Chaptr 13 Aggrgat Supply 0 1
Larning Objctivs thr modls of aggrgat supply in which output dpnds positivly on th pric lvl in th short run th short-run tradoff btwn inflation and unmploymnt known as th Phillips curv 1 2
1.Thr modls of aggrgat supply 1. Th sticky-wag modl 2. Th imprfct-information modl 3. Th sticky-pric modl All thr modls imply: = + ( ) agg. output natural rat of output Y Y α P P a positiv paramtr th actual pric lvl th xpctd pric lvl 2 3
1.1 Th sticky-wag modl Assums that: Firms and workrs ngotiat contracts and fix th nominal wag bfor thy know what th pric lvl will turn out to b. Employmnt is dtrmind by th quantity of labor firms dmand (downward sloping labor dmand curv) Output is dtrmind by th production function (concav production function) 3 4
1.1 Th sticky-wag modl Th nominal wag, W, thy st is th product of a targt ral wag, ω, and th xpctd pric lvl: W = ω P W P = ω P P 4 5
1.1 Th sticky-wag modl If it turns out that P = P P > P P < P W P P = ω P thn unmploymnt and output ar at thir natural rats Ral wag is lss than its targt, so firms hir mor workrs and output riss abov its natural rat Ral wag xcds its targt, so firms hir fwr workrs and output falls blow its natural rat 5 6
Ral wag, W/P (a) Labor Dmand Incom, output, Y (b) Production Function W/P 1 Y 2 Y 5 F(L) W/P 2 L 5 L d (W/P ) Y 1 4.... output,.. 2.... rducs th ral wag for a givn nominal wag,.. L 1 L 2 Labor, L 3....which raiss mploymnt,.. L 1 L 2 (c) Aggrgat Supply Labor, L Pric lvl, P Y 5 Y 1 a (P 2 P ) P 2 P 1 1. An incras in th pric lvl.. Y 1 Y 2 5.... and incom. 6. Th aggrgat supply curv summarizs ths changs. Incom, output, Y 6 7
1.1 Th sticky-wag modl Implis that th ral wag should b countr-cyclical, it should mov in th opposit dirction as output ovr th cours of businss cycls: In booms, whn P typically riss, th ral wag should fall. In rcssions, whn P typically falls, th ral wag should ris. This prdiction dos not com tru in th ral world. 7 8
1.2 Th imprfct-information modl Assumptions: all wags and prics prfctly flxibl, all markts clar ach supplir producs on good, consums many goods ach supplir knows th nominal pric of th good sh producs, but dos not know th ovrall pric lvl 8 9
1.2 Th imprfct-information modl Supply of ach good dpnds on its rlativ pric: th nominal pric of th good dividd by th ovrall pric lvl. Supplir dosn t know th pric lvl at th tim sh maks hr production dcision, so uss th xpctd pric lvl, P. Suppos P riss but P dos not. Thn supplir thinks hr rlativ pric has risn, so sh producs mor. With many producrs thinking this way, Y will ris whnvr P riss abov P. 9 10
1.3 Th sticky-pric modl Rasons for sticky prics: long-trm contracts btwn firms and customrs mnu costs firms do not wish to annoy customrs with frqunt pric changs Assumption: Firms st thir own prics (.g. as in monopolistic comptition) 10 11
1.3 Th sticky-pric modl An individual firm s dsird pric is p = P + a ( Y Y ) 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 know how P and Y will turn out: p = P + a ( Y Y ) 11 12
1.3 Th sticky-pric modl p = P + a ( Y Y ) Assum firms w/ sticky prics xpct that output will qual its natural rat. Thn, p = P To driv th aggrgat supply curv, w first find an xprssion for th ovrall pric lvl. Lt s dnot th fraction of firms with sticky prics. Thn, w can writ th ovrall pric 12 lvl as 13
