IS-LM Model
LM Function
1
Outline
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Introduction
Assets Market
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Money Demand Md = Mt + Ma
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Bond Market
Money Market
Transaction Demand Mt = dY
Asset Demand Ma = Ma’ - er
Money Supply Ms = Ms’
Money Market Equilibrium Md = Ms
2
Outline
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Deriving the LM Function
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Graphical Approach
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4-quadrant
Horizontal Summation of Mt and Ma
Simple Algebra
Slope of the LM Curve d/e
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Income Elasticity of Money Demand d
Interest Elasticity of Money Demand e
3
Outline
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Shift of the LM Curve
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Change in the Money Supply Ms’
Change in the Money Demand
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Change in the Asset Demand for Money Ma’
Change in the Transaction Demand for Money d
Interest Rate and Income Determination
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Equilibrium in the Goods Market (IS) &
Assets / Money Market (LM)
Simple Algebra of the IS-LM Model
4
Outline
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Implications of the IS-LM Model
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Effects of a change in IS E’ or T’
Effects of a change in LM Ms or Md
Disequilibrium
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in the goods market
in the money market
5
Introduction
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In the goods market, the IS curve is the
loci of different combinations of interest
rate and income that satisfy the
equilibrium condition (W = J)
In the assets market, the LM curve is
the loci of different combinations of
interest rate and income that satisfy the
equilibrium condition (Ms = Md)
6
Introduction
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Accordingly, we can determine the
interest rate and income that satisfy
the equilibrium conditions of both the
goods market (W = J) and assets
market (Ms = Md)
Still, the labour market may not be in
equilibrium.
There may be labour shortage (Y > Yf)
or unemployment (Y < Yf)
7
Assumption
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In this short-run IS-LM model, we still
assume the price level is fixed.
Hence, nominal income (Y) equals real
income (Q)
& nominal money balances (M) equals
real money balances (m = M/P)
8
Assets Market
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An individual has to face the choice of
allocating his financial wealth into different
assets, like money, bonds, stocks and
foreign currencies.
Here, only two types of assets, money and
bonds are considered.
It is assumed that an individual will store his
financial wealth in either money or bonds
9
Assets Market
Money Market & Bond Market
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The equilibrium condition of the assets market is
that the supply of financial assets equals the
demand for financial assets
Assets Supply=Money Supply+Bond Supply
Assets Demand=Money Demand+Bond Demand
In equilibrium, Assets Supply = Assets Demand
Ms + Bs = Md + Bd
10
Assets Market
Money Market & Bond Market
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Assets Market can be divided into
money market and bond market
If the money market is in equilibrium,
i.e., Ms = Md
The bond market will also be in
equilibrium, i.e., Bs = Bd
Thus, in the IS-LM model, only the
money market is considered.
11
Money Market
Money Supply Ms
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In the IS-LM model, money supply is
postulated as an exogenous function,
whose value is determined by the
monetary authority.
Ms = Ms’
Besides, there is no difference between
nominal money supply and real money
supply
12
Money Market
Money Demand Md
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In the IS-LM model, money demand Md
consists of transactions demand Mt and
asset demand Ma
Mt is assumed to be positively related to
income
Ma is assumed to be negatively related to
interest rate.
Thus, Md is hypothesised to be a function of
both income and interest rate Md = f(Y, r) 13
Money Demand
Transactions Demand Mt
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Money serves as the medium of exchange.
The higher the level of real / nominal income, the
higher will be the transactions demand for money
(real balances)
Mt = dY
d>0
The coefficient d is the income elasticity of money
demand.
Mt/Y = d
Mt/Y = d
14
Money Demand
Transactions Demand Mt
Mt
Slope of ray = slope of tangent = d
Mt = dY
Y
15
Money Demand
Transactions Demand Mt
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It is upward sloping as Mt is positively
related to income Y.
A change in income Y will lead to a
movement along the Mt curve, an
induced change Mt
When there is a rise in transactions
demand d for money, the slope of the
Mt curve will be larger, Mt is steeper
16
Money Demand
Transactions Demand Mt
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Factors affecting Mt
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Pay period shortened  Mt flatter, d
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Method 1: $100 daily
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Method 2: $700 weekly
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Average money holding =
Average money holding =
The use of Credit Cards  Mt flatter, d
17
Money Demand
Asset Demand Ma
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Liquidity is a measure of an asset’s
capacity to be rapidly resold at a price
close to its purchase price.
An asset is liquid if it can easily and
quickly be converted into cash at low cost.
Money is the most liquid asset.
Also, holding money involves lower risk
compared with other assets
18
Money Demand
Asset Demand Ma
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However, having a bank balance or a stock
of cash involves cost as it yields no
interest earnings.
Conversely, bonds yield interest earnings.
Moreover, there may be capital gain/loss
19
Money Demand
Asset Demand Ma
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Suppose all bonds are perpetuities (i.e. pay
interest forever and never repay the principal)
P = I/r
P
: the price of bond
I
: Interest earnings
r
: Market interest rate
When r is expected to fall, P is expected to rise,
and vice versa.
That means there’ll be capital gain
20
Money Demand
Asset Demand Ma
r
*
When r is relatively high,
holding bonds yield large interest returns
And r is expected to fall,
Price of bonds is expected to rise,
holding bonds can reap capital gain
More bonds will be held
Hence, demand for money as an asset will be less
Ma
21
Money Demand
Asset Demand Ma
r
When r is relatively low,
holding bonds yield less interest returns
And r is expected to rise,
Price of bonds is expected to fall,
holding bonds will suffer capital loss.
Less bonds will be held
*
Hence, demand for money as an asset will be greater
Ma
22
Money Demand
Asset Demand Ma
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When r rises, the cost of holding money
will increase.
Thus, people will hold less cash.
That explains why the asset demand for
money Ma is postulated as negatively
related to r
Ma = Ma’ - er
e >0
23
Money Demand
Asset Demand Ma
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The coefficient e is defined as the interest
elasticity of money demand
e = Ma/r
It measures the responsiveness of money
demand to interest rate.
The more interest elastic is the asset
demand for money, the greater will be the
fall in asset demand as a result of a rise in
interest rate
24
Money Demand
Asset Demand Ma
r
Ma = Ma’ - er
Ma2
Ma1
x-intercept =
Ma1 is more interest elastic
e is larger, i.e.,Ma is larger given a certain r
1/e is smaller, i.e., Ma1 is flatter
Ma
25
Money Demand
Asset Demand Ma
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It is downward sloping because r and
Ma are negatively related.
A change in interest rate r will cause a
movement along the Ma curve, i.e., an
induced change Ma
A change in the autonomous asset
demand for money Ma’ will shift the
Ma curve
26
Money Demand
Asset Demand Ma
The more interest elastic is the asset demand, the flatter will be the Ma curve
r
r
e=
e=0
Ma
Ma
27
Digression
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Price elasticity of demand Ed
= (Qxd/Qxd)/(Px/Px)
=slope of ray/slope of tangent
Price elasticity of supply Es = (Qxs/Qxs)/(Px/Px)
Income elasticity of demand Ei= (Qxd/Qxd)/(I/I)
Cross elasticity of demand Exy= (Qxd/Qxd)/(Py/Py)
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Goods x and y can be substitutes or complements
28
Digression
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Autonomous Consumption a
Interest Elasticity of Investment b = I/r
Marginal Propensity to Consume c = C/Y
Income Elasticity of Money Demand d = Mt/Y
Interest Elasticity of Money Demand e = Ma/ r
Marginal Propensity to Invest i = I/Y
Marginal Propensity to Import m = M/Y
Marginal Propensity to Save s = S/Y
Proportional Tax Rate t = T/Y
29
Digression
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Expenditure Multiplier k E
= Y/E’
= Y/C’ = Y/I’ = Y/G’ = Y/X’
= Y/M’
Tax Multiplier k T
= Y/T’
Balanced Budget Multiplier k B = k E + k
= Y/G’ + Y/T’
T
30
Deriving the LM Function
Money market equilibrium
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In money market equilibrium, Ms = Md
Ms
=
Ms’
Ma
=
Ma’ - er
Mt
=
dY
Md
=
Ma + Mt =
Ma’ - er + dY
Ms’
=
Ma + Mt
31
Deriving the LM Function
Money market equilibrium
If Ms = Ms’ = $1bn,
Ms = Mt + Ma
Mt
If Ma = 0, Mt =
45
It Mt = 0, Ma =
A $1 increase in Mt implies
a $1 decrease in Ma
given Ms = Ms’
45
A movement along the 45 line
Ma
32
Deriving the LM Function
Money market equilibrium
Mt
The 45 line is the loci of Mt and Ma which represents
money market equilibrium, i.e., Ms = Md
*
*
Ms > Md = Ma + Mt
*
*
Ms = Md = Ma + Mt
*
Ms < Md = Ma + Mt
Ma
33
Deriving the LM Function
Money market equilibrium
What happens if Ms = Ms’ increases?
Mt
Ma
Excess
Excess
Money
Money
Excess
Excess
Demand
Money
Money
Supply
Ma
Mt
34
Deriving the LM Function
4-Quadrant Method
Refer slide 15
Ma
Y
What happens if d ?
Mt = dY
Mt
35
Deriving the LM Function
4-Quadrant Method
r
Ma = Ma’ - er
What happens if there’s
 Ma’ or e ?
Ma
Refer slide 25
36
Deriving the LM Function
4-Quadrant Method
LM Curve
r
r1
r2
Ma
Ma2
*
*
Ma1
Mt2
Y2 Y1
Y
Mt1
Mt
37
LM Function
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Suppose the money market is initially in
equilibrium with Ms = Md.
Holding Ms constant,
a rise in Y will lead to a rise in Mt
since Mt  = dY
there’ll be an excess demand for money
Ms < Md = Mt  + Ma
38
LM Function
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r will increase to reduce Ma in order to
keep the money market in equilibrium
since Ma  = Ma’ - er 
Ms = Ms’ = Md = Mt  + Ma
This positive relationship between
interest rate r and national income Y in
the money market is represented by the
upward sloping LM curve in slide 37
39
Deriving the LM Function
Horizontal Summation
Since Mt = dY,
the transactions demand for money is independent of r
r
Mt1 = dY1
Mt2 = dY2
When Y increases, Mt will rise
at all levels of interest rate
Md
40
Deriving the LM Function
Horizontal Summation
r
Mt1 = dY1
If Y increases, Mt increases
Mt2 = dY2
Md = Ma + Mt
Ma = Ma’ - er
Ma, Mt, Md
41
Deriving the LM Function
Horizontal Summation
r
Ms = Ms’
r2
Y r
r1
Md, Ms
Md1 = Ma’ - er + d Y1
Md2 = Ma’ - er + d Y2
42
Deriving the LM Function
Horizontal Summation
r
LM
r2
r1
Y1
Y2
Y
43
Simple Algebra of the LM
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Ms = Ms’
Mt = dY
Ma = Ma’ - er
Md = Mt + Ma
In equilibrium, Ms = Md
44
Simple Algebra of the LM
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Money Market
Y=
r=
slope of the LM curve = r/Y =
Goods Market
Y=
r=
slope of the IS curve = r/Y =
45
Slope of the LM curve d/e
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The smaller d, the flatter LM
If there is a decrease in d (=Mt/Y),
the increase in Mt will be smaller given
any rise in income
The excess demand will be smaller
a smaller increase in r, which reduces Ma, is
enough to restore equilibrium in the money
market
46
Slope of the LM curve d/e
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The larger e, the flatter LM
If there is an increase in e (=Ma/r),
the decrease in Ma will be larger, given
any increase in interest
The excess supply will be larger
A larger increase in Y, which increases Mt,
is required to restore equilibrium in the
money market.
47
Revision
Slope of the IS curve -s/b
The smaller s, the flatter IS
 the increase in saving (s = S/Y) is
The increase in investment (b= I/r) is larger, given
smaller given any increase in income
any decrease in interest rate,
 excess supply is smaller
excess demand is larger
 a smaller decrease in interest rate, which
a larger increase in income, which increases saving, is
increases
investment,
is
required
to
restore
required to restore equilibrium in the goods market
equilibrium in the goods market


