm-spef ges rher hn unform ge fer ll, hen he unon hs he ly o hoose he pre hh supples lor o he frms nd he frms hve he poer o hoose he numer of orkers o employ, he unon s n exly he sme poson s monopols n produ mrke h mus hoose heher o hrge he sme pre o ll onsumers. As e kno from he lerure on pre dsrmnon, he suppler lys prefers o pre dsrmne hen possle. As for he frms h demnd lor, her ol profs n e hgher or loer h unform ge: hey prefer he unform ge hen hey re he more effen frm u ge dsrmnon hen hey re he less effen frm. Thus, s ler h here re nsnes n hh he frms ll prefer unform ge sruure. The prolem h he model nlyzed n Seon s h, sne does no llo for ge negoons, does no pure he frms sreg onsderons h re nheren n he kng lor ou of ompeon rgumen. We herefore urn o he generl model (oulned ove n Seons 3-5 hh uses he Nsh Brgnng Soluon o deermne ge res. In Seons 3 nd 4 e onsder he model hen sde pymens re no possle. We relx hs ssumpon n Seon 5. The mn resul s Seon 3 s h n he Mrshll-Merlo se-up, pern rgnng n never emerge s n equlrum ouome. We provde nuon for our resuls y solng o rues of he rgnng mehnsms h nfluene he gens preferenes. We rgue h oh he ly o lor ges o he frms nheren n sequenl rgnng nd he ly o ke lor ou of ompeon under pern rgnng enef he unon he expense of he frms. When frm-heerogeney s ek, he mp of he ge dsrmnon spe s smll nd hus he unon prefers o ke lor ou of ompeon hrough pern rgnng hle he frms prefer sequenl rgnng. Bu, hen frm- 5

7 heerogeney s suffenly srong, he pre dsrmnon spe s srong enough o reverse he gens preferenes. These rde-offs re, of ourse, key n deermnng he equlrum ouome of he negoons over he rgnng mehnsm. When he frms dffer only n lor produvy, e fnd h he rde-offs re suh h pern rgnng nno emerge n equlrum (Proposon 1. In Seon 4 e exend he model o llo he frms o dffer n non-lor oss nd sho h hs lers he rde-offs suh h pern rgnng n e n equlrum ouome (Proposon. We lso onsder n ssue h hs reeved surprsngly lle enon n he lerure he mp of rgnng mehnsm on onsumer elfre nd sho h hen he frms dffer n non-lor oss, onsumer surplus s mxmzed y sequenl rgnng (Proposon 3. Sne he onsumers ould e nerpreed s donsrem frms h use he upsrem frms oupu s n npu, hs provdes us h n explnon for hy pern rgnng mgh e preferred ll he gens negong ges hle onsumers nd donsrem frms loy he governmen o n s use. In Seon 5 e llo he gens o use sde pymens n order o nfluene he seleon of he rgnng mehnsm. Ths llos us o ge eer sense s o heher pern rgnng serves he neress of he unons, he frms, or oh. We egn y reonsderng our enhmrk model here he unon unlerlly ses he ge. In hs se, he ol surplus o e spl eeen he unon nd he frms s hgher h unform ge. Sne he frms prefer unform ge sruure, hey ould re he unon o ep hs rrngemen, hh runs onrry o onvenonl sdom. We hen sho h sde pymens mke possle for pern rgnng o emerge s n equlrum ouome n he Mrshll- Merlo model. The ly o mke sde pymens lso expnds he se of prmeers under hh pern rgnng ours hen he frms dffer n non-lor oss. We lso fnd h, s he enhmrk model suggess, f he frms dffer n lor produvy, pern rgnng only emerges s n equlrum ouome hen s he frms preferred mehnsm. If nsed, e fnd h hen he frms dffer n nonlor oss, pern rgnng n rse s n equlrum ouome hen s he unon s preferred mehnsm. We onlude he pper n Seon 6 y summrzng our resuls. 6

8 . Wge Seng y he Unon In hs seon e nrodue he s model nd, o provde enhmrk for ler omprsons, exmne he ouome hen he unon s lloed o se he ges. To fle omprsons h Mrshll nd Merlo (004, e dop mny of her ssumpons onernng funonl forms nd use muh of her noon. There re o frms ( nd h produe homogeneous good nd fe he follong lner demnd urve: P = 1 x x, here x denoes he oupu of frm. 8 We ssume h he orkers eh frm re represened y he sme ndusry-de unon. As for produon, lor s he only npu (e relx hs ssumpon n he Seon 4 u lor produvy eh frm s nlly unknon nd my hnge from one perod o he nex. I s ommon knoledge h n eh perod one frm ( ll e le o produe one un of oupu h eh orker hred; heres he oher frm ( ll ge only 1uns of oupu from eh orker. Thus, f e use l o denoe employmen for frm, hen e hve x = l nd x l =. Noe h frm s he effen frm heres frm s relvely neffen. The deny of he more effen frm s deermned y nure he egnnng of eh perod, h eh ouome eqully lkely. To ensure h oh frms produe n equlrum, e ssume h s suffenly lose o one (o e mde prese elo. In hs seon of he pper e ssume h n eh perod he unon ses he ges o e pd y eh frm. Follong Mrshll nd Merlo, e ssume h he unon s gol s o mxmze s expeed ge ll. Afer he ges re se, he frms ompee n he produ mrke n qunes. Thus, he o frms re engged n repeed gme n hh, n eh perod, nure deermnes he frms produves; hese vlues re reveled o ll plyers; ges re se y he unon; nd hen he frms 8 We normlze he demnd nerep n Mrshll nd Merlo (004 o 1, nd ssume h he goods re perfe susues. The degree of susuly plys no role n he resuls here or n Mrshll nd Merlo (004. 7

