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Unformatted text preview: Aggregate Supply and the Phillips Curve Road map to this lecture
We relax the assumption that the aggregate supply curve is vertical A version of the aggregate supply in terms of inflation (rather than the price level) is called the Phillips curve We present a more modern view of the IS ISLM model in terms of inflation and interest rates closer to current debates about monetary policy ECN 101  MACROECONOMICS slide 1 Objectives
Goal: determine the position and slope of the AS curve Together with our models for the AD curve we can complete the AD AS analysis ADAS The AS will be a middle step toward deriving the Phillips curve: = e  (u un) + ECN 101  MACROECONOMICS slide 2 Three models of aggregate supply
1. The stickywage model 2. The i 2 Th imperfectinformation model f ti f ti d l 3. The stickyprice model
All three models imply: Y = Y + (P  P )
e agg. output natural rate of output f t t the expected price level a positive parameter the actual price level i l l
slide 3 ECN 101  MACROECONOMICS The stickywage model stickyAssumes that firms and workers negotiate contracts and fix the nominal wage before they know what the price level will turn out to be. The nominal wage they set is the product of a target real wage and the expected price level:
Target real wage W = P e
W Pe = P P
ECN 101  MACROECONOMICS slide 4 The stickywage model stickyW Pe = P P
If it turns out that then
unemployment and output are l d at their natural rates Real wage is less than its target target, so firms hire more workers and output rises above its natural rate Real wage exceeds its target, so firms hire fewer workers and output falls below its natural rate
slide 5 P =P e P >Pe P <P
e ECN 101  MACROECONOMICS (a) Labor Demand Real wage, W/P W/P 1 (b) Production Function Income, output, Y Y 5 F(L) Y2 Y1 4. . .. output,. . W/P 2 L 5 Ld(W/P ) 2. 2 .. . reduces the real wage for a given nominal wage,. . L1 L2 Labor, L 3. . ..which raises employment, . . L1 L2 Labor, L (c) Aggregate Supply Price level, P Y 5 Y 1 a (P 2 Pe ) P2 P1 1. An inc ease . n increase in the price level. . 6. The aggregate supply curve summarizes these changes. Y1 Y2 Income, output, Y ECN 101  MACROECONOMICS 5. . .. and income. slide 6 The stickywage model stickyImplies that the real wage should be countercyclical , it should move in the opposite direction as output over the course of business cycles: In booms, when P typically rises, the real wage should fall. I recessions, when P t i ll falls, the real In i h typically f ll th l wage should rise. This Thi prediction does not come true in the real di ti d t t i th l world: ECN 101  MACROECONOMICS slide 7 The cyclical behavior of the real wage
Pe ercentag chan ge nge in real wa age
4 3 2 1 0
1982 1970 1991 1990 1993 1992 1996 1960 1998 1997 1999 2000 1984 1972 1965 1 2 3 4 5 1975 1974 1979 Percentage change in real GDP
1980 3 2 1 0 1 2 3 4 5 6 7 8 ECN 101  MACROECONOMICS slide 8 The imperfectinformation model imperfectAssumptions:
all wages and prices perfectly flexible, ll d i f tl fl ibl all markets clear each supplier produces one good, consumes h l d d many goods each supplier knows the nominal price of the good she produces, but does not know the overall price level ECN 101  MACROECONOMICS slide 9 The imperfectinformation model imperfectSupply of each good depends on its relative price: the nominal price of the good divided by the overall price level. Supplier doesn t know price level at the time doesn't she makes her production decision, so uses the e expected price level, P . Suppose P rises but P does not. Then supplier thinks her relative price has risen, so she produces more. h d With many producers thinking this way, Y will rise whenever P rises above P e.
