Why Do Labour Contracts Offer Guaranteed Annual Wage Increments?

Transcription

1 1 Why Do Lbour Conrcs Offer Gurneed Annul Wge Incremens? George Bulkley nd Greh D. Myles Universiy of Exeer Februry 1995 Absrc: Acdemic conrcs in he UK re chrcerised by wges h rise wih nnul incremens nd gurneed fuure employmen. In model bsed on he rrivl of ouside offers, i is shown how such senioriy wges cn rise in boh compeiive lbour mrkes nd when he employer enjoys some monopsony power. The model is hen reinerpreed o inroduce risk bou fuure produciviy. In his frmework, i is shown h senioriy wges cn co-exis wih he rionl offer of enure conrc by he firm. Key-words: long-erm conrcs, enure, wge profile JEL Clssificion Nos: 022, 026, 820 Posl ddress: Correspondence o firs uhor, Deprmen of Economics, Universiy of Exeer, EX4 4RJ, UK. Acknowledgemens: Thnks re due o Dvid de Mez nd n nonymous referee of his Journl.

2 2 I. Inroducion An ineresing feure of wge conrcs for enured cdemic sff in UK universiies is h hey formlly embody he principl h wges should increse wih senioriy. Individuls re hired, or ner, he boom of wge scle h hs 17 differen wge levels ech sepred by pproximely 5%. Once hired, lecurers re gurneed he righ o move les one sep up his py ldder ech yer 1. Of course his whole scle is renegoied nnully, resuling in ddiionl wge increses, superimposed on he uomic incremens. Mny oher UK public secor lbor conrcs employ similr wge ldder, for exmple hose of civil servns, locl governmen employees, school echers nd helh service workers. Alhough employmen of hese groups is very secure, conrcs of universiy lecurers re priculrly ineresing becuse enure gurnees o he individul, over some rnge, boh incresing wges nd fuure employmen. Thus, lhough he evidence for senioriy wges from economeric sudies hs been mixed [1; 2], we hve in hese conrcs cler cu cse o explin, nd one wih he ddiionl wrinkle of gurneed fuure employmen. In his pper we dop n explicily muli-period frmework in order o invesige gurneed wge incremens over ime. A criicl feure of he model is he ssumpion h consumpion is lloced cross periods ccording o he life-cycle hypohesis. Muli-period conrcs re herefore evlued by he lifeime uiliy which hey yield. I should be emphsized h even for conrcs where wge incremens re gurneed, here sill remins residul unceriny bou fuure ernings since he possibiliy exiss h worker my receive beer ouside offer. In secion II his unceriny is moived by incomplee serch nd in secion III by he fc h biliy only becomes known fer he firs period of employmen. These essenilly represen differen inerpreions of he sme model. The nlysis of secion II ssumes h ll workers re offered enure conrc nd i is shown h senioriy wges rise nurlly in such frmework. This in followed in secion III by join nlysis of senioriy wges nd he firm's decision wheher o offer enure conrc. In his cse, senioriy wges cn gin rise nd, impornly, enure conrcs cn cully be more profible for he firm hn conrcs wih no enure. Two resons for enure emerge in his model. I cs s insurnce for workers gins he income risk hey fce nd i llows employers o benefi from he ie-in cused by he exisence of relocion coss for workers who choose o swich employer. There is no pre-exising rionlision of senioriy wges h is consisen wih he sylised fcs we wish o explin. The convenionl explnion of incresing

3 3 wges is humn cpil heory [3] nd his could in principle lso explin gurneed fuure employmen higher wges if humn cpil were cquired common nd predicble re for ll workers in ech grde. However, his does no seem resonble explnion in he conex of universiy employmen, where he vs mjoriy of humn cpil is cquired erly in creer nd, s fr s reserch oupu is concerned, mos likely declines over ime. There re number of lernive heories of senioriy wges h build on he ssumpion of symmeric informion rher hn humn cpil. These include morl hzrd [10], dverse selecion [15], nd unceriny on he pr of firms bou workers' produciviy [7]. However, none of hese is consisen wih precommimen o boh higher fuure wges nd gurneed employmen. For exmple, one explnion for wge/experience scles h rise fser hn produciviy is h workers' effors cnno be direcly conrolled, or mesured nd rewrded, so worker erns less hn his mrginl produc when young, nd correspondingly more when old, in order o discourge shirking. This is proposed by Lzer [10] nd he ide is developed furher in Mlcolmson [11]. However in Lzer's model i is essenil h shirking workers, if cugh, be scked, nd in Mlcolmson's h hey re no promoed, so his cnno explin he commimen o incresing wges for enured cdemics. Kuhn [9] develops n ineresing model of why rde unions migh choose such py ldder, bsed on he ide h senioriy wges my be n effecive wy for union o exrc rens h ccrue o he firm's owners, nlogously o he use of nonliner price schedules in produc mrkes. However, senioriy is ssigned by he union rher hn ern over ime nd, s he nlysis is essenilly single period, here is nohing explici in his model which implies uomic py rises over ime for individul workers nd employmen is in no wy gurneed. Indeed uncerin employmen is he her of his model. The reminder of he pper is orgnised s follows. Secion II sudies he model under unceriny bou fuure wge offers. The opimliy of senioriy wges for firm offering enure conrc is demonsred. The issue of wheher firm would ever wish o offer enure conrc is inegred wih he issue of senioriy wges in secion III. Conclusions re given in secion IV.

