CHAPTER 18 INFLATION, UNEMPLOYMENT AND AGGREGATE SUPPLY. Themes of the chapter. Nominal rigidities, expectational errors and employment fluctuations

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1 CHAPTER 18 INFLATION, UNEMPLOYMENT AND AGGREGATE SUPPLY Themes of the chapter Nomnal rgdtes, expectatonal errors and employment fluctuatons The short-run trade-off between nflaton and unemployment The relatonshp between the theory of nflaton and the theory of structural unemployment Supply shocks and the New Economy The aggregate supply curve

2 WHERE WE ARE HEADING The theory of nflaton and unemployment developed n ths chapter may be summarzed n The expectatons-augmented Phllps curve e π =π +α α> ( u u ), 0 (1) π = actual rate of nflaton π e = expected rate of nflaton u = actual rate of unemployment u = natural rate of unemployment In the followng we wll derve the expectatons-augmented Phllps curve from a theory of wage and prce settng

3 PRICE SETTING Producton functon n sector Y = BL, 0 <α< 1 (3) 1 α The margnal product of labour ( 1 ) MPL dy / dl = α BL α (4) The demand curve for the product of sector σ P Y Y, = σ> P n 1 (5) Total revenue s TR PY, so accordng to (5) margnal revenue s

4 PRICE SETTING Margnal revenue n sector dtr dp dp Y MR = P + Y = P 1 + dy dy dyp 1 MR = P 1 σ (6) MC Margnal cost n sector W MPL = = W ( 1 α) BL α Maxmzaton of profts requres MR = MC, mplyng

5 PRICE SETTING Mark-up prcng MC p W p σ P = m, m > 1 ( 1 ) BL α α σ 1 (7) From (7) we obtan an expresson for P /P. Insert ths along wth (3) nto (5) to get Y 1 α BL σ P / P p m W / P Y = ( 1 ) α α BL n

6 LABOUR DEMAND IN SECTOR w, / ( 1 α) Y B ε L = w p, nb m W P ε σ ε σ 1 +α σ 1 ε ( ) (8) Thus labour demand s a declnng functon of the real wage w, and the numercal wage elastcty of labour demand at the sectoral level s gven by ε

7 WAGE SETTING UNDER PERFECT INFORMATION Workers n sector are educated and traned to work n that partcular sector, so they cannot move to another sector to look for a job. Hence ther outsde opton s smply equal to the real rate of unemployment beneft, b. All workers n sector are organzed n a monopoly trade unon whch seeks to maxmze The total rent accrung to workers n sector (trade unon objectve) ( ) ( ) ( ) Ω w = w b L w η (9) where the labour demand functon L (w ) s gven by (8), and where the parameter η measures the unon s preference for hgh employment relatve to the goal of a hgh real wage for employed members. If the unon has perfect nformaton about the current prce level P, t wll choose the nomnal wage rate W so as to maxmze Ω(w ) wth respect to w, mplyng the frst-order condton:

8 WAGE SETTING UNDER PERFECT INFORMATION ( ) dω w η η 1 dl = L + ( w b) η L = 0 dw dw = ε η( w b) dl w 1+ = 0 w dw L w w ηε w = m b, m ηε 1 (10) Thus the unon sets the real wage as a mark-up over the real rate of unemployment beneft. The mark-up s lower the hgher the values of η and ε

9 WAGE SETTING UNDER IMPERFECT INFORMATION Equaton (10) assumes that the unon has perfect nformaton on the current prce level. In practce, the unon must set the nomnal wage rate at the start of the current perod, based on the prce level expected to preval over that perod (P e ), so as to acheve an expected real wage equal to the target level m w b. Henceweget Note that The optmal nomnal wage rate under mperfect nformaton e w W = P m b (11) the nomnal wage rate s pre-set for one perod at a tme, so n the short run we have nomnal rgdty P e may devate from P, so there may be expectatonal errors

10 THE EXPECTATIONS-AUGMENTED PHILLIPS CURVE From (11) we get The actual real wage W P e P = P m w b whch may be nserted nto (8) to gve L Labour demand n sector ε/ Y σ B ( 1 α) P ε = nb m m b P p w e (12) In a symmetrc equlbrum aggregate employment s L=nL and total output s

11 THE EXPECTATIONS-AUGMENTED PHILLIPS CURVE Aggregate output n symmetrc equlbrum Y = ny = nbl α Substtutng ths nto (12) and usng the defnton of ε, we get Aggregate employment n symmetrc equlbrum 1 B ( 1 α) L = nl = n m m b P P p w e 1 / α Insertng the long run equlbrum condton P e =P nto (13), we fnd The natural level of employment L B = n p w m m b ( 1 α) 1 / α (13) (15)

