Pattern Bargaining as an Equilibrium Outcome. Rough Draft: not complete. Department of Economics, Michigan State University +

Transcription

1 Pattern Barganng as an Equlbru Outcoe Rough Draft: not coplete Anthony C. Creane * and Carl Davdson *,+ * Departent of Econocs, Mchgan State Unversty + GEP, Unversty of Nottngha Abstract: Pattern barganng s a negotatng strategy that s often eployed by ndustry-de unons n olgopolstc ndustres to set ages. Hoever, foral explanatons for ts exstence n equlbru are rare. The conventonal sdo s that pattern barganng takes labor out of copetton and therefore softens barganng beteen the unon and frs, resultng n hgher ndustry de ages. Hoever, ths does not explan hy frs agree to pattern barganng. In ths paper, e argue that the barganng echans cannot be posed upon the frs and that for pattern barganng to survve over te as a negotatng strategy t ust be agreed upon by all agents nvolved n the age settng process. Thus, e analyze a odel n hch the agents negotate over the barganng echans, the order of the negotatons and the ages n order to deterne the condtons under hch pattern barganng can eerge as an equlbru outcoe. We sho that hen sde-payents are possble, there are cases n hch pattern barganng ll be adopted n equlbru, but ths occurs hen pattern barganng s the frs ost preferred echans, not the unon s. We also sho that hen sde-payents are not possble, there are cases n hch all agents prefer pattern to sequental barganng, but the unon and the frs alays dsagree over the target fr. Fnally, e sho that ho frs ay dffer s crtcal, as hen frs also dffer n non-labor costs pattern barganng can arse n equlbru th the unon and the frs agreeng over the target fr.

2 Pattern barganng s a dely-used, soetes controversal negotatng strategy that s often eployed by ndustry-de unons to set ages. If pleented perfectly, the unon pcks one fr to bargan th frst (the target fr) and negotates a age. It then uses ths outcoe as a precedent, and akes take-orleave-t deands to the reanng frs for slar concessons. 1 Assung that the frs agree, and they usually do, ths practce results n a unfor age rate across frs. 2 Conventonal sdo s that ths practce, often attrbuted n the Unted States to the Unted Auto Workers (UAW) and the Teasters, provdes the unon th countervalng poer n ts relatonshp th the poerful frs that eploy ther ebers. It s argued that by takng labor out of copetton pattern barganng helps the unon secure hgher ages than they ould obtan otherse. Controversy over ts pact on ages recently led the Hoard Governent n Australa to outla ths practce under the WorkChoces legslaton (hch becae effectve on March 27, 2006). It s the contenton of unon leaders that the governent s obectve n dong so as to rrevocably shft barganng poer n ndustral relatons to eployers. 3 Explanatons of hy pattern barganng orks and ho t coes to be adopted are rare. Ths s surprsng gven that ths strategy clearly plays an portant role n age deternaton n ost OECD countres, often n portant ndustres. The takng labor out of copetton explanaton s the one ost coonly gven, although, as far as e kno, t has never been foralzed. The basc dea s sple. Ordnarly, unonzed olgopolstc frs have an ncentve to bargan tough snce any age concessons that they can pry fro the unon ll provde the th a copettve edge over ther product 1 What e have n nd s an ndustry n hch several unonzed olgopolstc frs negotate ages th the sae ndustry-de unon and then copete th each other n the product arket. Thus, the ages that are beng negotated are pad to orkers th slar sklls n slar occupatons. The U.S. autooble ndustry n hch the Unted Auto Workers negotates ages th Ford, Chrysler and General Motors or the U.S. arlnes ndustry n hch the Ar Lnes Plot Assocaton (ALPA) negotates ters th the aor arlnes both ft nto ths fraeork ncely. Pattern barganng s also used n other settngs by eployers to te-don the ages of orkers th dfferent skll sets and occupatons. For exaple, n the U.S. Arlne ndustry pattern barganng lnks the ages of plots, antenance orkers, and orkers n other crafts. Pattern barganng s also used dely n state and local governent negotatons th publc sector eployees th dfferent skll sets (e.g., frefghters and polce). In ths paper, e restrct attenton to pattern barganng of the forer type. 2 Related to pattern barganng s the concept of a e too agreeent n hch soe frs agree to accept the ters negotated by other frs. For exaple, orkers eployed by Las Vegas casnos have ther ages set through negotatons beteen ther unon and a ult-eployer barganng group. Casnos that are not ebers of the ult-eployer group often sgn e too agreeents that bnd the to accept those ters thout addtonal negotatons. 3 See the dscusson of pattern barganng and the recent changes n Australan Labor La on the Constructon Forestry Mnng Energy Unon eb ste:.cfeu.asn.au/constructon/research/secondave/pattern.htl. 2

