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MACROECONOMICS
Chapter 10: Aggregate Demand I:Building the IS -LM Model*
Chapter 10: Aggregate Demand I: Building the IS -LM Model 0/51
Seventh Edition
N. Gregory Mankiw
Slides based on Ron Cronovich's slides, adjusted for course in Macroeconomics at the Wang Yanan Institute for Studies in Economics at Xiamen University.
Learning Objectives
This chapter introduces you to understanding:
the goods market and the IS curve
the money market and the LM curve
Chapter 10: Aggregate Demand I: Building the IS -LM Model 1/51
the money market and the LM curve
the short-run equilibrium
• Simple closed economy model in which income is determined by expenditure.
• Notation: PE = C + I + G = planned expenditure (PE)Y = real GDP = actual expenditure=output
10.1) Goods Market and IS Curve� The Keynesian Cross
Chapter 10: Aggregate Demand I: Building the IS -LM Model 2/51
Y = real GDP = actual expenditure=output
• Think of PE as amount of goods households, firms and gvmt. wish to buy.
• Think of Y as goods which are actually produced.
• If PE<Y, firms cannot sell all they produced and put the difference into inventory (‘inventory investment’).
10.1) Goods Market and IS Curve� Elements of the Keynesian Cross
( )C C Y T= −
I I=
,G G T T= =
Consumption function:
For now, plannedinvestment is exogenous:
Govt policy variables:
Chapter 10: Aggregate Demand I: Building the IS -LM Model 3/51
I I=
( )E C Y T I G= − + +
=Y E
investment is exogenous:
Planned expenditure:
Equilibrium condition:
Actual expenditure = planned expenditure
P
P
10.1) Goods Market and IS Curve� Graphing Planned Expenditure
PE, Y
Planned expenditure PE =C +I +G
Chapter 10: Aggregate Demand I: Building the IS -LM Model 4/51
income, output, Y
PE =C +I +G
MPC1
10.1) Goods Market and IS Curve� Graphing the Equilibrium Condition
PE, YActual expenditure, Y=PE
Chapter 10: Aggregate Demand I: Building the IS -LM Model 5/51
income, output, Y
45º
10.1) Goods Market and IS Curve� The Equilibrium Value of Income
PE, YActual Expenditure, Y=PE
Planned expenditure,PE =C +I +G
Chapter 10: Aggregate Demand I: Building the IS -LM Model 6/51
income, output, Y
Equilibrium income
PE, Y Actual expenditure, ‘Output’,Y=E
Planned expenditure, ‘Output sold’,PE =C +I +G ;
10.1) Goods Market and IS Curve� The Equilibrium Value of Income (ctd.)
E.g. firms produced 120 cars (Y), however, according to spending plans they only sell 100 cars (PE). The
Y1
PE1
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income, output, Y
PE =C +I +G ; cars (PE). The difference, is put into inventory. Since firms don‘t like big inventories, they reduce production and economy moves towards equilbrium.
PE1
Y1
10.1) Goods Market and IS Curve� An Increase in Government Purchases
PE, Y
PE =C +I +G1
PE =C +I +G2At Y
1,
there is now an unplanned drop in inventory…
Chapter 10: Aggregate Demand I: Building the IS -LM Model 8/51
Y
PE1 = Y1 PE2 = Y2∆∆∆∆Y
…so firms increase output, and income rises toward a new equilibrium.
∆∆∆∆G
10.1) Goods Market and IS Curve� Solving for ∆YY C I G= + +
Y C I G∆ = ∆ + ∆ + ∆
MPC= × ∆ + ∆Y G
C G= ∆ + ∆
equilibrium condition
in changes
because I exogenous
∆∆∆∆C = (∆∆∆∆Y –∆∆∆∆T)
Chapter 10: Aggregate Demand I: Building the IS -LM Model 9/51
MPC= × ∆ + ∆Y G
(1 MPC)− ×∆ = ∆Y G
11 MPC
∆ = × ∆ − Y G
Because ∆∆∆∆C = MPC(∆∆∆∆Y –∆∆∆∆T)
with ∆∆∆∆T=0
Collect terms with ∆∆∆∆Y
on the left side of the equals sign:
Solve for ∆∆∆∆Y :
10.1) Goods Market and IS Curve� The Government Purchases Multiplier
Definition: the increase in income resulting from a $1 increase in G.
In this model, the govtpurchases multiplier equals
11 MPC
∆ =∆ −Y
G
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Example: If MPC = 0.8, then
1 MPC∆ −G
15
1 0.8∆ = =∆ −Y
G
An increase in G causes income to increase 5 times
as much!