The larger b, the flatter IS
48
The smaller d, the flatter LM
Steeper LM
r
Flatter LM
r1
r2
Ma
Ma2
Ma1
Mt2
*
*
Y2 Y1
*
Y
Y
Mt1
Mt
49
The larger e, the flatter LM
Steeper LM
r
r1 *
r2 *
Ma
Ma2
Ma1
Flatter LM
*
Y2 Y1 Y
Y
Mt2
Mt1
Mt
50
Two extreme cases
r
Larger slope, steeper LM r Smaller slope, flatter LM
slope = d/e = 
slope = d/e = 0
d=
d=
e=
e=
Y
Y
51
Shift of the LM Curve
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
Y=
when r = 0, Y =
which is the x-intercept of the LM curve
If there is a change in money supply Ms’
or money demand Ma’
the LM curve will shift.
52
Shift of the LM Curve
Increase in Ms’
LM Curve
r
r1
r2
Ma
Ma2
*
*
Ma1
Mt2
Y2 Y1
Y
Mt1
Mt
53
Shift of the LM Curve
Increase in Ms’
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LM equation, Y =
If we differentiate the equation w.r.t. Ms’
Y/Ms’= 1/d
OR
Y= Ms’/d
54
Shift of the LM Curve
Decrease in Ma’
LM Curve
r
r1
r2
Ma
Ma2
*
*
Ma1
Mt2
Y2 Y1
Y
Mt1
Mt
55
Shift of the LM Curve
Decrease in Ma’
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LM equation, Y =
If we differentiate the equation w.r.t. Ma’
Y/Ma’= - 1/d
OR
Y= - Ma’/d
56
Interest Rate & Income Determination
refer slide 6
LM
r
slope =
x-intercept =
re
IS
slope =
x-intercept =
Ye
Y
57
Simple Algebra of the IS-LM Model


