1. Aggregate supply Eva Hromádková, 3.5 2010 0VS452 + 5EN253 Lecture 11
Slides by: Ron Cronovich
Aggregate supply
Eva Hromádková,

2. Learning objectives
three models of aggregate supply in which output depends positively on the price level in the short run
Implication of SRAS curve: the short-run tradeoff between inflation and unemployment known as the Phillips curve

3. A new and improved short run AS curveY P
By now – difference between behavior of aggregate supply in the short run (price fixed) and long run (output fixed – classical theory) – 2 versions of AS curve
Now – look at more “realistic” aggregate function in the short run – positive dependence on price
Interpretation: a rise in price is associated with a rise in output (like in a firm)
+ can be explained as medium term AS – until the shock adjusts
Consider a more realistic case, in between the two extreme assumptions we considered before.

4. Three models of aggregate supply
Consider 3 stories that could give us this SRAS: 1. The sticky-wage model 2. The imperfect-information model 3. The sticky-price model
agg. output
natural rate of output
a positive parameter
the actual price level
the expected price level
3 stories that would explain why higher output is associated with higher price level.
Basic intuition: when price rises above what people expected, they can be induced into producing more => only unexpected movements in price cause deviations in the real economy

5. 1. The sticky-wage model Main idea
Assumes 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, W, they set is the product of a target real wage, , and the expected price level:
Main idea:
When nominal wage (W) is sticky, rise in price level lowers the real wage (W/P). Labor is cheaper so firms hire more and produce more.
W – real wage
Can be the equilibrium real wage
Can be higher (due to unions, efficiency wages, etc.)
Real wage = W/P is different from target real wage (w) if realized price level is different from the expected price level.
Reference:
Gray, J.A. (1976) – JME
Fischer, S. (1977) - JPE

6. Other strong assumption = employment is determined by the quantity of labor that firms demand – no say from workers

7. 1. The sticky-wage model Intuition
If it turns out that
then
unemployment and output are at their natural rates
Real wage is less than its target, so firms hire more workers and output rises above its natural rate
Summary of outcomes
Real wage exceeds its target, so firms hire fewer workers and output falls below its natural rate

8. 1. The sticky-wage model Problem
Implies that the real wage should be counter-cyclical , 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.
In recessions, when P typically falls, the real wage should rise.
This prediction does not come true in the real world:
This was initially noted by Keynes – first point of attack.

9. The cyclical behavior of the real wage Real world data
Percentage
change in real 4
1972
wage 3
1998
1965 2
1960
1997
1999 1
1996
2000
1970
1984
1982
1993
1991
1992 -1
Relation is more or less positive – think about the recent booms and behavior of wages.
If real wage is cyclical, it is slightly procyclical.
Main problem – unchanging labor demand curve over booms and recessions.
1990 -2
1975 -3
1979
1974 -4
1980 -5 -3 -2 -1 1 2 3 4 5 6 7 8
Percentage change in real GDP

10. 2. The imperfect-information model Assumptions
all wages and prices perfectly flexible, all markets clear
each supplier produces one good, consumes many goods
each supplier knows the nominal price of the good she produces, but does not know the overall price level
No price or wage rigidities.
Main idea: misperception about prices – consumers closely monitor price of good he produces + vaguely infers about the overall price level
Misperception: change in relative prices x changes in price level

11. 2. The imperfect-information model Main idea
Supply 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 she makes her production decision, so uses the expected price level, P e.
Suppose P rises but P e does not.
Then supplier thinks her relative price has risen, so she produces more.
With many producers thinking this way, Y will rise whenever P rises above P e.
Interesting study on the validity of this model by its inventor – Robert Lucas: comparison of countries with big volatility of aggregate demand (=> big price aggregate level price movement => consumers should have learned that =>should not respond by changes aggregate supply) and small volatility (here, the changes are mostly implied by the changes in relative prices => should generate response by changed volume of production.

12. 3. The sticky-price model Assumptions
Reasons for sticky prices:
long-term 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 – firms have some power on the market)
Firms do not instantly adjust prices in response to changes in demand.
Assumption of price setting – departure from assumption of perfect competition.

