Monopolistic Competition and Macroeconomic Dynamics

Transcription

1 Monopolsc Compeon and Macroeconomc Dynamcs Pasquale Commendaore, Unversà d Napol Federco II Ingrd Kubn, Venna Unversy of Economcs and Busness Admnsraon Absrac Modern macroeconomc models wh a Keynesan flavor usually nvolve nomnal rgdes n wages and commody prces. A ypcal model s sac and combnes wage barganng n he labor markes and monopolsc compeon n he commody markes. As cenral polcy mplcaon follows ha deregulang labor and/or commody markes ncreases equlbrum employmen. We reassess he consequences of deregulaon n a dynamc model. I sll ncreases employmen a he fxed pon, whch corresponds o he sac equlbrum soluon. However, he fxed pon loses sably hrough a Flp-bfurcaon wh sronger deregulaon; numercal smulaons llusrae ha deregulaon may even reduce average employmen. JEL: E1 Correspondng auhor: Ingrd Kubn Unversy of Economcs and Busness Admnsraon VWL7 e-mal: ngrd.kubn@wu-wen.ac.a Augasse 2-6 Tel.: A-1090 Venna, Ausra Fax:

2 1. Inroducon 1 Modern macroeconomc models wh a Keynesan flavor usually nvolve nomnal rgdes n wages and/or commody prces (see Gordon, 1990). A ypcal mcrofoundaon for he laer recurs o he Dx-Sglz model of monopolsc compeon (Dx and Sglz, 1977). Keynesan feaures suded n such models are he possbly of unemploymen (e.g. d Aspremon e al., 1990) and mulple equlbra (e.g. d Aspremon e al., 1995, Lnnemann, 2001) and ha fscal polcy has ncome mulpler effecs (Hejdra and Lghar, 1997; Hejdra e al., 1998; see also Solow, 1998). Blanchard and Kyoak (1987) proposed a prooype macro-model combnng monopolsc compeon n he commody markes wh labor marke mperfecons ha has now become a sandard framework for analyzng unemploymen problems. The wdely used approach of specfyng a wage seng and a prce seng equaon (see e.g. Nckel, 1990; Layard e al., 1991; or Blanchard, 2003; and for emprcal applcaons varous analyses by he European Commsson, e.g. McMorrow and oeger, 2000; Bans e al., 2002) ulmaely ress upon such mcro foundaons. Blanchard and Gavazz (2001) recenly presened a srucural model along hese lnes combng monopolsc compeon wh wage barganng (smlar also Jerger, 2001, n an open economy conex). A characersc resul n hose analyses s ha deregulang he labor markes (.e. reducng he barganng power of workers and/or reducng he unemploymen benefs) and/or deregulang he commody markes (.e. 1 An earler verson of he paper was presened a Workshops n Naples, Ax, Venna and Helsnk. We would lke o hank Ulrch Berger, Peer Flaschel, Leo Kaas, Carlo Panco, Floran Wagener and parcpans of he Workshops for helpful commens. The usual cavea apples. 2

3 reducng he marke power of commody supplers) ncreases equlbrum employmen (see also Gersbach, 1999 and 2000). However, hose models are ypcally sac models, whch do no specfy explcly he economc process n me. In he followng paper, we develop a dynamc macroeconomc model n whch commody markes are characerzed by monopolsc compeon and labor markes by wage barganng. In our analyss, he usual equlbrum soluon s a fxed pon of he dynamc model, whch exhbs he usual comparave sac properes (deregulang he labor and/or he commody marke ncreases employmen). However, dependng upon he parameers he fxed pon may lose sably hrough a Flp-bfurcaon gvng rse o cyclcal soluons and endogenous flucuaons. We show analycally ha commody and labor marke deregulaon may lead o nsably; n numercal smulaons, we even found cases n whch deregulaon leads o lower average employmen. Boh resuls, vald n a dynamc framework, conras wh he usual comparave sac properes. The paper s organzed as follows: In he second secon, we presen our model; s basc srucure closely follows Blanchard and Gavazz (2001). Monopolscally compeve frms bargan wh unons over employmen and nomnal wage raes on he bass of frms ancpaed demand funcons and workers nomnal reservaon wages. In he hrd secon, we explcly add wo dynamc componens. Frs, cenral o monopolsc compeon s ha frms neglec he reacons of oher frms. They herefore base her decsons on a oo hgh ancpaed prce elascy; ousde equlbrum, hey are necessarly surprsed by he marke resuls. As a consequence, hey wll adjus her ancpaed demand funcon over 3

4 me 2. Second, he nomnal reservaon wage also adjuss hrough me on he bass of he realzed employmen and he realzed nomnal wage rae. Whereas for he second process several plausble specfcaons do exs, he specfcaon of he frs one s drecly mpled by he exernal effec a he core of he monopolsc compeon model self. We show ha he frs process leads o dvergng me pahs: whle sll holds ha deregulaon ncreases saonary employmen, leads o fundamenal nsably. In he fourh secon, we sudy wo dfferen specfcaons for he reservaon wage adjusmen, each of whch mrrors a dfferen nsuonal se up. We show analycally ha hs second process may dampen he sharp nsably resul: deregulaon may sll desablze he economy; however, he me pah does no dverge bu s araced o a perod-wo cycle or evenually o a complex me pah. Some smulaons complee he dynamc exploraons. The las secon s lef for concludng remarks. 2. The economc frame work The analyss, beng framed n a dynamc seng, requres dealng explcly wh me. We assume ha durng he me un, whch for exposory purposes we call Week, all evens occur accordng o a well-defned sequence. On Monday of Week, frm and he assocaed unon bargan over employmen and he nomnal wage rae on he bass of frms ancpaed demand and workers nomnal reservaon wage. Producon occurs durng he 2 See Curre and Kubn (2002) for an exploraon of he monopolsc compeon dynamcs. D Aspremon e al. (1995) analyze endogenous flucuaons n wha hey call a Cournoan monopolsc compeon model. In conras o our approach, he dynamcs n her model s drven by an overlappng generaons srucure and varable mark-ups are cenral for he occurrence of endogenous flucuaons. 4