12 THE EXPECTATIONS-AUGMENTED PHILLIPS CURVE Dvdng (13) by (15) and denotng the labour force by N, we get ( 1 u) ( 1 ) L N P = = e L u N P 1 / α (16) Takng logs on both sdes of (16), and usng the approxmaton ln(1+x) x, we obtan p= p +α u u, p P, p P from whch we derve e ( ) ln ln e e e The expectatons-augmented Phllps curve ( u u ), p p, p e p 1 1 π=π +α π π (17)

13 EXPLAINING THE BREAKDOWN OF THE SIMPLE PHILLIPS CURVE IN THE LATE 1960s Up untl the 1960s the prce level was reasonably stable n peacetme. In such a stuaton t s reasonable to assume that π e = 0. From (17) we then get The smple Phllps curve π = α u u (18) ( ) However, n the late 1960s the nflaton rate had been postve and rsng for several years, so people started to expect a postve nflaton rate, π e > 0. In accordance wth (17), ths led to a gradual rse n the rate of nflaton assocated wth any gven rate of unemployment. Thus the apparent trade-off between unemployment and nflaton dscovered by Phllps s only a short-run trade-off whch wll hold only as long as the expected rate of nflaton stays constant. When the expected nflaton rate ncreases, the short-run Phllps curve wll shft upwards, and vce versa.

14 π u The expectatons-augmented Phllps curve

15 THE LINK BETWEEN UNEMPLOYMENT AND THE CHANGE IN INFLATION The natural rate of unemployment u s the rate of unemployment prevalng n a long-run equlbrum where expectatons are fulflled, π e = π. Suppose we have Statc expectatons e π = (19) π 1 From (17) we then get π π π ( ) 1 = α u u (20) whch shows that nflaton wll accelerate when unemployment s below the natural rate and decelerate when unemployment s above ts natural level. For ths reason the natural rate s sometmes called the Non-Acceleratng-Inflaton- Rate-of-Unemployment (NAIRU).

16 WHAT DETERMINES THE NATURAL RATE OF UNEMPLOYMENT? Recall that aggregate employment s L = nl. We may choose unts such that the labour force n each sector s 1 so that the total labour force (N) s equal to n. Thus we have The rate of employment L e = L N Aggregate output Y = ny = nbl = nbe 1 α 1 α Insertng these relatonshps along wth the symmetry condton W =W nto the labour demand curve (8) and solvng for e (usng the defnton of ε), we get e Aggregate labour demand ( ) 1/ α 1/ 1 α W B m P = p α (14)

17 WHAT DETERMINES THE NATURAL RATE OF UNEMPLOYMENT? By rearrangng (14), we obtan the real wage mplctly offered by frms, also termed W P The prce settng curve MPL 1 = B( 1 α p ) e m In a symmetrc equlbrum (W =W) where expectatons are correct (P e =P), equaton (11) gves the real wage clamed by workers, also termed α (PS) The wage settng curve W w m P = b (WS)

18 WHAT DETERMINES THE NATURAL RATE OF UNEMPLOYMENT? The natural rate of employment s the value of e whch makes the real wage clamed by workers consstent wth the real wage mplctly offered by frms. Equatng the rght-hand sdes of (PS) and (WS) and solvng for e, we thus get The natural rate of employment e B = p w m m b ( 1 α ) 1/ It s reasonable to assume that unemployment benefts are lnked to real ncome per capta whch s proportonal to total factor productvty n the long run. Hence we assume that b=cb. Insertng n the expresson above, we then obtan The natural rate of unemployment α u 1 α 1 e = 1 p w m m c 1/ α (22)

19 Implcatons of (22): WHAT DETERMINES THE NATURAL RATE OF UNEMPLOYMENT? The natural rate of unemployment s hgher the lower the degree of competton n product markets (a lower value of σ ncreases m p and m w ) the weaker the unon preference for hgh employment relatve to a hgh real wage (a lower value of η ncreases m w ) the more generous the level of unemployment benefts (the hgher the value of c ) Note that the natural unemployment rate s ndependent of the level of productvty (B). Ths s consstent wth emprcal evdence.