4 4 II. Conrcs wih Tenure In his secion we ssume wo-period enure conrc is grned o new hires nd sudy he chrcerisics of he ssocied wge profile. The offer of enure conrcs hs been jusified in number of wys in he lierure. The mos obvious pproch hs been o re i s device designed o proec cdemic freedom nd llow reserchers o pursue ides h my be in conflic wih he beliefs of he employer. An lernive suggesion is h enure hs evolved s socil cusom [5] h reflecs he collegie roos of universiies. In he economics lierure he rgumen h enure exiss becuse of he inheren risk involved in following n cdemic creer [6; 8] hs found some fvour. The bsis of he rgumen is h he rining required for cdemic work is long: from enering s n undergrdue o compleing docore kes minimum of six yers. Even fer his rining he finncil rewrds re no gre bu, more impornly, he level of performnce in he job, in erms of he re nd quliy of publicion, is no fully relised unil severl more yers hve pssed. A finl rgumen for enure hs been provided by Crmichel [4] on he bsis h i provides he securiy needed for hose lredy in pos o llow hem o ppoin new hires h will evenully be compeiors wih hem for he limied funds of he universiy. There re wo key feures of he models developed here. Firs we noe h worker who is offered enure conrc my neverheless be exposed o fuure income unceriny since hey cn qui if hey receive beer ouside wge offer he beginning of he second period. Secondly we ssume h he lifeime expeced income is opimlly lloced beween he wo periods, subjec o ny cpil mrkes consrins. The implicion of his ssumpion is h he supply of lbor in response o ny priculr wge offer will depend on he discouned vlue of lifeime expeced uiliy which is implied by he conrc. The model is sudied in he conex of wo formulions of he lbor mrke. In he firs, he firm is ssumed o hve some monopsony power, fcing n upwrd sloping lbor supply schedule (s funcion of expeced uiliy). This llows us o exmine how Kuhn's ide h senioriy wges my be viewed s n opiml price schedule migh work in his model. The second ssumes he lbor mrke is compeiive. The Lbor Mrke Assume lbor mrke chrcerised by wge dispersion, which is suppored by imperfec informion nd cosly serch. Persisence of such wge dispersion in equilibrium my be explined by heerogeneous firm mrginl revenue produc

5 5 schedules, see Reingnum [14]. There re mny idenicl workers who live for wo periods nd hey supply inelsiclly one uni of homogeneous lbor per period. Workers in heir firs period (he "young") re observionlly disinc from hose in heir second period (he "old"). A he beginning of ech period, workers hve he opporuniy o coslessly serch n exogeneously deermined number of firms, S, fer which furher serch becomes prohibiively expensive. Clerly S mus be smll, relive o he number of firms, o suppor wge dispersion. Workers' expecions he beginning of he firs period, over he bes wge offer hey will receive he beginning of he second period, re described by probbiliy densiy funcion f(), z which is ssumed o be coninuous on he inervl ( z, z ), wih disribuion funcion Fz (). Given he offer of wo period conrc wih wges { w 1, w 2 }, i is ssumed h he worker's expeced lifeime income is opimlly lloced beween periods coningen upon he degree of ccess o credi mrkes. We consider he wo limiing cses of perfec cpil mrkes, wih borrowing/lending fixed re of ineres, r, equl o he individul's ime discoun re, nd imperfec cpil mrkes wih no possibiliy of borrowing. I is ssumed h he preferences of ech worker cn be represened by n ddiively ime seprble expeced uiliy funcion. The expeced uiliy of wge offer, V( w 1,w 2 ), is hus given by Vw ( 1,w 2 )= Uw ( 1 + b)+ [ 11+ r] Fw 2 z ( )Uw ( 2 b[ 1+ r] )+ Uz ( b[ 1+ r] )f()dz z, (1) w 2 where b is he firs period borrowing which hs o be repid wheher he individul remins wih he firs period firm (he second erm on he righ-hnd side of (1)) or moves o beer job in he second period (he hird erm). The opiml level of borrowing, b*, is chosen o sisfy he necessry condiion z V b U' ( w 1 + b *) U' ( z b *1+ [ r] )f()dz z Fw ( 2 )U' ( w 2 b *1+ [ r] )= 0. (2) w 2 A he beginning of he firs period he conrc is chosen, ou of he S offered, which mximizes expeced uiliy nd he beginning of he second period he worker quis if he bes ouside offer, z, is beer hn he firms second period conrc wge, w 2. We now urn o chrcerise he opiml lbor conrc which single firm, hiring in his mrke, would offer.