5 Week from Tuesday o Frday. On Frday, commodes are delvered o he marke. Marke equlbrum deermnes he realzed prce. Fnally, on Saurday frms and unons updae he nformaon relevan for decsons n he followng perod concernng he employmen, he nomnal wage rae and he realzed prce. 2.1 Frms and Households The economy comprses a fxed number m of frms, each frm producng one dfferenaed good n a regme of monopolsc compeon; and L households, whch own he exsng frms, each household supplyng one un of labor. Each frm faces a unon composed of M L = members. m All frms share he same producon echnology, whch nvolves only one npu, labor, used n a fxed proporon. Assumng ha durng Week frm employs N workers, he producon of good s: x = f( N ) = N (1) for = 1 m. Followng Blanchard and Gavazz (2001), household j s preferences owards good (for = 1 m and j = 1 L) are represened by a CES uly funcon: 1 m 1 1 U j = m ( c ) (2) = 1 where 1 < < s he elascy of subsuon beween goods and c s he consumpon level of good for he perod. Noe ha he ncluson of he facor 1 m no he uly funcon mples ha he uly level depends only upon he overall consumpon quany and no on he number of dfferen consumpon goods. Ths specfcaon, herefore, does 5

6 no represen a preference for commody varey and s a parameer relaed only o he marke power of a sngle commody suppler (see Blanchard and Kyoak, 1987; and also he dscusson n Benassy, 1996). In Blanchard and Gavazz (2001), s he cenral parameer for sudyng he effecs of commody marke deregulaon. Household j s demand for good s gven by d j Yj p = mp P where Y j s he household j s nomnal ncome and where 1 1 m 1 1 P = ( p ) (3) m = 1 s a prce ndex correspondng o he prce of one un of uly. Summng hrough j, we oban he demand for commody durng Week d Y p = mp P (4) where Y s he overall nomnal ncome of he economy. We neglec he Prce Index Effec and he Ford Effec (see Yang and Hejdra, 1993; Dx and Sglz, 1993; and d Aspremon e al., 1990, 1996); he elascy of demand wh respec o he own prce herefore reduces o. 3 3 Lnnemeer (2001) showed ha boh effecs are a he roo of a possble mulplcy of equlbra. We prefer o demonsrae our resuls n he smples possble framework wh a unque equlbrum. 6

7 If he prce of each good s he same, p = p, he prce ndex becomes P = p and he demand for an ndvdual good smplfes o d Y = (5) mp In ha case, he elascy of demand wh respec o he prce s equal o 1. Movng on o he descrpon of he evens occurrng durng Week, mos of our dscusson wll be devoed o he crucal ones, ha s, he barganng process and he deermnaon of he marke equlbrum. 2.2 Barganng We employ he effcen barganng model (McDonald and Solow, 1983; Layard and Nckell, 1990): Durng he Monday of Week he pares (frm and he assocaed unon) bargan over employmen and he nomnal wage rae for he curren perod on he bass of a known se of daa relang o workers reservaon wage and frm s ancpaed demand funcon. The soluon maxmzes he followng Nash produc Z Z β Π Π β ( ) ( ) 1 (6) where 0 < β < 1 represens he relave barganng power of he unons, Z denoes he value of he unon s objecve funcon f an agreemen s reached and correspondng value for he frm. Z and Π Π he are he respecve values, f no conrac s concluded. We assume a ularan rade unon. Observng ha he CES ndrec uly funcon s gven by he nomnal ncome deflaed by an expeced prce ndex P, he value of he unons objecve funcon s gven by Z 7 ( ) NW + M N W = P (7)

8 where N denoes employmen, W he nomnal wage rae and W he nomnal reservaon wage, whch ndcaes he ncome opporunes expeced o preval ousde he frm under consderaon. Wh Z MW = P, he unon s conrbuon o he Nash bargan s N Z Z W W ( ) = P (8) Turnng now o he frm s conrbuon, we noe ha all profs are dsrbued o he owners households. Therefore, he frms s objecve s also defned n erms of he CES ndrec uly funcon. Wh Π = 0 and usng equaon (1), s hus gven by Π px WN N p W ( ) Π = P = P (9) where p denoes he ancpaed prce for commody. The framework of he Dx- Sglz model of monopolsc compeon suggess ha he ancpaed prce s deermned along he followng lnes. Typcally, each frm assumes ha oher frms wll no reac o s own prce decsons and ha when neglecng he Prce Index effec and he Ford effec he prce elascy of her demand funcon s consan and equal o. Therefore, a frm ha knows sold n he prevous perod a quany d 1 a a prce p 1 wll ancpae s demand funcon for he curren perod o be gven by: ˆ ˆ d ˆ ( ˆ d p ) K = = 1 1 ( p ) ( p ) (10) 8

9 where K s he poson of he ancpaed demand funcon. 4 Usng equaons (1) and (10) we oban he ancpaed prce p as 1 K p = (11) N We assume ha hs s common knowledge o boh barganng pares. Effcen (Nash) barganng beween frm s and he assocaed unon corresponds o choosng N and W so as o maxmze he followng expresson subjec o (11): Π Π ( Z Z ) ( ) = ( W W) ( p W ) N P β 1 β β 1 β (12) Observng ha consonan wh he monopolsc compeon se-up he pares assume he expeced prce ndex P o be ndependen of her decsons, he barganng resuls n: W 1+ β = W 1 (13) 1 M = p = W (14) N = K W 1 (15) Noe he famlar resul from he effcen barganng problem, namely ha a poson s chosen off he prof maxmum. In equaon (14), he margnal revenue s equaed o he 4 In oher words: Frms assume ha hey can sell he same quany a he same prce as n he prevous perod and hey assume ha her quany wll reac o a prce change accordng o an elascy of. 9