ECN 101  MACROECONOMICS
slide 10 e The stickyprice model stickyReasons for sticky prices: longterm contracts between firms and customers menu costs firms do not wish to annoy customers with frequent price changes Assumption: Firms set their own prices (e.g. as in monopolistic competition) ECN 101  MACROECONOMICS slide 11 The stickyprice model stickyAn individual firm's desired price is p = P + a (Y Y )
where a > 0. Suppose two types of firms: firms with flexible prices, set prices as above firms with sticky prices, must set their price before they know how P and Y will turn out: p = P e + a (Y e Y e ) ECN 101  MACROECONOMICS slide 12 The stickyprice model stickyp = P e + a (Y e Y e )
Assume sticky price firms expect that output will equal its natural rate. Then, p =Pe To derive the aggregate supply curve we first curve, find an expression for the overall price level. Let s denote the fraction of firms with sticky prices. Then, we can write the overall price level as
ECN 101  MACROECONOMICS
slide 13 The stickyprice model stickyP = sP
e + (1  s )[P + a (Y Y )]
price set by flexible price firms price set by sticky price firms Subtract (1s )P from both sides: sP = s P e + (1  s )[a(Y Y )]
Divide both sides by s : P = P e (1  s ) a + (Y Y ) s slide 14 ECN 101  MACROECONOMICS The stickyprice model stickyP = P
e High P e High P If firms expect high prices, then firms who must set prices in advance will set them high. i i d ill t th hi h Other firms respond by setting high prices. High Y High P When income is high, the demand for goods is high. p g p Firms with flexible prices set high prices. The greater the fraction of flexible price firms, the smaller is s and the bigger is the effect of Y on P. f
ECN 101  MACROECONOMICS
slide 15 (1  s ) a + (Y Y ) s The stickyprice model stickyP = P
e (1  s ) a + (Y Y ) s Finally, derive AS equation by solving for Y : Y = Y + (P  P e ),
s where = (1  s )a ECN 101  MACROECONOMICS slide 16 The stickyprice model stickyIn contrast to the stickywage model, the stickyprice model implies a pro cyclical real wage: procyclical Suppose aggregate output/income falls. Then, Firms see a fall in demand for their products. Firms with sticky prices reduce production, and hence reduce their demand for labor. The leftward shift in labor demand causes the real wage to fall. ECN 101  MACROECONOMICS slide 17 Summary & implications
P
LRAS Y = Y + (P  P e )
SRAS P >Pe
P =P
e P <Pe Y Y Each of the three models of agg. supply imply the relationship summarized b s mma i ed by the SRAS curve & equation qua o
slide 18 ECN 101  MACROECONOMICS Summary & implications
Suppose a positive AD shock moves output above its natural rate and P above the d b h level people had expected. SRAS equation: Y = Y + (P  P e ) P LRAS SRAS2 SRAS1 Over time, P2e = P1 = P1e P e rises, SRAS shifts up, and output returns to its t l t t it natural rate.
ECN 101  MACROECONOMICS P3 = P3e P2 AD2 AD1
Y 3 = Y1 = Y Y Y2
slide 19 Inflation, Unemployment, and the Phillips Curve
The Phillips curve states that depends on expected inflation, e pected inflation e cyclical unemployment: the deviation of the actual rate of unemployment from the natural rate supply shocks, shocks =  (u  u ) + where > 0 is an exogenous constant.
ECN 101  MACROECONOMICS
slide 20 e n Deriving the Phillips Curve from SRAS
(1)
(2) Y = Y + (P  P e )
P = P e + (1 ) (Y Y ) (3) P = P e + (1 ) (Y Y ) + (P  P1 ) = ( P e  P1 ) + (1 ) (Y Y ) + (4) (5)
(6) = e + (1 ) (Y Y ) + (1 ) (Y Y ) =  (u  u n ) (7) = e  (u  u n ) + ECN 101  MACROECONOMICS
slide 21 Three Faces of Aggregate Supply ECN 101  MACROECONOMICS slide 22 The Phillips Curve and SRAS
SRAS: Y = Y + (P  P e ) Phillips curve: = e  (u  u n ) + SRAS curve: output is related to unexpected movements in the price level Phillips curve: unemployment is related to unexpected movements in the inflation rate
ECN 101  MACROECONOMICS slide 23 The Phillips Curve
The slope of the Phillips curve depends on how sticky prices and wages are the stickier are wages and prices, the smaller is parameter , and the flatter is p the Phillips curve When the Phillips curve is flat, even large p , g changes in the unemployment rate have little effect on the price level ECN 101  MACROECONOMICS slide 24 Adaptive expectations
Adaptive expectations: an approach that assumes people form their expectations of future inflation based on recently observed inflation. A simple example: Expected inflation = last year's actual inflation e = 1
Then, the P.C. becomes Th th P C b = 1  (u  u n ) + ECN 101  MACROECONOMICS
slide 25 Inflation inertia = 1  (u  u n ) + In this form, the Phillips curve implies that inflation has inertia: In the absence of supply shocks or cyclical unemployment, inflation will continue indefinitely at its current rate. Past inflation influences expectations of current inflation, which in turn influences the wages & prices that people set. Disinflations are costly: any policy designed to reduce inflation will do so gradually over time
ECN 101  MACROECONOMICS slide 26 Two causes of rising & falling inflation
costpush cost push inflation: inflation resulting from supply shocks. Adverse supply shocks typically raise pp y yp y production costs and induce f firms to raise prices, "pushing" inflation up. What should the optimal policy response be? p p y p demandpull inflation: inflation resulting from demand shocks. Positive h k t P iti shocks to aggregate d t demand cause d unemployment to fall below its natural rate, which "pulls" the inflation rate up. What p p should the optimal policy response be?
