Is curve derivation

1. 1
CHAPTER 10CHAPTER 10 Aggregate Demand IAggregate Demand I
slide 20
The The ISIScurvecurve
def: a graph of all combinations of rand Y
that result in goods market equilibrium,
i.e.actual expenditure (output)
= planned expenditure
The equation for the
IScurve is:
()()YCY T Ir G=−++
CHAPTER 10CHAPTER 10 Aggregate Demand IAggregate Demand I
slide 21
Y
2
Y
1
Y
2
Y
1
Deriving the Deriving the ISIScurvecurve
↓r⇒↑I
Y
E
r
Y
E =C +I(r
1
)+G
E
=C +I(r
2
)+G
r
1
r
2
E =Y
IS
ΔI⇒↑E
⇒↑Y

2. 2
CHAPTER 10CHAPTER 10 Aggregate Demand IAggregate Demand I
slide 22
Understanding the Understanding the ISIScurve’s slopecurve’s slope
ƒThe IScurve is negatively sloped.
ƒIntuition:
A fall in the interest rate motivates firms to
increase investment spending, which drives
up total planned spending (
E ).
To restore equilibrium in the goods market,
output (a.k.a. actual expenditure,
Y ) must
increase.
CHAPTER 10CHAPTER 10 Aggregate Demand IAggregate Demand I
slide 23
The IS The IS curve and the Loanable Funds modelcurve and the Loanable Funds model
S, I
r
I(r)
r
1
r
2
r
Y
Y
1
r
1
r
2
(a)The L.F. model (b)The IScurve
Y
2
S
1
S
2
IS

3. 3
CHAPTER 10CHAPTER 10 Aggregate Demand IAggregate Demand I
slide 24
Fiscal Policy and the Fiscal Policy and the ISIScurvecurve
ƒWe can use the IS-LMmodel to see
how fiscal policy (
Gand T ) can affect
aggregate demand and output.
ƒLet’s start by using the Keynesian Cross
to see how fiscal policy shifts the
IS
curve…
CHAPTER 10CHAPTER 10 Aggregate Demand IAggregate Demand I
slide 25
Y
2
Y
1
Y
2
Y
1
Shifting the Shifting the ISIScurve: curve: ΔΔ GG
At any value of r,
↑
G⇒↑E⇒↑Y
Y
E
r
Y
E =C +I(r
1
)+G
1
E =C +I(r
1
)+G
2
r
1
E =Y
IS
1
The horizontal
distance of the
IS shift equals
IS
2
…so the IS curve shifts to the right.
1
1MPC
Y GΔ= Δ
−
ΔY

4. 4
CHAPTER 10CHAPTER 10 Aggregate Demand IAggregate Demand I
slide 26
Exercise: Shifting the IS curveExercise: Shifting the IS curve
ƒUse the diagram of the Keynesian Cross
or Loanable Funds model to show how
an increase in taxes shifts the
IScurve.
CHAPTER 10CHAPTER 10 Aggregate Demand IAggregate Demand I
slide 27
The Theory of Liquidity PreferenceThe Theory of Liquidity Preference
ƒdue to John Maynard Keynes.
ƒA simple theory in which the interest rate
is determined by money supply and
money demand.

5. 5
CHAPTER 10CHAPTER 10 Aggregate Demand IAggregate Demand I
slide 28
Money SupplyMoney Supply
The supply of
real money
balances
is fixed:
()
s
MP MP=
M/P
real money
balances
r
interest
rate
( )
s
MP
MP
CHAPTER 10CHAPTER 10 Aggregate Demand IAggregate Demand I
slide 29
Money DemandMoney Demand
Demand for
real money
balances:
M/P
real money
balances
r
interest
rate
( )
s
MP
MP
() ()
d
MP Lr=
L(r)

6. 6
CHAPTER 10CHAPTER 10 Aggregate Demand IAggregate Demand I
slide 30
EquilibriumEquilibrium
The interest
rate adjusts
to equate the
supply and
demand for
money:
M/P
real money
balances
r
interest
rate
( )
s
MP
MP
()MP Lr=
L(r)
r
1
CHAPTER 10CHAPTER 10 Aggregate Demand IAggregate Demand I
slide 31
How the Fed raises the interest rateHow the Fed raises the interest rate
To increase r,
Fed reduces
M
M/P
real money
balances
r
interest
rate
1
M
P
L(r)
r
1
r
2
2
M
P

7. 7
CHAPTER 10CHAPTER 10 Aggregate Demand IAggregate Demand I
slide 32
CASE STUDY CASE STUDY
Volcker’sVolcker’sMonetary TighteningMonetary Tightening
ƒLate 1970s: π> 10%
ƒOct 1979: Fed Chairman Paul Volcker
announced that monetary policy
would aim to reduce inflation.
ƒAug 1979-April 1980:
Fed reduces
M/P8.0%
ƒJan 1983: π= 3.7%
How do you think this policy change
would affect interest rates?
How do you think this policy change How do you think this policy change
would affect interest rates? would affect interest rates?
CHAPTER 10CHAPTER 10 Aggregate Demand IAggregate Demand I
slide 33
Volcker’sVolcker’sMonetary Tightening, Monetary Tightening, cont.cont.
Δi< 0Δi> 0
1/1983: i= 8.2%
8/1979: i= 10.4%
4/1980:
i= 15.8%
flexiblesticky
Quantity Theory,
Fisher Effect
(Classical)
Liquidity Preference
(Keynesian)
prediction
actual
outcome
The effects of a monetary tightening
on nominal interest rates
prices
model
long runshort run