1.3 Th sticky-pric modl P = sp + (1 s )[ P + a( Y Y )] pric st by sticky pric firms pric st by flxibl pric firms Subtract (1 s)p from both sids: sp = sp + (1 s )[ a( Y Y )] Divid both sids by s: (1 s) a P = P + ( Y Y ) s 13 14
1.3 Th sticky-pric modl (1 s ) a P = P + ( Y Y ) s High P High P If firms xpct high prics, thn firms who must st prics in advanc will st thm high. Othr firms rspond by stting high prics. 14 15
1.3 Th sticky-pric modl (1 s ) a P = P + ( Y Y ) s High Y High P Whn incom is high, th dmand for goods is high. Firms with flxibl prics st high prics. Th gratr th fraction of flxibl pric firms, th smallr is s and th biggr is th ffct of Y on P. 15 16
1.3 Th sticky-pric modl (1 s) a P = P + ( Y Y ) s Finally, driv AS quation by solving for Y : Y = Y + α ( P P ), whr α = s (1 s) a 16 17
1.3 Th sticky-pric modl In contrast to th sticky-wag modl, th stickypric modl implis a pro-cyclical ral wag: Suppos aggrgat output/incom falls. Thn, Firms s a fall in dmand for thir products. Firms with sticky prics rduc production, and hnc rduc thir dmand for labor. Th lftward shift in labor dmand causs th ral wag to fall. 17 18
1.4 Summary & Implications P LRAS Y = Y + α ( P P ) P > P P = P P < P Y SRS Y Each of th thr modls of agg. supply imply th rlationship summarizd by th SRAS curv & quation 18 19
1.4 Summary & Implications Suppos a positiv AD shock movs output abov its natural rat and P abov th lvl popl had xpctd. SRAS quation: Y = Y + α ( P P ) P = P P 3 3 P 2 Ovr tim, P 2 = P1 = P1 P riss, SRAS shifts up, and output rturns to its natural rat. Y 3 = 1 LRAS Y = Y Y 2 SRS 2 SRS 1 AD 1 AD 2 Y 19 20
2. Th Phillips Curv Th Phillips curv stats that π dpnds on xpctd inflation, π cyclical unmploymnt: th dviation of th actual rat of unmploymnt from th natural rat supply shocks, ν n π = π β ( u u ) + ν whr β > 0 is an xognous constant. 20 21
2. Th Phillips Curv (1) Y = Y + α ( P P ) (2) P = P + (1 α )( Y Y ) (3) P = P + (1 α )( Y Y ) + ν (4) ( P P ) = ( P P ) + (1 α )( Y Y ) + ν 1 1 (5) π = π + (1 α )( Y Y ) + ν n (6) (1 α )( Y Y ) = β ( u u ) n (7) π = π β ( u u ) + ν 21 22
2. Th Phillips Curv SRAS: Y = Y + α ( P P ) n Phillips curv: π = π β ( u u ) + ν SRAS curv: output is rlatd to unxpctd movmnts in th pric lvl Phillips curv: unmploymnt is rlatd to unxpctd movmnts in th inflation rat 22 23
2. Th Phillips Curv Adaptiv xpctations: an approach that assums popl form thir xpctations of futur inflation basd on rcntly obsrvd inflation. A simpl xampl: Expctd inflation = last yar s actual inflation π = π 1 Thn, th P.C. bcoms n π = π 1 β ( u u ) + ν 23 24
2. Th Phillips Curv n π = π 1 β ( u u ) + ν In this form, th Phillips curv implis that inflation has inrtia: In th absnc of supply shocks or cyclical unmploymnt, inflation will continu indfinitly at its currnt rat. Past inflation influncs xpctations of currnt inflation, which in turn influncs th wags & prics that popl st. 24 25
2. Th Phillips Curv n π = π 1 β ( u u ) + ν cost-push inflation: inflation rsulting from supply shocks. Advrs supply shocks typically rais production costs and induc firms to rais prics, pushing inflation up. 25 26
2. Th Phillips Curv dmand-pull inflation: inflation rsulting from dmand shocks. Positiv shocks to aggrgat dmand caus unmploymnt to fall blow its natural rat, which pulls th inflation rat up. 26 27
2. Th Phillips Curv In th short run, policymakrs fac a trad-off btwn π and u. π π + ν n π = π β ( u u ) + ν β 1 Th short-run Phillips Curv n u u 27 28
