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CHAPTER # 6
IS-LM MODEL
slide 0
In this chapter, you will learn…
 the IS curve, and its relation to
 the Keynesian cross
 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
slide 1
Introduction
 Hicks presented the concept of IS curve in 1937
 According to him, corresponding to equilibrium
level of NI where I=S, there is some particular
rate of interest.
 In other words hicks established the relationship
between Y and i where S = I, so this relationship
was given the name as Investment and saving
curve (IS curve)
slide 2
Definition
 IS Curve is a curve which shows
different combinations of rate of
interest (i) and level of NI (Y) where
saving (S) are equal to Investment (I ).
slide 3
Assumption of IS curve
 Y= C+I where C= C0+ cY, & I = I0 - Vi
 V= slope of investment curve which is affected by the
changes in the rate of interest




S= f(Y), S= -S0 + sY
I= f(Y)
Price level does not change
Wages remain the same
slide 4
Derivation of IS curve
 We know that Y=C+ I
 Putting the value of C & I in the equation
 So Y = C0 + cY +I0 –Vi
 Y - cY = C0 + I0 – Vi
 Y(1-c) = C0 + I0 – Vi
 Y= C0 + I0 – Vi
1-c
 Y = 1 (C0+I0-Vi)
IS equation
(1-c)
slide 5
Numerical explanation of IS curve
 Suppose C= 100 + 0.5Y, I= 100 – 10i
 Putting them in IS equation
 Y= 1 (100 +100 -10i),
(1-0.5)
Y = 200-10i ,
0.5
Y=
1
(200 -10i)
(1-0.5)
Y = 200- 10i
0.5 0.5
SO
Y = 400 - 20i
IS equation
slide 6
Example…..
 Now assuming different interest rates, we get different
values of Y where I=S,
 Taking i= 5% we have
 Y = 400 – 20i putting the value of i
 Y= 400 – 20(5%),Y= 400 -20(5/100), Y = 399
 So C= 100 +0.5(399), C= 299.5
 S= Y-C 399-299.5
S= 99.5
 I= I0-Vi
I=100-10(5%)
 Thus we have
i
Y
5%
399
I= 99.5
S
99.5
I
99.5
slide 7
The Keynesian Cross
 A simple closed economy model in which income
is determined by expenditure.
 Notation:
I = planned investment
E = C + I + G = planned expenditure
Y = real GDP = actual expenditure
slide 8
IS Curve: Graphical
Y
E
r
E =C +I +G
 I
 E
 Y
E =C +I +G
I
r
Y1
Y
Y2
r1
r2
IS
Y1
Y2
Y
slide 9
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 (E ).
 To restore equilibrium in the goods market,
output (actual expenditure, Y )
must increase.
slide 10
Shifts of the IS Curve
 The inverse relation between r
and Y is the IS curve
r
r1
Y
 For any particular value of r,
such as r1, Y increases if
 There is an increase in G or
in autonomous C or I, or if
 There is a decrease in T
Y1
IS1
Y2
IS2
Y
 Therefore, these changes shift
the IS curve to the right.
slide 11
THE MARKET FOR LOANABLE
FUNDS
 Financial markets coordinate the economy’s
saving and investment in the market for loanable
funds.
 Loanable funds refers to all income that people
have chosen to save and lend out, rather than
use for their own consumption.
slide 12
Supply and Demand for Loanable
Funds
 The supply of loanable funds comes from people
who have extra income they want to save and
lend out.
 The demand for loanable funds comes from
households and firms that wish to borrow to
make investments.
 The market for loanable funds is the market in
which those who want to save supply funds and
those who want to borrow to invest demand
funds.
slide 13
Interest rate for Loanable Funds
 The interest rate is the price of the loan.
 It represents the amount that borrowers pay for
loans and the amount that lenders receive on
their saving.
 The interest rate in the market for loanable funds
is the real interest rate.
slide 14
Figure 1 The Market for Loanable Funds
Interest
Rate
Supply
5%
Demand
0
$1,200
Loanable Funds
(in billions of dollars)
slide 15
Copyright©2004 South-Western
IS curve and Loanable funds
market
 The IS curve maps the
relationship between r and Y for
the loanable funds market in
equilibrium.
• Suppose Y increases from Y1 to
Y2. This raises savings from
S(Y1) to S(Y2) resulting in a lower
equilibrium interest rate.
r
• The IS curve maps out this
relationship between the
lower interest rate and
increased income.
r
S (Y1) S (Y2)
r1
r1
r2
r2
I
I
IS
Y1
Y2
Y
slide 16
The Theory of Liquidity Preference
 Keynes developed the theory of liquidity
preference in order to explain what factors
determine the economy’s interest rate.
 According to the theory, the interest rate adjusts
to balance the supply and demand for money.
slide 17
The Theory of Liquidity Preference
 Equilibrium in the Money Market
 According to the theory of liquidity preference:
 The interest rate adjusts to balance the supply
and demand for money.
 There is one interest rate, called the
equilibrium interest rate, at which the quantity
of money demanded equals the quantity of
money supplied.
slide 18
HOW FISCAL POLICY INFLUENCES
AGGREGATE DEMAND
 Fiscal policy refers to the government’s choices
regarding the overall level of government
purchases or taxes.
 Fiscal policy influences saving, investment, and
growth in the long run.
 In the short run, fiscal policy primarily affects the
aggregate demand.
slide 21
Changes in Government Purchases
 When policymakers change the money supply or
taxes, the effect on aggregate demand is
indirect—through the spending decisions of
firms or households.
 When the government increases or decreases
its own purchases of goods or services, it shifts
the aggregate-demand curve directly.
slide 22
Changes in Taxes
 When the government cuts personal income
taxes, it increases households’ take-home pay.
 Households save some of this additional
income and spend some of it on consumer
goods.
 Increased household spending shifts the
aggregate-demand curve to the right.
slide 23
LM Curve
 Introduction
according to Keynes, in money market
equilibrium takes place at the rate of interest
where Md=Ms. From this idea Hicks presented
the concept of LM curve
according to Hicks, corresponding to such rate
of interest where Md=Ms there is some
particular level of NI.
slide 24
Cont`d
 Thus LM curve establishes a relationship
between rate of interest and NI through
Md & Ms.
 Where L represent the demand for money
and M represent the supply of money
slide 25
Definition of LM curve
The LM curve is a graph of all combinations of r
(rate of interest) and Y (NI) that equate the
supply of money (Ms) and demand for money
(Md).
This direct relation between r and Y is the LM
Curve.
slide 26
Numerical explanation




