ECOS2002 – Intermediate Macroeconomics
Week 3: ’The IS-LM Model’
Copyright By PowCoder代写 加微信 powcoder
The University of 2 – 2022
ECOS2002 – Intermediate Macroeconomics The University of 1
Due: 21st August 6pm Sydney time
Portal opens August 16th
30 mins; 1 Attempt
12 equally weighted questions which address the topics we covered in
ECOS2002 – Intermediate Macroeconomics The University of Outline
Deriving the IS-Curve
Deriving the LM-Curve
Equilibrium in the IS-LM model
Policy in the IS-LM model
Extensions to the Model
I Endogeneity of Money
I The Zero Lower Bound
Readings: Blanchard and 5
ECOS2002 – Intermediate Macroeconomics The University of IS-LM Model
This model is the mathematical representation of Keynesian
macroeconomic theory described by J.M. Keynes in The General
It is a pure demand side model meaning that in its most basic form it
does not ask about supply constraints in the economy
By itself the model used to study the short run but it is often
considered as a path to explain the AS-AD model (next week)
Assumptions:
I Price level exogenous (no inflation considered)
I No supply constraints
ECOS2002 – Intermediate Macroeconomics The University of IS-LM Model
Two markets:
I The Goods Market: IS curve
I The Money Market: LM curve
ECOS2002 – Intermediate Macroeconomics The University of the IS-Curve
Let’s start with the equilibrium condition from the Keynesian Cross:
[c0 − c1T̄ + Ī + Ḡ ] (1)
So far, investment was exogenous, however, this is not realistic
Investment (I):
I Depends negatively on the interest rate i
I = I0 − I1i (2)
Taxes T and government spending G remain exogenous (for now)
ECOS2002 – Intermediate Macroeconomics The University of the IS-Curve algebraically
The new goods market equilibrium can be described as
[c0 − c1T̄ + I0 − I1i + Ḡ ] (3)
To derive the IS curve, we have to solve the goods market equilibrium
Y (1− c1) = [c0 − c1T̄ + I0 − I1i + Ḡ ] (4)
I1i = [c0 − c1T̄ + I0 + Ḡ ]− (1− c1)Y (5)
[c0 − c1T̄ + I0 + Ḡ ]
I Negative slope: − (1−c1)
ECOS2002 – Intermediate Macroeconomics The University of the IS-Curve graphically
1 Start with goods market graph
2 Draw a new graph below
3 Label x-axis Y and the y-axis i
4 Pick an initial nominal interest rate, i
5 Use this value to draw in a planned expenditure or goods market
demand curve
6 Now change i ⇒ i ′ > i
7 Now we can find two points in (Y , i) space
ECOS2002 – Intermediate Macroeconomics The University of the IS-Curve
ECOS2002 – Intermediate Macroeconomics The University of of the IS-Curve
In general:
I Movement along curve: Endogenous Variables
I Shifts: Exogenous Variables
The IS curve shifts due to changes in taxation T̄ and government
spending Ḡ
ECOS2002 – Intermediate Macroeconomics The University of in Taxation
ECOS2002 – Intermediate Macroeconomics The University of the LM-Curve
Let’s start with the equilibrium condition in the money market:(M
= L0Y − L1i (7)(M
LM relation: Real money supply equals real money demand(M
ECOS2002 – Intermediate Macroeconomics The University of the LM-Curve
= L0Y − L1i
L1i = L0Y −
I L0: The responsiveness of money demand to income
I L1: The responsiveness of money demand to the nominal interest rate
The LM (Liquidity Money) curve describes the relationship between
the interest rate, the stock of money, and output:
ECOS2002 – Intermediate Macroeconomics The University of the LM-Curve
1 Start with the money market graph
2 Draw a new graph to the right
3 Label x-axis Y and the y-axis i
4 Pick an initial nominal interest rate i and income level Y in the money
market graph
5 Place an initial point in the (Y , i) space
6 Now change Y ⇒ Y ′ > Y
7 Now we can find two points in (Y , i) space