An increase in G causes income to increase 5 times
as much!
• Initially, the increase in G causes an equal increase in Y: ∆∆∆∆Y = ∆∆∆∆G.
• But ↑Y ⇒ ↑C
⇒ further ↑Y
10.1) Goods Market and IS Curve� Why the Multiplier is Greater than 1
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⇒ further ↑Y
⇒ further ↑C
⇒ further ↑Y
• So the final impact on income is much bigger than the initial ∆∆∆∆G.
10.1) Goods Market and IS Curve� An Increase in Taxes
PE
PE =C2 +I +G
PE =C1 +I +GInitially, the tax increase reduces consumption, and therefore PE:
Chapter 10: Aggregate Demand I: Building the IS -LM Model 12/51
Y
PE2 = Y2 PE1 = Y1
∆∆∆∆Y
At Y1, there is now
an unplanned inventory buildup…
…so firms reduce output, and income falls toward a new equilibrium
∆∆∆∆C = −−−−MPC ∆∆∆∆T
10.1) Goods Market and IS Curve� Solving for ∆Y
Y C I G∆ = ∆ + ∆ + ∆
( )MPC= × ∆ − ∆Y T
C= ∆
eq’m condition in changes
I and G exogenous
Chapter 10: Aggregate Demand I: Building the IS -LM Model 13/51
( )MPC= × ∆ − ∆Y T
(1 MPC) MPC− ×∆ = − × ∆Y TSolving for ∆∆∆∆Y :
Final result: MPC1 MPC
−∆ = × ∆ − Y T
10.1) Goods Market and IS Curve� The Tax Multiplier
Def: the change in income resulting from a $1 increase in T :
MPC1 MPC
∆ −=∆ −Y
T
Chapter 10: Aggregate Demand I: Building the IS -LM Model 14/51
1 MPC∆ −T
0.8 0.84
1 0.8 0.2∆ − −= = = −∆ −Y
T
If MPC = 0.8, then the tax multiplier equals
10.1) Goods Market and IS Curve� The Tax Multiplier
…is negative:A tax increase reduces C, which reduces income.
…is greater than one(in absolute value):
Chapter 10: Aggregate Demand I: Building the IS -LM Model 15/51
(in absolute value): A change in taxes has a multiplier effect on income.
…is smaller than the govt spending multiplier:Consumers save the fraction (1 – MPC) of a tax cut, so the initial boost in spending from a tax cut is smaller than from an equal increase in G.
Use a graph of the Keynesian cross to show the effects of a decrease in planned investment on the equilibrium level of income/output.
10.1) Goods Market and IS Curve� 该你们了
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10.1) Goods Market and IS Curve�Definition of the IS Curve
def: a graph of all combinations of r and Y that result in goods market equilibrium
i.e.:� actual expenditure (output) = planned expenditure
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The equation for the IS curve is:
where I, as in chapter 3, is a function of the interest rate.
( ) ( )Y C Y T I r G= − + +
10.1) Goods Market and IS Curve�Deriving the IS Curve
↓r ⇒ ↑I
PE
PE =C +I (r1 )+G
PE =C +I (r2 )+GPE =Y
∆∆∆∆I⇒ ↑PE
Chapter 10: Aggregate Demand I: Building the IS -LM Model 18/51
Y2Y1
Y2Y1Y
r
Y
r1
r2
IS
⇒ ↑Y
• A fall in the interest rate motivates firms to increase investment spending, which drives up total planned spending (PE ).
10.1) Goods Market and IS Curve� Why the IS Curve is Negatively Sloped
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• To restore equilibrium in the goods market, output (a.k.a. actual expenditure, Y ) must increase.
r r
(a) The L.F. model (b) The IS curve
S1=Y-C-GS2
10.1) Goods Market and IS Curve� IS Curve & Loanable Funds Model
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S, I
I (r )r1
r2
YY1
r1
r2
Y2
IS
• We can use the IS-LM model to see how fiscal policy (G and T ) affects aggregate demand and output.
10.1) Goods Market and IS Curve� Fiscal Policy and the IS Curve
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• Let’s start by using the Keynesian cross to see how fiscal policy shifts the IS curve…
10.1) Goods Market and IS Curve�Shifting the IS Curve: ∆G
At any value of r, ↑G ⇒ ↑PE ⇒ ↑Y
PE
PE =C +I (r1 )+G1
PE =C +I (r1 )+G2
Y=PE
…so the IS curve shifts to the right.
Chapter 10: Aggregate Demand I: Building the IS -LM Model 22/51
Y2Y1
Y2Y1Y
r
Y
r1
IS1
The horizontal distance of the IS shift equals
IS2
shifts to the right.
