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1
IS-LM Model
LM Function
2
Outline Introduction Assets Market
Bond Market Money Market
Money Demand Md = Mt + Ma Transaction Demand Mt = dY Asset Demand Ma = Ma’ - er
Money Supply Ms = Ms’ Money Market Equilibrium Md = Ms
3
Outline Deriving the LM Function
Graphical Approach 4-quadrant Horizontal Summation of Mt and Ma
Simple Algebra Slope of the LM Curve d/e
Income Elasticity of Money Demand d Interest Elasticity of Money Demand e
4
Outline Shift of the LM Curve
Change in the Money Supply Ms’ Change in the Money Demand
Change in the Asset Demand for Money Ma’ Change in the Transaction Demand for Money d
Interest Rate and Income Determination Equilibrium in the Goods Market (IS) &
Assets / Money Market (LM) Simple Algebra of the IS-LM Model
5
Outline Implications of the IS-LM Model
Effects of a change in IS E’ or T’ Effects of a change in LM Ms or Md
Disequilibrium in the goods market in the money market
6
Introduction 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)
7
Introduction 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)
8
Assumption 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)
9
Assets Market 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
10
Assets MarketMoney Market & Bond Market
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
11
Assets MarketMoney Market & Bond Market 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.
12
Money Market Money Supply Ms
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
13
Money Market Money Demand Md
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)
14
Money DemandTransactions Demand Mt
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
15
Money DemandTransactions Demand Mt
Y
Mt
Mt = dY
Slope of ray = slope of tangent = d
16
Money DemandTransactions Demand Mt 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
17
Money DemandTransactions Demand Mt
Factors affecting Mt Pay period shortened Mt flatter, d
Method 1: $100 daily Average money holding =
Method 2: $700 weekly Average money holding =
The use of Credit Cards Mt flatter, d
18
Money DemandAsset Demand Ma
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
19
Money DemandAsset Demand Ma
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
20
Money DemandAsset Demand Ma
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
21
Money DemandAsset Demand Ma
Ma
rWhen 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
*
22
Money DemandAsset Demand Ma
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*
23
Money DemandAsset Demand Ma
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
24
Money DemandAsset Demand Ma
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
25
Money DemandAsset Demand Ma
r
Ma
Ma = Ma’ - er
x-intercept = Ma1
Ma2
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
26
Money DemandAsset Demand Ma 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
27
Money DemandAsset Demand Ma
r
Ma Ma
The more interest elastic is the asset demand, the flatter will be the Ma curve
r
e = e = 0
28
Digression 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) Goods x and y can be substitutes or complements
29
Digression 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
30
Digression 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 T
= Y/G’ + Y/T’
31
Deriving the LM FunctionMoney market equilibrium
In money market equilibrium, Ms = Md Ms = Ms’ Ma = Ma’ - er Mt = dY Md = Ma + Mt = Ma’ - er + dY Ms’ = Ma + Mt
32
Deriving the LM FunctionMoney market equilibrium
Mt
Ma
If Ms = Ms’ = $1bn,
Ms = Mt + Ma
If Ma = 0, Mt =
It Mt = 0, Ma =
45
45A $1 increase in Mt implies
a $1 decrease in Ma
given Ms = Ms’
A movement along the 45 line
33
Deriving the LM FunctionMoney market equilibrium
Mt
Ma
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
*
*
34
Deriving the LM FunctionMoney market equilibrium
Excess
Money
DemandExcess
Money
Supply
Mt
Ma
Ma
Mt
Excess
Money
Excess
Money
What happens if Ms = Ms’ increases?
35
Deriving the LM Function4-Quadrant Method
Mt
Ma
Y
Refer slide 15
Mt = dY
What happens if d ?
36
Deriving the LM Function4-Quadrant Method
Ma
r
Refer slide 25
Ma = Ma’ - erWhat happens if there’s
Ma’ or e ?