13. The sticky-price model Model
An individual firm’s desired price is
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:
Pricing decision of individual firm: price depends on
Overall level of prices P – it measures level of their costs
Aggregate income: higher income => higher demand for firm’s product

14. The sticky-price model Model II
Assume firms w/ sticky prices expect that output will equal its natural rate. Then,
To derive the aggregate supply curve, we first 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
S => fraction of firms with sticky prices
1-s => fraction of firms with flexible prices

15. The sticky-price model Model III
price set by sticky price firms
price set by flexible price firms
Subtract (1s )P from both sides:
General price level
Divide both sides by s :

16. The sticky-price model Implications
High P e  High P If firms expect high prices, then firms who must set prices in advance will set them high. Other firms respond by setting high prices.
High Y  High P When income is high, the demand for goods is high. 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.
Effect of income on the price level is based on the existence of flexible –pricing firms.
BUT we need sticky pricing firms in order to build expectation of price different than real one.

17. The sticky-price model AS curve
Finally, derive AS equation by solving for Y :

18. The sticky-price model Implications
In contrast to the sticky-wage model, the sticky-price model implies a procyclical real wage:
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.
What happens on the labor market:
Suppose recession => falling demand

19. Summary & implications
LRAS
SRAS
Each of the three models of agg. supply imply the relationship summarized by the SRAS curve & equation

20. Summary & implications
Suppose a positive AD shock moves output above its natural rate and P above the level people had expected.
SRAS2 Y P
LRAS
AD2
SRAS1
AD1
This graph has two lessons for students:
First, changes in the expected price level shift the SRAS curve (this should be clear from the equation, as should the fact that a change in the natural rate of output will shift the SRAS curve).
The second lesson concerns the adjustment of the economy back to full-employment output.
Over time, P e rises, SRAS shifts up, and output returns to its natural rate.

21. Aggregate Supply The Inflation-Unemployment Tradeoff
Increases in aggregate demand causes
A trade-off between unemployment and inflation.
REAL OUTPUT
PRICE LEVEL
UNEMPLOYMENT RATE
INFLATION RATE
Phillips curve
Aggregate
supply c C b B
AD3 a A
AD2
AD1
LO2

22. Aggregate Supply The Phillips Curve
The Phillips curve = historical inverse relationship (tradeoff) between the rate of unemployment and the rate of inflation.
A. W. Phillips: UK, years
Samuelson and Solow: USA, years
Now, more of a theoretical concept that captures relationship between unemployment and inflation

23. Phillips curve UK
The Phillips curve in the UK,

24. Phillips curve? US

25. Phillips curve Theoretical introduction
The Phillips curve states that  depends on
expected inflation, e
cyclical unemployment: the deviation of the actual rate of unemployment from the natural rate
supply shocks, 
Story with AD movements – unemployment X price tradeoff
- stagflation – movements of AS curve
- how the Phillips curve was developed – first clear relation + then expectation and uncertainty
 measures the responsiveness of inflation to cyclical unemployment.
where  > 0 is an exogenous constant.

26. Phillips curve How to derive the Phillips Curve from SRAS
Equation (1) is the SRAS equation.
Solve (1) for P to get (2).
To get (3), add the supply shock term to (2).
To get (4), subtract last year’s price level (P-1) from both sides.
To get (5), write  in place of (P- P-1) and e in place of (Pe- P-1). Note that the change in the price level is not exactly the inflation rate, unless we interpret P as the natural log of the price level.
Equation (6) captures the relationship between output and unemployment from Okun’s law (chapter 2): the deviation of output from its natural rate is inversely related to cyclical unemployment.
Substituting (6) into (5) gives (7), the Phillips curve equation introduced on the preceding slide.

27. Phillips curve The Phillips Curve and SRAS
SRAS curve: output is related to unexpected movements in the price level
Phillips curve: unemployment is related to unexpected movements in the inflation rate
Both equations show a link between real and nominal variables that causes the classical dichotomy to break down in the short run.

28. Phillips curve 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
What determines expected inflation – how can policymakers affect it?
Then, the P.C. becomes

29. Phillips curve Inflation inertia
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.
Existence of NAIRU – Non-Accelerating Inflation rate of unemployment
Un – NAIRU – Non-Accelerating Inflation Rate of Unemployment
Adaptive expectations
No supply shocks – v
No cyclical unemployment
(even without external factors existence of continuous inflation => Self-fulfilling “prophecies” of inflation)

30. Phillips curve Two causes of rising & falling inflation
demand-pull inflation: inflation resulting from demand shocks.
Positive shocks to aggregate demand cause unemployment to fall below its natural rate, which “pulls” the inflation rate up.
cost-push inflation: inflation resulting from supply shocks.
Adverse supply shocks typically raise production costs and induce firms to raise prices, “pushing” inflation up.
Demand – pull inflation – operates through labor market = unemployment rate

31. Graphing the Phillips curve
In the short run, policymakers face a trade-off between  and u. u 
The short-run Phillips Curve
Here, the “short run” is the period until people adjust their expectations of inflation.
Policymaker cannot affect pi and mu

32. Shifting the Phillips curve
People adjust their expectations over time, so the tradeoff only holds in the short run. u 
E.g., an increase in e shifts the short-run P.C. upward.