9 hoose oupu o mxmze profs. 9 Sne ne, ndependen dr on frm produves ours n eh perod, he ompeve posons of he frms hnge over me. I s mporn o noe h ges re hosen fer eh perod s produvy mesures hve een deermned nd reveled o ll pres. Thus, ge seng kes ple under omplee nformon ou he urren perod. In ddon, noe h sne he frms ompee n oupu fer he ges hve een se, he frms effevely deermne employmen (s s he se n lmos ll lor negoons. Srghforrd lulons yeld he Courno oupu, employmen, prof levels nd ge ll s: x, = l (, = / 3[ ] ( ( x, = l (, = / 3[ ] ( (3 π (, = x (, for =, ; (4 θ, l (, l (,. ( Wh π denong he profs erned y frm nd θ denong he ge ll. Follong Mrshll nd Merlo, e resr enon o he se n hh As noed ove, n ny gven perod eh frm s eqully lkely o e he effen frm or he neffen frm. Thus, ex ne, eh frm s expeed prof n ny gven perod s 5( π π. I follos. h he frms long-erm neress re ed o ol per perod profs. As for he unon, sne here s lys one effen frm nd one neffen frm, her gol ll e o mxmze he (ern ge ll s defned n (4. Sne he unon hs he poer o sele he ges pd y eh frm, here re o possles: he unon n demnd he sme ge from eh frm, or, he unon n sele frm-spef ges. Wh he unon hvng ll of he ge-seng poer, he order n hh he ges re hosen s no relevn. 9 Bsed on he log of Kreps nd Shenkmn 983, e n hnk of quny ompeon s redued form y of purng he noon h pres re eser o dus hn qunes n hs mrke. Thus, sne produon kes ple fr n dvne nd hen pres re negoed he me of purhse n he uo ndusry, quny ompeon seems lke resonle ssumpon for he uo ndusry. 10 Ths resron s no needed for hs seon of he pper. We dsuss he ppropre resron on n foonoe 11 elo. 8

10 Mxmzng (4 over nd sue o -( yelds he unon s opml frm-spef ges. We on = 1/ nd = /. Mxmzng (4 sue o -( nd = yelds he unon s opml ommon ge. We on u =, here he u susrp denoes h hs s he 4( 1 unform ge. For [.5,1 ], e hve u ; hus, sne eh frm s prof s deresng n s on ge nd nresng n s rvl s ge, he effen frm prefers he unform ge hle he neffen frm prefers he frm-spef ge sruure. And, susung hese ges k no, ( nd (4 nd omprng e fnd h he unon s lys eer-off h he frm-spef ges. None of hese resuls should e surprsng hey mm sndrd resuls from he lerure on pre dsrmnon under monopoly (nd do no depend upon he ssumed funonl forms. When he unon seles ommon ge, seles on one h s eeen he o frm-spef ges. Ths enefs he effen frm nd hrms he neffen frm. And, sndrd reveled preferene rgumen s enough o ensure h he unon nno e orse off hen he ges re frm-spef. Thus, veed from hs perspeve, one ould never expe he unon o prefer unform ge. As for he frms, hey kno h, over me, hey re lkely o e he effen frm hlf he me nd he neffen frm he remnder of he me. Thus, hey ould prefer he ge sruure h leds o he lrges per perod ol prof. I s srghforrd o sho h unform ge leds o hgher ol prof. I follos h ll e he frms, no he unon, h fvor unform ge sruure. Sne ges re no negoed, hs smple frmeork does no pure he fores h drve he kng ges ou of ompeon rgumen. Hoever, hs frmeork does provde us h some s nuon s o hy, onrry o prevlng sdom, n ndusry-de unon mgh prefer sequenl rgnng (n hh frm-spef ges re negoed. Thus, he kng ges ou of ompeon effe, hh e expe leds he unon o fvor pern rgnng, s no gong o e he only fore h deermnes he unon s preferenes h respe o rgnng sruure. 9

11 3. Usng Pern Brgnng o Tke Lor Ou of Compeon In hs seon e exend he model so h ges re negoed. We hen exmne he gens preferenes over rgnng mehnsms under he ssumpon h ges re deermned y he Nsh Brgnng Soluon (NBS. The non-ooperve foundons for he NBS re ell knon s he ouome of negoons n hh he gens rde offers unl n offer s eped (Runsen 198. There re no hree sges o he gme. In he frs o sges, he unon nd he frms negoe over he ge seng mehnsm (pern versus sequenl nd, f he order mers, he deny of he rge frm s deermned (he effen or he neffen frm. The ls sge onsss of repeed gme n hh, n eh perod, nure deermnes he frms produves; hese vlues re reveled o ll plyers; he unon nd frms hen pply he rgnng mehnsm o deermne ges; nd hen, fnlly, he frms engge n quny ompeon n he produ mrke. As n seon, euse ne, ndependen dr on frm produves ours n eh perod, he ompeve posons of he frms hnge over me. The frms ll keep hs n mnd hen seleng rgnng mehnsm nd hus, her gol ll e o fnd he rgnng mehnsm h mxmzes her expeed profs. I s orh nong h e re ssumng h here s sngle pon n he gme hh he rgnng mehnsm s deermned. Th s, gens do no renegoe he rgnng mehnsm n eh perod. The s de h e re ryng o pure s h negong over he rgnng mehnsm s lkely o e dfful nd osly sne he gens re lkely o hve very dfferen preferenes (e.g., he frms versus he unon; he effen frm versus he neffen frm. Thus, he gens ll no n o hve o re-vs hs ssue n eh perod. Insed, sne he frms nd he unon relze h hey re n long erm relonshp n hh he relve ompeve posons of he frms hnge over me, hey re lkely o ke long-run ve nd ry nd sele up fron rgnng mehnsm h orks ell for ll of hem over me. For exmple, frm my e llng o pu up h rgnng mehnsm hh s no del for hem hen hey re he effen frm f hey kno h hs sme mehnsm ll ork fr eer for hem hen hey re ompeve dsdvnge. When ges re negoed, he order of rgnng my mer, so e hve (poenlly four 10