3 arket rvals. Pattern barganng assures such frs that f they gve n to the unon s age deands, they ll not have to orry that ther ll rvals ll gan an advantage by beng tougher durng negotatons after all, all frs nd up payng the sae age rate. Thus, pattern barganng s veed as one ay to soften negotatons th olgopolstc frs. The proble th ths ratonale s that s does not explan hy the frs are llng to accept such an arrangeent. A foral ustfcaton for pattern barganng s provded by Marshall and Merlo (2004), but ther explanaton suffers fro slar crtcss. In ther odel, to unonzed frs that produce substtute products negotate ages th an ndustry-de unon. The frs face constant costs, but dffer n labor productvty. Four dfferent barganng echanss are consdered, th the Nash Barganng Soluton appled n each case. The unon can bargan sultaneously over ages th both frs, they can bargan sequentally, they can use pattern barganng that results n both frs payng the sae age, or they can use pattern barganng n labor costs hch results n age rates that equalze argnal costs across the frs. In the latter three cases, the order of barganng s portant, so both possble orderngs are consdered. Marshall and Merlo derve to aor results. Frst, they fnd that hen fr-heterogenety s eak, the unon prefers pattern barganng n ages; hereas hen fr-heterogenety s strong, the unon prefers pattern barganng n labor costs thus, the unon alays prefers soe type of pattern barganng. Second, the unon alays chooses to use the effcent fr as the target. The frst result s consstent th the perceved sdo that pattern barganng benefts unon ebers. Marshall and Merlo argue that the second result s consstent th a stylzed fact that unons alost never select the relatvely unproductve fr n the arket as the target. The proble th the Marshall and Merlo explanaton s that n ths settng the frs alays prefer an alternatve barganng echans. Ths s partcularly true of the non-target fr. Thus, t s hard to understand hy the frs ould ever agree to ths for of barganng. 4 Moreover, the non-target 4 Marshall and Merlo do recognze ths proble and address t n one of the latter sectons of the paper. Buldng on an nsght orgnally due to Wllason (1968), they extend ther analyss to allo for a potental entrant that ust use unon labor f t enters the arket. They then sho that n such a settng there are entry costs such that the thrd fr ould enter under sequental barganng but stay out under pattern barganng. Consequently, they argue that both the frs and the unon ay therefore prefer pattern barganng because t serves as a barrer to entry. To ake ths pont, they sho that there exsts a age that ould result n hgher payoffs for both the unon and the frs 3

4 fr should surely ve the unon s take-or-leave t age deand as non-credble. If the fr reects the unon s age deand, t ll alays be n the unon s nterest to reopen negotatons, effectvely resultng n the sae outcoe that ould be generated by sequental barganng. In ths paper, e argue that the barganng echans cannot sply be posed upon the frs and that for pattern barganng to survve as a long-run feature of the negotaton process t ust be agreed upon by all agents on both sdes of the labor arket. It follos that f e are to truly understand pattern barganng, e ust exane condtons under hch t eerges endogenously fro a settng n hch the agents negotate not only over the age rates but the barganng echans as ell. In order to do so, e develop a dynac odel that captures any of the essental features of the arkets n hch pattern barganng has been so portant (the US auto arket serves as our prary otvator). In partcular, e assue that the arket s characterzed by olgopolstc frs that produce substtute goods and that the frs producton costs are subect to rando shocks so that ther relatve copettve postons ay change over te. 5 The bulk of our odel borros heavly fro Marshall and Merlo (2002) n that there are to frs that face a lnear deand curve, costs are constant, the to frs dffer n ters of labor productvty, the unon s goal s to axze the age bll and ages are deterned by the Nash Cooperatve Barganng Soluton. Hoever, our odel dffers fro thers n three key ays. Frst, the dynac nature of the odel and exstence of the rando shocks ples that the frs ll prefer the barganng echans that axzes ther expected profts over te. Ths ples that frs ll prefer a echans that reards the hen they are the ost effcent fr n the arket thout penalzng the too uch hen they are at a copettve dsadvantage. Second, n addton to dfferences n labor productvty, e allo the frs to dffer n ther non-labor costs as ell. Fnally, as under duopoly than they ould earn th sequental barganng under tropoloy. Hoever, t s unclear hether or not ths age s an equlbru age th pattern barganng. We conecture that t s not and that f e restrct attenton to equlbru ages t s lkely to be the case that the frs prefer pattern barganng hle the unon prefers soe other barganng echans. We return to ths ssue and dscuss t a bt further n footnote??. 5 The assupton that costs are subect to rando shocks that alter the copettve postons of frs s becong ncreasngly coon n any appled areas. For exaple, ths assupton s a crucal coponent of the Mortensen-Pssardes (1994) odel of search generated uneployent n acroeconocs, the Hopenhayn ( ) odel of ndustry dynacs n ndustral organzaton and the Meltz (2004) odel of onopolstc copetton n nternatonal econocs 4

5 noted above, e expand the barganng envronent by allong the agents to negotate over the barganng echans and the order n hch the barganng takes place. Our dynac gae conssts of three stages. In the frst to stages, the agents negotate over the barganng echans and the order n hch barganng s to take place. Once these features have been pnned don, n the thrd stage the agents partcpate n a repeated gae of quantty copetton n hch each perod s age rate s negotated after the frs costs have been deterned and publcly revealed. We fnd that n ths settng there are portant nstances n hch both the unon and the frs prefer pattern barganng over sequental barganng, but that they alays dsagree about the order of negotatons. In soe nstances, t s possble to alternate the dentty of the target fr over a seres of contract negotatons n a ay that akes both the unon and the frs better off than they ould be th sequental barganng. When ths s not possble, e stll fnd nstances n hch the sub-gae perfect equlbru s characterzed by pattern barganng, although contrary to the perceved sdo, e fnd that ths s ost lkely to occur hen ths s the preferred echans of the frs, not the unon. The reander of the paper dvdes nto fve sectons. In Secton 2, n order to gan soe nsght nto the forces drvng our results, e look at pattern barganng fro a ne perspectve by analyzng an extree verson of the Marshall-Merlo odel n hch the unon has all the age settng poer. That s, rather than allo for negotatons, e start out by assung that the unon selects the age pad by each fr and then the frs choose eployent. In such a settng, pattern barganng s equvalent to the unon deandng the sae age fro each fr; hereas e nterpret a decson by the unon to deand dfferent ages as a preference for sequental barganng. When exaned fro ths perspectve, t ould be surprsng f the unon ever preferred pattern barganng after all, hen the unon has the ablty to choose the effectve prce at hch t supples labor to the frs and the frs have the poer to choose the nuber of orkers to eploy, the unon s n exactly the sae poston as a onopolst n a product arket that ust choose hether to charge the sae prce to all consuers. As e kno fro the lterature on prce dscrnaton, the suppler alays prefers to prce dscrnate hen possble. As for the frs that deand labor, ther total profts can be hgher or loer th a unfor age: they prefer the 5

