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Professor Yamin Ahmad, Money and Banking – ECON 354
Money and BankingECON 354
Professor Yamin Ahmad
Lecture 9: The Building Blocks of Aggregate Demand
Goods Market Equilibrium (IS Curve)
Money Market Equilibrium (LM Curve)
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Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Big Concepts in this lecture…
the IS curve, and its relation to the Keynesian cross the loanable funds model
the LM curve, and its relation to the theory of liquidity preference
how the IS-LM model determines income and the interest rate in the short run when P is fixed
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Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
The Big Picture
KeynesianCrossKeynesianCross
Theory of Liquidity Preference
Theory of Liquidity Preference
IScurve
IScurve
LM curveLM
curve
IS-LMmodelIS-LMmodel
Agg. demand
curve
Agg. demand
curve
Agg. supplycurve
Agg. supplycurve
Model of Agg.
Demand and Agg. Supply
Model of Agg.
Demand and Agg. Supply
Explanation of short-run fluctuations
Explanation of short-run fluctuations
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Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Context Second part of lecture 2 introduced the basic model of
aggregate demand and aggregate supply.
Long run prices flexible output determined by factors of production & technology unemployment equals its natural rate
Short run prices fixed output determined by aggregate demand unemployment negatively related to output
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slide 5
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
The Keynesian Cross A (simpler) closed economy model in which
income is determined by expenditure. (due to J.M. Keynes) – book does open economy version of model.
Notation: I = planned investmentAE = C + I + G = planned expenditureY = real GDP = actual expenditure
Difference between actual & planned expenditure = unplanned inventory investment
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Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Elements of the Keynesian Cross
AE GITYCAE
( )C C Y T
I I
,G G T T
Consumption function:
for now, plannedInvestment is exogenous:
planned expenditure:
equilibrium condition:
Govt policy variables:
actual expenditure = planned expenditure
AEY
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slide 7
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Graphing planned expenditure
income, output, Y
AE
planned
expenditure
AE =C +I +G
MPC1
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slide 8
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Graphing the equilibrium condition
income, output, Y
AE
planned
expenditure
AE =Y
45º
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Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
The equilibrium value of income
income, output, Y
AE
planned
expenditure
AE =Y
AE =C +I +G
Equilibrium income
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Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
An increase in government purchases
Y
AE AE
=Y
AE =C +I +G1
AE1 = Y1
AE =C +I +G2
AE2 = Y2
Y
At Y1,
there is now an unplanned drop in inventory…
…so firms increase output, and income rises toward a new equilibrium.
G
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Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Solving for YY C I G
Y C I G
MPC Y G
C G
(1 MPC) Y G
1
1 MPC
Y G
equilibrium condition
in changes
because I exogenous
because C = MPC Y
Collect terms with Y on the left side of the equals sign:
Solve for Y :
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Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
The government purchases multiplier
Example: If MPC = 0.8, then
Definition: the increase in income resulting from a $1 increase in G.
In this model, the govt purchases multiplier equals
1
1 MPC
YG
15
1 0.8
YG
An increase in G causes income to increase 5 times
as much!
An increase in G causes income to increase 5 times
as much!
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Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Why the multiplier is greater than 1
Initially, the increase in G causes an equal increase in Y: Y = G.
But Y C
further Y
further C
further Y
So the final impact on income is much bigger than the initial G.
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Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
An increase in taxes
Y
AE
AE =Y
AE =C2 +I +G
AE2 = Y2
AE =C1 +I +G
AE1 = 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
Initially, the tax increase reduces consumption, and therefore E:
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Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Solving for YY C I G
MPC Y T
C
(1 MPC) MPC Y T
eq’m condition in changes
I and G exogenous
Solving for Y :
MPC
1 MPC
Y TFinal result:
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slide 16
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
The tax multiplier
Def: the change in income resulting from a $1 increase in T :
MPC
1 MPC
YT
0.8 0.84
1 0.8 0.2
YT
If MPC = 0.8, then the tax multiplier equals
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Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
The tax multiplier
…is negative: A tax increase reduces C, which reduces income.
…is greater than one (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.