6 6 Conrcs wih Monopsony Power Consider firm which hires lbor in he mrke described bove o mximize he presen discouned vlue of profis, π, over he wo periods. Assume h lbor is he only inpu nd h here is liner producion echnology. We choose he unis of mesuremen so h 1 uni of lbor produces 1 uni of oupu. The firm receives price, p, per uni of oupu wih ceriny in boh periods. The monopsony power of he firm, nd workers' unceriny bou fuure wge offers, cn boh be moived in number of wys. One ssumpion used below is h he lbor mrke is chrcerised by serch nd informion coss. This boh implies some monopsony power for firms nd some second period wge unceriny for workers, if hey underke serch he beginning of ech ime period. However, one could eqully well moive he fuure wge unceriny by n ppel o uncerin promoion prospecs. The monopsony power of he firm could be due o i being he only employer for cerin clss of skilled lbor, s in he cse of universiies where he iniil moivion for his problem ws found. Thus i is hoped h his bsic ide hs some generliy of pplicion beyond h formlly modeled below. The monopsony power implies he lbor supply schedule of young workers o he firm is n incresing funcion of he expeced lifeime uiliy offered by he conrc. The probbiliy h his firm's offer is he bes of he S which rndom sercher hs received increses wih he level of he wge offer. The firm ses conrc nd employs ll who ccep i. The deerminion of he (single) wge offer h he firm will mke o ny old workers who re serching is no sudied here since i involves no new issues. The opiml conrc for ech ge group is independen of h offered o he oher under he preceding ssumpions h mrginl revenue produc is consn nd idenicl for boh groups nd h he wo groups re observionlly disinc. I should be noed now, for i will be used ler, h his specificion gurnees he monopsonis sricly posiive profis from employmen of young workers under convenionl single wge policy, providing h p is greer hn he wge offer h will elici les one uni of young lbor. The discussion in he inroducion suggess h he wge offer mde o he young will in generl be n offer of firs period employmen w 1, followed by second period w 2. Second period ouside offers re ssumed unobservble by he firm, nd hence w 2 cnno be mde coningen upon hese [12]. We mke his ssumpion becuse we wn o explin he observed non-se coningen commimen o higher fuure wges.

7 7 The problem for he firm is o choose he wo-period wge conrc { w 1, w 2 } which mximizes profis, π, where π = [ p w 1 ]NV ( ( w 1,w 2 ))+ [ 11+ [ r] ]p [ w 2 ]Fw ( 2 )NVw ( ( 1,w 2 )). (3) We hve ssumed firs period employmen is sufficienly lrge h he qui re 1 Fw ( 2 ) is effecively non-sochsic nd hence he resuls here re independen of he firm's iude o risk. NVw ( ( 1, w 2 ) is he upwrd sloping lbor supply curve discussed bove, so N' ()> 0. nd The firs order condiions for profi mximizion re π w 1 [ p w 1 + Fw ( 2 ) p w 2 [ ]]N' V w 1 N = 0, (4) [ ] 1 + r π w 2 [ p w 1 + Fw ( 2 )[ p w 2 ][ 1+ r] ]N' V w 2 + N[ p w 2 ]f( w 2 ) Fw ( 2 ) [ ]= 0. (5) Solving (4) nd (5) yields [ V w 2 ] V w 1 [ [ ] 1 + r [ ( )] 1+ r [ ]= Fw ( 2 ) [ p w 2 ]f w 2 [ ]. (6) Consider firs he soluion wih perfec cpil mrkes. In h cse he worker's choice of borrowing is chrcerized by (1) nd (2). Employing he envelope heorem nd V w 1 = U' ( w 1 + b *), (7) [ ( )] 1 + r V w 2 = Fw ( 2 )U' w 2 [ 1+ r]b * Subsiuing (7) nd (8) ino (6) gives [ ( )] U' ( w 1 + b *) Fw ( 2 )U' w 2 [ 1 + r]b * The firs proposiion follows direcly from (9). [ ]. (8) [ ]= Fw ( 2 ) [ p w 2 ]f( w 2 ). (9) Proposiion 1 When workers re risk neurl he profi-mximising conrc will specify senioriy wges wih w 2 > w 1. In priculr, second period wges will equl mrginl revenue produc bu firs period wges will be less hn mrginl revenue produc.