6 unfor age hen they are the ore effcent fr but age dscrnaton hen they are the less effcent fr. Thus, t s clear that there are nstances n hch the frs ll prefer pattern barganng. Moreover, as e kno fro the prce dscrnaton lterature (see, for exaple, Varan and ), the total surplus to be splt beteen the unon and the frs ay be hgher or loer th a unfor age. Ths ples that there ll be nstances n hch the frs ll prefer pattern barganng and can afford to brbe the unon to accept ths barganng echans (assung that lup su payents are possble). We close the secton by dscussng ays n hch such sde payents can be bult nto the negotated contract and provde exaples fro arkets n hch pattern barganng s prevalent. The proble th the odel analyzed n secton 2 s that, snce t does not allo for age negotatons, t does not capture the frs strategc consderatons that are nherent n the takng labor out of copetton arguent. We therefore turn to the general odel n sectons 3 and 4 (outlned above) hch uses the Nash Cooperatve Barganng Soluton to deterne age rates. In secton 3 e exane the agents preferences over barganng echanss hen, as n the Marshall-Merlo odel, the frs dffer only n labor productvty. Although not all results fro secton 2 generalze for exaple, there are no cases n hch the unon prefers a unfor age the general flavor of the results reans the sae. In partcular, e fnd that hen sde-payents are possble, pattern barganng can only eerge as an equlbru outcoe hen t s the frs preferred echans. Moreover, hen sde payents are not possble, equlbru s never characterzed by pattern barganng. In secton 3 e also provde ntuton for our results by solatng to attrbutes of the barganng echanss that nfluence the agents preferences. We argue that both the prce dscrnaton nherent n sequental barganng and the ablty to take labor out of copetton under pattern barganng beneft the unon at the expense of the frs. When fr-heterogenety s eak, the pact of prce dscrnaton s sall and thus the unon prefers to take labor out of copetton through pattern barganng hle the frs prefer sequental barganng. But, hen fr-heterogenety s suffcently strong, the prce dscrnaton effects are strong enough to reverse the agents preferences. These tradeoffs are, of course, key n deternng the equlbru outcoe of the negotatons over the barganng 6

7 echans. When the frs dffer only n labor productvty, e fnd that the trade-offs are such that thout sde-payents pattern barganng cannot eerge n equlbru. In secton 4 e extend the odel to allo the frs to dffer n non-labor costs and sho that ths alters the trade-offs such that pattern barganng can be an equlbru outcoe even n the absence of sde-payents. In secton 5 e turn to an ssue that has receved surprsngly lttle attenton n the lterature the pact of barganng echans on consuer elfare and sho that th non-labor costs consuers can prefer sequental barganng even hen producer surplus s greater th pattern barganng. As consuers can be nterpreted as donstrea frs, that use the duopolsts output as an nput, there s an explanaton for hy both pattern barganng eerges and governents (e.g., n Australa) could be lobbed aganst t. We conclude the paper n secton 6 by suarzng and dscussng our results. 2. Sequental Barganng as Prce Dscrnaton In ths secton e ntroduce the basc odel and then exane the outcoe hen the unon s alloed to set the ages. To facltate coparsons th Marshall and Merlo (2002), e adopt any of ther assuptons concernng functonal fors and use uch of ther notaton. There are to frs (a and b) that produce a hoogeneous good and face the follong lnear deand curve: P = 1 x a xb, here x denotes the output of fr. We assue that the orkers at each fr are represented by the sae ndustry-de unon. As for producton, labor s the only nput (e relax ths assupton n the next secton) but labor productvty at each fr s ntally unknon and ay change fro one perod to the next. It s coon knoledge that n each perod one fr (a) ll be able to produce one unt of output th each orker hred; hereas the other fr (b) ll get only t 1unts of output fro each orker. Thus, f e use to denote eployent for fr then e have xa = a and x b = t. Note that fr a s the effcent fr hereas fr b s relatvely neffcent. The dentty b of the ore effcent fr s deterned by nature at the begnnng of each perod, th each outcoe 7

8 equally lkely. To ensure that both frs produce n equlbru, e assue that t s suffcently close to one (to be ade precse belo). There are three stages to the gae. In the frst to stages, the unon and the frs negotate over the age settng echans (pattern versus sequental) and the dentty of the target fr (the effcent or the neffcent fr -- f the order atters). The last stage conssts of a repeated gae n hch, n each perod, nature deternes the frs productvtes, these values are revealed to the unon, the unon and frs then apply the barganng echans to deterne ages and then, fnally, the frs engage n quantty copetton n the product arket. Snce a ne, ndependent dra on fr productvtes occurs n each perod, the copettve postons of the frs are lkely to change over te. The frs ll keep ths n nd hen selectng a barganng echans and thus, ther goal ll be to fnd the barganng echans that axzes ther expected profts. We assue that the unon s goal s to axze ts expected age bll. There are several aspects of ths set-up that are orth notng. To begn th, there s a sngle pont n the gae at hch the barganng echans s deterned. That s, agents do not renegotate the barganng echans n each perod. The basc dea that e are tryng to capture s that negotatng over the barganng echans s lkely to be dffcult and costly snce the agents are lkely to have very dfferent preferences (e.g., the frs versus the unon; the effcent fr versus the neffcent fr). Thus, the agents ll not ant to have to re-vst ths ssue n each perod. Instead, snce the frs and the unon realze that they are n a long ter relatonshp n hch the relatve copettve postons of the frs ay change over te, they are lkely to take a long-run ve and try and select up front a barganng echans that orks ell for all of the over te. A fr ay be llng to put up th a barganng echans hch s not deal for the hen they are the effcent fr f they kno that ths sae echans ll ork far better for the hen they are at a copettve dsadvantage. The second aspect of our set-up orth notng s e are assung that the ages are deterned after each perod s productvty easures have been deterned and revealed to all partes. Thus, age settng takes place under coplete nforaton about the current perod. Fnally, note that snce the frs 8