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Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Walkthrough Example I:
Economic Scenario:
In the Keynesian Cross, assume that the consumption function is given by:
C = 475 + 0.75(Y-T)Planned Investment, I = 150, G = 250, T = 100.
a. Graph planned expenditure as a function of income
b. What is the equilibrium level of income
c. If government purchases increase by 125, what is the new equilibrium income?
d. What level of government purchases is needed to achieve an income of 2600?
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slide 19
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
A Balanced Budget Approach
Problem: Suppose that we face our canonical problem where
C=475 + 0.75(Y-T), T = 100 I = 150, G = 250
Suppose that the government wishes to increase its spending by 100, but uses a balanced budget approach, thereby raising taxes by the same amount to finance its expenditures.
Question: Is there any impact on GDP? Does it change? If so, by how much?
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Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Balanced Budget Change in GSolution:
Suppose G = T=100.
Hence
i.e. so our balanced budget multiplier = 1
Why?
1
10
1 cTcGIc
Y
AEY m,equilibriu In
10011 1
1
1
1
Gc
GcG
c
TcGY
1G
Y
GTcTcTcTc
GcGcGcGcGY
...
...41
31
211
41
31
211
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Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
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
The equation for the IS curve is:
( ) ( )Y C Y T I r G
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slide 22
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Y2Y1
Y2Y1
Deriving the IS curve
r I
Y
AE
r
Y
AE =C +I (r1 )+G
AE =C +I (r2 )+G
r1
r2
AE =Y
IS
I AE
Y
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Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Why the IS curve is negatively sloped
A fall in the interest rate motivates firms to increase investment spending, which drives up total planned spending (AE ).
To restore equilibrium in the goods market, output (a.k.a. actual expenditure, Y ) must increase.
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slide 24
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Market For Loanable Funds – Closed Economy
Define SpY-T-C(Y-T) and Sg T-G
S Sp + Sg = Y – C(Y-T) – G = S(Y; G, T)
Capital Markets Equilibrium: S(Y;G,T) = I(r)(Loanable Funds)
Or Equivalently: Y = Yd C(Y-T) + I(r) + G
(+)
(+) (-) (+)
(-)
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Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
The IS curve and the loanable funds model
S, I
r
I (r ) r1
r2
r
YY1
r1
r2
(a) The L.F. model (b) The IS curve
Y2
S1S2
IS
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slide 26
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Algebra Of The IS Curve
Suppose C = c0 + c1(Y-T) and I = I0 – br
(Note: Blanchard also considers the effect of sales on Investment by incorporating Y, i.e. I=b0+b1Y-b2r)
Then Y= C + I + G
= c0 + I0 + G + c1(Y-T) – br
If we collect like terms:
rc
b
c
TcGIcY
11
100
11
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slide 27
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Slope of the IS curve
Hold everything except Y and r fixed:
Thus IS is relatively flat if either:
(i) b is very large; or
(ii) (ii) c close to unity.
rc
b
c
TcGIcY
11
100
11
01
11
1
b
c
Y
rr
c
bY
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slide 28
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Walkthrough Example II:
Economic Scenario: Consider the following IS-LM model:
Goods Market: C = 200+0.5(Y-T); I = 200 – 1000r; G = 250; T = 200
Question:
Derive the IS relation (i.e. an equation with Y on one side and everything else on the other)
Solution
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slide 29
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Fiscal Policy and the IS curve
We can use the IS-LM model to see how fiscal policy (G and T ) affects aggregate demand and output.
Let’s start by using the Keynesian cross to see how fiscal policy shifts the IS curve…
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slide 30
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Y2Y1
Y2Y1
Shifting the IS curve: G
At any value of r, G
AE Y
Y
AE
r
Y
AE =C +I (r1 )+G1
AE =C +I (r1 )+G2
r1
AE =Y
IS1
The horizontal distance of the IS shift equals
IS2
…so the IS curve shifts to the right.
1
1 MPC
Y G Y
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slide 31
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Recall: The Theory of Liquidity Preference
Due to John Maynard Keynes.
A simple theory in which the interest rate is determined by money supply and money demand.
Money supply is exogenous – determined by Fed!
