1

IS-LM MODEL

Miscellaneous

2

Simple Keynesian Model v.s.IS-LM Model G’ (b = 0)

C, I, G, G’, AD

Y

r

Y

IS1

Slope = s/b =

b = I/r = 0

(C’-cT’+I’+G’)/s(C’-cT’+I’+G’)/s

IS2 LM

3

Simple Keynesian Model v.s.IS-LM Model G’ (b = 0)

Simple Keynesian Model Ye = kE G’ = G’/s

IS-LM Model Ye = kE G’ = G’/s interest rate has increased but

investment would not decrease since b=0, i.e., investment is perfectly interest inelastic

No crowding-out effect

4

Simple Keynesian Model v.s.IS-LM Model G’ (b 0)

C, I, G, G’, I’,AD

Y

r

Y

(C’-cT’+I’+G’)/s

Slope = s/b

IS1

(C’-cT’+I’+G’)/s

IS2 LM

5

Simple Keynesian Model v.s.IS-LM Model G’ (b 0)

Simple Keynesian Model Ye kE G’ G’/s

IS-LM Model Shift of the IS curve: Y = kE G’ = G’/s Ye kE G’ G’/s interest rate has increased and investment would

decrease since b 0, the IS-LM multiplier = Ye/ G’ = crowding-out effect

1

s+b (d/e)

6

Simple Keynesian Model v.s.IS-LM Model G’ (e = )

C, I, G, G’, AD

Y

r

Y

(C’-cT’+I’+G’)/s(C’-cT’+I’+G’)/s

Slope = d/e = 0

e = Ma/r =

Liquidity Trap

d = Mt/Y = 0

LM

IS1 IS2

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Simple Keynesian Model v.s.IS-LM Model G’ (e = )

Simple Keynesian ModelYe = kE G’ = G’/s

IS-LM ModelYe = kE G’ = G’/s• Mt has increased when Y, normally, interest rate has to

increase to induce people to hold less Ma, as r would raise the return from holding bond

• However, when there’s a liquidity trap, people’s demand for money as an asset, which provides liquidity, is unlimited (e = Ma/r = ) , they would hold as much Ma as possible, r would remain constant, thus no crowding-out effect.

8

Simple Keynesian Model v.s.IS-LM Model G’ (d = 0 )

The diagram is the same as slide no.6 Simple Keynesian Model

Ye = kE G’ = G’/s

IS-LM ModelYe = kE G’ = G’/s• When there’s an increase in government expenditure,

income increase by kE G’ , but transaction demand for money would not increase (d = Mt/Y = 0), Ma need not decrease and r need not increase. With the same interest rate, there’s no crowding-out effect.

9

Simple Keynesian Model v.s.IS-LM Model G’ (Vertical LM)

C, I, G, G’, I’,AD

Y

r

Y

(C’-cT’+I’+G’)/s

Slope = d/e =

d=Mt/Y=

e=Ma/r=0

IS1

(C’-cT’+I’+G’)/s

IS2 LM

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Simple Keynesian Model v.s.IS-LM Model G’ (Vertical LM)

Simple Keynesian ModelYe = 0

IS-LM ModelYe = 0• Full Crowding Out Effect • When d=Mt/Y=, G’ Y by kEG’ Mt by so Y

has to reduce to the original level • When e=Ma/r=0, G’ Y by kEG’ Mt but Ma would

not decrease, so Mt has to reduce to the original level to restore equilibrium in the money market

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Simple Keynesian Model v.s.IS-LM Model G’ = T’ (b = 0)Balanced-Budget ChangeC, I, G, G’, T’, AD

Y

r

Y

IS1

Slope = s/b =

b = I/r = 0

(C’-cT’+I’+G’)/s(C’-cT’+I’+G’)/s

IS2 LMIS3

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Simple Keynesian Model v.s.IS-LM Model Simple Keynesian Model

Cannot be used to analyze monetary policy

IS-LM Model Can be used to analyze monetary policy

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Demand CurveP

Qd

Slope of tangent = P/Qd = 0

Ed = (Qd/Qd)/(P/P) =

It measures the responsiveness of Qd of a good to a change in the price of the good

Ed = slope of ray / slope of tangent

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Deriving the IS FunctionTwo-Sector Injection = WithdrawalI = S

r

Y

S

I

I= I’ - br

y-intercept =I’/b

x-intercept = I’

slope =1/b

b = I/r

J = W

I = S

C’ = 0 = S’

S = sY

slope = s

s =S/Y

*

*

IS

y-intercept = I’/b

x-intercept = I’/s

slope = s/b

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Deriving the IS FunctionFour-Sector Injection = WithdrawalI + G + X = S + T + M

r

YJ

J = G’ + X’ + I’ - br

x-intercept = G’+X’+I’

slope = 1/b

b = I/r

J = W

*

IS

x-intercept

slope = s/b

W = S’ - sT’ + T’ + M’ + sY

*

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Deriving the IS FunctionThree-Sector (w/ b = 0) Injection = Withdrawal

I + G = S + T r

W

J Y

J = I’ + G’

b = 0 = I/r

slope =1/b = **

IS:

slope = s/b =

Y =

x-intercept =

What happens when

there’s G’?