10 nomnal reservaon wage and no o he margnal cos (correspondng o he nomnal wage W, rae). I follows ha he prce s se as a mark-up over he reservaon wage, p = ( 1+µ ) where µ 1 ( 1). Followng Blanchard and Gavazz (2001), we nerpre a decrease n he mark-up µ (.e. an ncrease n ) as commody marke deregulaon. I reduces he sze of frm s ancpaed surplus per un of oupu, ( ) p W = µ W. Labor marke deregulaon s refleced n Blanchard and Gavazz (2001) by a decrease n he relave barganng power of he unon, β. As equaon (13) shows, β deermnes he dsrbuon of he ancpaed surplus beween wages and profs. Decreasng β reduces he workers share n he surplus, βµ W. In addon, our model, as developed n he followng secons, allows for labor marke deregulaon n he form of changng he unemploymen nsurance scheme. Ths form of labor marke deregulaon may also mpnge on he barganng oucome (and on he sze of he surplus) hrough s effecs on he nomnal reservaon wage. Noe fnally ha equaons (14) and (15) are no ndependen resuls, equaon (15) can be obaned from equaon (14) by akng consran (11) no accoun. Durng Week, a he end of conracng, frm employs N workers, pays he nomnal wage rae W and ancpaes he prce p. Fgure 1 depcs he barganng equlbrum. Gven he reservaon wage W and he poson of he ancpaed demand funcon K, he bargan deermnes he employmen level N and he wage rae W n frm. Each frm expecs o sell s oupu a an ancpaed prce p. 10

11 2.3 Shor erm commody markes equlbrum The characerscs of he commody markes equlbrum follow from he assumpon ha all frms behave dencally wha Blanchard and Gavazz (2001) call he symmery assumpon. Each frm pays he same wage W = W, hres he same number of workers, N = N, and produce he same quany x = x, whch s equal o her respecve supples s = s = x. They envsage o sell hese quanes a an dencal ancpaed prce p = p. A he end of he producon perod, on Frday, each frm supples s o he (dencal) rue demand funcon d (see Eq. (5)). In conras o he ancpaed demand funcons, he rue demand funcons ake no accoun he reacons of all oher frms; each of hem has an elascy of 1 (nsead of ). Therefore, producers canno realze her prce and quany ancpaons. In he followng we assume ha frms sell he enre quany produced a he marke-clearng prce p ˆ (dfferen from he ancpaed prce) 5. Usng (5), he realzed prce s deermned as: dˆ = s = x = N pˆ Y Y = = (16) mx mn Fgure 2 depcs he shor run commody markes equlbrum. 5 In prncple, producers as monopolss can also decde o sell a smaller quany han he produced one when enerng he marke. However, hey do no have an ncenve o do so: On he bass of an elascy of demand greaer (ancpaed demand) or equal o 1 (rue demand) n absolue erms, revenues do no ncrease wh a quany resrcon. In addon, a ha momen, producon coss are already sunk and maxmzng revenues also maxmzes profs. Therefore, quany resrcons canno ncrease profs. Curre and Kubn (2002) also explore an alernave quany raonng scheme. 11

12 A ha pon n he paper, mgh be worhwhle o race explcly he money crcu correspondng o he marke ransacons descrbed so far. The quany of money, denoed by Q, s assumed o be gven and money s only used as a means of ransacon. On Monday mornng, he households n her qualy of frms owners hold he enre quany of money. A he concluson of he barganng process, frms borrow par of o pay he workers wages. If any ax s leved o fnance an unemploymen benef, par of he quany of money s redsrbued o he unemployed. On Frday mornng, he enre quany of money s n he hand of he households n he form of wages, unemploymen benefs and money holdngs. On Frday, he households consumpon demand s deermned under a cash n advance consran. Marke prces are herefore deermned as pˆ Q Q = = ;.e. by he mx mn pure quany heory of money. Frms receve as revenue he enre quany of money, whch hey redsrbue oally o households as realzed profs, gven by he dfference beween revenues and wage paymens, and as deb repaymens correspondng o he wages pad n advance. 6 Therefore, oal realzed nomnal ncome Y as he sum of nomnal wage paymens and realzed nomnal profs s always equal o he quany of money Q; he cash n advance consran concdes wh an ncome consran n he consumer maxmzaon problem. From now on, we ake he quany of money and hus he nomnal ncome as numérare. Fnally, on Saurday frms and unons updae her nformaon. The poson of frm s ancpaed demand curve changes on accoun of he realzed prce p ˆ and he realzed demand d ˆ. Inserng hs nformaon n equaon (10) deermnes he poson of he ancpaed demand for he perod +1: 6 In order o keep our analyss smple, we assume no neres paymens. 12

13 K ˆ ˆ 1 dp + = (17) Smlarly, workers reservaon wage adjuss n he lgh of he realzed nomnal wage W and of he realzed employmen N. 3. The dynamc sysem 3.1. Oulne The dynamc behavor of he model, herefore, nvolves wo processes. Frs, snce producers do no know he rue elascy of he demand funcon, he poson of he ancpaed demand funcon (and hus of he ancpaed margnal revenue) shfs over me. For a gven nomnal reservaon wage and margnal revenue curve, he effcen barganng oucome, M = W, deermnes employmen. Snce all frms are dencal, equaon (15) can be wren as: m e = K W L 1 (18) where e mn = denoes he employmen rae. Takng no accoun equaons (16) and (17), L can also be wren as Y 1 1 ( ) e = e W L 1 (19) Second, he nomnal reservaon wage, W, s also adjused over me. For exposory purposes, n wha follows we begn our sudy wh he dynamcs of he frs process n solaon by assumng a nomnal reservaon wage nvaran over me. Afer ha 13