8 8 Proof Risk neurliy implies U' () is consn. From (9) i hen follows h w 2 = p. Since he monopsony power of he firm implies h i mkes sricly posiive profis, i follows from (3) h w 1 < p. The inuiion for his resul is h he worker's second period expeced surplus cn be effecively "sold", bundled wih firs period employmen, by lowering he firs period wge. Therefore, w 2 is chosen so h second period join firm-worker surplus is mximized. This is somewh nlogous o he well-known resul, 0i [13], h in produc mrke monopolis should cpure consumers surplus by n enry fee, nd herefer price oupu mrginl cos. This conrc provides useful benchmrk since i mximizes he join expeced surplus of firm nd is workers. I is n efficien conrc, bu leves he worker exposed o unceriny in he second period. If workers re risk verse here my be insurnce gins in modifying i. The oucome when workers re risk-verse is summrised in Proposiion 2. Proposiion 2 If workers re risk verse workers he profi-mximising conrc will specify senioriy wges. The second period wge will exceed mrginl revenue produc nd he firs period wge will be less hn mrginl revenue produc. Proof From he firs-order condiion for he choice of b i follows h U' ( w 1 + b[ 1+ r] )= U' ( χ b[ 1 + r] )1 F( χ) for some vlue w 2 < χ < z. Risk version implies hence U' χ b[ 1 + r] [ ]+ Fw ( 2 )U' ( w 2 b[ 1+ r] ), (10) ( )< U' ( w 2 b[ 1 + r] ), (11) U' ( w 2 b *1+ [ r] )> U' ( w 1 + b *). (12) From (9) i cn be seen h (12) implies w 2 > p. Posiive profis require, from (3), h p > w 1 nd hence w 2 > w 1. Risk version serves o lower he firs period wge, nd rise he second period wge, compred o risk neurliy. This mkes pr of he lower firs period wge look like n insurnce premium gins no finding beer job in ler period, nd is hus disinc componen of senioriy wges from he monopsony power. Thus

9 9 we would expec i o be observed even in compeiive lbor mrke. We invesige he ruh of his observion in he following subsecion. I is widely rgued h consumers hve limied biliy o borrow gins humn cpil nd, ccordingly, we now consider he oher polr cse where no borrowing is possible. When workers hve no ccess o credi, worker my sve in he firs period bu no borrow, so b* 0. In his cse he mximizion of uiliy is subjec o he consrin b* 0. I is srighforwrd o show h his consrin binds, since b* > 0 in he unconsrined problem, nd we my herefore proceed o nlyse his cse by seing b* = 0. Se b* = 0 in (9) nd suppose w 2 w 1, which implies U' ( w 2 ) U' ( w 1 ) under risk version. This implies, from (9), h p w 2. Bu if w 2 w 1, hen i mus be rue h p w 1. This is inconsisen wih firm's profi being sricly posiive, which i mus be under he echnology nd mrke ssumpions mde in his secion. Hence w 2 > w 1 which implies, from (9), if b* = 0, h p > w 2. Therefore, wih imperfec cpil mrkes, he form of he profi-mximising conrc remins s described in Proposiion 2. Compeiive Lbour Mrke We now mend he lbor mrke described in he previous subsecion by ssuming h he serch coss he beginning of he firs period re zero. The se-up for he second period is unchnged. If i seems lile forced o hve zero serch coss for young workers, nd posiive for old, i migh be emphsized h he principl objecive here is o isole wo disinc forces work in he preceding secion. Also he serch frmework ws only one jusificion for second period wge unceriny. If second period wge unceriny is due o unceriny bou he individul's produciviy in oher jobs nd his unceriny is resolved he beginning of he second period, hen i is quie consisen wih his h he firs period should be compeiive. The purpose here is o cpure in n uncluered frmework he everydy feure h workers in prcice ypiclly recognise, when hey ccep one job, h hey my receive beer offer some de in he fuure, nd his holds rue even if hey found heir firs job in compeiive lbor mrke. For exmple, heir promoion o higher grdes wihin he sme firm my be uncerin. The lbor mrke now clers in he firs period, under full informion bou conrcs on offer ll oher firms in he curren period. The firm fces n infiniely elsic supply of young lbor n exogeneously deermined level of expeced uiliy since workers compre expeced uiliies of conrcs. Inegring he preceding model of he firm wih his lbor mrke implies h profis re liner in oupu nd employmen, nd hence firm size is indeermine. Rher hn mend he model so