9 copete n output after the ages have been deterned, the frs effectvely deterne eployent (as s the case n alost all labor negotatons). We begn our analyss by descrbng the product arket outcoe. Straghtforard calculatons yeld the Cournot output, eployent, proft levels and age bll as: (1) x, ) = (, ) = (1/ 3t)[ t(1 2 ) + ] a ( a b a a b a b (2) x, ) = t (, ) = (1/ 3t)[ t(1 + ) 2 ] b ( b a b b a a b (3) 2 π (, ) = x (, ) for = a, b; (4) θ, ) (, ) + (, ). th π ( a b a a a b b b b a denotng the profts earned by fr and θ denotng the age bll. In ths settng, to ensure that both frs produce n equlbru, e requre that t. 5. As noted above, n any gven perod each fr s equally lkely to be the effcent fr or the neffcent fr. Thus, ex ante, each fr s expected proft n any gven perod s 5( π + π ). It follos. a b that the frs ll be nterested n selectng the barganng echans that axzes total per perod profts. As for the unon, snce there s alays one effcent fr and one neffcent fr, ther goal ll be to axze the (certan) age bll as defned n (4). In ths secton e assue that the unon has the poer to select the ages pad by each fr. There are to possbltes: the unon can deand the sae age fro each fr (as n pattern barganng), or, the unon can select fr-specfc ages. Wth the unon havng all of the age-settng poer, the order of negotatons s not relevant. Maxzng (4) over a and b subect to (1)-(2) yelds the unon s optal fr-specfc ages. We obtan a = 1/ 2 and b = t / 2. Maxzng (4) subect to (1)-(2) and a = b yelds the unon s optal coon age. We obtan p = t(1 + t) 2, here the p subscrpt denotes that ths s 4( t t + 1) 9

10 the pattern age. For t [.5,1 ], e have b p a ; thus, snce each fr s proft s decreasng n ts on age and ncreasng n ts rvals age, the effcent fr prefers the pattern age hle the neffcent fr prefers the fr-specfc age structure. And, substtutng these ages back nto (1), (2) and (4) and coparng e fnd that the unon s alays better-off th the fr-specfc ages. None of these results should be surprsng they c standard results fro the lterature on prce dscrnaton under onopoly (and do not depend upon the assued functonal fors). When the unon selects a coon age, t settles on one that s beteen the to fr-specfc ages. Ths benefts the effcent fr and hars the neffcent fr. And, a standard revealed preference arguent s enough to ensure that the unon cannot be orse off hen the ages are fr-specfc. Thus, veed fro ths perspectve, one ould never expect the unon to prefer a coon age,.e., pattern barganng. In our set-up, the agents settle on a barganng echans before productvtes are revealed. Ths s partcularly portant for the frs. They kno that, over te, they are lkely to be the effcent fr half the te and the neffcent fr the reander of the te. Thus, they ould prefer the echans that leads to the largest per perod total proft. It s straghtforard to sho that th lnear deand and constant costs, a coon age leads to hgher total proft. It follos that n the ntal stage, t ll be the frs, not the unons, argung for a pattern age. Whether the frs can convnce the unon to adopt a pattern age structure depends upon the ay n hch the barganng echans s chosen. We ll not deal th that ssue at ths pont. Instead, e ll assue that sde payents are possble n the ntal stage so that the negotatons alays lead to the barganng echans that axzes the ont surplus of the unon and the frs. The type of sde payents that e have n nd ould be any payent ade by the frs to the unon (or vce versa) that ould not affect the frs argnal costs of producton. So, for exaple, any contrbuton ade by the frs n the auto ndustry to the UAW s ob fund ould qualfy; as ould a sgnng bonus pad to all unon ebers ho vote yes on a ne proposed contract. Another exaple ould be an agreeent to change the penson forula that results n a ore favorable retreent package for orkers. 6 6 We thank Paula Voos for provdng these exaples. 10

11 Wth lnear deand, constant costs and both frs actve n equlbru, t s once agan straghtforard to sho that the total surplus to be splt by the unon and the frs (.e., π π + θ ) s e + alays larger th a coon age (although ths need not be true for other functonal fors). Thus, the frs should be able to brbe the unon to use set the pattern age n each perod. Note that n ths case the outcoe s consstent th pattern barganng n that the frs nd up payng the sae age. Hoever, ths outcoe eerges because the coon age s n the frs best nterest and because a coon age generates ore value to the agents than fr-specfc ages. As e noted above, there s nothng ne n these results. Wth the unon settng the age, these results are exactly hat e expect gven hat e kno about the pact of thrd-degree prce dscrnaton. Moreover, snce ages are not negotated, ths fraeork does not capture the forces that drve the takng ages out of copetton arguent. So, the reader ght onder hy e bothered to present these results at all. The anser s that frst there s a strong sple reason to expect, contrary to sdo, that unons ould prefer sequental barganng and that the takng ages our of copetton ust be a strong effect to over turn ths. As e ll see, the flavor of these results survves hen the odel s extended to allo for age negotatons. 3. Usng Pattern Barganng to Take Labor Out of Copetton In ths secton e extend the odel so that ages are negotated. We then exane the agents preferences over barganng echanss under the assupton that ages are deterned by the Nash Barganng Soluton (NBS). The non-cooperatve foundatons for the NBS are ell knon t s the outcoe of negotatons n hch the agents trade offers untl an offer s accepted (Rubnsten 1982). When ages are negotated, the order of barganng ay atter, so e have (potentally) four cases to consder. Snce all four cases are algebra ntensve, e sketch the soluton ethod n the text and relegate the detals to Appendx A here all analytc solutons are provded. We begn th pattern barganng th fr s the target. As s standard, e use backards nducton. If the unon fals to 11

