Review of the labour market
• In last week’s lecture, we introduced into our
system two new endogenous variables (wages
W, price level P) and four new exogenous
variables (expected price level Pe, labour supply
L, factors affecting wage-setting z, firm mark-up
over wages μ).
• We have two equations
W = Pe F(u, z)
W = P / (1 + μ )
• To add to our IS-LM framework.
Deriving aggregate supply
• Setting these two equations equal and dropping W, we
get:
Pe F(u, z) = P / (1 + μ )
• Remember that unemployment u = 1 – Y/L, so we can
solve for output as a function of today’s price level. We
will call this relationship “aggregate supply” or AS:
F(1 - Y/L, z) = P / [Pe (1 + μ )]
• Now F(u, z) was decreasing in u as wages rise slower if
unemployment is high. This means that the higher is
the right-hand side, the lower is unemployment.
Deriving aggregate supply
• But the lower is unemployment, the higher is
output, Y.
• Combining all these we see that the higher is
the right-hand side, the higher is output. Y is
higher when P is higher, holding fixed Pe and μ.
• Our aggregate supply curve graphs output as a
function of P, so our AS curve is upward-sloping
in P.
• What else do we know about our AS curve?
Deriving aggregate supply
• We know that if P = Pe then u = un. As we
showed last week, if P = Pe:
F(un, z) = 1 / (1 + μ )
• We can solve this for the natural rate of
unemployment, un, as all the other terms
are constants. If we have a natural rate of
unemployment, then we must also have a
“natural rate of output”, Yn:
Yn = Nn =(1 – un) L
Deriving aggregate supply
• The AS curve for a
given level of
expected price must
go through the point
(Yn, Pe), or in other
terms if Y = Yn, then
P = Pe.
Deriving aggregate supply
• This is true for all AS
curves, so higher
expected prices must
shift the AS curve
upwards.
Deriving aggregate demand
• We have derived an AS equation expressing a
relationship between output by firms and the
price level. Obviously we will complement this
with an equation expressing demand for goods
as a function of price. We call this our
“aggregate demand” or AD curve.
• Our IS equation showed goods demand as a
function of government spending G, taxes T and
the interest rate i. But i also depended on
equilibrium in the LM equation.
Deriving aggregate demand
• Our IS-LM equations are:
IS: Y = C(Y – T) + I(Y, i) + G
LM: M/P = Y L(i)
• Assume the RBA holds M fixed.
• A rise in price will lower the real money supply
(M/P) so real money demand has to fall. This
means that i must rise.
• For a higher i, investment will be lower so goods
demand as a whole must also be lower. Our AD
graph for output must be downward-sloping in P.
Deriving aggregate demand
• We could think of a rise in
P as shifting the LM curve
up, so leading to lower Y
and higher i.
• A rise in G shifts the IS
curve to the right, raising
Y for any P, so shifts AD
right.
Y = Y(M/P, G, T)
Derivatives: + , + , -
What if RBA sets cash rate?
• We can add a complication. Suppose the RBA targets
interest rates and allows real money stock to vary- a
cash rate- while aiming for a target price level. (This is
the way the RBA actually operates.)
• In this case the RBA follows an “interest rate rule”, which
might be:
i = in + a(P – PT)
• If the price level exceeds the target price level, the RBA
will raise interest rates above the “natural rate of
interest”, in. If the price level is below the target rate, the
RBA will lower the interest rate below in.
• The natural rate of interest is the interest rate when P =
Pe, so Y = Yn and u = un.
Interest rate rule
• Now we have 3 equations, with 3 endogenous
variables (Y, i, P):
Y = C(Y – T) + I(Y, i) + G
M/P = Y L(i)
i = in + a(P – PT)
• We can substitute for i to reduce this system to:
Y = C(Y – T) + I(Y, in + a(P – PT)) + G
M/P = Y L(in + a(P – PT))
• These two equations are independent of each
other. Once we know P then i is fixed by the
interest rate rule, we can determine Y without
referring to the LM equation.
Interest rate rule
• Output is determined by:
Y = C(Y – T) + I(Y, in + a(P – PT)) + G
• Money supply is determined by:
M/P = Y L(in + a(P – PT))
• Our AD curve is given by:
Y = Y(in + a(P – PT), G, T)
Derivatives: ,+,• Intuition: A rise in the price level causes the RBA to
respond using its interest rate rule and raise i. The rise
in i is what causes the AD curve to be sloping down.
Since it is the response of the RBA that determines the
rise in i, the slope of the AD curve depends on the RBA.
AD equation
• Our IS-LM equations are two equations in 3
endogenous variables (Y, i, P). We have
substituted out for i and derived our AD
equation. So we have one equation in two
endogenous variables (Y, P).
• There are two forms for our AD equation:
Fixed M: Y = Y(M/P, G, T)
Target P: Y = Y(in + a(P – PT), G, T)
• Important: Both of these AD curves slope
downwards in P, but note that they slope down
for different reasons!
AS-AD equilibrium
• In our new AS-AD system, we have two
equations in (Y, P):
AS: P = Pe F(1 – Y/L, z) (1 + μ )
AD: Y = Y(M/P, G, T)
Or
AD: Y = Y(in + a(P – PT), G, T)
• But once we solve for (Y, P), we can go back
into the LM equation or interest rate rule:
M/P = Y L(i)
• To solve for i.
or
i = in + a(P – PT)
AS-AD equilibrium in short-run
• For a given Pe (and PT, if
the RBA has one), we
have the AS curve going
through (Yn, Pe).
• At point A, where As and
AD intersect, we have
short-run equilibrium in
the goods and money
market (on the AD curve)
and in the labour market
(AS curve).
AS-AD equilibrium in medium-run
• But this can’t be an equilibrium for long. In
wage-setting, workers and firms assumed that P
would be equal to Pe. But prices were higher,
and so output higher, than expected.
• Workers and firms will negotiate higher wages in
the future, which will drive prices up even further.
• Higher prices will lead to higher interest rates, so
driving output down. We move along the AD
curve up and to the left.
• This continues until expected prices equal
prices, and output is back at natural rate.
AS-AD equilibrium in medium-run
• Higher expected
prices shifts the AS
curve up, raising
current prices and
reducing Y.
• In the medium-term,
we shift along the AD
until we are back at
equilibrium with P =
Pe and Y =Yn.
Where do we end up?
• In the long-run, we will end up with prices
equal to expected prices and output equal
to the natural rate. We will also be at the
intersection of the AS-AD. AND we will
have interest rates equal to their natural
rate.
Talking through some scenarios
• For the rest of today and in the tutorial, we
will talk through some “stories” or
“scenarios” using this AS-AD framework.
It is important that you can replicate both
the economic logic of the story and the
graphs of the story.
Monetary policy contraction
• Let’s say that the RBA
wants to reduce the price
level in the economy.
• The RBA lowers the
target price, meaning that
current price is above
target price, so i has to be
raised.
• A higher i shifts the AD
curve to the left to our
new short-run equilibrium.
PT
P´
A
A´
●
●
PT´
AD´
Y´
Yn
Monetary policy contraction
• However we are now
below expected
prices, so wages
have to be reduced.
This shifts out AS
curve to the right.
• In the medium-run we
move down along the
AD curve back to LR
equilibrium.
PT
P´
A
A´
●
●
A´´
AD´
●
PT´
Y´
Yn
AS´´
Thursday tutorial
• For Thursday, practice the example of the
budget deficit decrease in Section 7.5 of
the book and Question 7 from the back of
the book.