10 10 sufficien condiion for unique firm size cn be idenified, we proceed by considering only necessry condiion which mus be sisfied. This suffices o chrcerise he opiml wge conrc { w 1, w 2 } which necessrily mus sisfy { w 1, w 2 } rgmx π = p w 1 + Fw 2 ( )[ p w 2 ][ 1+ r] s.. Vw 1, w 2 ( ) V. (13) Employing he resricion h b* solves (2), he derivives of he Lgrngen describing he opimizion in (13) re nd L w 1 = 1 + λu' ( w 1 + b *), (14) [ ( )] 1 + r L w 2 = [ p w 2 ]f( w 2 ) Fw 2 [ ( )] 1+ r [ ]+ λ Fw ( 2 )U' w 2 b *1+ [ r] [ ], (15) where λ is he lgrnge muliplier on he minimum-uiliy consrin. Proposiion 3 cn hen be proved. Proposiion 3 When workers re risk verse, he profi-mximizing conrc specifies wges which increse wih senioriy. The second period wge will exceed mrginl revenue produc, nd firs period wge will be less hn mrginl revenue produc. Proof Subsiuing (14) ino (15) gives L w 2 = [ p w 2 ]f( w 2 ) Fw 2 ( )+ [ Fw ( 2 )U' ( w 2 b *1+ [ r] )]U' ( w 1 + b *). (16) Consider pir of wges such h w ˆ 1 = w ˆ 2 nd noe (i) h w ˆ 2 p for profis o be non-negive; nd (ii) w ˆ 1 = w ˆ 2 implies b* > 0 so U' ( w ˆ 2 b *1+ [ r] ) > U' ( w ˆ 1 + b *). Now evluing (14) w ˆ 1 = w ˆ 2 gives L w 2 ˆ w 1 = ˆ w 2 p > 0. (17) This implies h he opimum mus hve w 1 < p < w 2. Thus even in compeiive lbor mrke, if risk verse workers hve ccess o credi, senioriy wges will be observed. If workers re risk neurl hen he wge will equl mrginl revenue produc in ech period. This is obvious from (16). The inuiion for his resul is he following: second period uiliy for he worker is mx{ Uw ( 2 b *1+ [ r] ),U( z b *1+ [ r] )}. Since z w 2, rising w 2 will reduce second period risk. Under risk version, mrginl uiliy will be highes when he

11 11 worker remins wih he firm second period. Thus, from posiion wih w 1 = w 2, mrginl increse in w 2 nd mrginl reducion in w 1 will resul in firs-order insurnce gins, bu second-order efficiency losses. Now consider he cse where he workers cnno borrow. The firm is price ker in he oupu mrke, nd hence equilibrium requires zero profis. This gives Proposiion 4. Proposiion 4 If workers do no hve ccess o cpil mrkes, he only equilibrium is where wges re consn, nd equl o mrginl revenue produc in ech period. Proof I cn gin be shown h he consrin b 0 is binding. From (16), he necessry condiion for he firm's opimision reduces o [ p w 2 ]f( w 2 ) Fw ( 2 )+ Fw ( 2 )U' ( w 2 ) U' ( w 1 )= 0, when b* = 0. Assume h w 2 > w 1. From he bove equliy, his implies h p > w 2 nd hence h profis re posiive. Conversely, ssume h w 2 < w 1. Then p < w 2 nd profis re negive. Only he oucome w 1 = w 2 = p is consisen wih he zeroprofi oucome. Discussion The inuiion for hese resuls srs from considerion of he bse line cse of workers who re risk neurl, where heir expeced uiliy is mximized by mximision of expeced wge receips. Inroducing risk version implies he disribuion of wge receips mers. If workers hve ccess o borrowing, nd consumpion is deermined by lifecycle uiliy mximision, hen under eiher monopsony or in compeiive lbor mrke, mrginl uiliy of income is highes, becuse of repymen of firs period borrowing, in he second period if he worker doesn' find beer second period job. This implies h hey will rde-off some expeced wge income, for redisribuion of wges ino he se where hey don' qui. On he oher hnd, under monopsony, if hey hve no ccess o cpil mrkes, he mrginl uiliy of income is highes in he firs period, nd herefore here needs o be mrginl re-disribuion from he second o he firs period, compred o he conrc which mximizes expeced wges. In compeiive lbor mrke he wge conrc for risk neurl workers implies he sme wge in boh periods. Thus if workers cnno borrow, heir mrginl uiliy of income is he sme in boh periods, if hey don' qui, nd here is no reson for wge redisribuion. These inuiions ber