14 we specfy he adjusmen of he reservaon wage explcly and explore he dynamc properes of he full sysem Commody marke dynamcs n solaon If we assume a reservaon wage fxed a an arbrarly chosen level, dynamc process s W = W, he mpled Y 1 1 ( ) e = e W L 1 (20) Equaon (20) s a one-dmensonal frs-reurn map wh he followng fxed pon and frs dervave e Y = L 1 1 ( W ) 1 (21) FP e Y = ( ) ( 1 ) 1 = 1 1 W e e L 1 (22) As long as > 1, he fxed pon, gven by equaon (21), ncreases wh, e e = > 0, bu loses sably a = 2. Eq. (22) shows ha he dervave of he ( 1) frs reurn map s negave for all values of he employmen rae; herefore, he me pah dverges for > 2. Deregulang he commody marke ncreases he saonary employmen bu may evenually lead o nsably. Fgure 3 llusraes he perod 2 cycle occurrng precsely a = 2. The employmen rae alernaes beween e 1 and e 2 ; he ancpaed demand and ancpaed margnal revenue funcons shf accordngly. Sarng wh he ancpaed demand funcon 1 and he correspondng ancpaed margnal revenue funcon 1 he barganng process resuls n he hgher employmen rae e 1. The realzed marke prce s below he ancpaed one. The 14

15 ancpaed demand and margnal revenue curves shf downward o he poson 2. The nex barganng resuls n he lower employmen rae e 2. The marke prce s now above he ancpaed one nducng an upward shf of he ancpaed demand and margnal revenue back o her respecve poson The nomnal reservaon wage as a funcon of he employmen rae Nex, we nroduce a posve dependence on he employmen rae of he nomnal reservaon wage, W = W( e 1 ): A hgher employmen rae s consdered o ncrease he expeced employmen probables ousde he frm under consderaon and hus o ncrease he reservaon wage. As a consequence, he adjusmen of he nomnal reservaon wage affecs he commody marke dynamcs. The resulng dynamc sysem s sll onedmensonal: Y ( ( )) e = e W e L 1 (23) The fxed pon s 1 Y e = W e L 1 ( ( )) 1 (24) Noe ha rsng sll ncreases he equlbrum employmen rae e e e W = 1 + > 0 ( 1) W e The frs dervave of (23) s 1 e Y Y 1 W = ( W) (1 ) e 1 + e 1 ( )( W) e L 1 L 1 e 1 1 FP e W = 1 W ( e) e 1 (25) 15

16 The fxed pon now loses sably a < 2; beyond ha value he me pah dverges. Therefore, a posve nfluence of he employmen rae on he nomnal reservaon wage desablzes he economy. 7 Fgure 3 also llusraes hs desablzng effec. Sar from he marke resul 1 and consder he deermnaon of poson 2. The ancpaed demand funcon and he ancpaed margnal revenue shf agan owards her poson 2; bu now, n addon, he nomnal reservaon wage s ncreased because of he hgh realzed employmen rae e 1. Therefore, he new employmen rae 2 wll be below e 2 n Fgure 3. The ncrease n he nomnal reservaon wage hus ncreases he flucuaons. The process s desablzed The nomnal reservaon wage as a funcon of he employmen rae and of s lagged value Fnally we allow also for a posve nfluence of he lagged reservaon wage upon s curren value: (, 1 1 ) W = W e W (26) For he momen 8, we assume he funcon W () o be monooncally ncreasng n boh argumens. The raonale for he dependence of he nomnal reservaon wage on he employmen rae s as skeched above; for he second one runs along he followng lnes: 7 Blanchard and Gavazz (2001) consder he real reservaon wage o be an mplc funcon of he employmen rae. However, s no possble o assess he sably properes of her model whou specfyng a relaonshp beween he reservaon wage and he employmen rae. In wha follows we pu forward such a specfcaon. 8 Bu see below he dscusson n secon

17 a hgh reservaon wage n -1 wll resul n a hgh barganed nomnal wage rae n -1, whch n urn s expeced o rase he nomnal reservaon wage n. The cenral dynamc sysem s now wo-dmensonal and gven by equaons (19) and (26). In he fxed pon he followng holds e Y = L 1 1 ( W ) 1 (27) W ( ew, ) = θ (28) The Jacoban evaluaed a he fxed pon s gven by J e W e W 1 1 W e 1 W W = E W W 1 e 1 W (29) The race and he deermnan are e W W r J E = 1 + W e W 1 1 (30) W de J E = (1 ) W 1 (31) Fgure 3 can be used o llusrae ha he addonal effec nroduced by equaon (26) s poenally sablzng. Sar agan wh he marke poson realzed n perod 1 and consder he deermnaon of he poson 2. The ancpaed demand funcon and he ancpaed margnal revenue shf o her respecve poson 2. Two facors change he nomnal reservaon wage. As n he prevous case, he hgh employmen rae e 1 ends o ncrease. A he same me, he hgh employmen rae e 1 mples ha he barganed nomnal wage n 17