ECN 101  MACROECONOMICS
slide 27 = 1  (u  u n ) + Graphing the Phillips curve
In the short run, policymakers face a tradeoff between and u. b d
e + = e  (u  u n ) + 1 The shortrun Phillips Curve un u ECN 101  MACROECONOMICS slide 28 Shifting the Phillips curve
People adjust their expectations over time, so the tradeoff only holds in the short run run. = e  (u  u n ) + e 2 +
e 1 + E.g., an increase g, in e shifts the shortrun P.C. upward. d
ECN 101  MACROECONOMICS un u slide 29 The sacrifice ratio
To reduce inflation, policymakers can contract AD, causing unemployment to AD rise above the natural rate. The sacrifice ratio measures p g y the percentage of a year's real GDP that must be foregone to reduce y percentage point. g p inflation by 1 p Estimates vary, but a typical one is 5.
ECN 101  MACROECONOMICS
slide 30 The sacrifice ratio
Suppose policymakers wish to reduce unemployment from 6% to 5% Hence, Hence the Phillips curve may be something like
with 1 = 2% or 0.02 The reduction in unemployment results in an increase in inflation given by the Phillips curve, i.e., , = 0.02 2(0.05 0.06) = 0.04 = 1 2(u 0.06) Alas, the following period, the Phillips curve becomes = 0 04 2( 0 06) 0.04 2(u 0.06)
ECN 101  MACROECONOMICS
slide 31 Lowering Unemployment 4% 2% New Phillips Curve p Old Phillips Curve 5% 6% ECN 101  MACROECONOMICS slide 32 Rational expectations
Ways of modeling the formation of expectations:
adaptive expectations: People base their expectations of future inflation on recently observed inflation. rational expectations: People base their expectations on all available information, including information about current and prospective future policies.
ECN 101  MACROECONOMICS slide 33 Painless disinflation?
Proponents of rational expectations believe that the sacrifice ratio may be very small: Suppose u = u n and = e = 6%, and suppose the Fed announces that it will do whatever is necessary to reduce inflation from 6 to 2 percent as soon as possible. If the announcement is credible, then e will fall, perhaps by the full 4 points. Then, ideally, can fall without an increase in u.
ECN 101  MACROECONOMICS
slide 34 The natural rate hypothesis
Our analysis of the costs of disinflation, and of economic fluctuations in the preceding chapters, p g p , is based on the natural rate hypothesis: Changes in aggregate demand g gg g affect output and employment only in the short run. In the long run, the economy returns to the levels of output, employment, th l l f t t l t and unemployment described by the classical model
ECN 101  MACROECONOMICS
slide 35 A Modern ISLM Model for Monetary ISPolicy Analysis
In policy and public environments, we typically discuss in terms of inflation and interest rates, not in terms of the price level and money supply. y pp y Hence, let's adapt the AD model based on the ISLM in terms of inflation and interest IS LM rates to match the Phillips curve ECN 101  MACROECONOMICS slide 36 A Modern AD curve
First, let's rewrite investment demand in terms of nominal interest rates (which the Fed can set) and inflation, I(r) = I(i  e)
For a given level of e ,different levels i will deliver different levels of planned expenditure, and hence an IS curve in terms of nominal interest rates ECN 101  MACROECONOMICS slide 37 The IS with nominal interest rates
E E =C +I (i2)+G E =C +I (i1)+G i I E Y
I
i i1 i2 Y1 Y2 Y IS Y1 Y2 Y
slide 38 ECN 101  MACROECONOMICS The AD Curve in terms of Inflation
Now consider tracing the AD curve by tracing the different IS curves that result from allowing fluctuations in (which p previously we assumed constant) y ) To this end, we replace the LM with a more modern treatment of how monetary policy is set by the Fed. This is called the Taylor rule ECN 101  MACROECONOMICS slide 39 The Taylor Rule
The Taylor rule (named after John Taylor, an economist at Stanford formerly Stanford, undersecretary of the Treasury with Bush) suggests the Fed should set interest rates gg according to: i = (r+ *) + (  *) + (Y Y *) (r Hence, if = * then Y = Y * and i = r + * ECN 101  MACROECONOMICS slide 40 The ISTR Graph ISAt Y1 the economy is p below potential and inflation is below target Hence, the Fed will follow the Taylor rule and lower i which will bring the economy g y closer to potential i TR1(1) TR2( e) i1 i2 IS( e) Y Y1 Y2 = Y* ECN 101  MACROECONOMICS slide 41 ADADPC
For different values of inflation, the TR will shift around which we can use to trace the around, AD curve, just as we did with the ISLM model Together with the Phillips Curve (PC), we have a modern framework for economic analysis ECN 101  MACROECONOMICS slide 42 ADADPC
At lower levels of inflation, the TR curve calls for lower i Given the PC, output is below potential. Hence, policy to H li t stimulate AD from AD1 to AD2 is required. This will result in more inflation and more output
ECN 101  MACROECONOMICS i TR(1) TR(2) IS( e) i1 i2
Y1 Y* * 1 Y PC AD2 AD1 Y1 Y* Y
slide 43 ...
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 Spring '09
 PONTUSRENDAHL
 Macroeconomics, Inflation, Phillips Curve

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