People hold wealth in the form of either: Money Bonds Demand for money and demand for
bonds!
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slide 32
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Money supply
The supply of real money balances is fixed:
sM P M P
M/P real money
balances
rinterest
rate sM P
M P
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Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Money demand
People either hold: Money Bonds
Demand forreal money balances:
M/P real money
balances
rinterest
rate sM P
M P ( )d
M P L r
L (r )
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slide 34
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Equilibrium
The interest rate adjusts to equate the supply and demand for money:
M/P real money
balances
rinterest
rate sM P
M P
( )M P L r L (r )
r1
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Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
How the Fed raises the interest rate
To increase r, Fed reduces M
M/P real money
balances
rinterest
rate
1M
P
L (r )
r1
r2
2M
P
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slide 36
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
CASE STUDY:
Monetary Tightening & Interest Rates Late 1970s: > 10%
Oct 1979: Fed Chairman Paul Volcker announces that monetary policy would aim to reduce inflation
Aug 1979-April 1980: Fed reduces M/P 8.0%
Jan 1983: = 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?
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Monetary Tightening & Rates, cont.
i < 0i > 0
8/1979: i = 10.4%
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
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slide 38
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
The LM curve
Now let’s put Y back into the money demand function:
( , )M P L r Y
Note: In Blanchard:
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:
dM P L r Y ( , )
idYdiYLP
Md
21
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slide 39
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Nominal or Real Rates in Money Demand?
What is real return to saving $1?
This is known as the Fisher Equation.
So:
Treat Ms as exogenous; for present set = 0.
iri
r
1
11
),( YiLd
PM
P
M :mEquilibriu MarketMoney (-)(+)
YrLP
M,
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slide 40
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Deriving the LM curve
M/P
r
1M
P
L (r ,
Y1 )
r1
r2
r
YY1
r1
L (r ,
Y2 )
r2
Y2
LM
(a) The market for real money balances (b) The LM curve
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slide 41
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
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 initial interest rate.
The interest rate must rise to restore equilibrium in the money market.
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slide 42
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
There are two assets (money and bonds), but only one equilibrium condition. Do we need to worry about bond market equilibrium as well? Answer:
dBsBd
PM
P
dBd
PMAsB
P
sM : So
wealth.realAwith
sM
This is an example of Walras Law.
Equilibrium in the Bond Market?
No!
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slide 43
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Algebra of the LM Curve
With M and P fixed: 0 = kY - h r
Slope of LM Curve :
LM curve relatively flat if either:
(i) k small; or
(ii) (ii) h large ( “ Liquidity Trap”)
hrkYmd
0PM :Write
0
h
k
Y
r
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slide 44
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
How M shifts the LM curve
M/P
r
1M
P
L (r , Y1 ) r1
r2
r
YY1
r1
r2
LM1
(a) The market for real money balances (b) The LM curve
2M
P
LM2
![Page 45: Professor Yamin Ahmad, Money and Banking – ECON 354 Money and Banking Money and Banking ECON 354 Professor Yamin Ahmad Lecture 9: The Building Blocks of](https://reader036.vdocument.in/reader036/viewer/2022062308/56649d6a5503460f94a493a5/html5/thumbnails/45.jpg)
slide 45
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Shifts in LM curve (r fixed)
So vertical shift is independent of k
PhMrrh
PkMYYk
1
1
PM
:fixed YHold
0? k if happens What
PM
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slide 46
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Walkthrough Example III:
Economic Scenario:
Suppose that the money demand function is:(M/P)d = 1000 – 100r
where r is the interest rate (in percent). The money supply M is 1000, and the price level is 2.
a. Graph the supply and demand for real money balances.
b. What is the equilibrium interest rate?
c. Assume that the price level is fixed. What happens to the equilibrium interest rate if the supply of money is raised from 1000 to 1200?
d. If the Fed wishes to raise the interest rate to 7 percent, what money supply should it set?