12 reach an agreeent th fr, fr becoes a onopolst n the product arket. Let denote the age negotated by fr hen t s a onopolst and let ( ) and x ( ) denote ths fr s labor deand and output at ths age. Then, accordng to the NBS, axzes the product of the unon s age bll and the fr s proft; that s 2 axzes ( )[ x ( )] over. Turn next to the orgnal negotatons beteen the unon and fr. The age bll evaluated at serves as the unon s threat pont durng these negotatons, hereas fr s threat pont s zero (snce t does not produce f no agreeent s reached). Snce under pattern barganng t s understood that both frs ll end up payng the sae age, then usng (3)-(4) and a straght-forard applcaton of the NBS, the age that the unon settles on hen usng fr as the target solves (5) ax { θ (, ) ( )} x (, ) 2 p( ) We use to denote ths age, th the super-scrpt denotng that ths age eerges under pattern barganng and that fr s used as the target. The analytc solutons for p( ) and are provded n the Appendx A. Turn next to sequental barganng under the assupton that fr negotates th the unon frst. Let ) denote the age that coes out of these ntal negotatons note that the sub-scrpt refers to the fact that ths age s the result of sequental barganng th fr as the target hle the sub-scrpt sgnfes that ths s the age pad by fr. Then, hen fr negotates th the unon, the NBS soluton age that eerges solves (6) ax { ) ( ), ) + (, ) ) ) ( ) )} x (, ) ) 2 Note that f the unon fals to reach an agreeent th fr, fr becoes a onopolst n the product arket, but ust stll pay the (already) negotated age of ). Ths explans hy the unon s threat 12

13 ) ) ) ) pont s gven by ( ). Let ( ) denote the soluton to (6). As before, the super-scrpt refers to the fact that ths age eerges under sequental barganng th fr as the target; hereas the sub-scrpt sgnfes that ths s the age to be pad by fr. It s portant to note that ) s ncreasng n ) th a slope less than one. The reason for ths s straght-forard: an ncrease n fr s age ncreases the surplus to be splt by fr and the unon hch trggers an ncrease n fr 's age. Hoever, does not ncrease by the full ncrease n snce ths ould copletely undo the copettve advantage ust ganed by fr (there s also a stablty arguent that restrcts the slope to be belo one). Fnally, e turn the ntal negotatons beteen fr and the unon n order to descrbe ho ) s deterned. If the unon and fr fal to reach an agreeent, fr does not produce (and therefore earns nothng) hle fr becoes a onopolst and the unon and fr settle on a age of. Ths ples that the unon s threat pont s gven by ( ) and ) solves (7) ax { (, ) ( )) + ) ( ) ( ) ( ), ) ( )} x (, ) ( )) 2 Note that n negotatng over ts on age, fr takes nto account ho the outcoe ll affect the barganng beteen fr and the unon. Ths s the aspect of age barganng n olgopolstc ndustres that pattern barganng s eant to elnate. The analytc solutons for ) ) and ( ) are ) provded n Appendx A. Wth the ages deterned, e can use (3) and (4) to calculate the unon s age bll and the frs profts. In addton, sung these values allos us to deterne the ont surplus to be splt beteen the agents (producer surplus). To assess the preferences over the dfferent barganng echanss for the agents, e restrct. 5 t 1 (hch ples that both frs are actve n 13

14 equlbru). Ths leaves us th the sae odel analyzed by Marshall and Merlo and allos for a drect coparson of our results. As they deonstrate, th the frs dfferng only n labor productvty, the order of barganng does not atter hen sequental barganng s used. Thus, e have three barganng echanss to consder. We start th the unon s preferences, hch are depcted n Fgure 1a. The frst result s not surprsng: under pattern barganng, the unon alays prefers to bargan th the ore effcent fr frst. Ths follos fro the fact that the effcent fr generates a larger surplus and can therefore afford to pay a hgher age than ts counterpart. As e sho n the next secton, ths result generalzes to stuatons n hch the frs dffer n non-labor costs as ell t s alays n the nterest of the unon to use the ore effcent fr as the target. The second result that s evdent fro Fgure 1a s that hen the degree of fr-heterogenety s eak ( t 1), the unon prefers pattern over sequental barganng regardless of hch fr s used as the target. When fr-heterogenety s oderate ( t ), the unon stll prefers pattern barganng to sequental, as long as the target s the effcent fr. It s only hen the frs dffer draatcally n labor productvty (. 5 t ) that the unon prefers to bargan sequentally. Marshal and Merlo (2002) provde ntuton for the unon s preference orderng and t s the an result of ther paper. Hoever, e offer a soehat dfferent explanaton for these results. As e shoed n the prevous secton, the prce dscrnaton aspects of sequental barganng beneft the unon at the expense of the frs. Hoever, the takng labor out of copetton aspect of pattern barganng results n hgher average ages n the ndustry. Ths follos fro the fact that frs are ore llng to agree to age ncreases hen they kno that ther rval s age ll rse by the sae aount that ther age s ncreasng (and, as e sa above, th sequental barganng any ncrease n leads to an ncrease n of saller agntude). Thus, sequental barganng benefts the unon by allong for prce dscrnaton but hars the unon by generatng loer average ages. The beneft fro prce 14