Refer slide 45
Do the following past paper questions.
58
1999 A#6
Refer to the following information about an economy
C = 600 + 0.75Y
I = 400 - 4000r
Mt = 0.25Y
Ma = 190 - 600r
Ms = 500
C = consumption expenditure
Y = national income
I = investment expenditure
r = interest rate
Mt = transaction demand for money
Ma = asset demand for money
Ms = money supply
The equilibrium levels of income and interest rate in this
economy are ___ and ___ respectively.
A. 1200..17.5%
C. 1600..15%
B. 1500..20%
D. 1800..13.75%
59
Implications of the IS-LM Model
Effect of a change in IS: E’
If there is a +ve G’,
r
the IS curve will shift to the right
by the amount of k E G’
With an upward-sloping LM,
both r and Y will increase
Y
X - intercept =
60
Implications of the IS-LM Model
Effect of a change in IS: T’
If there is a -ve T’,
r
the IS curve will shift to the right
by the amount of -c k E T’
With an upward-sloping LM,
both r and Y will increase
Y
X - intercept =
61
Implications of the IS-LM Model
Effect of a change in LM: Ms’
If there is a +ve Ms’,
r
the LM curve will shift to the right
by the amount of Ms’/d
With a downward-sloping IS,
r will decrease
but Y will increase
X - intercept
Y
62
Implications of the IS-LM Model
Effect of a change in LM: Ma’
If there is a -ve Ma’,
r
the LM curve will shift to the right
by the amount of -Ma’/d
With a downward-sloping IS,
r will decrease
but Y will increase
X - intercept
Y
63
2000 A#5

