macro Road map to this lecture Objectives Aggregate Supply and the Phillips Curve Three models of aggregate supply W = ω P The sticky-wage model

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Prudence McGee
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Road map to this lctur macro Aggrgat Supply ad th Phillips Curv W rlax th assumptio that th aggrgat supply curv is vrtical A vrsio of th aggrgat supply i trms of iflatio (rathr tha th pric lvl is

1 Road map to this lctur macro Aggrgat Supply ad th Phillips Curv W rlax th assumptio that th aggrgat supply curv is vrtical A vrsio of th aggrgat supply i trms of iflatio (rathr tha th pric lvl is calld th Phillips curv W prst a mor modr viw of th IS- LM modl i trms of iflatio ad itrst rats closr to currt dbats about motary policy slid Objctivs Goal: dtrmi th positio ad slop of th AS curv Togthr with our modls for th AD curv w ca complt th AD-AS aalysis Th AS will b a middl stp toward drivig th Phillips curv: = - β (u u + ν Thr modls of aggrgat supply. Th sticky-wag modl 2. Th imprfct-iformatio modl 3. Th sticky-pric modl All thr modls imply: = + α ( P P agg. output atural rat of output a positiv paramtr th actual pric lvl th xpctd pric lvl slid 2 slid 3 Th sticky-wag modl Assums that firms ad workrs gotiat cotracts ad fix th omial wag bfor thy kow what th pric lvl will tur out to b. Th omial wag thy st is th product of a targt ral wag ad th xpctd pric lvl: W = ω P W P = ω P P Targt ral wag Th sticky-wag modl If it turs out that P = P P > P P < P W P = ω P P th umploymt ad output ar at thir atural rats Ral wag is lss tha its targt, so firms hir mor workrs ad output riss abov its atural rat Ral wag xcds its targt, so firms hir fwr workrs ad output falls blow its atural rat slid 4 slid 5

2 Ral wag, W/P W/P W/P 2 L 5 L d (W/P rducs th ral wag for a giv omial wag,.. (a Labor Dmad L L 2 Labor, L Icom, output, output, which raiss mploymt,.. Pric lvl, P. A icras i th pric lvl.. (b Productio Fuctio 2 P 2 P L L 2 (c Aggrgat Supply ad icom. 5 F(L 5 a (P 2 P Labor, L 6. Th aggrgat supply curv summarizs ths chags. Icom, output, slid 6 Th sticky-wag modl Implis that th ral wag should b coutrcyclical, it should mov i th opposit dirctio as output ovr th cours of busiss cycls: I booms, wh P typically riss, th ral wag should fall. I rcssios, wh P typically falls, th ral wag should ris. This prdictio dos ot com tru i th ral world: slid 7 Th cyclical bhavior of th ral wag Prctag chag i ral wag Prctag chag i ral GD slid 8 Th imprfct-iformatio iformatio modl Assumptios: all wags ad prics prfctly flxibl, all markts clar ach supplir producs o good, cosums may goods ach supplir kows th omial pric of th good sh producs, but dos ot kow th ovrall pric lvl slid 9 Th imprfct-iformatio iformatio modl Supply of ach good dpds o its rlativ pric: th omial pric of th good dividd by th ovrall pric lvl. Supplir dos t kow pric lvl at th tim sh maks hr productio dcisio, so uss th xpctd pric lvl, P. Suppos P riss but P dos ot. Th supplir thiks hr rlativ pric has ris, so sh producs mor. With may producrs thikig this way, will ris whvr P riss abov P. Th sticky-pric modl Rasos for sticky prics: log-trm cotracts btw firms ad customrs mu costs firms do ot wish to aoy customrs with frqut pric chags Assumptio: Firms st thir ow prics (.g. as i moopolistic comptitio slid 0 slid 2

