Three Models of Aggregate Supply

1
Three Models of Aggregate Supply

• The sticky wage, imperfect-information, and
  sticky price models.

2
Model Background

• Most economists analyze short-run fluctuations in
  aggregate income and the price level using the
  AD/AS model.
• Earlier we introduced long-run AS as a vertical
  line which implied perfect flexibility for
  prices.
• Our short-run AS curve was perfectly horizontal
  which implied perfect rigidity for prices.
• Now we will propose theories for a positively
  sloped AS curve. This implies a tradeoff between
  between inflation and unemployment.
• All three models adhere to the following
  functional form.

where agt0, Y is output,
is the natural rate of output, P is the
price level, and Pe is the expected price level.
3
Model Background

• This equation states that output deviates from
  its natural rate when the price level deviates
  from the expected price level. a indicates how
  much output responds to unexpected changes in P
  and 1/a is the slope of the AS curve.

• Although each of the three theories adheres to
  the given functional form, each highlights a
  different reason why unexpected movements in the
  price level are associated with fluctuations in
  aggregate output.

4
The Sticky Wage Model
W/P

• Many economists believe that nominal wages are
  sticky in the short run.

When the nominal wage is stuck, a rise in P from
P0 to P1 lowers the real wage, making labour
cheaper.
W/P0
The lower real wage induces firms to hire more
labour.
DL
W/P1
The additional labour hired produces more output.
The positive relationship between P and Y means
AS slopes upward.
L
L0
L1
Y
P
Y1
YF(L)
P1
Y0
P0
L
Y
L0
L1
Y1
Y0
5
The Sticky Wage Model

• The downfall of the sticky wage model is that it
  predicts a countercyclical relationship between
  the real wage and output. Actual data suggests a
  procyclical relationship.

6
The Imperfect-Information Model

• Unlike the sticky wage model, this model assumes
  that wages and prices are free to adjust and that
  the labour market clears. The imperfect-informati
  on model attributes the positively sloped AS
  curve to temporary misperceptions about prices.

7
The Imperfect-Information Model

• With some simple algebra we can rewrite our
  supply curve in inverse form getting

Each individual supplier observes their own price
closely
but must guess at the overall price level and
form an expectation.
P
If all prices in the economy (unobserved)
increase including the suppliers own price
(observed) and the supplier expected it then PPe
and output remains unchanged. The perception is
that the relative price for the supplier has not
changed.
P1P1e
P0P0e
Y
Y0
8
The Imperfect-Information Model
If all prices in the economy (unobserved)
increase including the suppliers own price
(observed) and the supplier did not expect it
then the supplier perceives mistakenly that the
relative price of their own product has increased
(PgtPe). The supplier then produces more output.
P
P1gtP1e
P0P0e
Y
Y0
Y1
So, when actual prices exceed expected prices,
suppliers raise their output. The positive
relationship between P and Y means AS slopes
upward.
9
The Sticky Price Model

• This model explains an upward sloping AS curve by
  assuming that some prices are sticky because
• firms have long term contracts with customers,
• firms hold prices steady in order not to annoy
  regular customers with frequent price changes,
  and
• for firms who have printed and distributed a
  catalog or price list it is too costly to alter
  prices.

10
The Sticky Price Model

• The typical firms desired price p depends on
  two macroeconomic variables

The overall price level P, where a higher price
level implies that the firms costs are higher so
the firm wants to charge more for its own product.
And the level of aggregate income Y, where a
higher level of income raises the demand for the
firms product so firms raise prices to cover the
higher marginal costs.
The parameter a measures how much the firms
desired price responds to the level of aggregate
output.
11
The Sticky Price Model

• Now we assume there are two types of firms.

Some have flexible prices. They always set their
prices according to this equation.
Others have sticky prices. They announce their
prices in advance based on what they expect
economic conditions to be.
For simplicity, assume that these firms expect
output to be at its natural rate, so that the
last term is zero. These firms set their price
based on what they expect other firms to charge.
12
The Sticky Price Model

• With the pricing rules of these two groups we can
  derive the aggregate supply equation.
• We want the overall price level in the economy,
  which is the weighted average of the prices set
  by the two groups.

If s is the fraction of firms with sticky
prices and 1 s the fraction with flexible
prices, then the overall price level is
The second term is the price of the flexible
price firms weighted by their fraction.
The first term is the price of the sticky-price
firms weighted by their fraction in the economy.
Now subtract (1 s)P from both sides getting
Dividing both sides by s gives us
13
The Sticky Price Model

• So when firms expect a high price level, they
  expect high costs. Those firms that fix prices
  in advance set their prices high. These high
  prices cause the other firms to set high prices
  also. Hence, a high expected price level Pe
  leads to a high actual price level P.
• When output is high, the demand for goods is
  high. Those firms with flexible prices set their
  prices high, which leads to a high price level.
  The effect of output on the price level depends
  on the proportion of firms with flexible prices.
• So, the overall price level depends on the
  expected price level and on the level of output.

Algebraic rearrangement of the price formula
Yields the familiar AS function.
Where...
14
The Sticky Price Model
W/P

• Like the other models the sticky-price model says
  that the deviation of output from the natural
  rate is positively associated with the deviation
  of the price level from the expected price level.
  
• The sticky price model is also consistent with a
  procyclical real wage.

SL
W/P
DL
If a firms price is stuck in the short run then
a decrease in AD reduces the amount the firm is
able to sell. The firm responds by reducing
demand for labour.
L
P
L0
L1
So fluctuations in output are associated with a
shifting labour demand curve.
P1
If a firms price is flexible in the short run
then a decrease in AD reduces the amount the firm
is able to sell. The firm responds by reducing
its price.
P0
Y
Y0
Y1
15
Conclusion

• This section presents three models of AS that why
  it is upward sloping in the short run. One model
  assumes nominal wages are sticky the second
  assumes information about prices is imperfect
  the third assumes prices are sticky. The world
  may contain all three of these market
  imperfections, and all may contribute to the
  behavior of short-run AS. All can be summarized
  by the equation