12 ses o onsder. Sne ll four ses re lger nensve, e skeh he soluon mehod n he ex nd relege he dels o Appendx A here ll nly soluons re provded. We egn h pern rgnng h frm s he rge, hh e denoe y P(. As s sndrd, e use krds nduon. If he unon fls o reh n greemen h frm, frm eomes monopols n he produ mrke. Le m m denoe he ge negoed y frm hen s monopols nd le l ( nd m x m ( m denoe hs frm s lor demnd nd oupu hs ge. Then, ordng o he NBS, m mxmzes he produ of he unon s ge ll nd he frm s prof; h s m mxmzes l ( [ x ( ] over. Turn nex o he orgnl negoons eeen he unon nd m m frm. The ge ll evlued m serves s he unon s hre pon durng hese negoons, heres frm s hre pon s zero (sne does no produe f no greemen s rehed. Sne under pern rgnng s undersood h oh frms ll end up pyng he sme ge, hen usng (3-(4 nd srgh-forrd pplon of he NBS, he ge h he unon seles on hen usng frm s he rge solves (5 mx { θ (, m l m ( m } x (, We use p( o denoe hs ge, h he super-srp denong h hs ge emerges under pern rgnng h frm s he rge. The soluons for m nd p( re provded n he Appendx A. Turn nex o sequenl rgnng under he ssumpon h he unon negoes h frm frs, hh e denoe y S(. Le denoe he ge h omes ou of hese nl negoons noe h he super-srp refers o he rgnng sruure (sequenl rgnng h frm s he rge hle he su-srp sgnfes h hs s he ge pd y frm. Then, hen frm negoes h he unon, he NBS soluon ge h emerges solves (6 mx { l (, l (, l m ( } x (, Noe h f he unon fls o reh n greemen h frm, frm eomes monopols n he produ 11

13 mrke, u mus sll py he (lredy negoed ge of. Ths explns hy he unon s hre m pon s gven y l (. Le ( denoe he soluon o (6. As efore, he super-srp refers o he rgnng sruure; heres he su-srp sgnfes h hs s he ge o e pd y frm. I s mporn o noe h s nresng n h slope less hn one. The reson for hs s srgh-forrd: n nrese n frm s ge nreses he surplus o e spl y frm nd he unon hh rggers n nrese n frm s ge. Hoever, does no nrese y he full nrese n sne hs ould ompleely undo he ompeve dvnge us gned y frm (here s lso sly rgumen h resrs he slope o e elo one. Fnlly, e urn he nl negoons eeen frm nd he unon n order o desre ho s deermned. If he unon nd frm fl o reh n greemen, frm does no produe (nd herefore erns nohng hle frm eomes monopols nd he unon nd frm sele on ge of m m m. Ths mples h he unon s hre pon s gven y l ( nd m solves (7 mx { l (, ( ( l ( (, m l m ( m } x (, ( Noe h n negong over s on ge, frm kes no oun ho he ouome ll ffe he rgnng eeen frm nd he unon. Ths s he spe of ge rgnng n olgopols ndusres h pern rgnng s men o elmne. The nly soluons for nd ( re provded n Appendx A. Wh he ges deermned, e n use (3 nd (4 o lule he unon s ge ll nd he frms profs. In ddon, summng hese vlues llos us o deermne he surplus o e spl eeen he gens (produer surplus. To ssess he preferenes over he dfferen rgnng mehnsms for he gens, e resr enon o he se n hh Ths leves us h he sme model 11 We mke hs ssumpon o fle omprson o Mrshll nd Merlo (004 ho resr enon o > ½. Hoever, s possle o sho h here s n neror equlrum n hh oh frms produe for ny greer hn (roughly 1/3. The expl expresson for derved from he frs order ondon s no defned = ½ -- 1

14 nlyzed y Mrshll nd Merlo nd llos for dre omprson of our resuls. As hey demonsre, h he frms dfferng only n lor produvy, he order of rgnng does no mer hen sequenl rgnng s used. Thus, e hve hree rgnng mehnsms o onsder, P( h =, nd S S( = S(: pern h he effen frm ( s he rge, pern h he neffen frm ( s he rge nd sequenl rgnng. We sr h he unon s preferenes, hh follo from Fgure 1. The frs resul s no surprsng: under pern rgnng, he unon lys prefers o rgn h he more effen frm frs: θ( p(, p( θ( p(, p( for [.5,1]. Ths follos from he f h he effen frm generes lrger surplus nd n herefore fford o py hgher ge hn s ounerpr. As e sho n he nex seon, hs resul generlzes o suons n hh he frms dffer n non-lor oss s ell s lys n he neres of he unon o use he more effen frm s he rge. The seond resul h s evden from Fgure 1 s h hen he degree of frm-heerogeney s ek ( , he unon prefers pern over sequenl rgnng regrdless of hh frm s used s he rge. When frmheerogeney s modere ( , he unon sll prefers pern rgnng o sequenl, s long s he rge s he effen frm. I s only hen he frms dffer drmlly n lor produvy ( h he unon prefers o rgn sequenlly. Mrshl nd Merlo (004 provde nuon for he unon s preferene orderng nd s he mn resul of her pper. Hoever, e offer someh dfferen explnon for hese resuls. As e shoed n he prevous seon, he ly o lor ges o he frms, hh s hrers of sequenl rgnng, enefs he unon he expense of he frms. Hoever, he kng lor ou of ompeon spe of pern rgnng resuls n hgher verge ges n he ndusry. Ths follos from he f h frms re more llng o gree o ge nrese hen hey kno h her rvl s ge ll rse y he sme moun h her ge ll rse (nd, s e s ove, h sequenl u s srghforrd o verfy h = ½ here exss h ssfes he frs order ondon ( = ¼. Ths ge s he expl soluon o he frs order ondon hen he lm s ken s pprohes ½. I s no dfful o hek h he equlrum s ell ehved (.e., sly ondons re ssfed for /3,1/]. Inuvely, e n o resr suh h he unon ould prefer o hve oh frms produe. The qulvely nure of our resuls do no hnge y expndng he rnge of n f, pern rgnng eomes more lkely for lo. 13