15 dscrnaton s not partcularly portant hen the frs are slar, so that th eak heterogenety the latter force donates and the unon prefers pattern barganng. The advantages fro prce dscrnaton gro as the frs becoe less alke, and ths effect donates hen fr-heterogenety s strong. As a result, hen the frs are qute dsslar, the unon prefers sequental barganng. The proble th the Marshall-Merlo result s evdent fro Fgure 1b here the frs total profts ( Π ) are depcted for each of the three barganng echanss. As e noted above, the frs goal s to select the barganng echans that axzes ts expected profts, hch, gven our set-up, s equvalent to axzng total ndustry profts. Fgure 1b ndcates that hen fr-heterogenety s eak ( t 1), the frs prefer sequental barganng over any for of pattern barganng. Note, hoever, that hen fr-heterogenety s oderate or draatc (. 5 t ), the frs prefer pattern barganng, provded that the neffcent fr s that target. The fact that the frs prefer that the eak fr serves as the target should not be surprsng snce the neffcent fr generates a saller surplus, usng t as the target results n a loer age and hgher profts. The explanaton for the frs preferences s slar to that gven above for the unon. The prce dscrnaton nherent n sequental barganng hars the frs; hereas the ablty to take labor out of copetton through pattern barganng also hars the fr (due to the hgher average ages). When the negatve aspects fro sequental barganng are donate, the frs prefer pattern barganng; otherse, they prefer sequental barganng. If the frs are slar, the pact of prce dscrnaton s sall and the frs prefer sequental barganng. As the dfference beteen the frs gros, the pact of prce dscrnaton ncreases so that the frs eventually stch and prefer pattern barganng. Snce the unon and the frs preferences are so dfferent, t s useful to look at ho the total surplus to be splt by the agents, producer surplus (PS), vares th the barganng echans. Ths s shon n Fgure 1c. When fr-heterogenety s eak to oderate ( t 1 ), Fgure 1c ndcates that the PS s largest th sequental barganng. Thus, even though the unon prefers pattern barganng, the frs ll refuse to adopt ths echans; and, even f sde payents are possble, the unon ll not 15

16 be able brde to brbe the frs to accept ths outcoe. In fact, f sde payents are possble and fr heterogenety s eak to oderate, e ould expect sequental barganng to be the outcoe snce t axzes producer surplus (e dscuss the case n hch sde payents are not possble belo). Fgure 1c also ndcates that hen fr-heterogenety becoes draatc (. 5 t ) the ont surplus s largest hen the frs get ther preferred outcoe: pattern barganng th the neffcent fr as the target. Thus, f sde-payents are possble and fr-heterogenety s suffcently strong, e ould expect pattern barganng to be the outcoe th the neffcent fr used as the target and sdepayents should be pad by the frs to the unon. It follos that th sde payents, pattern barganng eerges only hen t s the outcoe desred by the frs, not the unons. These results are entrely consstent th those presented n secton 2 hen e assued that the unon has the ablty to select the age. The explanaton for the relatonshp beteen barganng structure and producer surplus can be explaned as follos. As th the frs and the unon, there are to forces at ork. Snce sequental barganng leads to loer average ages, one should expect sequental barganng to generate a greater surplus loer ages ply greater output and a larger surplus to be shared. 7 Hoever, th sequental barganng the neffcent fr nds up payng a loer age rate than t ould under pattern barganng. Therefore, under sequental barganng the neffcent fr has a greater arket share, plyng that a greater fracton of the output s produced neffcently. Thus, even though sequental barganng leads to loer average ages, output can decrease th sequental barganng. (We ll see later that th postve non-labor costs ths also leads to ore neffcent producton.) When the frs are slar, the frst effect donates and producer surplus s hgher th sequental barganng. As fr-heterogenety becoe ore pronounced, the loss output fro neffcent producton gros so that producer surplus eventually becoes larger th pattern barganng. When sde payents are possble, e expect the agents to select the echans that axzes ther ont surplus (here e are assung that sde payents can be used to nfluence both the barganng 7 The effcent (producer surplus and elfare axzng) age s equal to zero. 16

17 echans and the order of negotatons). Thus, Fgure 1c s suffcent to predct the outcoe of the barganng process. We no turn to the case n hch sde payents are not possble. To analyze ths case, e ust no copletely descrbe the three-stage gae that the agents face. In the frst stage, the agents ust select the barganng echans. If pattern barganng s selected, then n stage 2 the dentty of target fr s deterned. In ths secton, e start by consderng to extree cases for stage 2. In the frst case, the unon alays has the poer to select the target (ths case sees to be consstent th the nsttutons n several arkets). In the second case, t s the frs that alays get to select the target. Gven the agents preferences, sub-gae perfecton dctates that n the frst case the unon alays selects the effcent fr hle n the second case the frs alays select the neffcent fr. Fnally, th the target set, n the last stage the agents engage n a repeated gae of quantty-copetton n the product arket n hch the frs productvty levels vary (but are alays publcly revealed) fro perod to perod. We assue that n the frst stage, knong ho the target ll be selected, the agents sultaneously announce ther choce as sequental (S) or pattern (P). Hoever, t s possble to pleent pattern barganng f all agents do not agree to adopt t. Thus, e assue that f all agents select P, then pattern barganng s adopted; otherse, sequental barganng s the outcoe. In the frst case, th the effcent fr as the target, Fgure 1a ndcates that the unon prefers S to P for all t <.5785; hereas Fgure 1b ndcates that the frs prefer S to P for all t > Thus, sequental barganng s alays the outcoe. In case 2, th the neffcent fr as the target, Fgure 1a ndcates that the unon prefers S to P as long as t <.7338; hereas Fgure 1b ndcates that the frs prefer S to P for all t > Thus, n these to extree cases, sequental barganng s the only possble equlbru outcoe. We can push ths a bt further by consderng one other possblty for stage 2. We can assue that s understood that f pattern barganng s selected then th probablty q the unon ll get to select the target; hereas th the reanng probablty the frs ll select the target. In ths secton e ake 17