ECOS2002 – Intermediate Macroeconomics The University of the LM-Curve
ECOS2002 – Intermediate Macroeconomics The University of of the LM-Curve
Changes in M
will shift the LM curve
I Changes in the nominal money stock M
I Changes in the price level P
ECOS2002 – Intermediate Macroeconomics The University of in the IS-LM model
An algebraic example
Y = C + I + G
C = c0 + c1(Y − T )
= L0Y − L1i
I = I0 − I1i
ECOS2002 – Intermediate Macroeconomics The University of in the IS-LM model
Goods market equilibrium:
[c0 − c1T̄ + I0 − I1i + Ḡ ]
Money market equilibrium:
ECOS2002 – Intermediate Macroeconomics The University of in the IS-LM model
General Equilibrium in the Economy:
c0 − c1T̄ + I0 − I1i + Ḡ
c0 − c1T̄ + I0 − I1
Solve for Y:
Y (1− c1) =
c0 − c1T̄ + I0 − I1
Y (1− c1) + I1
c0 − c1T̄ + I0 +
1− c1 + I1L0L1
c0 − c1T̄ + I0 +
ECOS2002 – Intermediate Macroeconomics The University of in the IS-LM model
General Equilibrium in the Economy:
1− c1 + I1L0L1︸ ︷︷ ︸
IS-LM Multiplier
c0 − c1T̄ + I0 +
IS-LM Autonomous Spending
The multiplier is smaller than in the traditional Keyensian-Cross model
1− c1 + I1L0L1
ECOS2002 – Intermediate Macroeconomics The University of in the IS-LM model
ECOS2002 – Intermediate Macroeconomics The University of in the IS-LM Model
Fiscal Policy: The use of government spending and taxation to
influence macroeconomic conditions
Contractionary fiscal policy:
I Fiscal policy that decreases the demand for goods and services by the
government, business, or consumers ⇒ G ↓, T ↑
Expansionary fiscal policy:
I Fiscal policy that increases the demand for goods and services by the
government, business, or consumers ⇒ G ↑, T ↓
Let’s consider that the government increases taxes to consolidate the
ECOS2002 – Intermediate Macroeconomics The University of in the IS-LM Model
Let’s consider the IS/LM GDP Equilibrium
1− c1 + I1L0L1
c0 − c1T̄ + I0 +
1− c1 + I1L0L1
∆c0 − c1∆T̄ + I0 +
Because we are considering only a change in ∆T ,all other changes are
equal to zero
1− c1 + I1L0L1
ECOS2002 – Intermediate Macroeconomics The University of in the IS-LM Model
An increase in taxation reduces output by:
1− c1 + I1L0L1
Note that the change in taxation is negative
If taxes increase, then output will decrease
ECOS2002 – Intermediate Macroeconomics The University of Fiscal Policy in the IS-LM Model
ECOS2002 – Intermediate Macroeconomics The University of in the IS-LM model
Spending multipliers and crowding out
The IS-LM model predicts, that an increase in public spending,
increases the nominal interest rate
A higher nominal interest rate crowds out private investment
When interest rates increase, it is more expensive to get a loan or
build up capital
Crowding out is explicit in the IS/LM model and results in a smaller
multiplier
Crowding out
ECOS2002 – Intermediate Macroeconomics The University of in the IS-LM Model
Monetary Policy: Monetary policy in the IS/LM is conducted
through changes in the money supply M.
These are shifting the LM curve up or down
Contractionary monetary policy:
I Decrease in money supply and an subsequent increase in interest rates
⇒ M ↓ → i ↑ (LM curve shifts upward/leftward)
Expansionary fiscal policy:
I Increase in money supply (and a subsequent decrease in interest rates)
⇒ M ↑ → i ↓ (LM curve shifts downward/rightward)
ECOS2002 – Intermediate Macroeconomics The University of Monetary Policy in the IS-LM Model
ECOS2002 – Intermediate Macroeconomics The University of in the IS-LM Model
ECOS2002 – Intermediate Macroeconomics The University of Policy Mix
Monetary and fiscal policy is never conducted in complete isolation.
The combination of monetary and fiscal policies is known as the
monetary–fiscal policy mix, or simply, the policy mix.