15 rgnng ny nrese n leds o n nrese n of smller mgnude. Thus, sequenl rgnng enefs he unon y llong for frm-spef ge sruure u hrms he unon y generng loer verge ges. The enef from ge dsrmnon s no prulrly mporn hen he frms re smlr, so h h ek heerogeney he ler fore domnes nd he unon prefers pern rgnng. The dvnges from frm-spef ge sruure gro s he frms eome less lke, nd hs effe domnes hen frm-heerogeney s srong. As resul, hen he frms re que dssmlr, he unon prefers sequenl rgnng. The prolem h he Mrshll-Merlo resul s evden from Fgure 1 here he frms ggrege profs ( Π re deped for eh of he rgnng mehnsms. As e noed ove, he frms gol s o sele he rgnng mehnsm h mxmzes s expeed profs, hh, gven our se-up, s equvlen o mxmzng ol ndusry profs. To egn, s ler h h pern rgnng, he frms lys prefer he neffen frm o e he rge. So, even f e resr our enon o pernrgnng, here s dsgreemen eeen he unon nd he frms over he nure of he rgnng proess. When e nlude sequenl rgnng, he possly of greemen seems even more remoe. Fgure 1 ndes h hen frm-heerogeney s ek (.767 1, he frms prefer sequenl rgnng over ny form of pern rgnng. Noe, hoever, h hen frm-heerogeney s modere or drm (.5.767, he frms prefer pern rgnng. More speflly, her frs hoe s lys pern rgnng h he neffen frm s he rge h s, P(. The f h he frms prefer h he ek frm serves s he rge should no e surprsng sne he neffen frm generes smller surplus, usng s he rge resuls n loer ge nd hgher profs. 1 The explnon for he frms preferenes s smlr o h gven ove for he unon. The frmspef ge sruure, hh s nheren n sequenl rgnng, hrms he frms; heres he ly o ke lor ou of ompeon hrough pern rgnng lso hrms he frm (due o he hgher verge ges. When he negve spes from sequenl rgnng re domne, he frms prefer pern 1 Noe h h suffen heerogeney (.5.59 he frms ll prefer ny sor of pern rgnng over sequenl rgnng. 14

16 rgnng; oherse, hey prefer sequenl rgnng. If he frms re smlr, he mp of ge dsrmnon s smll nd he frms prefer sequenl rgnng. As he dfferene eeen he frms gros, he mp of pre dsrmnon nreses so h he frms evenully sh nd prefer pern rgnng. I s ler from Fgures 1 nd 1 h no ommon rgnng mehnsm s he frs hoe for oh sdes. For <.5785, he unon prefers S hle he frms prefer P(. For >.767 he frms prefer sequenl rgnng u he unon prefers P(. Fnlly for (.5785,.767, oh sdes prefer pern rgnng, hoever hey dsgree s o he deny of he rge. To hrerze equlrum, e mus no desre he frs-o sges of he gme h he gens fe n more del. We egn h he seond sge, n hh he order of he negoons s deermned (fer he rgnng mehnsm hs een seleed. If pern rgnng hs een seleed, hen e ssume h h proly q [0,1] nure ssgns he unon he poer o deermne he deny of rge frm. We herefore use q s mesure of he unon s ly o nfluene he seleon of he rge. For exmple, f q = 1, hen he unon lys hooses he rge heres f q = 0, hen he frms lys hoose he rge. By vryng q e n onsder ll possle sge o ouomes nd nvesge he mnner n hh he unon s ly o nfluene he seleon of he rge ffes he lkelhood of pern rgnng rsng n equlrum. 13 Turn nex o he frs sge, n hh he gens sele he rgnng mehnsm. We ssume h n hs sge, knong ho he rge ll e seleed n sge o, he gens smulneously nnoune her hoe s sequenl (S or pern (P. Hoever, s mpossle o mplemen pern rgnng f ll gens do no gree o dop. Thus, e ssume h f ll gens sele P, hen pern rgnng s doped; oherse, sequenl rgnng s he ouome. We egn our nlyss y onsderng he o exreme ses: he unon lys hooses he rge (q = 1 or he frms lys hoose he rge (q = 0. When he unon hooses he rge, su-gme 13 We noe h vlues of q (0,1 re onssen h ommonly oserved phenomenon ssoed h pern rgnng n h he rge frm nd s hrerss hnge over me (.e., somemes he unon ll sele he mos effen frm s he rge hle oher mes ll sele md-level frm s he rge. 15

17 perfeon des h he effen frm s lys seleed. Fgure 1 ndes h he unon prefers S o P( for ll <.5786; heres Fgure 1 ndes h he frms prefer S o P( for ll >.591. For ll, S s nnouned y les one sde, nd so S s lys he ouome. When he frms hoose he rge, su-gme perfeon des h he neffen frm s lys seleed. Fgure 1 ndes h he unon prefers S o P( s long s <.7338; heres Fgure 1 ndes h he frms prefer S o P( for ll >.767. Agn, for ll, S s nnouned y les one sde. Thus, n hese o exreme ses, sequenl rgnng s he only possle equlrum ouome. We no onsder nermede vlues for q. In he frs sge, he gens kno h f pern rgnng s hosen he effen frm ll e seleed s he rge h proly q. As resul, he pyoff o he unon hen P s he ouome s qθ p( qθ p( (rell h he super-srp P( ndes h pern rgnng hs een doped h frm s he rge. On he oher hnd, under sequenl rgnng he unon erns θ S (sne he order of rgnng does no mer. The pyoff for he frms s luled n n nlogous fshon. I should e ler h for.767 nd.5785, S ll e he ouome. In he former se, he frms prefer (nd so nnoune S even hen hey ge o hoose rge frm h proly one; heres n he ler se s he unon h nsss on S regrdless of q. For , he unon ll only nnoune P f q s suffenly hgh; heres he frms ll nnoune P only hen q s suffenly lo. Le q U denoe he vlue of q h eques he expeed ge ll h pern rgnng o he expeed ge ll h sequenl rgnng, nd defne q F s he vlue of q h eques expeed ol prof h pern rgnng o expeed ol profs h sequenl rgnng. Clerly, vlue of q suh h oh he unon nd he frms prefer P over S exss ff q U q F.. Hoever, for ll n hs rnge q U > q F, so h here s no vlue for q suh h oh he unon nd he frms prefer pern rgnng! Thus, hen sde pymens re no possle, e onlude h n he Mrshll-Merlo frmeork e ould lys expe sequenl rgnng o e hosen n equlrum. I follos h he f h he unon my prefer pern rgnng s no suffen o expln ho emerges s n equlrum ouome. 16

