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

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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

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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

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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

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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

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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)

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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)

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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)

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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

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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

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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.

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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

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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)

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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

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Y

Mt

Mt = dY

Slope of ray = slope of tangent = d

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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


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

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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

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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

20


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

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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


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


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


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

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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

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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

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r

Ma Ma

The more interest elastic is the asset demand, the flatter will be the Ma curve

r

e = e = 0

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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

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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’

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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

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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

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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

*

*

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Excess

Money

DemandExcess

Money

Supply

Mt

Ma

Ma

Mt

Excess

Money

Excess

Money

What happens if Ms = Ms’ increases?

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Deriving the LM Function4-Quadrant Method

Mt

Ma

Y

Refer slide 15

Mt = dY

What happens if d ?

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Ma

r

Refer slide 25

Ma = Ma’ - erWhat happens if there’s

Ma’ or e ?

37


r

Ma

Mt

r1

Ma1

Mt1

Y1

*r2

Ma2

Mt2Y2

*

LM Curve

Y

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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

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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

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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

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r

Ma, Mt, Md

Ma = Ma’ - er

Mt1 = dY1

Md = Ma + Mt

If Y increases, Mt increases

Mt2 = dY2

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Md, Ms

r

Md1 = Ma’ - er + d Y1 Md2 = Ma’ - er + d Y2

Ms = Ms’

r1

r2

Y r

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r

YY1 Y2

r1

r2

LM

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Simple Algebra of the LM Ms = Ms’ Mt = dYMa = Ma’ - er Md = Mt + Ma In equilibrium, Ms = Md

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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 =

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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.

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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

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The smaller d, the flatter LM

r

Ma

Mt

r1

Ma1

Mt1

Y1

*r2

Ma2

Mt2 Y2

*

Steeper LM

YY

*

Flatter LM

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The larger e, the flatter LMr

Ma

Mt

r1

Ma1

Mt1

Y1

*r2

Ma2

Mt2

Y2

*

Steeper LM

YY

*Flatter LM

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Two extreme casesSmaller slope, flatter LM

slope = d/e = 0

d =

e =

r

YY

r Larger slope, steeper LM

slope = d/e =

d =

e =

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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.

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Shift of the LM CurveIncrease in Ms’

r

Ma

Mt

r1

Ma1

Mt1

Y1

*r2

Ma2

Mt2Y2

*

LM Curve

Y

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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

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Shift of the LM CurveDecrease in Ma’

r

Ma

Mt

r1

Ma1

Mt1

Y1

*r2

Ma2

Mt2Y2

*

LM Curve

Y

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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

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Interest Rate & Income Determination refer slide 6

r

Y

LM

slope =

x-intercept =

IS

slope =

x-intercept =

re

Ye

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Simple Algebra of the IS-LM Model

Refer slide 45 Do the following past paper

questions.

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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%

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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

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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

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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

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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

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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

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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

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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

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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.

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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)

Documents

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