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Deriving the IS FunctionThree-Sector (w/ b = ) Injection = WithdrawalI + G = S + T

W

YJ

rb = = I/r

slope = 1/b =0

r is a constant

* *

IS

slope = s/b = 0

What happens when

there’s G’?

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Deriving the IS FunctionThree-Sector (w/ s = 0) Injection = WithdrawalI + G = S + T

S = S’

s = S/Y = 0

slope = 0

W = S’ + T’

Y

W

J

r

* *IS

slope = s/b = 0

What happens when

there’s G’?

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Deriving the IS FunctionThree-Sector (w/ s = ) Injection = WithdrawalI + G = S + T

r

W

J Y

s= S/Y=

slope =

**

IS

slope = s/b =

What happens when

there’s G’?

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Deriving the LM FunctionMs = Md = Ma + Mte = Liquidity Trap

r

Y

Mt

Ma

e = Ma/r =

slope = 1/e = 0

* *

LM

slope = d/e = 0

What happens when

there’s Ms’?

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Deriving the LM FunctionMs = Md = Ma + Mtd = 0

r

Y

Mt

Ma

d = Mt/Y = 0

slope = 0

* *

LM

slope = d/e =0

What happens when

there’s Ms’?

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Deriving the LM FunctionMs = Md = Ma + Mte = 0

r

Y

Mt

Ma

e = Ma/r = 0

slope = 1/e = **

LM

slope = d/e =

What happens when

there’s Ms’?

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Deriving the LM FunctionMs = Md = Ma + Mtd =

r

Y

Mt

Ma

d = Mt/Y =

slope =

**

LM

slope = d/e =

What happens when

there’s Ms’?

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Deriving the LM FunctionMs = Md = Ma + Mte = when r to a low level liquidity trap

r

Y

Mt

Ma

**

LM

slope = d/e

* LMslope = d/e = 0

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1990 A#13

Which of the following correctly explains the rightward shift of the asset demand function from MA0 to MA1?

A. a rise in the interest rateB. a rise in the marginal efficiency of investment

C. an increase in the sale of government bondsD. a rise in the risk of holding bonds

Asset demand for money

Interest Rate MA0 MA1

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1990 A#30 Refer to the diagram below:

Which of the following statements is INCORRECT?A. The expenditure multiplier will increaseB. The IS curve will shift to the right.C. The average propensity to save will increaseD. There will be a rise in realized injection

S

I+G

(I+G)’

Y

S, I, G S = saving

I = investment

G = government expenditure

Y = income

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1991 A#5 A monetary policy will be more effective if

the liquidity preference function is more ___ and the marginal efficiency of capital function is more ___ .

A. elastic, elasticB. inelastic, inelasticC. inelastic, elasticD. elastic, inelastic

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1991 A#8 An increase in money supply will be likely to lead to an

increase in national income. Which of the following would affect the extent of the change in national income?

(1) the interest elasticity of investment(2) the marginal propensity of withdraw(3) the interest elasticity of demand for moneyA. (1) and (2) onlyB. (1) and (3) onlyC. (2) and (3) onlyD. All of the above

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1992 A#2 Which of the following will have a greater impact upon

equilibrium income when there is a change in the money supply?

A. the flatter the money demand curve; the steeper the investment demand curve; and the larger the MPC

B. the steeper the money demand and investment demand curves; and the smaller the MPC

C. the flatter the money demand and investment demand curves; and the larger the MPC

D. the steeper the money demand curve; the flatter the investment demand curve; ;and the larger the MPC

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1993 A#5 There’re 3 hypothetical economies. They’ve different

sets of IS and LM functionIS Function LM

FunctionEconomy A Y = 1000 - 500r Y = 400 + 500rEconomy B Y = 1800 - 200r Y = 500 + 500rEconomy C Y = 2400 Y = 700 + 500rSuppose the central banks of the 3 economies reduce the

money supply by the same amount. The national income will decrease most in __ and least in __.

A. Economy A, Economy B B. Economy A, Economy CC. Economy B, Economy C D. Economy C, Economy A