18 perod 1 was comparavely low. Ths would reduce he nomnal reservaon wage, hus nroducng a sablzng elemen. Whou specfyng explcly he dynamc adjusmen process for he nomnal reservaon wage, s dffcul o assess he sably properes. We provde such a specfcaon n he followng secon and explore he dynamcs of he full model. 4. Fully specfed dynamcs and numercal smulaons 4.1. The dynamc adjusmen process for he nomnal reservaon wage The reservaon wage n he barganng process represens he ncome expeced by he rade unon for members who do no fnd employmen n he frm under consderaon (see Layard and Nckel, 1990). I herefore depends on he expeced probably of fndng employmen n oher frms, on he wage rae expeced o be pad by oher frms and on he unemploymen benef B. 9 Consonan wh he monopolsc compeon se up, we assume 9 We dd no ncorporae explcly he fnancng of he unemploymen benef. However, we suded he case of fnancng ou of a general labor ncome ax ha apples boh o workers and unemployed (smlar o Calmfors and Johansson, 2001): Equ. (12) would be modfed o β ( Z Z ) ( Π Π ) = ( 1 τ )( W W) ( p W ) N P. β 1 β 1 β where τ denoes he ancpaed ax rae, wh τ = τ 1, and where Z and Z are now ne of axaon. On Tuesday, he ax rae s adjused o mach he benef paymens requred by WN WeL B e L and money holdngs he realzed unemploymen: τ = τ = ( 1 τ) ( 1 ) are redsrbued accordngly. The barganng resuls and he followng analyss are no changed by hs exenson. 18

19 ha he rade unons do no ake no consderaon reacons of oher frms and he mpac of her own decsons on he aggregae varables. The expeced probably of fndng employmen n oher frms and he expeced wage rae ousde he frm under consderaon s herefore gven by he respecve values realzed n he prevous perod. W = e W + (1 e ) B (32) or usng equaon (13) + β 1 W = e W + ( 1 e ) B (33) For he unemploymen benef we consder wo dfferen specfcaons (see e.g. Layard e al., 1991, and Pssardes, 1998) mrrorng wo possble nsuonal se-ups. The frs s close o a socal asssance scheme accordng o whch he compensaon for he unemployed s fxed n real erms (correspondng o a ceran CES uly level ω ) and he nomnal paymen s adjused each perod o he realzed prce, B ˆ = ω p 1. In he second, he compensaon for he unemployed worker corresponds o a fracon of he nomnal wage rae she was recevng n he prevous perod, B = φw 1, where 0 < φ < 1 s he replacemen rao. The unemploymen benef sysems n he OECD counres are found n beween hose wo exreme cases (see Goerke, 2000). Such specfcaons wll allow us o clarfy he role of changes n parameers, whch relae o he unemploymen benef, as measures of (de)regulaon n he labor marke. 4.2 Unemploymen benef fxed n real erms We consder frs he nsuonal se up for he unemploymen benef close o a socal asssance sysem. The real unemploymen benef corresponds o a CES uly level of ω, s nomnal counerpar s gven by B = ω ˆ p 1. The dynamc sysem s 19

20 Y 1 1 e = e W L 1 (34) 1+ β W = e W + e 1 ( 1 ) Y Le 1 ω (35) A crucal feaure of hs specfcaon s ha he realzed marke poson mpacs on he dynamcs boh hrough shfs of he demand funcon, mplc n equaon (34), and hrough he deermnaon of he nomnal reservaon wage, as shown n equaon (35). The fxed pon, he paral dervaves, he race and deermnan are gven by 1 ω Y 1 e = and W = 1+ β ω el (36) FP W 1+ β Y 1 W 1 and + = = β > 0 e L e W 1 FP W ω e (37) rje = 1 + ω ( 1+ β) e deje = ( 1+ β) e 1 (38) Noe ha n conras o he assumpon n secons 3.3 and 3.4 he paral dervave W e 1 need no be posve snce wh he assumed specfcaon a hgh employmen rae n perod -1 no only means a hgh expeced re-employmen probably n perod bu also va a low realzed prce n -1 a low nomnal unemploymen benef n. The laer ndrec effec of he employmen rae on he nomnal reservaon wage was negleced n he prevous secons. Appendx 1 nvesgaes analycally he properes of he dynamc sysem (34)-(35). I s shown ha he fxed pon exhbs he usual comparave sac resuls: Commody and labor marke deregulaon as refleced n a hgher value of and n lower values of β and ω, respecvely engender a hgher employmen rae. The analyss furher shows ha he 20

21 fxed pon s only sable for low values of and for hgh values of β and ω. However, n conras o he one-dmensonal models suded prevously, he sably loss now occurs hrough a Flp bfurcaon gvng rse o aracng cycles and evenually o chaoc flucuaons. Therefore, commody and labor marke deregulaon hough expeced o ncrease he saonary employmen rae may desablze he economy, bu does no lead o dvergng me pahs. So far, we have explored analycally he dynamcs properes of he sysem (34)-(35). We now urn o a small calbraon exercse. Noe ha he fxed pon soluons and he sably properes only depend upon hree parameers: he parameer reflecng he degree of monopoly power n he commody markes, or µ; and he wo parameers relaed o he exen of labor marke regulaon, namely he barganng power of rade unons β and he parameer concernng he specfcaon of he real unemploymen benef ω. These parameers are subjec o he followng boundares: 0 < β < 1, 0 < ω < w and 1 <, where w 1 = represens he saonary real reservaon wage. Choosng an upper lm for herefore allows sudyng he enre parameer space numercally. In our exercse, we assumed 5 (or µ 0.25 ). We searched numercally for values of β, ω and such ha he fxed pon approxmaes wo macroeconomc sylzed facs; namely ha n 1990s Connenal Europe he employmen rae ypcally assumes values above 0.8 and ha he wage share ypcally assumes values slghly below In addon, we ask whch dynamc properes he me 10 Takng he average over a sgnfcan group of European Counres, Gammarol e al. (2002) esmae ha n he 1990s he labor share was n he Busness secor, 0.58 n Indusry and n he Tradable Servces. 21