18 Proposon 1: When he frms dffer n lor produvy, hen equlrum s hrerzed y sequenl rgnng for ll produvy dfferenes (. Proposon 1 my e someh surprsng gven he preferene orderngs of he gens. Afer ll, here re prmeer vlues suh h ll gens prefer pern rgnng o sequenl rgnng (hs ours hen s modere;.e., The prolem s h he gens dsgree ou he rge. When he frms dffer only n lor produvy, hs dsgreemen over he rge s srong enough h eomes mpossle o ge pern rgnng n equlrum hou sde pymens. As e sho elo, hs s no longer he se hen he frms dffer n non-lor oss. 4. Dfferenes n Non-Lor Coss We no exend he model o llo he frms o dffer n non-lor oss. We do so y ssumng h eh me h frm (he neffen frm produes un of oupu mus nur non-lor os of. Frm, on he oher hnd, fes no ddonl per un oss. In order o hghlgh he mporne of hs exenson, e se = 1so h hs s he only dfferene ross frms. Ths mples h frm s mrgnl os of produon s ; heres frm s mrgnl os s. As e sho, hs ssumpon lers he rde-offs fed y he frms nd he unons nd mkes possle for pern rgnng o emerge s n equlrum ouome. Wh hs se-up, Courno ompeon n he produ mrke leds o he follong equlrum ouomes (oh frms re ve n equlrum under ll relevn rgnng mehnsms provded h s suffenly lo h s, (8 x (, = l (, = / 3[1 ( ] (9 x (, = l (, = / 3[1 ( ] h he frms profs nd he unon s ge ll sll gven y (3 nd (4, respevely. Furhermore, he NBS ges under he dfferen rgnng mehnsms re sll defned y (5-(7, h he nly 14 The ondon nds for hen here s pern rgnng h he effen frm. 17

19 soluons provded n he Appendx A. Wh > 0, he ouome from sequenl rgnng no depends on hh frm s used s he rge. Thus, e no hve four dfferen mehnsms o onsder. Sne he ouome does no depend on he orderng n he Mrshll-Merlo frmeork, hs s he frs ndon h he soure of frmheerogeney my e mporn. Moreover, he ouome h non-lor oss seems more nuve, s one ould normlly expe he order of negoons o mer. Turnng o he unon s preferenes, s eser o follo he ensung dsusson y referrng o desrpon of he gens preferene orderngs (provded n Appendx B, sne h four ses no he nlogs of Fgures 1 nd 1 re exessvely omplex o e useful. As s ler from he orderngs of he ge lls, he unon prefers pern rgnng over sequenl rgnng for ll. 15 Thus, hen he frms dffer only n non-lor oss, he kng lor ou of ompeon effe ssoed h pern rgnng lys domnes he dvnges from he frm-spef ge sruure ssoed h sequenl rgnng. Ths resul s onssen h he onvenonl sdom ou pern rgnng s ell s he s messge of Mrshl nd Merlo he unon prefers pern rgnng. The orderngs lso ndes h, s n he Mrshll-Merlo frmeork (nd for he sme resons, he unon lys prefers o rgn h he effen frm frs (regrdless of he rgnng mehnsm. Turnng o he frms, e fnd h her preferenes re onssen h he se of produvy dfferenes dsussed n Seon 3 (see Appendx B. Th s, hey prefer sequenl rgnng hen frm heerogeney s ek (.63 u prefer pern rgnng hen frm heerogeney s srong (.63. The nuon follos h n prevous seons for he frms here re oh posve nd negve spes of sequenl rgnng. The posve spe s h resuls n loer verge ges. The negve spe, hh domnes hen he frms re suffenly heerogeneous, s h hey re hrmed 15 Ths resul s prly he rf of exmnng neror soluons n ll ses, hh requres h <.34 (hs resron s requred under pern rgnng h he effen frm s he rge. If e llo for orner soluons, hen here exss smll regon of he prmeer spe hen frms re suffenly heerogeneous n hh sequenl rgnng h he effen frm s he rge s preferred y he unon o pern rgnng h he effen frm s he rge. 18

20 y he pre dsrmnon nheren n sequenl rgnng. We lso see h, s efore nd for he sme resons, he frms lys prefer h he neffen frm rry ou her negoons frs. We re no n poson o solve for equlrum. As n Seon 3, e egn h he o exreme ses. Suppose frs h he unon hs omplee onrol over he rge (q = 1. Then, y su-gme perfeon he effen frm ll e seleed s he rge nd from Appendx B e kno h he unon ll op for pern rgnng. Turnng o he frm, e see h for srong heerogeney ( >.646 he frms ould lso prefer pern rgnng. Thus, pern rgnng n emerge s n equlrum ouome f here s heerogeney n non-lor oss. Turnng o he se n hh he frms n sele he rge (q = 0, e kno h hey ll lys sele he neffen frm. In hs se (from Appendx B, he unon ould sele pern rgnng s long s he frms re no oo dfferen ( <.317. The frms, on he oher hnd, prefer pern rgnng henever >.630; oherse, hey prefer sequenl rgnng. Ths mples h pern rgnng ll e he equlrum ouome for ll [.630,.317]. 16 Exendng he nlyss o llo for ll possle q, follos for [.646,.317] pern rgnng rses regrdless of he rge frm. Th s, for ll q, pern rgnng s he equlrum ouome. Furher, for ll.630, here exss rnge of vlues for q suh h equlrum s hrerzed y pern rgnng. For <.630, sequenl rgnng s lys he equlrum ouome. We summrze hese resuls n Proposon : Proposon : Suppose h he frms dffer n non-lor oss, hen f frms re suffenly homogeneous ( <.630, equlrum s hrerzed y sequenl rgnng. For [.630,.646], here exss q* suh h e ge pern rgnng f q < q*; 16 I s orh nong h he equlrum ge soluons provded n Appendx A re suffen o llo for onsderon of he generl model n hh he frms dffer n oh lor produvy nd non-lor oss. We hve exmned hs model nd he resuls re qulvely denl o hose desred n hs seon. The key resul remns: for sgnfn poron of he prmeer spe he rde-offs re suh h ll gens prefer pern rgnng o sequenl rgnng. Thus, s long s he frms dffer n non-lor oss, pern rgnng n emerge n equlrum even hen sde pymens re no possle. 19