3 Th sticky-pric modl A idividual firm s dsird pric is p = P + a ( whr a > 0. Suppos two typs of firms: firms with flxibl prics, st prics as abov firms with sticky prics, must st thir pric bfor thy kow how P ad will tur out: p = P + a ( Th sticky-pric modl p = P + a ( Assum sticky pric firms xpct that output will qual its atural rat. Th, p = P To driv th aggrgat supply curv, w first fid a xprssio for th ovrall pric lvl. Lt s dot th fractio of firms with sticky prics. Th, w ca writ th ovrall pric lvl as slid 2 slid 3 Th sticky-pric modl P = s P + ( s[ P + a( ] pric st by sticky pric firms Subtract ( s P from both sids: sp = s P + ( s [ a( ] Divid both sids by s : pric st by flxibl pric firms ( s a P = P + ( s slid 4 Th sticky-pric modl ( s a P = P + ( s High P High P If firms xpct high prics, th firms who must st prics i advac will st thm high. Othr firms rspod by sttig high prics. High High P Wh icom is high, th dmad for goods is high. Firms with flxibl prics st high prics. Th gratr th fractio of flxibl pric firms, th smallr is s ad th biggr is th ffct of o P. slid 5 Th sticky-pric modl ( s a P = P + ( s Fially, driv AS quatio by solvig for : = + α ( P P, whr s α = ( s a Th sticky-pric modl I cotrast to th sticky-wag modl, th stickypric modl implis a pro-cyclical ral wag: Suppos aggrgat output/icom falls. Th, Firms s a fall i dmad for thir products. Firms with sticky prics rduc productio, ad hc rduc thir dmad for labor. Th lftward shift i labor dmad causs th ral wag to fall. slid 6 slid 7 3

4 P > P P = P P < P P Summary & implicatios LRAS = + α ( P P SRAS Each of th thr modls of agg. supply imply th rlatioship summarizd by th SRAS curv & quatio slid 8 Suppos a positiv AD shock movs output abov its atural rat ad P abov th lvl popl had xpctd. Summary & implicatios Ovr tim, P riss, SRAS shifts up, P = P = P 2 ad output rturs to its atural rat. SRAS quatio: = + α ( P P P = P P 3 3 P 2 LRAS = = 3 SRAS 2 2 SRAS AD 2 AD slid 9 Iflatio, Umploymt, ad th Phillips Curv Th Phillips curv stats that dpds o xpctd iflatio, cyclical umploymt: th dviatio of th actual rat of umploymt from th atural rat supply shocks, ν = β( u u + ν whr β > 0 is a xogous costat. Drivig th Phillips Curv from SRAS ( = + α ( P P (2 P = P + ( α ( (3 P = P + ( α ( + ν (4 ( P P = ( P P + ( α ( + ν (5 = + ( α( + ν (6 ( α( = β( u u (7 = β( u u + ν slid 20 slid 2 Thr Facs of Aggrgat Supply Th Phillips Curv ad SRAS SRAS: = + α ( P P Phillips curv: = β( u u + ν SRAS curv: output is rlatd to uxpctd movmts i th pric lvl Phillips curv: umploymt is rlatd to uxpctd movmts i th iflatio rat slid 22 slid 23 4

5 Th Phillips Curv Th slop of th Phillips curv dpds o how sticky prics ad wags ar th stickir ar wags ad prics, th smallr is paramtr β, ad th flattr is th Phillips curv Wh th Phillips curv is flat, v larg chags i th umploymt rat hav littl ffct o th pric lvl Adaptiv xpctatios Adaptiv xpctatios: a approach that assums popl form thir xpctatios of futur iflatio basd o rctly obsrvd iflatio. A simpl xampl: Expctd iflatio = last yar s actual iflatio Th, th P.C. bcoms = β( u u + ν = slid 24 slid 25 Iflatio irtia = β( u u + ν I this form, th Phillips curv implis that iflatio has irtia: I th absc of supply shocks or cyclical umploymt, iflatio will cotiu idfiitly at its currt rat. Past iflatio iflucs xpctatios of currt iflatio, which i tur iflucs th wags & prics that popl st. Disiflatios ar costly: ay policy dsigd to rduc iflatio will do so gradually ovr tim slid 26 Two causs of risig & fallig iflatio = β( u u + ν cost-push iflatio: iflatio rsultig from supply shocks. Advrs supply shocks typically rais productio costs ad iduc firms to rais prics, pushig iflatio up. What should th optimal policy rspos b? dmad-pull iflatio: iflatio rsultig from dmad shocks. Positiv shocks to aggrgat dmad caus umploymt to fall blow its atural rat, which pulls th iflatio rat up. What should th optimal policy rspos b? slid 27 Graphig th Phillips curv Shiftig th Phillips curv I th short ru, policymakrs fac a trad-off btw ad u. + ν = β( u u + ν β Th short-ru Phillips Curv Popl adjust thir xpctatios ovr tim, so th tradoff oly holds i th short ru. + ν 2 + ν = β( u u + ν u u E.g., a icras i shifts th short-ru P.C. upward. u u slid 28 slid 29 5