11 MPC
∆ = ∆−
Y G∆∆∆∆Y
Use the diagram of the Keynesian cross to show how a decrease in taxes shifts the IS curve.
10.1) Goods Market and IS Curve� 该你们了: Shifting the IS Curve
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Learning Objectives
This chapter introduces you to understanding:
the goods market and the IS curve
the money market and the LM curve
Chapter 10: Aggregate Demand I: Building the IS -LM Model 24/51
the money market and the LM curve
the short-run equilibrium
• LM curve plots the relation between the interest rate and the level of income on the market for money balances.
10.2) Money Market and LM Curve � The Theory of Liquidity Preference
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• To understand this relationship Keynes introduced the theory of liquidity preference.
• A simple theory in which the interest rate is determined by money supply and money demand.
10.2) Money Market and LM Curve � Money Supply
The supply of real money balances is fixed:
rinterest
rate( )sM P
Chapter 10: Aggregate Demand I: Building the IS -LM Model 26/51
( )sM P M P=
M/Preal money
balances
M P
10.2) Money Market and LM Curve � Money Demand
Demand forreal money balances:
rinterest
rate( )sM P
( ) ( )d
M P L r=
Chapter 10: Aggregate Demand I: Building the IS -LM Model 27/51
M/Preal money
balances
M P
( ) ( )d
M P L r=
L (r )
10.2) Money Market and LM Curve � Equilibrium
The interest rate adjusts to equate the supply and demand for
rinterest
rate( )sM P
Chapter 10: Aggregate Demand I: Building the IS -LM Model 28/51
demand for money:
M/Preal money
balances
M P
( )M P L r= L (r )
r1
10.2) Money Market and LM Curve � How the Fed Raises the Interest Rate
To increase r, Fed reduces M
rinterest
rate
r2
1M
P
2M
P
Chapter 10: Aggregate Demand I: Building the IS -LM Model 29/51
M/Preal money
balances1
M
P
L (r )
r1
2M
P
10.2) Money Market and LM Curve � Monetary Tightening & Interest Rates
• Late 1970s: ππππ > 10%
• Oct 1979: Fed Chairman Paul Volcker announces that monetary policy would aim to reduce inflation
• Aug 1979-April 1980:
Chapter 10: Aggregate Demand I: Building the IS -LM Model 30/51
• Aug 1979-April 1980: Fed reduces M/P 8.0%
• Jan 1983: ππππ = 3.7%
How do you think this policy change would affect nominal interest rates? How do you think this policy change would affect nominal interest rates?
10.2) Money Market and LM Curve � Monetary Tightening & Rates, cont.
Quantity theory, Fisher effect
Liquidity preference
The effects of a monetary tightening on nominal interest rates
model
long runshort run
Chapter 10: Aggregate Demand I: Building the IS -LM Model 31/51
∆i < 0∆i > 0
8/1979: i = 10.4%
1/1983: i = 8.2%
8/1979: i = 10.4%
4/1980: i = 15.8%
flexiblesticky
Fisher effect(Classical)
preference(Keynesian)
prediction
actual outcome
prices
model
10.2) Money Market and LM Curve �Definition of the LM Curve
Now let’s put Y back into the money demand function:
The LM curve is a graph of all combinations of
( )dM P L r Y= ( , )
Chapter 10: Aggregate Demand I: Building the IS -LM Model 32/51
( , )M P L r Y=
The LM curve is a graph of all combinations of r and Y that equate the supply and demand for real money balances.
The equation for the LM curve is:
10.2) Money Market and LM Curve � Deriving the LM Curve
r r
LM
(a) The market for real money balances (b) The LM curve
Chapter 10: Aggregate Demand I: Building the IS -LM Model 33/51
M/P1
M
P
L (r ,Y1 )
r1
r2
YY1
r1
L (r ,Y2 )
r2
Y2
10.2) Money Market and LM Curve � Why the LM Curve is Upward Sloping
• An increase in income raises money demand.
• Since the supply of real balances is fixed, there is now excess demand in the money market at the
Chapter 10: Aggregate Demand I: Building the IS -LM Model 34/51
now excess demand in the money market at the initial interest rate.
• The interest rate must rise to restore equilibrium in the money market.
r r
LM1
(a) The market for real money balances
(b) The LM curve
LM2
10.2) Money Market and LM Curve � How ∆M Shifts the LM Curve
Chapter 10: Aggregate Demand I: Building the IS -LM Model 35/51
M/P1
M
P
L (r ,Y1 )r1
r2
YY1
r1
r2
2M
P
10.2) Money Market and LM Curve � 该你们了: Shifting the LM Curve
Suppose a wave of credit card fraud causes consumers to use cash more frequently in transactions. Use the liquidity preference model to show how these events shift the LM curve.