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slide 47
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
The short-run equilibriumThe short-run equilibrium is the combination of r and Y that simultaneously satisfies the equilibrium conditions in the goods & money markets:
( ) ( )Y C Y T I r G
Y
r
( , )M P L r Y
IS
LM
Equilibriuminterestrate
Equilibriumlevel ofincome
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slide 48
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Equilibrium With Fixed Prices
IS Curve
11
11
100)(),;(cbr
c
TcGIcYrITGYS or
LM Curve
(+)(-)(+)
)0P
M(or ),( hrkYmYrLPM
(-)(+)
Solve for Y and r in terms of G,T, M and P.
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slide 49
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Equilibrium in the IS-LM Model
Income and Output
r
Y
LMIn
tere
st R
ate
IS
Equilibrium interest rate
Equilibrium level of income
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slide 50
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Is there any reason to expect it to converge to this equilibrium from arbitrary r and Y?
If there is an excess demand for money (excess supply of bonds) this should drive the return on bonds up, and vice versa.
If savings exceeds planned investment, then consumers must be spending less and producers will be accumulating unwanted inventories. So they will cut back production, and vice versa.
Hence the system should converge.
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slide 51
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
What is this???
hbkc
hPbMhbmTcGIc
h
PMkYm
c
b
c
TcGIcY
/1
1
//0100
)/
0(1
11
1100
h or 0b as 0 and MY
0h as 0 and
Hence:
0)/
11(
0/
11
1
hbkchPb
hbkcGY
![Page 52: Professor Yamin Ahmad, Money and Banking – ECON 354 Money and Banking Money and Banking ECON 354 Professor Yamin Ahmad Lecture 9: The Building Blocks of](https://reader036.vdocument.in/reader036/viewer/2022062308/56649d6a5503460f94a493a5/html5/thumbnails/52.jpg)
slide 52
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Walkthrough Example IV:Economic Scenario: Consider the following IS-LM model:
Goods Market: C = 200+0.5(Y-T); I = 200 – 1000r; G = 250; T=200
Money Market: M = 3000; P = 2; L(r,Y)= 2Y – 10000r
a. Derive the IS relation (i.e. an equation with Y on one side and everything else on the other)
b. Derive the LM relation
c. Solve for equilibrium real GDP (Y*) and interest rate (r*)
d. Solve for the equilibrium values of C, I and G (- verify you get Y by adding up C+I+G)
e. Suppose that the Fed increases money supply by 280, i.e. DM=280. Solve for Y*, r*, C and I. Describe what happens
f. Set M back to its initial value. Now suppose the government increases spending by 70, i.e. DG = 70. Solve for Y*, r*, C and I. Describe what happens.
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slide 53
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Fiscal Expansion
IS2
hbkc
G
/1
Y2
Income and Output
r
Y
LM
Inte
rest
Rat
e
IS1
Y1
r1
r2
c
G
1
A
B
![Page 54: Professor Yamin Ahmad, Money and Banking – ECON 354 Money and Banking Money and Banking ECON 354 Professor Yamin Ahmad Lecture 9: The Building Blocks of](https://reader036.vdocument.in/reader036/viewer/2022062308/56649d6a5503460f94a493a5/html5/thumbnails/54.jpg)
slide 54
Professor Yamin Ahmad, Money and Banking – ECON 354
Note: These lecture notes are incomplete without having attended lectures
Monetary Expansion
LM2
r2
LM1
Income and Output
r
Y
Inte
rest
Rat
e
IS
r1
Y1 Y2
A
B
![Page 55: Professor Yamin Ahmad, Money and Banking – ECON 354 Money and Banking Money and Banking ECON 354 Professor Yamin Ahmad Lecture 9: The Building Blocks of](https://reader036.vdocument.in/reader036/viewer/2022062308/56649d6a5503460f94a493a5/html5/thumbnails/55.jpg)
Summary
1. Keynesian cross basic model of income determination takes fiscal policy & investment as exogenous fiscal policy has a multiplier effect on income.
2. IS curve comes from Keynesian cross when planned
investment depends negatively on interest rate shows all combinations of r and Y
that equate planned expenditure with actual expenditure on goods & services
slide 55
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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 interest
rate
4. LM curve comes from liquidity preference theory when
money demand depends positively on income shows all combinations of r and Y that equate
demand for real money balances with supply
slide 56
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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.
slide 57