22 pah exhbs close o ha fxed pon. Our numercal exploraon shows ha parameer consellaons exs whch resul n plausble fxed pons, whch are sable for hghly regulaed markes and whch lose sably wh commody or labor marke deregulaon. The resulng flucuaons are relavely small, whch conrbues o he plausbly of he resuls. As an llusraon, Fgure 4 shows he me pahs for he employmen rae e + 1 and W+ 1e+ 1L he wage share w + 1 = for ω = and = Wh hese parameer values, Y he bfurcaon value relang o he barganng power of workers s β bf For β = 0.02 fxed pon s sable; for β = 0.01 s unsable. The resulng perod-wo me pahs exhb flucuaons wh comparavely small ampludes, hng no boundary condon. Fgure 4 also shows ha on a perod wo cycle boh he upper and he lower values for he employmen rae may le below s equlbrum value; average employmen raes over he cycle may be lower han s saonary counerpars. The ndrec effec of he employmen rae on he nomnal reservaon wage s n hs case sronger han he drec one and causes a declne n average employmen. Ths resul s n sark conras o he convenonal comparave sac analyss Furher smulaons wh dfferen values for show ha commody marke deregulaon may also reduce average employmen raes below her equlbrum values. In addon, n ha case average employmen raes may even declne wh ncreased commody marke deregulaon. A smlar resul emerges wh deregulang labor marke va reducng unemploymen benefs. 22

23 4.3. The unemploymen benef as a fxed proporon of he nomnal wage rae We now consder anoher nsuonal se up accordng o whch he unemploymen benef s a fxed replacemen rao φ of he nomnal wage rae earned n he los job, B = φw 1. The sysem (19) and (33) can be wren as Y 1 1 e = e W L 1 (39) 1+ β 1+ β W = e W + ( 1 e ) φ W (40) Noe ha he analycal srucure of hs specfcaon s smpler han he prevous one gven ha he realzed marke poson only affecs he dynamcs hrough shfs of he demand funcon as shown n equaon (39). The fxed pon, he paral dervaves, he race and he deermnan are gven by ( 1)(1 φ) φβ Y 1 e = and W = ( 1 + β)(1 φ) el (41) FP W 1+ β W = W(1 φ) > 0 and = 1 e 1 W 1 FP 1 (42) rje = 2(1 ) + 1+ β φ de E = 1 1 ( ) J ( ) (43) The major conclusons from he prevous case carry over: As s shown n Appendx 2, deregulaon n he labor or he commody marke ncreases he saonary employmen rae, bu may evenually lead o a Flp bfurcaon of he fxed pon gvng rse o aracng perod wo cycles. Therefore, he basc rade off remans presen: Deregulaon ncreases employmen raes bu may desablze he economy. Compuer smulaons (no presened here) show ha n hs case s more dffcul o fnd plausble parameer values for sable equlbrum pons. We have been able o denfy 23

24 sable wo-cycles. The amplude of he cyclcal me pah, however, s much hgher han n he prevous case, and he employmen rae hs que ofen s upper boundary of one. 12 In he unsable regon, furher deregulaon usually ncreases average employmen raes even above her correspondng equlbrum values. 5. Concluson In he prevous paper, we have analyzed he dynamcs of a model followng closely he prooype specfcaon pu forward by Blanchard and Gavazz (2001) whch combnes monopolsc compeon n he commody marke and effcen barganng n he labor marke. The dynamcs resuls from wo sources: Frs, nheren o monopolsc compeon s ha each sngle suppler overesmaes he prce-elascy of hs demand funcon; each sngle suppler s herefore necessarly surprsed by he marke oucome and wll adap hs ancpaed demand funcon accordngly. Second, effcen barganng processes are based on a reservaon wage ndcang he expeced ncome ousde he frm under consderaon. Ths ancpaon s also adjused n he lgh of realzed marke resuls. Whle he second process may be specfed n varous forms, he frs one s drecly mpled by he exernal effec a he core of he monopolsc compeon model self. I s dffcul o magne fundamenally dfferen specfcaons whou leavng he assumed marke srucure. We showed n he paper, ha he frs process desablzes he economy: Deregulaon does ncrease he saonary employmen rae, bu engenders dvergng me pahs. Inroducng varous plausble specfcaons for he adjusmen process of he 12 We found n compuer smulaons he nsably problem o be less severe wh adapve expecaons, whch dampen he flucuaons of he ancpaed demand funcon. 24

25 reservaon wage dampens hs sharp resul: The sably loss occurs hrough a Flp bfurcaon gvng rse no o dvergng me pahs bu o aracng perod-wo cycles and evenually o complex me pahs. However, he basc rade-off remans: Deregulaon ncreases he saonary employmen bu may lead o nsably wh me pahs exhbng n some cases even lower average employmen raes. eferences: Bans, M. and A. Derx, K. Pchlmann, W. oeger, 2002, Srucural reforms n labour and produc markes and macroeconomc performance n he EU, The EU Economy: 2002 evew, Chaper 2. Benassy, J.-P., 1996, Tase for varey and opmum producon paerns n monopolsc compeon, Economc Leers 52, Blanchard, O. and F. Gavazz, 2001, Macroeconomc effecs of regulaon and deregulaon n goods and labor marke, NBE-Workng Paper Blanchard, O. and N. Kyoak, 1987, Monopolsc Compeon and he Effecs of Aggregae Demand, The Amercan Economc evew 77, Blanchard, O., 2003, Macroeconomcs (Prence Hall). Calmfors, L. and A. Johansson, 2001, Unemploymen benefs conrac lengh and nomnal wage flexbly, CESIfo Workng Paper 514. Curre, M. and I. Kubn, 2002, Complex Dynamcs and Monopolsc Compeon, Beräge zur Wrschafsforschung 02-01, Johannes Guenberg-Unversä Manz, Fachberech echs- und Wrschafswssenschafen. D Aspremon, C. and. Ferrera dos Sanos, L. Gérard-Vare, 1990, On monopolsc compeon and nvolunary unemploymen, Quarerly Journal of Economcs 105, D Aspremon, C. and. Ferrera dos Sanos, L. Gérard-Vare, 1995, Marke power, coordnaon falures and endogenous flucuaons, n: H. Dxon and N. ankn, The new 25