Which of the following will lead to a leftward
shift of an LM curve?
A. A fall in interest rate
B. more widespread use of credit cards
C. an increase in the liquidity preference
D. a decrease in national income
64
2000 A#12
If the amount of money held for
transaction purposes is 40% of the national
income, then a $200 increase in the money
supply will lead to a rightward shift in the
LM curve by an amount of
A. $80
B. $200
C. $250
D. $500

65
2000 A#13

An increase in the marginal propensity to
consume would result in
A. a parallel shift of the IS curve to the right
B. a parallel shift of the IS curve to the left
C. a flatter IS curve
D. a steeper IS curve
66
2000 A#14

In the IS-LM model, if there is a
simultaneous cut in government expenditure
and money supply, then
A. national income will decrease while interest rate
will rise
B. national income will decrease while interest rate
will fall
C. interest rate can either rise or fall
D. national income can either increase or decrease
67
2000 A#15

Which of the following concerning the value of a
bond is correct?
A. The closer to maturity the bond is, the greater will be
the change in its value for a change in interest rate.
B. The further to maturity the bond is, the greater will be
the change in its value for a change in interest rate.
C. A change in interest rate will not affect the value of a
bond.
D. The impact of a change in interest rate on the value of
the bond does not depend on its maturity date.
68
2000 A#21

In the IS-LM model, which of the following are
correct if investment is independent of interest
rate?
(1) An increase in money supply will have no effect on
national income
(2) An increase in money supply will have no effect on
interest rate.
(3) An increase in government expenditure will lead to an
increase in interest rate
A. (1) and (2) only C. (2) and (3) only
B. (1) and (3) only D. (1), (2) and (3)
69