1. Aggregate Supply & SR Tradeoff between Inflation and Unemployment
CHAPTER THIRTEEN
Aggregate Supply & SR Tradeoff between Inflation and Unemployment
Chapter 13 has two parts. The first concerns aggregate supply. In the preceding chapters, we made the simple and extreme assumption that all prices were “stuck” in the short run. This assumption implied a horizontal short-run aggregate supply curve. More realistic models of aggregate supply imply an upward-sloping SRAS curve. Chapter 13 presents three of the most prominent models.
The second half of the chapter is devoted to the Phillips curve and related issues. The section uses a few lines of algebra to derives an expression for the Phillips curve from the SRAS equation. This is followed by a discussion of adaptive and rational expectations, and the sacrifice ratio. The chapter concludes by contrasting the notion of hysteresis to the natural rate hypothesis.
Homework or in-class exercises in which students use the models to analyze the effects of policies and shocks would be assigned. Before the introduction of the Phillips curve would be a good place to have students work an exercise using the IS-LM-AD-AS model with a positively-sloped SRAS curve.
The key difference is that, in the short run, a shift in AD causes P to change, which changes M/P, which shifts LM a bit, which explains why the short-run change in output is smaller when SRAS is upward-sloping than when it is horizontal.

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

3. Three models of aggregate supply
The sticky-wage model
The imperfect-information model
The sticky-price model
All three models imply:
; α>0
agg. output
a positive parameter
the actual price level
the expected price level
natural rate of output
;α>0

4. The sticky-wage model
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 they set is the product of a target real wage and the expected price level:
Target real wage

5. The sticky-wage model 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
Real wage exceeds its target, so firms hire fewer workers and output falls below its natural rate

6. An assumption of the sticky price model is that employment is determined by the quantity of labour that firms demand. Firms hiring decision is based on the labour demand function; L= Ld(W/P).
If the Nominal wage W is fixed, an increase in the price level from P1 to P2 reduces the real wage from W/P1 to W/P2. The lower real wage raises the quantity of labour demanded from L1 to L2.
Panel (b) shows the production function. An increase in the quantity of labour from L1 to L2 raises output from Y1 to Y2.
Panel (c) shows the aggregate supply curve summarizing the relationship between the price level and output. An increase in the price level form P1 to P2 raises output from Y1 to Y2.

7. The sticky-wage model
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:
Now let us read and discuss Case study on page 379.

8. The cyclical behavior of the real wage4
1972 3
1998
1965 2
Percentage change in real wage
1960
1997
1999 1
1996
2000
1970
1984
1982
1993
1991
1992 -1
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

9. 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

10. The imperfect-information model
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.

11. The sticky-price model
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)
Monopolistic competition implies firms have some market power.
This is one of the models that explains an upward sloping SRAS
Firms do not instantly adjust the prices they charge in response to changes in demand
Slide provide some of the main reasons

12. The sticky-price model
An individual firm’s desired price is
where a > 0.
The firms’ desired price depends on two macro variables:
The overall price level P
The level of aggregate income, Y
The higher the overall price level, the more the firm would like to set for its product.
A higher the level of income increases the demand for the firms product. Because, the marginal costs increase at higher levels of production, the greater the demand the higher the firm’s desired price
slide 11 11

13. The sticky-price 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:

14. The sticky-price model
Assume sticky price firms 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

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

16. The sticky-price model
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.

17. The sticky-price model
Finally, derive AS equation by solving for Y :
Deviation of output from the natural level is positively associated with the deviation of the price level from the expected price level.

18. The sticky-price model
In contrast to the sticky-wage model, the sticky-price model implies a pro-cyclical 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.

19. Summary & Implications
We have seen three models of the aggregate supply that explains an upward sloping SRAS:
Sticky price model- assumes some prices are sticky
Sticky nominal wages models
Assumes information about prices are imperfect
Imperfect information model
These models are not incompatible with one another
Models differ in their assumptions and emphasis but implications for aggregate output are similar
Deviations of output from the natural level is positively associated with the deviation of the price level from the expected price level.
slide 18 18

20. Summary & implications
Figure 13-3, p.357
Idiosyncracy alert:
If  is constant, then the SRAS curve should be linear, strictly speaking. However, in the text, it is drawn with a bit of curvature (which I have reproduced here). Y P
LRAS
SRAS
Each of the three models of agg. supply imply the relationship summarized by the SRAS curve & equation
If the price level is higher than the expected price level, output exceeds its natural level.
If the price level is lower than the expected price level, output falls short its natural level.
Note that the SRAS is drawn for a given Pe and that a change in Pe would shift the curve.

21. 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.