26 macroeconomcs: mperfec markes and polcy effecveness (Cambrdge Unversy Press, Cambrdge) D Aspremon, C. and. Ferrera dos Sanos, L. Gérard-Vare, 1996, On he Dx-Sglz Model of Monopolsc Compeon, The Amercan Economc evew 86, Dx, A. and J. Sglz, 1977, Monopolsc Compeon and Opmum Produc Dversy, The Amercan Economc evew 67, Dx, A. and J. Sglz, 1993, Monopolsc Compeon and Opmum Produc Dversy: eply, The Amercan Economc evew 83, Gersbach, H., 1999, Produc Marke Compeon, Unemploymen and Income Dspares, Welwrschaflches Archv 135, Gersbach, H., 2000, Promong Produc Marke Compeon o educe Unemploymen n Europe: An Alernave Approach?, Kyklos 53, Gammarol, N. and J. Messna, T. Senberger, C. Srozz, 2002, European Labor Share Dynamcs: An Insuonal Perspecve, European Unversy Insue, Workng Paper Eco Goerke, L., 2000, The Wedge, The Mancheser School 68, Gordon,., 1990, Wha s New-Keynesan Economcs?, Journal of Economc Leraure 28, Hejdra, B. and J. Lghar, 1997, Keynesan Mulplers, Drec Crowdng Ou, and he Opmal Provson of Publc Goods, Journal of Macroeconomcs 19, Hejdra, B. and J. Lghar, F. van der Ploeg, 1998, Fscal polcy, dsoronary axaon, and drec crowdng ou under monopolsc compeon, Oxford Economc Papers 50, Jerger, J., 2001, Globalzaon, Wage Seng and he Welfare Sae, Journal of Polcy Modellng 23. Layard,. and S. Nckell, 1990, Is unemploymen lower f unons bargan over employmen?, The Quarerly Journal of Economcs 105, Layard,. and S. Nckell,. Jackman, 1991, Unemploymen (Oxford Unversy Press, Oxford). 26

27 Lnnemann, L., 2001, The Prce Index Effec, Enry, and Endogenous Markups n a Macroeconomc Model of Monopolsc Compeon, Journal of Macroeconomcs 23, McDonald, I. and. Solow, 1983, Wage Barganng and Employmen, Amercan Economc evew LXXIII, McMorrow, K. and W. oeger, 2000, Tme - Varyng Naru / Naru Esmaes for he EU s Member Saes, ECFIN - Economc Papers 145. Nckel, S., 1990, Unemploymen: A Survey, The Economc Journal 100, Pssardes, C., 1998, The mpac of employmen ax cus on unemploymen and wages; The role of unemploymen benefs and ax srucure, European Economc evew 42, Solow,., 1999, Monopolsc Compeon and Macroeconomc Theory (Cambrdge Unversy Press, Cambrdge). Yang, X. and B. Hejdra, 1993, Monopolsc Compeon and Opmum Produc Dversy: Commen, The Amercan Economc evew 83,

28 Appendx 1 In hs appendx we sudy he dynamc sysem relaed o he case n whch he employmen benef s fxed n real erms and s nomnal counerpar s adjused o he realzed prce, B = ω pˆ. The dynamc sysem s 1 Y 1 1 e = e W L 1 (A1.1) W 1+ β 1 e = e W e 1 Y ω L (A1.2) A1.1 Fxed pon and comparave sacs The saonary real reservaon wage and he saonary real wage are 1 1+ β w = w = (A1.3) I follows ha w ω Y 1 Y e = W = p= w ω el el (A1.4) Noe ha f condon ω < w (A1.5) holds and β > 0, hen w < w and 0< e < 1. Noe ha he saonary real reservaon wage depends only on whereas he saonary real wage rae depends on β and and he saonary employmen rae depends on ω, β and. We have 28

29 ( ) ( ) + w w ( w ) 2 e β ω 1 β ( ω) = ω > 0 W Y e w 1 β w 1 = 2 ( 1) = > 0 = > e Le (A1.6) (A1.7) W e e wh ( < 0) for ( > ) ( 1) The mpac of changes n β s gven by e w ω = < β ( w ω) 2 0 (A1.8) W 1 Y e w 1 = = > 0 2 β Le β β (A1.9) The mpac of changes n ω s gven by e β 1 = < 0 2 ω ( w ω) (A1.10) W 1 Y e = > 0 2 ω Le ω (A1.11) A1.2 Bfurcaon analyss The Jacoban evaluaed a he fxed pon s J E 2 + β 1 Y e + β 1 1 e ω 1 LeW W 1 = + β 1 Y + β 1 W ω e 2 1 Le 1 Deermnan and Trace are: ( β ) dej = + 1 e (A1.12) E 29