12 12 some resemblnce o hose in he insurnce lierure, where firs-order insurnce gins re obined he expense of second-order efficiency losses. III. Endogeneous Tenure Choice In his secion we exend he model o show how fuure income unceriny my explin he decision of firm o offer enure conrc. In his wy we provide new explnion o enure conrcs, differen o hose discussed in he inroducion o secion II. In shor, we now demonsre how minor modificion of he model we hve lredy considered cn hve enure emerging s he preferred soluion for boh workers nd firms. In ddiion, i will be shown h i is possible for enure o rise in conjuncion wih senioriy wges. The srucure h we dop is he following. As in he second subsecion of II, ech worker serches he poenil employees before cceping he bes conrc offered. A his sge, he biliy of he worker in he occupion is unknown o eiher he worker or ny of he firms. In he universiy conex, he inerpreion is h he workers hve compleed heir Ph.D.s bu hve ye o prove heir cpbiliy chieving publicions. The biliy of ech worker is relised during he firs period nd, he end of his period, is public knowledge. The consequence of his srucure is h he firs period wge mus represen he reurn o some verge level of biliy wheres i is possible for he second period wge o be condiionl upon biliy. We ssume h he lbor mrke is compeiive so he opimision for he firm is consrined, s in (11), by he uiliy level chievble elsewhere on he mrke. There is one furher modificion h is inroduced. We ssume h i is no cosless for worker o move beween jobs he end of he firs period. Such removl coss cn be significn in prcice. For ypicl cdemic in he UK wih five yers of experience, he direc coss involved in selling one house nd purchsing noher plus he cos of removl of personl belongings cn esily rech 25% of he nnul slry of Alhough new employer my choose o offse some of hese direc coss here re ddiionl indirec coss, mos nobly hose involved wih spouse securing employmen in new locion. As such, hese moving coss reduce he freedom of movemen wihin he sysem nd provide ie-in o he iniil employer. As will become ppren, one spec of enure cn hen be inerpreed s mechnism o preven employers from exploiing his ie-in. An lernive inerpreion of his cos could be h of cquiring he specific humn cpil required o funcion effecively fer job swich.

13 13 To formlise his discussion, ssume h ech worker hs n inne biliy level,, where [, ]. Abiliy in he populion of workers is rndomly disribued nd cn be described by he densiy funcion f() wih cumulive disribuion F (). A he beginning of period 1, biliy cnno be observed bu i becomes common knowledge he end of his period. The mesure of biliy is chosen so h he vlue of worker of biliy o firm is equl o. If worker wishes o chnge employer he end of he firs period, moving cos of c mus be pid. Firs consider he oucome h rises in he bsence of enure. Assuming h he lbor mrke is compeiive wih mny firms compeing for he vilble workers. Since ll firms re essenilly idenicl, in ech ime period hey mus ll offer he sme wges. The firs sep is o deermine he wge offered in he second period when biliy hs become public knowledge. The vlue of worker o firm is given by heir reveled biliy nd, if worker were o move o new firm, his is he wge hey would receive. However, he employer which hey joined in period 1 hs degree of monopoly power over heir incumben employees since worker wishing o move beween firms mus py cos of c. In fc, he wge hey need o py o rein ll heir workforce is given by - c nd his mus be he equilibrium wge in period 2 s funcion of biliy. Alhough enry of new firms cnno upse his equilibrium wge in he second period, he consequence of enry is h expeced profi for firms mus be driven o zero. Since he second period wge is below he mrginl vlue produc of worker, he firs period wge mus be sufficienly bove o ensure zero profi. This resoning implies h he non-enure oucome is given by n w 1 = E ()+ c [ 1+ r ], n w 2 =, E( π n )= 0. From he srucure of his non-enure conrc, he uiliy level h is obined is given by V = Uw ( n 1 + b)f ()d [ ] Uw n 2 b 1+ r [ r] = U( E ()+ c [ 1 + r]+ b)f()d r ( [ ])f ()d [ [ ] U c b[ 1+ r] ( )f ()d (18) This is he minimum uiliy level h ny enure conrc mus supply in order for firm offering enure o rc ny workers.

