MACROECONOMIC MODELS PART 2 GECO6400. THE AGGREGATE EXPENDITURE MODEL THE EXPENDITURE MULTIPLIER Changes in autonomous expenditure lead to greater changes

MACROECONOMIMACROECONOMIC MODELSC MODELS

PART 2PART 2

GECO6400GECO6400

THE AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL

THE EXPENDITURE MULTIPLIERTHE EXPENDITURE MULTIPLIERChanges in autonomous expenditure Changes in autonomous expenditure

lead to greater changes in the level of lead to greater changes in the level of output.output.

This concept is encapsulated in the This concept is encapsulated in the Multiplier (k).Multiplier (k).

The multiplier concept derives from the The multiplier concept derives from the relationships that exist within the relationships that exist within the macroeconomy.macroeconomy.

THE EXPENDITURE MULTIPLIERTHE EXPENDITURE MULTIPLIER

One person’s expenditure becomes another’s incomeOne person’s expenditure becomes another’s income

The Circular Flow of income depicts The Circular Flow of income depicts interdependence between each sector of the interdependence between each sector of the economy – what happens in one sector influences economy – what happens in one sector influences what happens in another.what happens in another.

The initial change in expenditure comes from The initial change in expenditure comes from outside the system – it is not due to a change in outside the system – it is not due to a change in income but is autonomous.income but is autonomous.


THE EXPENDITURE MULTIPLIERTHE EXPENDITURE MULTIPLIER

Such changes can be due to factors that Such changes can be due to factors that influence household Autonomous influence household Autonomous Consumption such as prices and wealth.Consumption such as prices and wealth.

Such changes can also be due to factors that Such changes can also be due to factors that influence businesses’ Autonomous influence businesses’ Autonomous Investment expenditure such as expectations Investment expenditure such as expectations or interest rates.or interest rates.


The Multiplier ProcessThe Multiplier ProcessThe initial expenditure in spent and re-The initial expenditure in spent and re-

spent multiple times.spent multiple times.

The eventual increase in income is The eventual increase in income is greater in magnitude than the initial greater in magnitude than the initial increase in expenditure that caused it.increase in expenditure that caused it.

This is the expenditure multiplier This is the expenditure multiplier effect.effect.


The Multiplier ProcessThe Multiplier Process Round 1Round 1:: the initial increase in expenditure causes the initial increase in expenditure causes

an increase in income.an increase in income.

Round 2Round 2: part of the increase in income of round 1 : part of the increase in income of round 1 is saved (MPS), the rest is spent (MPC), causing is saved (MPS), the rest is spent (MPC), causing another increase in income.another increase in income.

Round 3Round 3: part of the increase in income of round 2 : part of the increase in income of round 2 is saved (MPS), the rest is spent MPC), causing is saved (MPS), the rest is spent MPC), causing another increase in income.another increase in income.

Round nRound n:: The total effect of the initial increase in The total effect of the initial increase in expenditure is exhausted. There is no more expenditure is exhausted. There is no more expenditure occurring.expenditure occurring.


The Multiplier ProcessThe Multiplier Process

Not all of the initial expenditure is re-spent. Some Not all of the initial expenditure is re-spent. Some leaks out of the system through savings. The leaks out of the system through savings. The multiplier also works in reverse.multiplier also works in reverse.

The leakage from savings at each level or round of The leakage from savings at each level or round of expenditure means that the Multiplier process expenditure means that the Multiplier process eventually comes to an end.eventually comes to an end.

The change in expenditure gradually becomes The change in expenditure gradually becomes

smaller and smaller as it works its way through smaller and smaller as it works its way through the economy (circular flow) until it eventually is the economy (circular flow) until it eventually is completely spent. completely spent.


The Multiplier ProcessThe Multiplier Process

An initial change in autonomous expenditure can be due to a change in an exogenous An initial change in autonomous expenditure can be due to a change in an exogenous variable (external influence) such as interest rates, wealth, expectations or prices.variable (external influence) such as interest rates, wealth, expectations or prices.


The investment schedule would shift up on the 45 degree-line diagram, causing the AE schedule to also shift up, producing a multiplied increase in income (GDP).

rr AEAEII YY

A drop in interest rates for instance would cause the following to occur:

EXAMPLEEXAMPLE

C=60+0.8YC=60+0.8Y

S=-60+0.2YS=-60+0.2Y

I1=10I1=10

Increase in autonomous Investment Increase in autonomous Investment due to improved business due to improved business expectationsexpectations

I2=20I2=20


Working out Equilibrium IncomeWorking out Equilibrium IncomeEquilibrium occurs where:Equilibrium occurs where:

Y=AEY=AEAE=C+IAE=C+IAE=60+0.8Y+10AE=60+0.8Y+10AE=70+0.8YAE=70+0.8Y


Working out Equilibrium IncomeWorking out Equilibrium Income

Y=AEY=AEY=70+0.8YY=70+0.8YY-0.8Y=70Y-0.8Y=700.2Y=700.2Y=70Y=70/0.2Y=70/0.2Y=350Y=350


Working out Equilibrium IncomeWorking out Equilibrium IncomeLeakages-Injections ApproachLeakages-Injections Approach

Equilibrium occurs also where:Equilibrium occurs also where:Leakages = InjectionsLeakages = Injections

S=IS=IS=1-CS=1-CS=1-(60+0.8Y)S=1-(60+0.8Y)S=-60+0.2YS=-60+0.2YI=10I=10


Equilibrium Income:Equilibrium Income:S=IS=I

-60+0.2Y=10-60+0.2Y=100.2Y=700.2Y=70Y=70/0.2Y=70/0.2Y=350Y=350


YY CC II AEAE

0 60 10 70

50 100 10 110

100 120 10 130

150 180 10 190

200 220 10 230

250 260 10 270

300 300 10 310

350 340 10 350

400 380 10 390

450 420 10 430

500 460 10 470


A Change in Autonomous A Change in Autonomous ExpenditureExpenditure

Autonomous investment increases by Autonomous investment increases by $20B$20B

Working out Equilibrium IncomeWorking out Equilibrium IncomeY=AEY=AE

AE=C+IAE=C+IAE=60+0.8Y+30AE=60+0.8Y+30AE=90+0.8YAE=90+0.8Y


Finding Equilibrium IncomeFinding Equilibrium Income

Equilibrium occurs where:Equilibrium occurs where:Y=AEY=AE

Y=90+0.8YY=90+0.8YY-0.8Y=90Y-0.8Y=900.2Y=900.2Y=90Y=90/0.2Y=90/0.2Y=450Y=450


Finding Equilibrium IncomeFinding Equilibrium IncomeEquilibrium occurs also where:Equilibrium occurs also where:

Leakages = InjectionsLeakages = InjectionsS=IS=I

S=1-CS=1-CS=1-(60+0.8Y)S=1-(60+0.8Y)S=-60+0.2YS=-60+0.2YI=30I=30


Equilibrium Income:Equilibrium Income:S=IS=I

-60+0.2Y=30-60+0.2Y=300.2Y=900.2Y=90Y=90/0.2Y=90/0.2Y=450Y=450


YY CC II AEAE

0 60 30 90

50 100 30 130

100 120 30 150

150 180 30 210

200 220 30 250

250 260 30 290

300 300 30 330

350 340 30 370

400 380 30 410

450 420 30 450

500 460 30 490


OUTPUT

AGGREGATE EXPENDITURE

AE=70+0.8YAE=90+0.8Y

$20B

$350B $450B

$20B

$100B

$100B

I2=30

I1=10

S=-60+0.2Y

45O

OUTPUT

SAVINGS AND INVESTMENT

$70B

$90B

$10B

$30B

0 $350B $450B

$350B

$450B


Calculating the Size of the MultiplierCalculating the Size of the MultiplierChange in autonomous expenditure Change in autonomous expenditure

(Investment) of $20B has induced a change in (Investment) of $20B has induced a change in Income of $100B.Income of $100B.

This can be represented:This can be represented:k=k=ΔΔY/ Y/ ΔΔAEAE

k=$100B/$20Bk=$100B/$20Bk=5k=5

That is, the change in Autonomous Expenditure That is, the change in Autonomous Expenditure has caused Income to increase by five times.has caused Income to increase by five times.

This is the value of the multiplier.This is the value of the multiplier.


EXPENDITUEXPENDITURE ROUNDRE ROUND

CHANGE IN CHANGE IN INCOMEINCOME

CHANGE IN CHANGE IN CONSUMPTIOCONSUMPTIO

NN

CHANGE IN CHANGE IN SAVINGSSAVINGS

First RoundFirst Round 2020 1616 44

Second RoundSecond Round 1616 12.812.8 3.23.2

Third RoundThird Round 12.812.8 10.2410.24 2.562.56

Fourth RoundFourth Round 10.2410.24 8.198.19 2.052.05

Fifth RoundFifth Round 8.198.19 6.556.55 1.641.64

Sixth RoundSixth Round 6.556.55 5.245.24 1.311.31

Other RoundsOther Rounds 26.2226.22 20.9820.98 5.245.24

TOTALTOTAL 100.00100.00 80.0080.00 20.0020.00

The Multiplier process can be represented in the following way:


Using algebra to determine the multiplierUsing algebra to determine the multiplier ΔΔY= Y= ΔΔC + C + ΔΔII ΔΔC=MPC x C=MPC x ΔΔYY ΔΔY=(MPC x Y=(MPC x ΔΔY) + Y) + ΔΔII (1-MPC) (1-MPC) ΔΔY= Y= ΔΔII ΔΔY=1/(1-MPC) x Y=1/(1-MPC) x ΔΔII ΔΔY/Y/ΔΔI=1/(1-MPC)I=1/(1-MPC) k=1/(1-MPC)k=1/(1-MPC) k=1/MPSk=1/MPSSo, changes in the MPS affect the size of the So, changes in the MPS affect the size of the

multipliermultiplier


Calculating the Multiplier Using Calculating the Multiplier Using AlgebraAlgebra

k=1/MPSk=1/MPS k=1/0.2k=1/0.2 k=5k=5


THE PUBLIC SECTORTHE PUBLIC SECTOR

Government ExpenditureGovernment Expenditure

Government expenditure is considered Government expenditure is considered autonomous of income in the simple autonomous of income in the simple Aggregate Expenditure model.Aggregate Expenditure model.

G=AG=A

The impact of a change in G is identical to The impact of a change in G is identical to a change in I – it shifts the AE curve up a change in I – it shifts the AE curve up and has a multiplier effect on income.and has a multiplier effect on income.


C+I+G

C+I


OUTPUT


45O

0

C

TaxationTaxationTaxation has 2 components:Taxation has 2 components:1.1. AutonomousAutonomous Taxation (a): independent Taxation (a): independent

of income. This is like sales Tax; andof income. This is like sales Tax; and2.2. Induced Induced Taxation (Taxation (tt): taxation that ): taxation that

changes as income changes. This is changes as income changes. This is like income taxlike income tax

The equation for Taxation is:The equation for Taxation is:T=a+T=a+ttYY


Government Expenditure and Taxation Government Expenditure and Taxation can be represented on the leakages-can be represented on the leakages-injections diagram (similar to injections diagram (similar to Investment and Savings)Investment and Savings) T=a+tY

G=A


OUTPUT

G and T

DISPOSABLE INCOMEDISPOSABLE INCOME

The introduction of taxation causes a The introduction of taxation causes a difference between Gross Income and difference between Gross Income and Disposable Income.Disposable Income.

Disposable Income is calculated by Disposable Income is calculated by subtracting taxes from Gross Income:subtracting taxes from Gross Income:

Yd=(1-NT)YYd=(1-NT)Y

Disposable Income is then used as the Disposable Income is then used as the basis for calculating equilibrium income.basis for calculating equilibrium income.


THE EXTERNAL SECTORTHE EXTERNAL SECTOR

ExportsExports

Export expenditure is considered autonomous Export expenditure is considered autonomous of income in the simple Aggregate of income in the simple Aggregate Expenditure model.Expenditure model.

Export expenditure depends on other Export expenditure depends on other economies’ income.economies’ income.

X=AX=A

The impact of a change in X is identical to a The impact of a change in X is identical to a change in I and G– it shifts the AE curve up change in I and G– it shifts the AE curve up and has a multiplier effect on income.and has a multiplier effect on income.


C+I+G

C+I

AE=C+I+G+NX


OUTPUT


0

45O

ImportsImports

Imports are considered to have 2 aspects Imports are considered to have 2 aspects – autonomous and induced.– autonomous and induced.

1.1. AutonomousAutonomous Imports (a): independent Imports (a): independent of income; andof income; and

2.2. InducedInduced Imports ( Imports (mm): imports ): imports expenditure that depends on the level expenditure that depends on the level of national income.of national income.

The equation for Imports is:The equation for Imports is:

M=a+M=a+mmYY


Net ExportsNet Exports

Net exports are the balance of Net exports are the balance of international trade in the model – international trade in the model – the amount of exports sold overseas the amount of exports sold overseas minus the value of imports minus the value of imports consumed.consumed.

NX=X-(a+NX=X-(a+mmY)Y)


Export Expenditure and Imports can Export Expenditure and Imports can be represented on the leakages-be represented on the leakages-injections diagraminjections diagram

M=a+mY

X=A

NX


OUTPUT

X and M

0

OUTPUT


AE=C+IAE=C+I+G

I+G

45O

OUTPUT

LEAKAGES AND INJECTIONS

0

AE=C

I

AE=C+I+G+NX

I+G+XS+T+M

S

S+T


The Multiplier in the Full Aggregate The Multiplier in the Full Aggregate Expenditure ModelExpenditure Model

The more leakages there are from the The more leakages there are from the macroeconomy, the lower the impact of macroeconomy, the lower the impact of the expenditure multiplier. So, when the the expenditure multiplier. So, when the full open macroeconomy multiplier is full open macroeconomy multiplier is calculated, the following formula is used:calculated, the following formula is used:

k=1/1-[k=1/1-[bb(1-(1-tt)-)-mm]]


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MACROECONOMIC MODELS PART 2 GECO6400. THE AGGREGATE EXPENDITURE MODEL THE EXPENDITURE MULTIPLIER Changes in autonomous expenditure lead to greater changes