IS - LM Model

By Wong Chuen-Ping

2 markets

• Goods Market

Equilibrium:

E = Y

C + I = C + S

I = S

• Money Market

Equilibrium:

Md = Ms

• S = 0.2Y - 40 I = 260 - 2000r• In equilibrium: S = I

• 0.2Y - 40 = 260 - 2000r

• Y = 1500 - 10000r

The Goods Market

1500

Y S I r

60 60 0.10

700 100 100 0.08

900 140 140

1100 180 180 0.04

1300 220 220 0.02

260 260 0

500

0.06

IS equation

The Goods Market • Y = 1500 - 10000r

The IS curve

00.020.040.060.080.1

0.12

500 700 900 1100 1300 1500 Y

r

Y r

500 0.1700 0.08900 0.06

1100 0.041300 0.021500 0

IS curve

• IS curve shows all the combinations of real national income (Y) and real interest rate (r) at which the goods market is in equilibrium.

How to derive IS curve?

r

Y

S

I 450

ISI

r1

S

r2

I2 I1

S1

S2

Y1 Y2

ED & ES in product market

r

Y

IS

I=SE=Y

A (Y , S )C

(Y . S )

B

S>I

Y>E

ES

S<IY<E

ED

Disequilibrium in product marketr

Y

IS

ED

ES

I>SE>Y

I<SE<Y

I=SE=Y

rr

I

I

Y

Y

SS

45

I

S

r1

I1

S1

Y1

IS

r2

Y2I2

S2

The IS Curve

IS Curve

S, I

Y Y

r

Y1 Y2

I1

S

Y1

I2

Y2

r1

r2

IS

at r1, investment = I1

at r2, investment = I2

Lower r, higher I

• Ms =400 Mt = 0.25Y Ma = 250 – 2000r• In equilibrium: Ms = Mt + Ma

• 400 = 0.25Y + 250 - 2000r

• Y = 600 + 8000r

The Money Market

0.125

600

0.05

LM equation

Y Ms Mt Ma r

400 150 250 0

1000 400 250 150

1600 400 400 0

The Money Market • Y = 600 + 8000r

The LM curve

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

600 1000 1400 1800 Y

rY R

600 0

1000 05

1400 0.1

LM curve

• LM curve shows all the combinations of real national income (Y) and real interest rate (r) at which the money market is in equilibrium.

How to derive LM curve?

r

Y

Mt

Ma

LM

Ma

r1

Mt

r2

A2A1

T1

T2

Y1 Y2

K

OH

Ms=OH=OK

ED & ES in Money market

r

Y

LMMd=Ms

A (Y , Mt )C(Y . Mt )

B

Md>Ms

ES

Md<Ms

ED

Disequilibrium in Money market

r

Y

LM

ED

ES

Md>Ms

Md<MsMd=Ms

rr

Ma

Ma

Y

Y

MtMt

Ma

Mt

r1

A1

T1

Y1

LMr2

Y2A2

T2

The LM Curve

O

H

K

Ms=OH=OK

LM Curve

r

M Y

r

Md1

Ms

Y1

Md2

Y2

r1

r2

LM

at Y1, Md = Md1

at Y2, Md = Md2Higher Y, higher Md

r1

r2

Equilibrium in Product & Money Market

rLM

IS

YY1

r1A

Disquilibrium in Product & Money Market

r

LM

IS

Y

F

G

H

J

Ms Md

Ms Md

Ms Md

Ms Md

>

>

<

<

I S

I S

I S

I S

>

>

<

<

IS-LM Equations

• Goods Market• C = 100 + 0.8Y• I = 200 - 400r

In equilibrium:

Y = E = C + I

IS equation:

Y = 1500 - 2000r

• Money Market• Ms = 300• Mt = 0.2Y• Ma = 50 - 100r

In equilibrium:

Ms = Md =Mt + Ma

LM equation:

Y = 1250 + 500r

R = 0.1 i.e. 10% Y = 1300

IS-LM Equations

• Goods Market• C = 100 + 0.75Yd• I = 300 - 7000r• G = 525• T = 20%(Y-100)

IS equation ?