33. Phillips curve The sacrifice ratio
To reduce inflation, policymakers can contract agg. demand, causing unemployment to rise above the natural rate.
The sacrifice ratio measures the percentage of a year’s real GDP that must be foregone to reduce inflation by 1 percentage point.
Estimates vary, but a typical one is 5.
Contraction of aggregate demand => Lower output (and GDP)

34. Phillips curve The sacrifice ratio II
Suppose policymakers wish to reduce inflation from 6 to 2 percent.
If the sacrifice ratio is 5, then reducing inflation by 4 points requires a loss of 45 = 20 percent of one year’s GDP.
This could be achieved several ways, e.g.
reduce GDP by 20% for one year
reduce GDP by 10% for each of two years
reduce GDP by 5% for each of four years
The cost of disinflation is lost GDP. One could use Okun’s law to translate this cost into unemployment.
Do example:
Suppose Phillips curve is: pi = pie – 0.4 (u -un )
Where pie = pi(-1) and un=0.05
If want to reduce inflation from 0.06 to 0.02:
0.02 = 0.06 – 0.4(u )
so = -0.4(u )
so 0.10 = u – 0.06
So u = 0.16 (so have to raise u by 10 %pts)
Next year: pi(-1) = 0.02
0.02 = 0.02 – 0.4(u -0.06)
So u = 0.06
(no need for extra unemployment)

35. Phillips curve 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.
A good example to illustrate the difference between adaptive and rational expectations.
Suppose the Fed announces a shift in priorities, from maintaining low inflation to maintaining low unemployment w/o regard to inflation; this shift will start affecting policy next week.
If expectations are adaptive, then expected inflation will not change, because it is based on past inflation. The Fed’s announcement pertains to the future, and has no impact on past inflation.
If expectations are rational, then expected inflation will increase right away, as people factor this announcement into their forecasts.

36. Phillips curve 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,  can fall without an increase in u.

37. CASE STUDY The sacrifice ratio for the Volcker disinflation
1981:  = 9.7%
1985:  = 3.0%
Total disinflation = 6.7%
year u
u n
uu n
1982
9.5%
6.0%
3.5%
1983
9.5
6.0
3.5
1984
7.4
1.4
1985
7.1
1.1
Beginning of 80’s – very high inflation levels
Tight monetary policy => lower aggregate demand => lower unemployment => lower inflation
The natural rate of unemployment is assumed to be 6.0% during the early 1980s.
Total 9.5%

38. CASE STUDY The sacrifice ratio for the Volcker disinflation
Previous slide:
inflation fell by 6.7%
total of 9.5% of cyclical unemployment
Okun’s law: each 1 percentage point of unemployment implies lost output of 2 percentage points.
So, the 9.5% cyclical unemployment translates to 19.0% of a year’s real GDP.
Sacrifice ratio = (lost GDP)/(total disinflation)
= 19/6.7 = 2.8 percentage points of GDP were lost for each 1 percentage point reduction in inflation.

39. The natural rate hypothesis
Our analysis of the costs of disinflation, and of economic fluctuations in the preceding chapters, is based on the natural rate hypothesis:
Changes in aggregate demand affect output and employment only in the short run.
In the long run, the economy returns to the levels of output, employment, and unemployment described by the classical model.
The natural rate hypothesis allows us to study the long run separately from the short run.
Challenge = hysteresis = long-lasting effect of irregularities in AD on natural rate of unemployment
Loss of skills of workers
Attitudes towards work
Wage-setting process : shift of market power

40. Chapter summary 1. Three models of aggregate supply in the short run:
sticky-wage model
imperfect-information model
sticky-price model
All three models imply that output rises above its natural rate when the price level rises above the expected price level.

41. Chapter summary 2. Phillips curve derived from the SRAS curve
states that inflation depends on
expected inflation
cyclical unemployment
supply shocks
presents policymakers with a short-run tradeoff between inflation and unemployment