NI will be in equilibrium where Md=Ms
While Md has two components i.e. Mtd & Msd
Where Mtd = kY ,
Msd= mo - mi
 where m0 represent Msd at zero rate of interest
 m is the slope of Msd curve, and
 i is the rate of interest.
slide 27
Numerical explanation…..








Now Suppose Mtd =0.25Y, Msd =124 -200i, Ms =300
So MD = 0.25Y +124 -200i , & Ms= 300
As Ms=Md so
300= 0.25Y+ 124 - 200i
300-124=0.25Y -200i
176=0.25Y-200i
0.25Y =176 +200i
Y= 704 + 800i
LM equation
slide 28
Numerical explanation….
 Suppose i= 5%
 Y= 704 +800i
Y = 704 +800(5%)
 So Mtd = 0.25Y Mtd= 0.25(744)
 & Msd= 124 -200(5%) Msd= 124 -10
 We know that Md= Mtd + Msd
Y=744
Mtd= 186
Msd=114
Md =186+114=300
 Thus Md= Ms =300
i
Y
Mtd + Msd = Md
Ms
5%
744
186 + 114 = 300
300
 Similarly we can get different value of Y where Md=Ms
slide 29
Deriving the LM curve
(a) The market for
r
real money balances
(b) The LM curve
r
LM
r2
r2
L (r , Y2 )
r1
r1
L (r , Y1 )
Ms
M/P
Y1
Y2
Y
slide 30
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.
slide 31
How M shifts the LM curve
(a) The market for
r
real money balances
(b) The LM curve
r
LM2
LM1
r2
r2
r1
r1
L ( r , Y1 )
M2/P M1/P M/P
Y1
Y
slide 32
Shifts of the LM Curve
 We see that r decreases when either
 P or Y decreases, or
 M increases, or
 Autonomous money demand
LM0
r0
LM1
r1
decreases
Therefore, the LM curve shifts right
if there is an increase in M or a
decrease in either P or autonomous
money demand.
Y0
slide 33
Exercise: 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……????
slide 34
IS=LM: The Short Run
Equilibrium
 Given our IS and LM equation we
can now determine the short run
equilibrium interest rate and output
• By mapping out the relationship
between Y and r when the goods
market is in equilibrium we get
the IS curve.
• By mapping out the relationship
•
between Y and r when the money
market is in equilibrium we get the
LM curve.
When we set IS=LM we can solve
for the equilibrium levels of r and
Y. This represents simultaneous
equilibrium in the goods market
(or loanable funds market) and the
money market.
r
LM
r*
IS
Y*
Y
slide 35
The Big Picture
Keynesian
Cross
Theory of
Liquidity
Preference
IS
curve
LM
curve
IS-LM
model
Agg.
demand
curve
Agg.
supply
curve
Explanation
of short-run
fluctuations
Model of
Agg.
Demand
and Agg.
Supply
slide 36
Recap: Shifts of IS and LM Curves
 The IS curve shifts right if
 G increases, or
 autonomous C or I
increases, or
 T decreases
 The LM curve shifts right
if
 M increases, or
 P decreases, or
 Autonomous money
demand decreases.
r
r
LM
LM0
LM1
IS0
IS1
Y
IS
Y
slide 37
Chapter 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 38
Chapter 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 39
Chapter 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 40
slide 41