Popl adjust thir xpctations ovr tim, so th tradoff only holds in th short run. 2. Th Phillips Curv π 2 π 1 + ν + ν π n π = π β ( u u ) + ν E.g., an incras in π shifts th short-run P.C. upward. n u u 28 29
2. Th Phillips Curv To rduc inflation, policymakrs can contract agg. dmand, causing unmploymnt to ris abov th natural rat. Th sacrific ratio masurs th prcntag of a yar s ral GDP that must b forgon to rduc inflation by 1 prcntag point. Estimats vary, but a typical on is 5. 29 30
2. Th Phillips Curv Suppos policymakrs wish to rduc inflation from 6 to 2 prcnt. If th sacrific ratio is 5, thn rducing inflation by 4 points rquirs a loss of 4 5 = 20 prcnt of on yar s GDP. This could b achivd svral ways,.g. rduc GDP by 20% for on yar rduc GDP by 10% for ach of two yars rduc GDP by 5% for ach of four yars Th cost of disinflation is lost GDP. On could us Okun s law to translat this cost into unmploymnt. 30 31
2. Th Phillips Curv Ways of modling th formation of xpctations: adaptiv xpctations: Popl bas thir xpctations of futur inflation on rcntly obsrvd inflation. rational xpctations: Popl bas thir xpctations on all availabl information, including information about currnt and prospctiv futur policis. 31 32
2. Th Phillips Curv Proponnts of rational xpctations bliv that th sacrific ratio may b vry small: Suppos u = u n and π = π = 6%, and suppos th Fd announcs that it will do whatvr is ncssary to rduc inflation from 6 to 2 prcnt as soon as possibl. If th announcmnt is crdibl, thn π will fall, prhaps by th full 4 points. Thn, π can fall without an incras in u. 32 33
2. Th Phillips Curv Our analysis of th costs of disinflation, and of conomic fluctuations in th prcding chaptrs, is basd on th natural rat hypothsis: Changs in aggrgat dmand affct output and mploymnt only in th short run. In th long run, th conomy rturns to th lvls of output, mploymnt, and unmploymnt dscribd by th classical modl (chaptrs 3-8). 3 33 34
2. Th Phillips Curv Hystrsis: th long-lasting influnc of history on variabls such as th natural rat of unmploymnt. Ngativ shocks may incras u n, so conomy may not fully rcovr: Th skills of cyclically unmployd workrs dtriorat whil unmployd, and thy cannot find a job whn th rcssion nds. Cyclically unmployd workrs may los thir influnc on wag-stting; insidrs (mployd workrs) may thn bargain for highr wags for thmslvs. Thn, th cyclically unmployd outsidrs may bcom structurally unmployd whn th rcssion nds. 34 35
Chaptr summary 1. Thr modls of aggrgat supply in th short run: sticky-wag modl imprfct-information modl sticky-pric modl All thr modls imply that output riss abov its natural rat whn th pric lvl falls blow th xpctd pric lvl. 35 36
Chaptr summary 2. Phillips curv drivd from th SRAS curv stats that inflation dpnds on xpctd inflation cyclical unmploymnt supply shocks prsnts policymakrs with a short-run tradoff btwn inflation and unmploymnt 36 37
Chaptr summary 3. How popl form xpctations of inflation adaptiv xpctations basd on rcntly obsrvd inflation implis inrtia rational xpctations basd on all availabl information implis that disinflation may b painlss 37 38
Chaptr summary 4. Th natural rat hypothsis and hystrsis th natural rat hypothss stats that changs in aggrgat dmand can only affct output and mploymnt in th short run hystrsis stats that agg. dmand can hav prmannt ffcts on output and mploymnt 38 39