Up until now, we have assumed that the central bank chooses the
nominal money supply, M, and sticks with it.
But, normally, the central bank decides to keep the interest rate
constant rather than M constant (or more precisely, the interest rate
equal to some short-term target, i0).
Consider a fiscal contraction (G ↓ orT ↑), with 2 alternative
approaches to monetary policy:
1 Central bank keeps M constant
2 Central bank keeps i constant at i0
ECOS2002 – Intermediate Macroeconomics The University of Mix
The fiscal policy contraction leads to a much lower level of output if
the central bank keeps the interest rate constant.
The reason is that investment would have been stimulated by the
falling interest rate, thus partly compensating for the reduction in
aggregate demand from the fiscal contraction.
ECOS2002 – Intermediate Macroeconomics The University of and Monetary Policy in Same Direction
Deficit Reduction and Monetary Contraction
Tight fiscal and tight monetary policy has severe adverse effects on
ECOS2002 – Intermediate Macroeconomics The University of and Monetary Policy in Opposite Direction
Fiscal Contraction and Monetary Expansion
Tight fiscal and easy monetary policy allows output to continue to
grow modestly
ECOS2002 – Intermediate Macroeconomics The University of I: Endogeneity of Money
So far we were assuming the central bank chooses the money stock
and then just lets the interest rate adjust
This is not how modern monetary policy is conducted
Let’s think of the central bank as choosing the interest rate and doing
what it needs to do with money supply to achieve it
In this scenario the LM curve becomes a horizontal line
LM relation: i = ī
ECOS2002 – Intermediate Macroeconomics The University of I: Endogeneity of Money
ECOS2002 – Intermediate Macroeconomics The University of II: The ZLB
Liquidity trap
”After the rate of interest has fallen to a certain level, liquidity preference
may become virtually absolute in the sense that almost everyone prefers
holding cash rather than holding a debt which yields so low a rate of
interest.” (Keynes, 1936 General Theory)
After the financial crisis and especially during Covid many central
banks around the world have moved interest rate to the Zero-Lower
bound (ZLB)
This is essentially the liquidity trap Keynes was talking
Let’s adjust our model so that it can capture the ZLB
ECOS2002 – Intermediate Macroeconomics The University of Question
What do you think happens to the curves in the IS-LM model if the
economy is at the ZLB?
a The IS curve is horizontal and the LM curve is unchanged.
b The LM curve is horizontal and the IS curve is unchanged.
c The LM curve and the IS curve are unchanged.
d The LM curve is vertical and the IS curve is unchanged.
ECOS2002 – Intermediate Macroeconomics The University of II: The ZLB
When interest rates are close or equal to zero, the central bank
cannot push interest rates further down. Why?
I Outside option to hold cash if rates go negative
I Financial assets are not as desirable because their liquidity is lower and
the return is close to zero
In this scenario the LM curve becomes horizontal as well even when
we assume quantity-setting monetary policy:
I Agents are indifferent between holding money or other assets
I Demand for money becomes infinitely elastic
ECOS2002 – Intermediate Macroeconomics The University of II: The ZLB
What happens if the government decides to conduct expansionary
fiscal policy?
ECOS2002 – Intermediate Macroeconomics The University of
The IS-LM model combines the implications of equilibria in both the
goods and the financial market
The IS curve shows combinations of interest rate and output
consistent with the equilibrium in the goods market
The LM curve shows combinations of interest rate and output
consistent with the equilibrium in the financial market
Fiscal policy leads to crowding out if the LM curve is upward sloping
Assumptions matter! Change the assumption and you will see
different results
ECOS2002 – Intermediate Macroeconomics The University of
The model captures aggregate demand for goods and services
However, we also need think about the supply side of the economy
This means we have to look at employment and prices
ECOS2002 – Intermediate Macroeconomics The University of
Expand the model to the AS-AD model
Bringing prices and employment into the model
Next week: The Labour Market
ECOS2002 – Intermediate Macroeconomics The University of Sydney
程序代写 CS代考 加微信: powcoder QQ: 1823890830 Email: powcoder@163.com