18 no attept to explan ho q s deterned; nstead, e are sply nterested n askng hether there exst values of q that result n pattern barganng beng selected as the equlbru barganng echans. In the frst stage, the agents kno that f pattern barganng s chosen the effcent fr ll be selected as the target th probablty q. As a result, the payoff to the unon hen P s the outcoe s qθ p( a) p( b) + (1 q) θ, here the super-scrpt p( ) ndcates that pattern barganng has been adopted th fr as the target. On the other hand, under sequental barganng the unon earns θ s (snce the order of barganng does not atter). The payoff for the frs s calculated n an analogous fashon. It should be edately clear that for t and t. 5785, sequental barganng ll eerge as the outcoe of the gae. In the forer case, the frs prefer S even hen they get to choose target fr th probablty one; hereas n the latter case t s the unon that nssts on S regardless of q. For t. 7265, the fr ll only choose P f q s suffcently hgh; hereas the frs ll choose P only hen q s suffcently lo. Let q U ( q ) denote the value of q that equates the expected age bll (expected total proft) th pattern barganng th the age bll (total proft) fro sequental barganng. Then there exsts a value of q such that both the unon and the frs prefer P over F S ff q q. Hoever, hen the frs dffer only n labor productvty e fnd that for all t n ths U F range q > q -- so that there s no value for q such that both the unon and the frs prefer pattern U F barganng! Thus, hen sde payents are not possble, e conclude that n the Marshall-Merlo fraeork e ould alays expect sequental barganng to be chosen n equlbru. It follos that the fact that the unon ay prefer pattern barganng s not suffcent to explan ho t eerges as an equlbru outcoe. 4. Dfferences n Non-Labor Costs We no extend the odel to allo the frs to dffer n non-labor costs. We do so by assung that each te that fr b produces a unt of output t ust ncur a non-labor cost of c. Fr a, on the 18

19 other hand, faces no addtonal per unt costs. In order to hghlght the portance of ths extenson, e set t = 1so that ths s the only dfference across the frs. Ths ples that fr a s argnal cost of producton s a ; hereas fr b s argnal cost s b + c. As e sho, ths assupton alters the trade-offs faced by the frs and the unons and akes t possble for pattern barganng to eerge as an equlbru outcoe n even n the absence of sde payents. Wth ths set-up, Cournot copetton n the product arket leads to the follong equlbru outcoes (both frs are actve n equlbru under all relevant barganng echanss provded that c 3 / 8 =.375 ) (8) x (, ) = (, ) = (1/ 3)[1 2 + ( c)] a a b a a b a b + (9) x (, ) = (, ) = (1/ 3)[1 + 2( c)] b b a b b a a b + th the frs profts and the unon s age bll stll gven by (3) and (4), respectvely. Furtherore, the NBS ages under the dfferent barganng echanss are stll defned by (5)-(7), th the analytc solutons provded n the Appendx A. Wth c > 0, the outcoe fro sequental barganng no depends on hch fr s used as the target. Thus, e no have four dfferent echanss to consder. As n the Marshall-Merlo fraeork, and for the sae reasons, the unon alays prefers to bargan th the effcent fr frst (regardless of hether sequental or pattern barganng s chosen); hereas the frs alays prefer that the neffcent fr carry out ther negotatons frst. Ths case s slar n any ays to the case covered n secton 3. For exaple, the unon prefers pattern barganng hen the frs are slar (c s lo), but prefers pattern barganng hen the frs are sgnfcantly dfferent. The frs preferences are reversed they prefer sequental barganng hen the c s lo but prefer pattern barganng hen c s hgh. As for producer surplus, t s agan axzed hen the neffcent fr s the target (snce these results n loer ages). Moreover, producer surplus s axzed under sequental barganng hen the frs are slar, but pattern 19

20 barganng generates a larger surplus hen the frs are sgnfcantly dfferent (a coplete descrpton of the preference orderngs s provded n Appendx B). As a result, hen sde payents are possble, one ght expect the to odels to yeld alost dentcal conclusons. And, for the extree values of c ths s the case. When c s suffcently lo ( c.1965 ), the unon ould lke to see pattern barganng used, but the frs prefer sequental barganng and pattern barganng does not generate enough surplus to allo the unon to brbe the fr nto acceptng ts shes. On the other hand, hen c s suffcently hgh ( c ) the frs prefer pattern barganng th the neffcent fr as the target and can afford to brbe the unon to accept ths barganng echans. Hoever, for nteredate values of c soe nterestng possbltes arse. Consder, for exaple, the case th c ; n hch total profts and producer surplus are both largest hen pattern barganng s pleented and the neffcent fr s used as the target. Thus, the frs should be able to use sde payents to ensure that they get ther ost preferred outcoe. The tst here s that sde payents ay not be necessary -- for these values of c the unon also prefers pattern over sequental barganng, provded that the effcent fr s used as the target. That s, hen c.3648 all agents ve pattern barganng as the best outcoe, hoever they do not agree on the dentty of the target. If, as e assued at the end of the prevous secton, the order of barganng s randoly selected, t ay be possble to fnd values of q such that all agents prefer pattern barganng to sequental. In fact, for all c n ths range, e fnd that such values of q alays exst. Ths represents the frst exaple that e kno of n hch pattern barganng can eerge as an equlbru outcoe thout the use of sde payents. We explore ths case n greater detal belo. Another nterestng case arses for c In ths case, the frs frst choce s S th the neffcent fr as the target; hereas ther second choce s usually P th the neffcent fr as the target (f c. 2052, the frs second choce s actually S th the effcent fr as the target). The unon prefers both types of pattern barganng over ether type of sequental, and, as alays, 20