37
Deriving the LM Function4-Quadrant Method
r
Ma
Mt
r1
Ma1
Mt1
Y1
*r2
Ma2
Mt2Y2
*
LM Curve
Y
38
LM Function 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
39
LM Function 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
40
Deriving the LM FunctionHorizontal Summation
r
Md
Since Mt = dY,
the transactions demand for money is independent of r
Mt1 = dY1 Mt2 = dY2
When Y increases, Mt will rise
at all levels of interest rate
41
Deriving the LM FunctionHorizontal Summation
r
Ma, Mt, Md
Ma = Ma’ - er
Mt1 = dY1
Md = Ma + Mt
If Y increases, Mt increases
Mt2 = dY2
42
Deriving the LM FunctionHorizontal Summation
Md, Ms
r
Md1 = Ma’ - er + d Y1 Md2 = Ma’ - er + d Y2
Ms = Ms’
r1
r2
Y r
43
Deriving the LM FunctionHorizontal Summation
r
YY1 Y2
r1
r2
LM
44
Simple Algebra of the LM Ms = Ms’ Mt = dYMa = Ma’ - er Md = Mt + Ma In equilibrium, Ms = Md
45
Simple Algebra of the LM Money Market Y = r = slope of the LM curve = r/Y = Goods Market Y = r = slope of the IS curve = r/Y =
46
Slope of the LM curve d/e 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
47
Slope of the LM curve d/e 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.
48
RevisionSlope of the IS curve -s/b
The smaller s, the flatter IS the increase in saving (s = S/Y) is smaller
given any increase in income excess supply is smaller a smaller decrease in interest rate, which
increases investment, is required to restore equilibrium in the goods market
The larger b, the flatter IS
The increase in investment (b= I/r) is larger, given
any decrease in interest rate,
excess demand is larger
a larger increase in income, which increases saving, is
required to restore equilibrium in the goods market
49
The smaller d, the flatter LM
r
Ma
Mt
r1
Ma1
Mt1
Y1
*r2
Ma2
Mt2 Y2
*
Steeper LM
YY
*
Flatter LM
50
The larger e, the flatter LMr
Ma
Mt
r1
Ma1
Mt1
Y1
*r2
Ma2
Mt2
Y2
*
Steeper LM
YY
*Flatter LM
51
Two extreme casesSmaller slope, flatter LM
slope = d/e = 0
d =
e =
r
YY
r Larger slope, steeper LM
slope = d/e =
d =
e =
52
Shift of the LM Curve 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.
53
Shift of the LM CurveIncrease in Ms’
r
Ma
Mt
r1
Ma1
Mt1
Y1
*r2
Ma2
Mt2Y2
*
LM Curve
Y
54
Shift of the LM CurveIncrease in Ms’
LM equation, Y =
If we differentiate the equation w.r.t. Ms’
Y/Ms’= 1/d OR Y= Ms’/d
55
Shift of the LM CurveDecrease in Ma’
r
Ma
Mt
r1
Ma1
Mt1
Y1
*r2
Ma2
Mt2Y2
*
LM Curve
Y
56
Shift of the LM CurveDecrease in Ma’
LM equation, Y =
If we differentiate the equation w.r.t. Ma’
Y/Ma’= - 1/d OR Y= - Ma’/d
57
Interest Rate & Income Determination refer slide 6
r
Y
LM
slope =
x-intercept =
IS
slope =
x-intercept =
re
Ye
58
Simple Algebra of the IS-LM Model
Refer slide 45 Do the following past paper
questions.
59
1999 A#6Refer to the following information about an economy
C = 600 + 0.75Y C = consumption expenditureI = 400 - 4000r Y = national incomeMt = 0.25Y I = investment expenditureMa = 190 - 600r r = interest rateMs = 500 Mt = transaction demand for money
Ma = asset demand for moneyMs = 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%
60
Implications of the IS-LM ModelEffect of a change in IS: E’
X - intercept =
r
Y
If there is a +ve G’,
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
61
Implications of the IS-LM ModelEffect of a change in IS: T’
X - intercept =
r
Y
If there is a -ve T’,
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
62
Implications of the IS-LM ModelEffect of a change in LM: Ms’
r
YX - intercept
If there is a +ve Ms’,
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
63
Implications of the IS-LM ModelEffect of a change in LM: Ma’
r
YX - intercept
If there is a -ve Ma’,
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
64
2000 A#5 Which of the following will lead to a
leftward shift of an LM curve?
A. A fall in interest rateB. more widespread use of credit cardsC. an increase in the liquidity preferenceD. a decrease in national income
65
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. $80B. $200C. $250D. $500
66
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 leftC. a flatter IS curveD. a steeper IS curve
67
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 fallD. national income can either increase or decrease
68
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.
69
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) onlyB. (1) and (3) only D. (1), (2) and (3)