14 14 Turning o he cse of enure, he expeced pyoff o worker of cceping conrc w 1,w 2 { } is given by Vw ( 1,w 2 )= Uw 1 + b ( ) [ ] Uw 2 b 1 + r [ r] w 2 +c ( [ ] ) f()d + w 2 +c U ( c b[ 1 + r] ) f()d, (19) where he worker will only choose o chnge jobs if reveled biliy is greer hn w 2 + c. Now ssuming s we did bove h he number of workers employed is sufficienly gre h o llow he populion proporions o be pplied o he firm, he profi level of firm offering enure conrc will be π w ( 1,w 2 )= N f()d w 1 + Fw2+ c w 2 +c [( )[ 1 + r] ] f()d w 2, (20) where only hose receiving n offer in excess of w 2 + c will leve. As in he second subsecion of II, we do no emp o deermine he scle of operion of he firm bu insed chrcerize he opiml conrc for given level of operion. s The Lgrngen describing he opimizion fcing he firm cn hen be wrien L = f()d w 1 + Fw 2 + c w 2 +c [( )[ 1 + r] ] f()d w 2 + λ EV w [ ( 1, w 2 ) V]. (21) Given he conex, he consrining level of uiliy is chosen o be equl o he expeced uiliy h worker cn expec o chieve if hey simply ccep he non-enure mrkedeermined conrc, w n i, i = 1, 2, in ech period. This is given by (18). Since he opimision of he firm is consrined by he uiliy level chievble by he worker in he bsence of enure, ne surplus is genered by he enure conrc if he mximized level of profis rising from (21) is posiive. This will be one of he poins of focus below. From (21) he opiml enure conrc offered by he firm will sisfy he necessry condiions L w λv 1 = 0, (22)

15 15 nd L w 2 [ [ ]] 2 + c [ [ ] Fw ( 2 + c) 1 + r + f( w 2 + c) 1 + r [ ]f( w 2 + c) 1] w 2 +c f()d w 2 + λv 2 = 0. (23) Solving (22) nd (23) chrcerizes he wge in he second period of he enure conrc s he soluion o [ [ ] 1 w 2 + c [ [ ] V 2 V 1 = Fw ( 2 + c) 1 + r f( w 2 + c) 1 + r [ [ ]f( w 2 + c) ] w 2 +c f()d w 2. (24) There re now wo poins h mus be demonsred. Firsly, i mus be shown h here re circumsnces in which senioriy wges cn emerge from (24). The reson why his is possible is cler. Since he second-period wge plces n upper limi on he biliy of employees h remin wih he firm, he firm hs n incenive o defer pymen in enure conrc o h period in order o rise he men level of biliy. The benefi from doing his is offse o some degree by he fc h ll workers hve o be pid he higher wge bu, s long s biliy disribuion is no oo concenred low levels, i should prove beneficil for he firm. The second fc h mus be esblished is, s lredy noed, h enure conrc wih senioriy wges cn led o posiive profis for he firm. When i does, i sricly domines he non-enure conrc. To mke our poin h senioriy wges nd profible enure cn co-exis, we clcule he oucome for he cse of worker risk-neurliy. Adoping risk-neurliy bises he cse s much s possible gins enure becuse he firm is unble o profi from offering insurnce o he workers. So, if enure is profible in his cse, i will be more so when workers re risk verse nd would py risk premium o insure gins he rndomness in he second-period oucome. Using (7) nd (8), wih riskneurliy (24) reduces o ( + c)w [ 2 + c]= w 2 Fw 2 w 2 + c f ()d. (25) Now ssume h = 0 nd h f()= 2 2 so h F ()= Subsiuing ino (25), he second-period wge mus solve