Chapter 10: Aggregate Demand I: Building the IS -LM Model 36/51
r r
LM1
(a) The market for real money balances
(b) The LM curve
LM2
10.2) Money Market and LM Curve � How increase in (M/P)D Shifts LM Curve
Chapter 10: Aggregate Demand I: Building the IS -LM Model 37/51
M/P1
M
P
L 1(r ,Y 1)r1
r2
YY1
r1
r2L 2(r ,Y 1)
Learning Objectives
This chapter introduces you to understanding:
the goods market and the IS curve
the money market and the LM curve
Chapter 10: Aggregate Demand I: Building the IS -LM Model 38/51
the money market and the LM curve
the short-run equilibrium
10.3) The Short-Run Equilibrium� Definitions and Equations
The short-run equilibrium is the combination of r and Ythat simultaneously satisfies the equilibrium conditions in the goods & money markets:
r
LM
Chapter 10: Aggregate Demand I: Building the IS -LM Model 39/51
the goods & money markets:
( ) ( )Y C Y T I r G= − + +
Y( , )M P L r Y=IS
Equilibriuminterestrate
Equilibriumlevel ofincome
10.3) The Short-Run Equilibrium� The Big Picture
KeynesianCrossKeynesianCross
Theory of Liquidity Preference
Theory of Liquidity Preference
IScurve
IScurve
LMcurveLM
curve
IS-LMmodelIS-LMmodel Explanation
of short-run fluctuations
Explanation of short-run fluctuations
Chapter 10: Aggregate Demand I: Building the IS -LM Model 40/51
PreferencePreferencecurvecurve
Agg. demand
curve
Agg. demand
curve
Agg. supplycurve
Agg. supplycurve
Model of Agg.
Demand and Agg. Supply
Model of Agg.
Demand and Agg. Supply
fluctuationsfluctuations
Preview of Chapter 11
In Chapter 11, we will
– use the IS-LM model to analyze the impact of policies and shocks.
– learn how the aggregate demand curve comes
Chapter 10: Aggregate Demand I: Building the IS -LM Model 41/51
– learn how the aggregate demand curve comes from IS-LM.
– use the IS-LM and AD-AS models together to analyze the short-run and long-run effects of shocks.
– use our models to learn about the Great Depression.
→ Behind the bald figures
Economic Text:
1) What is a leading indicator?2) Why are pet businesses, condom, and business sales said to
be leading indicators of the economic situation? 3) Why do some people suggest to take the shortness of skirts
(‘hemlines’) or countries leaders’ hairlines to be indicators of the economic situation?
Chapter 10: Aggregate Demand I: Building the IS -LM Model 42/51
economic situation?4) Even if the previous suggestions were good to predict where the
economy is heading, why are they only of limited use as leading economic indicators?
5) Which mechanism could explain the relation between the number of google searches for ‘gold price’ and the U.S. consumer confidence? What is the big advantage of this indicator if the relation proves to be stable?
Chapter SummaryChapter Summary
1. Keynesian cross
– basic model of income determination
– takes fiscal policy & investment as exogenous
– fiscal policy has a multiplier effect on income.
Chapter 10: Aggregate Demand I: Building the IS -LM Model 43/51
– fiscal policy has a multiplier effect on income.
Chapter SummaryChapter Summary
2. IS curve
– comes from Keynesian cross when planned investment depends negatively on interest rate
– shows all combinations of r and Y that equate
Chapter 10: Aggregate Demand I: Building the IS -LM Model 44/51
– shows all combinations of r and Y that equate planned expenditure with actual expenditure on goods & services
Chapter SummaryChapter Summary
3. Theory of Liquidity Preference
– basic model of interest rate determination
– takes money supply & price level as exogenous
– an increase in the money supply lowers the
Chapter 10: Aggregate Demand I: Building the IS -LM Model 45/51
– an increase in the money supply lowers the interest rate
Chapter SummaryChapter Summary
4. LM curve
– comes from liquidity preference theory when money demand depends positively on income
– shows all combinations of r and Y that equate
Chapter 10: Aggregate Demand I: Building the IS -LM Model 46/51
– shows all combinations of r and Y that equate demand for real money balances with supply
Chapter SummaryChapter Summary
5. IS-LM model
– Intersection of IS and LM curves shows the unique point (Y, r ) that satisfies equilibrium in both the goods and money markets.
Chapter 10: Aggregate Demand I: Building the IS -LM Model 47/51