20 ALTERNATIVE MICRO FOUNDATIONS FOR THE EXPECTATIONS-AUGMENTED PHILLIPS CURVE the trade unon model wthout ntersectoral labour moblty (see above) or wth labour moblty (see exercse 18.1) the effcency wage model (see Chapter 23, secton 4) the worker-mspercepton model of a compettve labour market (see Chapter 18, secton 3) The worker-mspercepton model does not nclude nomnal rgdtes, so to obtan an expectatons-augmented Phllps curve t s only necessary to assume expectatonal errors. However, as shown n secton 18.3, the exstence of nomnal rgdtes wll amplfy the employment fluctuatons generated by nomnal rgdtes. Our model abstracts from nomnal prce rgdtes, but n practce such rgdtes may help to explan the sluggsh adjustment of nflaton and unemployment to ther long run equlbrum levels.

21 SUPPLY SHOCKS In practce, the level of productvty and the wage and prce mark-ups wll fluctuate around ther long-run trend levels (whch we denote by bar superscrpts). It s plausble to assume that the rate of unemployment beneft s lnked to the trend level of productvty. In that case we may rewrte (13) as Actual employment ( ) 1/ α e B 1 α P L ( 1 u) N = n mmcb P p w (31) The long-run equlbrum level of employment s the employment level prevalng when expectatons are fulflled and when productvty as well as the mark-ups are at ther trend levels. Hence we have Natural employment 1 α L ( 1 u ) N = n p w m m c 1 / α (32)

22 THE EXPECTATIONS-AUGMENTED PHILLIPS CURVE WITH SUPPLY SHOCKS Dvdng (31) by (32), we get p w 1 u Bm m P = p w e 1 u Bm m P 1/ α (33) Takng logs n (33) and usng the approxmaton ln(1+x) x plus the defntons of π e and π, we end up wth u u s, e π=π +α + ( ) s p w m m B ln ln ln p w m + m B (34)

23 TESTING THE PHILLIPS CURVE THEORY Wth statc expectatons, π e = π -1, we may wrte (34) as π = α β u+ s, E s = 0 (35) [ ] A regresson analyss based on U.S. data for yelds The expectatons-augmented Phllps curve n the USA π = u, R = s.e.=1.081 s.e.= (26) Estmate of the natural unemployment rate n the USA u = α /β = 4.467/0.723 = 6.2%

24 PRODUCTIVITY GROWTH, THE PHILLIPS CURVE AND THE NEW ECONOMY The combnaton of low unemployment and nflaton n the U.S. snce 1995 may be explaned by a postve productvty shock, reflected n an acceleratng rate of productvty growth. When productvty growth accelerates, we have lnb lnb > 0 s < 0 Recall that the target real wage of workers s w * = m w cb so n a perod of acceleratng productvty growth, the target real wage lags behnd the growth n actual productvty growth, thereby reducng nflatonary pressure.

25 THE AGGREGATE SUPPLY CURVE Snce Y = ny, L 1 u N = nl ( ) t follows from the producton functon (3) that 1 α L α Y = nb = n B ( 1 u) N n 1 α Takng logs on both sdes of (38) and usng ln(1-u) -u, we get α y lny = lnn + lnb+ ( 1 α) ln ( 1 u) N α lnn + lnb+ 1 α lnn 1 α u ( ) ( ) lnn α + lnb y u = lnn + 1 α (38) (39)

26 THE AGGREGATE SUPPLY CURVE In parallel to (38), we may specfy natural output as and take logs to get u α 1 Y = n B 1 u N α = lnn + ( ) lnn + lnb y 1 α (41) Substtutng (39) and (41) nto the expectatons-augmented Phllps curve (34), we get The Short-Run Aggregate Supply (SRAS) curve e π=π +γ + y y s, ( ) p w α m m ln( B/B) γ, s ln + ln p w 1 α m m 1 α (42)

27 PROPERTIES OF THE AGGREGATE SUPPLY CURVE the SRAS curve slopes upwards, because hgher output hgher employment lower MPL hgher MC hgher prces va the mark-up prcng behavour of frms the SRAS curve shfts upwards n case of a rse n the expected nflaton rate or n case of an unfavourable supply shock (hgher mark-ups or a negatve productvty shock) the Long-Run Aggregate Supply (LRAS) curve s obtaned when expectatons are fulflled (π e =π) and mark-ups and productvty are at ther trend levels. The LRAS curve s vertcal n (y,π)-space, that s, n the long run there s no trade-off between nflaton and output (employment) Note that n a model wth ntersectoral labour moblty a rse n actvty leads to ncreased wage pressure whch contrbutes to the postve slope of the SRAS curve.

28 π y Aggregate supply n the short run (SRAS) and n the long run (LRAS)

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