• Money Market• Ms = 800• Mt = 120 + 0.4Y• Ma = 240 - 3000r

LM equation ?

r = 0.05 i.e. 5% Y = 1475

Y = 2350 - 17500r Y = 1100 + 7500r

Shifts in the IS curve

r

Y

S

I 450

IS1I1

r1

S

r2

I2 I1

S1

S2

Y1 Y2

I2IS2

I

Increase in Investment ( or↑G)

r

IS1

YY1

r1A

IS2

Y2

↑I, at same r, Y↑, △Y =△I x MPS

1

B

IS shifts to the right

Shifts in the IS curve

r

Y

S

I 450

IS1I1

r1

S1

I1

S1

Y1 Y2

IS2

S2

S

Decrease in Saving ( or↓T)

r

IS1

YY1

r1A

IS2

Y2

↓S, at same r, E↑, Y↑,

B

IS shifts to the right

Shifts in the LM curve

r

Y

Mt

Ma

LM1

Ma

r1

Mt

A1

T1

Y1

MsLM2

Increase in Money Supply

r LM1

YY1

r1A

LM2

B

at same Y, ↑Ms, Ms > Md, r↓

LM shifts to the right

Increase in Money Supply

r LM1

YY1

r1A

LM2

B

Y2

↑Ms, at same r, Y↑, LM shifts to the right△Y =△Ms x d

1

Shifts in the LM curve

r

Y

Mt

Ma

LM1

Ma

r1

Mt1

A1

T1

Y1

O

MtLM2

Mt2

Decrease in Mt

r LM1

YY1

r1A

LM2

B

at same Y, Mt↓, Ms > Md, r↓

LM shifts to the right

Shifts in the LM curve

r

Y

Mt

Ma

LM1

Ma1

r1

Mt1

A1

T1

Y1

O

LM2

Ma2

Ma

Increase in Ma

r LM1

YY1

r1A

LM2

B

at same Y, Ma↑, Ms < Md, r↑

LM shifts to the left

Increase in Investment (↑G, ↑C)

r

LM

IS1

YY1

r1A

IS2

Br2

Y2

Increase in Saving (↑Tax)

r

LM

IS1

YY1

r1A

IS2

Br2

Y2

Increase in Money Supply (↓Md)

r

LM1

IS

YY1

r1A

LM2

Br2

Y2

Increase in demand for Money (↓Ms)

r

LM1

IS

YY1

r1A

LM2

Br2

Y2

Slope of the IS curve & MPS

Smaller MPS, greater multiplier, flatter IS

r↓, I↑→↑Y

YY1

r1

Y2

r2

r

IS1

IS2

larger MPS, steeper IS

Smaller MPS, flatter IS

Y3

MPS1(ΔY = ΔI x )

Slope of IS & Interest elasticity of I

more interest elastic investment, flatter IS

r↓, I↑,

YY1

r1

Y2

r2

r

IS1

IS2

Less interest elastic I, steeper IS

Y3

flatter IS

more interest elastic, larger ΔI, largerΔY

More interest elastic I,

Slope of LM & Income elasticity of Mt

more income elastic Mt, steeper LM

Y↑, Mt↑,

YY1

r1

Y2

r

LM1

LM2

more income elastic Mt, steeper LM

Less income elastic Mt, flatter LM

more income elastic Mt, larger ↑in Mt, largerΔr

Slope of LM & Interest elasticity of Ma

less interest elastic Ma, steeper LM

Y↑, Mt↑,

YY1

r1

Y2

r

LM1

LM2

less interest elastic Ma, steeper LM

more interest elastic Ma, flatter LM

Md > Ms, r↑to ↓Ma, less r elastic Ma, largerΔr

Fiscal Policy - ↑G

r

LMIS1

YY1

r1A

IS2

Br2

Y2

F

MPS1

AF =ΔG x

Crowding-out effect

• The crowding-out effect refers to the reduction in income resulting from an increase in interest rate.