8. 8
CHAPTER 10CHAPTER 10 Aggregate Demand IAggregate Demand I
slide 34
The LM curveThe LM curve
Now let’s put Yback into the money demand
function:
(, )MP LrY=
The LMcurveis a graph of all combinations of
rand Ythat equate the supply and demand
for real money balances.
The equation for the
LMcurve is:
( )
d
MP LrY=(, )
CHAPTER 10CHAPTER 10 Aggregate Demand IAggregate Demand I
slide 35
Deriving the LM curveDeriving the LM curve
M/P
r
1
M
P
L(r,Y
1
)
r
1
r
2
r
Y
Y
1
r
1
L(r,Y
2
)
r
2
Y
2
LM
(a)The market for
real money balances
(b)The LM curve

9. 9
CHAPTER 10CHAPTER 10 Aggregate Demand IAggregate Demand I
slide 36
Understanding the Understanding the LMLMcurve’s slopecurve’s slope
ƒThe LMcurve is positively sloped.
ƒIntuition:
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 initial interest rate.
The interest rate must rise to restore
equilibrium in the money market.
CHAPTER 10CHAPTER 10 Aggregate Demand IAggregate Demand I
slide 37
How How ΔΔMMshifts the LM curveshifts the LM curve
M/P
r
1
M
P
L(r,Y
1
)
r
1
r
2
r
Y
Y
1
r
1
r
2
LM
1
(a)The market for
real money balances
(b)The LM curve
2
M
P
LM
2

10. 10
CHAPTER 10CHAPTER 10 Aggregate Demand IAggregate Demand I
slide 38
Exercise: Shifting the LM curveExercise: Shifting the LM curve
ƒSuppose a wave of credit card fraud
causes consumers to use cash more
frequently in transactions.
ƒUse the Liquidity Preference model
to show how these events shift the
LMcurve.
CHAPTER 10CHAPTER 10 Aggregate Demand IAggregate Demand I
slide 39
The shortThe short--run equilibriumrun equilibrium
The short- run equilibrium is
the combination of
rand Y
that simultaneously satisfies
the equilibrium conditions in
the goods & money markets:
()()YCY T Ir G=−+ +
Y
r
(, )MP LrY=
IS
LM
Equilibrium
interest
rate
Equilibrium level of income

11. 11
CHAPTER 10CHAPTER 10 Aggregate Demand IAggregate Demand I
slide 40
The Big PictureThe Big Picture
Keynesian
Cross
Theory of Liquidity
Preference
IS
curve
LM
curve
IS-LM
model
Agg.
demand
curve
Agg.
supply
curve
Model of
Agg.
Demand
and Agg.
Supply
Explanation
of short-run
fluctuations
CHAPTER 10CHAPTER 10 Aggregate Demand IAggregate Demand I
slide 41
Chapter summaryChapter summary
1.Keynesian Cross
ƒbasic model of income determination
ƒtakes fiscal policy & investment as exogenous
ƒfiscal policy has a multiplied impact on income.
2.IScurve
ƒcomes from Keynesian Cross when planned
investment depends negatively on interest rate
ƒshows all combinations of rand Ythat
equate planned expenditure with actual
expenditure on goods & services

12. 12
CHAPTER 10CHAPTER 10 Aggregate Demand IAggregate Demand I
slide 42
Chapter summaryChapter summary
3.Theory of Liquidity Preference
ƒbasic model of interest rate determination
ƒtakes money supply & price level as exogenous
ƒan increase in the money supply lowers the
interest rate
4.LMcurve
ƒcomes from Liquidity Preference Theory when
money demand depends positively on income
ƒshows all combinations of randYthat equate
demand for real money balances with supply
CHAPTER 10CHAPTER 10 Aggregate Demand IAggregate Demand I
slide 43
Chapter summaryChapter summary
5.IS-LMmodel
ƒIntersection of ISand LMcurves shows the
unique point (
Y, r) that satisfies equilibrium
in both the goods and money markets.

13. 13
CHAPTER 10CHAPTER 10 Aggregate Demand IAggregate Demand I
slide 44
Preview of Chapter 11Preview of Chapter 11
In Chapter 11, we will
ƒuse the
IS-LMmodel to analyze the impact
of policies and shocks
ƒlearn how the aggregate demand curve
comes from
IS-LM
ƒuse the IS-LMand AD-ASmodels together
to analyze the short-run and long-run
effects of shocks
ƒlearn about the Great Depression using our
models
CHAPTER 10CHAPTER 10 Aggregate Demand IAggregate Demand I
slide 45