21 oherse e ge sequenl rgnng. For [.646,.317], equlrum s lys hrerzed y pern rgnng for ll q. Fnlly, for. 317, here exss q** suh h pern rgnng s he equlrum ouome for ll q > q**; oherse equlrum s hrerzed y sequenl rgnng. The onrs eeen he ses n hh [.630,.646] nd. 317 s orh hghlghng. In he former se, e ge pern rgnng only f q s suffenly lo. Ths s due o he f h for hese vlues of, he unon lys prefers pern rgnng (regrdless of he rge hle he frms prefer pern rgnng only f hey hve suffen onrol over he rge. In onrs, n he ler se, e only ge pern rgnng f q s suffenly hgh. Ths follos from he f h hen he frms re suffenly heerogeneous he frms lys prefer pern rgnng u he unon ll only gree o pern rgnng hen hs suffen onrol over he rge. Proposon s our mos mporn resul n h hs s he frs exmple (h e re re of n hh pern rgnng emerges s n equlrum ouome n model n hh ll gens ply role n deermnng he rgnng sruure. We lose hs seon y urnng o n ssue h hs reeved surprsngly lle enon n he lerure he mp of rgnng sruure on onsumer elfre. 17 Sne he good s homogenous, onsumers prefer he rgnng sruure h leds o he loes oupu pre. Ths mens h ll hey re neresed n s ggrege oupu he dsruon of oupu s no mporn. We hve rgued ove h sequenl rgnng lys leds o loer verge ges. Thus, hs s lso he rgnng sruure h resuls n hgher ol oupu. Thus, onsumers lys prefer sequenl rgnng over pern rgnng regrdless of he order of he negoons (for he prese preferene orderng, see Appendx B. 18 We summrze hs resul n Proposon In our orkng pper, Crene nd Dvdson (007, e lso exmne he relonshp eeen rgnng sruure nd ol elfre. 18 For he sme reson onsumers prefer h he neffen frm e he rge frm. 0

22 Proposon 3: When he frms dffer n non-lor oss, onsumer surplus s mxmzed y sequenl rgnng. In he nroduon e noed h he Hord Governmen n Ausrl reenly doped legslon med oulng pern rgnng nd h unon leders rgued h he mn gol of hs legslon s o shf rgnng poer ords frms. Hoever, he f h e fnd h sequenl rgnng generes greer onsumer elfre hn pern rgnng provdes n nrgung lernve explnon for he Hord Governmen s ons he Workhoes legslon ould hve een n emp o proe onsumer s neress. In ddon, sne onsumers n e nerpreed s donsrem frms, our nlyss lso offers n explnon s o hy some frms ould volunrly gree o pern rgnng hle donsrem frms n oher ndusres ould loy gns. We lso noe h, regrdless of he governmen s movon n oulng pern rgnng, Proposon 3 suggess h hs on my hve enefed Ausrln onsumers. 5. Sde Pymens For ompleeness, e no onsder he se n hh sde pymens n e used o nfluene he rgnng mehnsm. One reson for dong so s o exmne hh gens neres re mos nvesed n he mplemenon of pern rgnng. Afer ll, gven he sruure of our hree-sge gme, n he sene of sde pymens ll gens mus gree o pern rgnng for o e doped. When sde pymens re possle, one sde my e llng o re he oher o ep hs rgnng sruure. Anoher reson o onsder hs se s h here pper o e nsnes n hh lump sum rnsfers re nluded s pr of nely negoed onr. Wh sde pymens possle, e ould expe he ge sruure h mxmzes he on surplus of he unon nd he frms o emerge n equlrum. The ype of sde pymens h e hve n 19 The relonshp eeen rgnng sruure nd onsumer surplus s slghly more ompled n he Mrshll- Merlo frmeork. In prulr, f frms re suffenly heerogeneous, hen n he Mrshll-Merlo seng onsumers my prefer pern rgnng. See he dsusson preedng Proposon 4 elo (long h foonoe 3 nd our orkng pper (Crene nd Dvdson 007 for dels. 1

23 mnd ould e ny pymen mde y he frms o he unon (or ve vers h ould no ffe he frms mrgnl oss of produon. So, for exmple, ny onruon mde y he frms n he uo ndusry o he UAW s o fund ould qulfy; s ould sgnng onus pd o ll unon memers ho voe yes on ne proposed onr. Anoher exmple ould e n greemen o hnge he penson formul h resuls n more fvorle reremen pkge for orkers. 0 We egn h our enhmrk model of Seon here he unon ses he ges nd hooses eher unform ge or sepre ges for eh frm. Wh lner demnd, onsn oss nd oh frms ve n equlrum, s srghforrd o sho h he ol surplus o e spl y he unon nd he frms (.e., π π θ s lys lrger h unform ge (lhough hs need no e rue for oher e funonl forms. Thus, n he frs perod, efore produves re reveled, he frms should e le o re he unon o omm o seng unform ge n eh perod. Noe h n hs se he ouome s onssen h pern rgnng n h he frms nd up pyng he sme ge. Hoever, hs ouome emerges euse he ommon ge s n he frms es neres nd euse unform ge generes more vlue o he gens hn frm-spef ges. Sne hs runs ouner o onvenonl sdom, e nex exmne hs ssue hen ges re rgned. As e s n Seons 3 nd 4, hen sde pymens re no possle he Mrshll-Merlo frmeork yelds very dfferen resuls from he model n hh he frms dffer n non-lor oss. In he Mrshll-Merlo frmeork, pern rgnng s never n equlrum ouome; heres h dfferenes n non-lor oss, e ge pern rgnng s long s he frms re suffenly heerogeneous. In onrs, he o models yeld qulvely smlr predons hen sde pymens re possle. Therefore, for onreeness, e fous enon one model. Sne yelds lener resuls, e ork h he Mrshll-Merlo frmeork. A he end of he seon, e desre ho he resuls mus e modfed hen frms dffer n non-lor oss. Ineresed reders re referred o our orkng pper, Crene nd Dvdson (007, n hh omplee hrerzon for oh models s provded. 0 We hnk Pul Voos for suggesng hese exmples.