30 w ω rje = 1 ( + β 1) e+ w (A1.13) wh < dej E < 0and < rj E < 1. The volaon of one of he followng condons would nvolve nsably for he sysem (n brackes he ype of bfurcaon nvolved): () J ( β) 1 de = e > 0 (Hopf bfurcaon); E w ω () 1 rje + deje = > 0 w (Saddle node bfurcaon); w ω 1+ rje + deje = e > 0 w () ( β) (Flp bfurcaon). Condons () and () always hold as long as > 1 and only possble. Condon () corresponds o w > ω. The Flp bfurcaon s he [(3 2) ω + (4 3 ) w] βw ( 1)( w ω)(3 [ 4) w ω ] [( 1)( w ω) + βw] w > 0 (A1.14) In hs condon for sably, he denomnaor s always posve. Therefore, he sysem s sable for [(3 2) ω+ (4 3 ) w ] βw > ( 1)( w ω)(3 [ 4) w ω ] We may dsngush hree cases dependng on. Case 1: 4 <. The sably condon s sasfed for all oher parameer values: 3 Case 2: 4 < 2 3 <. The sably of he sysem depends upon he parameer values. There are hree sub-cases ha we have o ake no accoun dependng on ω: 30

31 Case 2a: 3 4 ω < 3 2 w. I follows ( ) w ( ) 3 4 > 3 2 ω > 2ω. In hs case, he sably condon s never sasfed. Case 2b: w ω 4 < < w. The sysem s sable for 3 2 β bf ( 1)( w ω)[(3 4) w ω] > β = > 0 [(3 2) ω + (4 3 ) w ] w (A1.15) If β falls below hs value, he sysem loses sably hrough a Flp bfurcaon. Case 2c: w 4 < w < ω < w. The sysem s sable for 3 2 β bf ( 1)( w ω)[(3 4) w ω ] > 0 > β = [(3 2) ω + (4 3 ) w ] w Tha s, he sysem s always sable. Case 3: 2 <. As for Case 2, he sably of he sysem depends upon he parameer values. Dependng on ω we may denfy wo sub-cases: Case 3a: 3 4 ω < w. As n Case 2a, he sably condon s never sasfed. 3 2 Case 3b: w ω 4 < < w < w. As n Case 2b, he sysem s sable for 3 2 β bf ( 1)( w ω)[(3 4) w ω] > β = > 0 [(3 2) ω + (4 3 ) w ] w (A1.16) If β falls below hs value, he sysem loses sably hrough a Flp-bfurcaon. 31

32 Appendx 2 In hs appendx we examne some of he properes of he dynamc sysem relaed o he case n whch he employmen benef s a proporon of he nomnal wage rae earned n he los job, B = φw 1. The dynamc sysem s Y 1 1 e = e W L 1 (A2.1) 1+ β W = [ 1 (1 φ)(1 e 1) ] W 1 1 (A2.2) A2.1 Fxed pon and comparave sacs From (40) and (39), we solve for he saonary employmen rae and reservaon wage e ( 1)(1 φ) φβ = ( 1 + β)(1 φ) (A2.3) W 1 Y = (A2.4) el Noe ha f condon ( 1)(1 φ) φβ > 0 (A2.5) holds and β > 0, hen 0< e < 1. The saonary prce s Y p = and he saonary nomnal wage s el 1+ β W = W. I 1 follows ha he saonary real wage and he saonary real reservaon wage are dencal o he prevous case: 1+ β 1 w= w = (A2.6) 32

33 From (A2.3), he saonary employmen rae depends on φ, β and. The comparave sacs of he saonary sae nvolves: e β = > ( 1 + β)(1 φ) 2 0 (A2.7) W 1 2 ( 1) Y e w β w = = > = > e L ( e ) (A2.8) W e e wh ( < )0 for ( > ) ( 1) The mpac of changes of β s gven by e 1 = < 0 2 β ( 1 + β)(1 φ) (A2.9) W 1 Y e w 1 = > 0 = > 0 2 β Le β β (A2.10) The mpac of changes of φ s gven by e β = < φ ( 1 + β)(1 φ) 2 0 (A2.11) W 1 Y e = > 0 2 φ Le φ (A2.12) A2.2 Bfurcaon analyss The Jacoban evaluaed a he fxed pon s J E 1+ β e 1 (1 φ) e 1 W = 1 + β ( 1 φ ) W

34 Deermnan and Trace are: dej = 1 (A2.13) E rj E = 2(1 ) + ( 1+ β) φ 1 (A2.14) wh < dej E < 0. The volaon of one of he followng condons would nvolve nsably for he sysem (n brackes he ype of bfurcaon nvolved): () 1 dej = > 0 (Hopf bfurcaon); E 1 r E + de E = ( 1)(1 ) > 0 1 () J J [ φ φβ ] 1+ r E + de E = 1+ 3(1 ) + 1+ β φ > 0 1 () J J ( ) (Saddle node bfurcaon); (Flp bfurcaon). Condons () and () always hold as long as condon (A2.5) holds. The Flp bfurcaon s he only possble. Condon () corresponds o [ ] 2 (3 φ ) 7 (1 βφ ) < (A2.15) If condon (A2.15) s no sasfed, he sysem loses sably hrough a Flp-bfurcaon. Defne ha value of correspondng o he hghes roo ha sasfes condon (A2.15) wh an equaly sgn as z( φ, β) = (1 ) (1 ) + 2(1+ 7 ) βφ β φ βφ 2(3 φ) (A2.16) The sysem s sable for φ > φbf 1+ β 34

35 ( ) 3 φ 4 1 β > βbf φ < bf where bf = z(φ, β) for 0 < β < 1 and 0 < φ < 1. Noe fnally ha 0 < φ bf < 1, ff z(0, β) < < z(1, β) and 0 < β bf < 1 ff z(φ, 0) < < z(φ, 1); and ha z(0, β) = < bf < + 17 = z(1,1)

36 36

37 37

38 38

39 39