• G E E >Y Y Mt Md > Ms r

• r I Y (crowding-out effect)

The crowding-out effect

The crowding-out effect

r

LMIS1

YY1

r1A

IS2

Br2

Y2

F

MPS1

AF =ΔG x

Crowding-out effect

• condition of employment (unemployment, ? crowding-out effect) (full employment, ? Crowding-out effect)

• interest elasticity of demand for money, more interest elastic, smaller change in r, crowding-out effect ? .

• interest elasticity of investment, less interest elastic, when r , smaller in I, crowding-out effect ? .

Factors affecting the crowding-out effect

smaller

smaller

larger

smaller

Fiscal Policy - ↑Tax

r LM

IS1

YY1

r1A

IS2

Br2

Y2

r LM

IS1

YY1

r1A

IS2

Br2

Y2

Lump sum tax ↑, IS shifts left

Tax rate↑, IS steeper

Fiscal Policy - Equal↑in G & T

r

LMIS1

YY1

r1A

IS2

Br2

Y2

F

AF =ΔG = ΔT

Crowding-out effect

Monetary Policy - ↑Ms

r

LM1

IS

YY1

r1A

LM2

Br2

Y2

Fiscal & Monetary Policies - ↑Ms + ↑G

r

LM1

IS1

YY1

r1 A

LM2

B

Y2

IS2

Effectiveness of Monetary Policy & slope of IS

r

LM1

IS1

YY0

r0A

LM2

r1

Y1

IS2

Y2

r2 C

Ms ↑→r↓→I↑,LM →right ,

Monetary Policy is more effective if IS is flatter

B

more interest elastic (flatter IS), larger ↑I, larger↑Y

smaller MPS (flatter Y), larger ↑Y

Effectiveness of Fiscal Policy & slope of LM

r

LM1

IS1

YY1

r1A

IS2

Br2

Y2

Crowding-out effect

LM2

Cr3

Y3Fiscal Policy is more effective if LM is flatter

G↑, IS →right , Y↑ → Mt↑,

Mt less income elastic, Ma more interest elastic,

r↑smaller, crowding-out smaller

rr

Ma

Ma

Y

Y

MtMt

Ma

Mt

r1

T1

Y1

LM

The LM Curve with liquidity trap

O

H

K

Ma – perfectly interest elastic

Horizontal LM

Y2

rr

Ma

Ma

Y

Y

MtMt

Ma

Mt

r1

Y1

LM

The LM Curve with Ma perfectly interest inelastic

O

H

K

Ma – perfectly interest inelastic

r2vertical LM

rr

I

I

Y

Y

SS

45

I

S

r1

I1

S1

Y1

IS

r2

The IS Curve with perfectly interest inelastic IInvestment perfectly interest elastic

IS vertical

Horizontal LM

r

LM

IS1

YY1

r1 A

IS2

B

Y2

r

LM

IS1

YY1

r1 A

Fiscal Policy effective

Monetary Policy ineffective

G↑ Ms↑

Vertical LM

r LM

IS1

YY1

r1 A IS2

B

r

LM1

IS1

YY1

r1 A

Fiscal Policy ineffective

Monetary Policy effective

r2

G↑ Ms↑LM2

r2

Y2

B

Vertical IS

r

LMIS1

YY1

r1 A

IS2

B

r LM1IS

YY1

r1 A

Fiscal Policy effective

Monetary Policy ineffective

r2

G↑ Ms↑LM2

r2 B

Y2

Horizontal IS

r

IS

LM

YY1

r1 A

r

LM1

IS

YY1

r1 A

Fiscal Policy ineffective

Monetary Policy effective

G↑ Ms↑

LM2

B

Y2