21 they prefer that the effcent fr serve as the target. Producer surplus s axzed under pattern barganng th the neffcent fr as the target. Ths ples that no one has any hope of gettng ther ost preferred outcoe. The frs cannot afford to brbe the unon to accept sequental barganng th the neffcent fr as the target and the unon cannot brbe the fr to accept the effcent fr as the target. But, both agents can get ther second choce, pattern barganng th the neffcent fr as the target, and ths s the lkely outcoe th sde payents. It s nterestng to note that n ths case t s the unon that ust brbe the frs to accept pattern barganng. To see ths, sply note that the preference orderngs n Appendx B ndcate that for these values of c the frs ll alays prefer S over P regardless of the dentty of the target. Thus, the unon, hch prefers ether for of P over ether for of S, ll have to brbe the frs pattern barganng. It s orth notng that hen c. 2630, unlke the prevous case, gven the frs preferences, pattern barganng cannot eerge as the equlbru outcoe hen sde payents are not possble. Ths s due to the fact for these values of c the frs alays prefer S to P regardless of the dentty of the target. Thus, f the unon cannot use sde payents to brbe the fr, S ll alays be the equlbru outcoe. We no turn to a ore careful analyss of the three stage gae hen sde payents are not possble. For our purpose, t s suffcent to focus on the to extree cases n hch one agent has the ablty to select the target n stage 2. Consder frst the case n hch the unon selects the target so that, by sub-sae perfecton, the effcent fr ust alays bargan frst. Checkng the preference orderngs reported n Appendx B, e fnd that the frs prefer P to S henever c >.2646; otherse, ther preferences are reversed. In contrast, the unon prefers P to S hen c <.3648; otherse ther preferences are reversed. It follos that e get all agents selectng P n stage 1 for all c [.2646,.3648]. Thus, for a sgnfcant porton of the paraeter space, pattern barganng s the equlbru outcoe even though the agents cannot use sde payents. 21

22 Slar results are obtaned hen the frs select the target n stage 2. Fro Appendx B, hen the neffcent fr s the target the frs prefer P to S as long as c >.2630; hereas the unon prefers P to S f c < Thus, pattern barganng s the equlbru outcoe for all c [.2630,.3127]. 8 In ths latter case (n hch the frs select the target), t s orth notng that a sall change n the structure of the gae akes pattern barganng a ore lkely equlbru outcoe. To see ths, suppose that e reverse the order of the frst to stages so that the order of barganng s deterned before the agents select ther preferred barganng echans. Then the frs can nduce the unon to select pattern barganng n stage 2 by offerng to randoze the target fr over te. If e use q to (once agan) denote the probablty that the effcent fr bargans frst, then, as e ust shoed, the frs can set q = 0 for all c [.2630,.3127] and stll get P as the equlbru outcoe. Hoever, for all c [.3127,.3646] the fr can also get P as the outcoe by settng q at a value hgh enough that the unon ll be llng to accept pattern barganng over sequental. The value of q that s suffcent to do so s defned by qθ p( a) p( b) a) b) + (1 q) θ = qθ + (1 q) θ. It s easy to check that for all c [.3127,.3646] there exsts a value for q [0,1] that satsfes ths expresson. Thus, th ths alternatve gae structure e get pattern barganng as the equlbru outcoe for a uch der range of values for c. Ths provdes us th an explanaton for one coonly observed phenoenon assocated th pattern barganng: n any arkets, the target fr and ts characterstcs change over te (.e., soetes the unon ll select the ost effcent fr as the target hle at other tes t ll select a d-level fr as the target). We close ths secton by consderng an ssue that has receved surprsngly lttle attenton n the lterature: What s the pact of barganng structure on consuer elfare? As far as consuers are 8 It s orth notng that the equlbru age solutons provded n Appendx A are suffcent to allo for consderaton of the general odel n hch the frs dffer n both labor productvty and non-labor costs. We have exaned ths odel and the results are qualtatvely dentcal to those descrbed n ths secton. The key result reans: for a sgnfcant porton of the paraeter space the trade-offs are such that all agents prefer pattern barganng to sequental barganng. Thus, as long as the frs dffer n non-labor costs, pattern barganng can eerge n equlbru even hen sde payents are not possble. 22

23 concerned, they prefer the barganng structure that leads to the loest consuer prce. Ths eans that all they are nterested n s aggregate output the dstrbuton of output s not portant. Whle dscussng the pact of barganng structure on producer surplus n Secton 3 e noted that sequental barganng alays leads to loer average ages and greater aggregate output. Thus, consuers alays prefer sequental over pattern barganng regardless of the order of the negotatons. In the ntroducton e noted that the Hoard Governent n Australa recently adopted legslaton aed at outlang pattern barganng and that unon leaders argued that the an goal of ths legslaton as to shft barganng poer toards frs. Hoever, the fact that e fnd that sequental barganng generates greater consuer elfare than pattern barganng provdes an ntrgung alternatve explanaton for the Hoard Governent s actons. 23