6 Th sacrific ratio To rduc iflatio, policymakrs ca cotract AD, causig umploymt to ris abov th atural rat. Th sacrific ratio masurs th prctag of a yar s ral GDP that must b forgo to rduc iflatio by prctag poit. Estimats vary, but a typical o is 5. slid 30 Th sacrific ratio Suppos policymakrs wish to rduc umploymt from 6% to 5% Hc, th Phillips curv may b somthig lik = - 2(u 0.06 with - = 2% or 0.02 Th rductio i umploymt rsults i a icras i iflatio giv by th Phillips curv, i.., = ( = 0.04 Alas, th followig priod, th Phillips curv bcoms = (u 0.06 slid 3 Lowrig Umploymt Ratioal xpctatios Ways of modlig th formatio of xpctatios: 4% adaptiv xpctatios: Popl bas thir xpctatios of futur iflatio o rctly obsrvd iflatio. 2% Nw Phillips Curv Old Phillips Curv ratioal xpctatios: Popl bas thir xpctatios o all availabl iformatio, icludig iformatio about currt ad prospctiv futur policis. 5% 6% slid 32 slid 33 Pailss disiflatio? Propots of ratioal xpctatios bliv that th sacrific ratio may b vry small: Suppos u = u ad = = 6%, ad suppos th Fd aoucs that it will do whatvr is cssary to rduc iflatio from 6 to 2 prct as soo as possibl. If th aoucmt is crdibl, th will fall, prhaps by th full 4 poits. Th, idally, ca fall without a icras i u. slid 34 Th atural rat hypothsis Our aalysis of th costs of disiflatio, ad of coomic fluctuatios i th prcdig chaptrs, is basd o th atural rat hypothsis: Chags i i aggrgat dmad affct output ad ad mploymt oly oly i i th th short ru. ru. I I th th log log ru, ru, th th coomy rturs to to th th lvls of of output, mploymt, ad ad umploymt dscribd by by th th classical modl slid 35 6

7 A Modr IS-LM Modl for Motary Policy Aalysis I policy ad public viromts, w typically discuss i trms of iflatio ad itrst rats, ot i trms of th pric lvl ad moy supply. Hc, lt s adapt th AD modl basd o th IS-LM i trms of iflatio ad itrst rats to match th Phillips curv A Modr AD curv First, lt s rwrit ivstmt dmad i trms of omial itrst rats (which th Fd ca st ad iflatio, I(r = I(i - For a giv lvl of,diffrt lvls i will dlivr diffrt lvls of plad xpditur, ad hc a IS curv i trms of omial itrst rats slid 36 slid 37 Th IS with omial itrst rats Th AD Curv i trms of Iflatio i I E E I E =C +I (i 2 +G E =C +I (i +G Now cosidr tracig th AD curv by tracig th diffrt IS curvs that rsult from allowig fluctuatios i (which prviously w assumd costat i i 2 To this d, w rplac th LM with a mor modr tratmt of how motary policy is st by th Fd. This is calld th Taylor rul i 2 2 IS slid 38 slid 39 Th Taylor Rul Th IS-TR Graph Th Taylor rul (amd aftr Joh Taylor, a coomist at Staford, formrly udrscrtary of th Trasury with Bush suggsts th Fd should st itrst rats accordig to: i = (r+ * + α ( - * + β ( * Hc, if = * th = * ad i = r + * At th coomy is blow pottial ad iflatio is blow targt Hc, th Fd will follow th Taylor rul ad lowr i which will brig th coomy closr to pottial i i 2 i TR ( TR 2 ( IS( 2 = * slid 40 slid 4 7

8 AD-PC For diffrt valus of iflatio, th TR will shift aroud, which w ca us to trac th AD curv, just as w did with th IS-LM modl Togthr with th Phillips Curv (PC, w hav a modr framwork for coomic aalysis slid 42 At lowr lvls of iflatio, th TR curv calls for lowr i Giv th PC, output is blow pottial. Hc, policy to stimulat AD from AD to AD 2 is rquird. This will rsult i mor iflatio ad mor output AD-PC i i i 2 * * * TR( TR( 2 IS( PC AD 2 AD slid 43 8

Learning objectives. Three models of aggregate supply. 1. The sticky-wage model 2. The imperfect-information model 3. The sticky-price model

Learning objectives. Three models of aggregate supply. 1. The sticky-wage model 2. The imperfect-information model 3. The sticky-price model Larig objctivs thr modls of aggrgat supply i which output dpds positivly o th pric lvl i th short ru th short-ru tradoff btw iflatio ad umploymt kow as th Phillips curv Aggrgat Supply slid 1 Thr modls