24 There re o ses o onsder sne here re o poenl soures of dsgreemen eeen he unon nd he frms. In he frs se, e ssume h sde pymens n e used o nfluene oh he rgnng mehnsm nd he seleon of he rge. In he seond se, e ssume h he gens re unle o onr on he rge. In he frs se, e expe h negoons ll resul n he mehnsm h mxmzes he on surplus of he unon nd he frms. Fgure 1 shos ho hs produer surplus (PS vres h he rgnng mehnsm hen he frms dffer n lor produvy. 1 When frmheerogeney s ek o modere ( , Fgure 1 ndes h he PS s lrges h sequenl rgnng. Thus, n hs se, even h sde pymens, pern rgnng nno rse n equlrum. Fgure 1 lso ndes h hen frm-heerogeney s srong ( produer surplus s lrges hen he frms ge her preferred ouome: P(. Ths suggess h pern rgnng s lkely o emerge hen s he ouome desred y he frms, no he unons. These resuls re enrely onssen h he enhmrk model here he unon seles he ge. The explnon for he relonshp eeen rgnng sruure nd produer surplus n e explned s follos. As h he frms nd he unon, here re o fores ork. Sne sequenl rgnng leds o loer verge ges, one should expe sequenl rgnng o genere greer surplus loer ges mply greer oupu nd lrger surplus o e shred. Hoever, h sequenl rgnng he neffen frm nds up pyng loer ge re hn ould under pern rgnng. Ths mples h under sequenl rgnng, he neffen frm hs greer mrke shre nd hus, greer fron of ol oupu s produed neffenly. Consequenly, even hough sequenl 1 Mrshll nd Merlo (004 do no exmne produer surplus. Hoever, he ssue does ome up mplly n he fnl seon of her rle hen hey dsuss poenl enry y hrd frm. As dsussed n foonoe 4, Mrshll nd Merlo sho h n he presene of poenl enry, here s ommon ge h ould mke oh he unon nd he o numens eer-off hn hey ould e h sequenl rgnng (hs ommon ge loks enry hle sequenl rgnng llos he hrd frm o ener. They hen rgue h pern rgnng ould herefore e n he neres of he unon nd he o numens. The f h suh ge exss merely shos h produer surplus ould e hgher h ommon ge hn h sequenl rgnng. Wh needs o e shon s h hs ommon ge s lso n equlrum ge h pern rgnng. The effen ge (he one hh mxmzes produer surplus s lys less hn eher he pern or sequenl rgnng ges due o doule mrgnlzon. 3

25 rgnng leds o loer verge ges, ol oupu n e loer h sequenl rgnng. 3 When he frms re smlr, he frs effe domnes nd produer surplus s hgher h sequenl rgnng. As frm-heerogeney eome more pronouned, he loss n oupu from neffen produon gros, so h produer surplus evenully eomes lrger h pern rgnng. 4 Summrzng, e hve: Proposon 4: Suppose h he frms dffer n lor produvy nd h sde pymens n e used o nfluene oh he rgnng mehnsm nd he rge frm, hen f he frms re suffenly homogenous (.650 1, sequenl rgnng s he equlrum ouome. Oherse, equlrum s hrerzed y pern rgnng h he neffen frm s he rge. If sde pymens nno e used o nfluene he seleon of he rge, hen he vlue of q eomes mporn. To see hs, onsder h ours n he o exreme ses. Frs, ssume h he unon lys hs he poer o sele he rge (.e., q = 1. Gven he unon s preferene, su-gme perfeon des h f pern rgnng s seleed n sge one, hen he unon lys seles he effen frm s he rge. Hoever, Fgure 1 ndes h produer surplus h sequenl rgnng lys exeeds s vlue under pern rgnng hen he effen frm s he rge. Thus, hen q = 1 nd sde pymens n only e used o deermne he mehnsm, sequenl rgnng s he only ouome no. Th s, for pern rgnng o rse n hs se, sde pymens mus e le o nfluene oh he mehnsm nd he rge. Noe h n hs se, f >.5786, hen sne he unon prefers P(, e ould expe sde pymens o flo from he frm o he unon. Th s, f hey ould, he frms ould re he unon n order o on sequenl rgnng. No urn o he oher exreme n hh frms sele he rge (.e., q = 0. In he seond sge of 3 Ths s presely hy he relonshp eeen he rgnng mehnsm nd onsumer surplus s slghly more ompled n he Mrshll-Merlo frmeork. 4 As e dsussed n foonoe 7, e do no onsder pern rgnng n oss sne leds o smller on surplus hn sequenl rgnng nd/or pern rgnng n ges. The reson for hs s h pern rgnng n oss omnes he ors spes of he oher o mehnsms (n erms of generng lrge on surplus y sofenng negoons leds o hgher verge ges hn sequenl rgnng nd y equlzng mrgnl oss ross frms resuls n less effen dsruon of produon hn pern rgnng n ges. 4

