Transcript The Sticky Price Model - The Economics Network

Three Models of
Aggregate Supply
The sticky wage, imperfectinformation, and sticky price
models.
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.
Y  Y   (P  Pe )
where α>0, Y is output,Y is the natural rate of output, P is the
price level, and Pe is the expected price level.
Model Background
• This equation states that output deviates from its natural rate
when the price level deviates from the expected price level. α
indicates how much output responds to unexpected changes in P
and 1/α is the slope of the AS curve.
Y  Y   (P  P )
e
• 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.
The Sticky Wage Model
W/P
• Many economists believe that
nominal wages are sticky in the short
run.
P
When the nominal wage is
stuck,
rise inreal
P from
P0 to
Thea lower
wage
P1 lowers
thetoreal
induces
firms
hirewage,
more
The
additional
labour
hired
making
labour
cheaper.
labour.
produces more output.
The positive relationship
between P and Y means AS
slopes upward.
W/P0
W/P1
DL
L0
L1
Y
Y1
P1
Y  Y   (P  Pe )
L
Y=F(L)
Y0
P0
Y0
Y1
Y
L0
L1
L
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.
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-information model attributes
the positively sloped AS curve to temporary misperceptions
about prices.
The Imperfect-Information Model
• With some simple
algebra we can rewrite
our supply curve in
inverse form getting…
Y Y
P
 Pe

Each individual
supplier
…but
must guess
at the
observes
own
overall
pricetheir
level
andprice
form
an closely…
expectation.
P
If all prices in the economy
(unobserved) increase
including the supplier’s own
price (observed) and the
supplier expected it then
P=Pe and output remains
unchanged. The perception
is that the relative price for
the supplier has not
changed.
Y  Y   (P  Pe )
P1=P1e
P0=P0e
Y0
Y
The Imperfect-Information Model
Y Y
P
 Pe

If all prices in the economy
(unobserved) increase including
the supplier’s 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
(P>Pe). The supplier then
produces more output.
So, when actual prices exceed
expected prices, suppliers raise
their output. The positive
relationship between P and Y
means AS slopes upward.
P
Y  Y   (P  Pe )
P1>P1e
P0=P0e
Y0
Y1
Y
The Sticky Price Model
•
This model explains an upward sloping AS curve by assuming that
some prices are sticky because
1.
firms have long term contracts with customers,
2.
firms hold prices steady in order not to annoy regular customers
with frequent price changes, and
3.
for firms who have printed and distributed a catalog or price list it is
too costly to alter prices.
The Sticky Price Model
• The typical firm’s desired price
“p” depends on two
macroeconomic variables…
The overall price level “P”, where
a higher price level implies that
the firm’s costs are higher so the
firm wants to charge more for its
own product.
The parameter “a” measures how
much the firm’s desired price responds
to the level of aggregate output.
p  P  a(Y  Y )
And the level of
aggregate income “Y”,
where a higher level of
income raises the
demand for the firm’s
product so firms raise
prices to cover the higher
marginal costs.
The Sticky Price Model
• Now we assume there are two
types of firms.
p  P  a(Y  Y )
Some have flexible prices. They always set
their prices according to this equation.
e
p  P  a(Y  Y )
e
p  Pe
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.
e
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 first term is the price of the stickyprice firms weighted by their fraction in
the economy.
P  sPe  (1  s)[P  a(Y  Y )]
The second term is the price of the
flexible price firms weighted by their
fraction.
Now subtract (1 – s)P from both sides
getting…
sP  sPe  (1  s)[a(Y  Y )]
Dividing both sides by “s” gives us…
P  Pe  [(1  s)a / s](Y  Y )
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...
P  Pe  [(1 s)a / s](Y  Y )
Y  Y   (P  Pe )
  s /[(1  s)a]
The Sticky Price Model
• 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.
W/P
SL
W/P
• If The
sticky
model
is also
a firm’s
price price
is stuck
in the short
run then a
consistent
a procyclical
realfirm is
decrease
in ADwith
reduces
the amount the
wage.
able
to sell. The firm responds by reducing
demand for labour.
DL
P
L1
L
L0
p  P  a(Y  Y )
So fluctuations in output are associated with
a shifting labour demand curve.
Y  Y   (P  Pe )
P1
If a firm’s 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
Y1
Y0
Y
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…
Y  Y   (P  P )
e