16 16 5[ w 2 + c] 3 = 3w 2 2. (26) The ssumpion of risk neurliy implies h he uiliy funcion is liner. From (18) he consrin h he enure conrc offers he sme uiliy s h expeced wihou enure cn be wrien s w 1 + w 2 +c [ 2w2 2 ]d + [ 2[ c] 2 ]d 0 w 2 +c = [ r]. (27) Finlly, he expeced profi from he employmen of ech worker is given by Eπ = 2 3 w 1 [ w 2 + c] 5 4 [ 1 + r]. (28) Tble I describes he soluion of he sysem (26) - (28) for rnge of prmeer vlues. As cn be seen from he ble, boh senioriy wges nd he exisence of enure re suppored by hese resuls. The explnion for his is h he moving cos ies he worker o he firm so h lhough he firm is rewrding some workers more hn heir mrginl produc, he mrginl worker is being pid moun c less hn mrginl produc. Alhough he firm sill mkes loss in he second period, his is more hn offse by he profi i chieves in he firs period. Alhough we cknowledge he disribuion funcion employed is unusul, his ws chosen only for compuionl ese. Afer ll, he min poin ws o esblish h cses exised under which senioriy nd enure could boh be simulneously rionl. Tble I Plced Here IV. Conclusions Alhough his pper ws iniilly moived by puzzling propery of conrcs for Universiy lecurers in he UK, i is hoped h he resuling model hs served o isole generl forces work in shping lbor conrcs. If he employer hs some monopsony power senioriy my be n efficien wy o exrc worker's surplus, rher like non-uniform prices in oupu mrkes. Secondly, nd quie independenly of he compeiive srucure of he lbor mrke, if life-cycle opimising workers hve ccess o credi mrkes, hey will hve preference for jobs wih n incresing wge profile, ou of h se of wge profiles which holds consn he expeced wge bill o he employer. This insurnce moivion ws highlighed by he model where he lbor mrke ws compeiive, nd workers were risk verse.

17 17 We hve lso provided formulion of unceriny bou fuure produciviy combined wih coss of relocion which provides moives for boh senioriy in wges nd he provision of enure in employmen. I is possible for he firm o increse is profis by offering he workers some insurnce gins boh unceriny in he oucome nd he need o reloce in he form of second-period wge h exceeds h pid in he firs-period. Alhough we hve presened he coss s being conneced wih relocion, hey could eqully be reed s being cused by he need for rerining fer job swich (for insnce by he need o lern firm-specific skills). Doing his nurlly brodens he inerpreions h cn be given o he model. References 1. Abrhm, Kherine G. nd Henry S. Frber, "Job Durion, Senioriy nd Ernings." Americn Economic Review, June 1987, Alonji, Joseph G. nd Rober A. Shkoko "Do Wges wih Job Senioriy?" Review of Economic Sudies, April 1987, Becker, Gry S. Humn Cpil, 2nd ed. New York: Columbi Universiy Press for Nionl Bureu of Economic Reserch, Crmichel, H. Lorne "Incenives in Acdemics: Why is here Tenure?" Journl of Poliicl Economy, June 1988, Elser, Jon "Socil Norms nd Economic Theory." Journl of Economic Perspecives, Fll 1989, Freemn, Smih "Wge Trends s Performnce Revels Producive Poenil: A Model nd Applicion o Acdemic Erly Reiremen." Bell Journl of Economics, Auumn 1977, Hrris, Milon nd Beng Holmsrom "A Theory of Wge Dynmics." Review of Economic Sudies, April 1982, Hrris, Milon nd Yorm Weiss "Job Mching wih Finie Horizon nd Risk Aversion." Journl of Poliicl Economy, Augus 1984, Kuhn, Peer "A Nonuniform Pricing Model of Union Wges nd Employmen." Journl of Poliicl Economy, June 1988,

18 Lzer, Edwrd P. "Agency, Ernings Profiles, Produciviy nd Hours Resricions." Americn Economic Review, Sepember 1981, Mlcolmson, Jmes M. "Work Incenives, Hierrchy, nd Inernl Lbour Mrkes." Journl of Poliicl Economy, June 1984, Moore, John "Opiml Lbour Conrcs when Workers hve Vriey of Prively Observed Reservion Wges." Review of Economic Sudies, June 1984, Oi, Wler Y. "A Disneylnd Dilemm: Two-Pr Triffs for Mickey Mouse Monopoly." Qurerly Journl of Economics, Februry 1971, Reingnum, Jennifer F. "A Simple Model of Equilibrium Price." Journl of Poliicl Economy, Augus 1979, Slop, Jonne nd Seven Slop "Self-Selecion nd Turnover in he Lbour Mrke." Qurerly Journl of Economics, November 1976,

19 19 * Thnks re due o Dvid de Mez nd n nonymous referee of his journl. 1 Formlly, he move up from he 7h poin is given fer review of performnce bu his is usully no rigorously pplied. In ddiion, he finl hree poins re given on specil meri. 2 The rgumen does no work for uniform disribuion. The one we use could pproxime he norml below he men.