26 he gme, he frms lys sele he neffen frm s he rge. Gven hs, he relve vlues of produer surplus n Fgure 1 nde h f (.650, 1, S s he equlrum ouome. Moreover, he sde-pymens go from he unon o he frm henever >.767. Thus, hen q = 0 nd s suffenly hgh, he unon ould e llng o re he frms n order o on sequenl rgnng. Fnlly, f (.5,.650, P( s he equlrum ouome. I s orh nong h y Proposon 4, ssgnng he frms he poer of seleng he rge frm rses produer surplus. Exendng he nlyss o he nermede ses n hh q (0,1 s srghforrd, sne e smply ke eghed verge of he pyoffs. For (.650,1, oh sdes prefer sequenl rgnng regrdless of q. If (.5,.650, hen he ouome depends on heher, gven, produer surplus h sequenl rgnng exeeds q PS p( q PS p( here he super-srp P( ndes h pern rgnng hs een doped h frm s he rge. Sne for ny <.650, produer surplus h he effen frm s he rge s srly greer hn produer surplus h sequenl rgnng, here lys exss q rrrly lose o 0 suh h produer surplus h pern rgnng s greer hn h sequenl rgnng. 5 Proposon 5: Suppose h he frms dffer n lor produvy nd h sde pymens n e used o nfluene he rgnng mehnsm u no he rge, hen f he frms re suffenly homogenous (.650 < 1, sequenl rgnng s he equlrum ouome. In ddon, hen he frms re suffenly heerogeneous, ( here exss q* (0, 1 suh h for q > q* here s sequenl rgnng; oherse equlrum s hrerzed y pern rgnng h he neffen frm s he rge. 5 I s orh nong h hen he gens nno onr on he deny of he rge, sequenl rgnng s he ouome hen <.650 nd q s suffenly lrge n spe of he f h produer surplus ould e greer under pern rgnng. 5

27 Proposon 5 ndes h pern rgnng n sll rse n equlrum, u only hen he frms hve suffen nfluene on he seleon of he rge. To summrze our resuls n he Mrshll-Merlo frmeork, Proposon 1 ndes h hou sde pymens, pern rgnng n never emerge s n equlrum ouome. Proposons 4 nd 5 nde h hen sde pymens re possle, equlrum my e hrerzed y pern rgnng, u only hen he neffen frm s used s he rge. Moreover, from Fgures 1 nd 1, pern rgnng only emerges n equlrum hen s he preferred rgnng mehnsm of he frms. As e noed he egnnng of hs seon, resuls que smlr o hose n Proposons 4 nd 5 hold hen he frms dffer n non-lor oss. To egn h, he exsene of sde pymens mkes more lkely h equlrum ll e hrerzed y pern rgnng -- hou sde pymens pern rgnng n only rse hen >.630, h sde pymens he ondon eomes > In ddon, pern rgnng usully rses hen s he frms preferred rgnng mehnsm. The one sgnfn dfferene s h hen he frms nno onr over he deny of he rge s possle o hve pern rgnng emerge hen s n he unon s neres, no he frms. Ths s onssen h he onvenonl sdom h he unon s neres h s mos served y he dopon of pern rgnng. Thus, here re les o resons o prefer model n hh frms dffer n non-lor oss o he Mrshll-Merlo frmeork. Frs, provdes n explnon of ho pern rgnng n rse n equlrum hou sde pymens. Seond, hen sde pymens re possle, provdes n explnon of ho pern rgnng n rse endogenously hen s suppor y he unon nd opposed y he frms. 6 6 In our orkng pper, Crene nd Dvdson (007, e hghlgh hrd reson o prefer he model h dfferene n non-lor oss: provdes n explnon for he onroversy h surrounds he use of pern rgnng. Ths n e explned s follos. In he Mrshll-Merlo se-up, e fnd h henever he use of sde pymens resuls n he dopon of pern rgnng, hs resuls n n nrese n onsumer surplus. Thus, n he Mrshll-Merlo se-up, hou sde pymens pern rgnng ll never e doped, nd h sde pymens ll gens ll gn y s dopon. When he frms dffer n non-lor oss, Proposon 3 mkes ler h onsumers (nd donsrem frms lys prefer sequenl rgnng. Thus, here ll lys e some gens ho oppose he dopon of pern rgnng. 6

28 6. Conluson Pern rgnng s ommon negong sregy h s no ell undersood. The onvenonl sdom s h hs sregy s used y ndusry-de unons o sofen rgnng nd seure hgher ges. Ths nuon s onfrmed n reen pper y Mrshll nd Merlo (004 n hh hey sho h unons prefer hs rgnng mehnsm o smulneous nd/or sequenl rgnng. Hoever, hs does no expln hy he frms re llng o ep suh n rrngemen. Buldng on he nsghs of Mrshll nd Merlo, e hve presened model n hh he gens negoe over ges nd he rgnng mehnsm. We hve shon h hen omprng sequenl nd pern rgnng, here re ompeng fores ork for oh he unon nd he frms. For he unon, pern rgnng s dvngeous euse sofens he negoons h he frms y kng lor ou of ompeon, resulng n hgher ndusry ges. On he oher hnd, sequenl rgnng llos he unon o explo dfferene ross he frms y demndng dfferen ges muh n he sme y h monopols ould hrge dfferen pres o onsumers h dfferen levels of llngness o py. When frms re smlr, he enefs from ge dsrmnon re smll nd he unon prefers pern rgnng. The enefs ed o ge dsrmnon re muh more mporn hen he frms re suffenly dfferen, so h h suffen frm-heerogeney, he unon prefers sequenl rgnng. In our model he relve ompeve posons of he frms hnge over me due o rndom shoks o eher lor produvy or non-lor oss. The frms my herefore prefer pern rgnng euse llos he relvely more effen frm o py loer ge hn ould h sequenl rgnng nd hs n led o hgher expeed lfeme profs. On he oher hnd, s noed ove, pern rgnng sofens negoons nd resuls n hgher verge ges. As resul, e fnd h hen frm-heerogeney s ek (srong, he frms prefer sequenl (pern rgnng. Ths s presely he oppose of he y n hh he unon s preferenes re lnked o he degree of frmheerogeney, mplyng h my no e possle o fnd suons n hh ll gens prefer pern rgnng o sequenl. 7