MACROECONOMIC MACROECONOMIC MODELS MODELS PART 2 PART 2 GECO6400 GECO6400
MACROECONOMIMACROECONOMIC MODELSC MODELS
PART 2PART 2
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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 AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
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 AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
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 AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
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 AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
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 AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
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 AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
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
THE AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
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
THE AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
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
THE AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
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
THE AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
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
THE AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
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
THE AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
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
THE AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
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
THE AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
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
THE AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
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
THE AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
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
THE AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
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
THE AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
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.
THE AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
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:
THE AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
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
THE AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
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 AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
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.
THE AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
C+I+G
C+I
THE AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
OUTPUT
AGGREGATE EXPENDITURE
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
THE AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
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
THE AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
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 AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
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.
THE AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
C+I+G
C+I
AE=C+I+G+NX
THE AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
OUTPUT
AGGREGATE EXPENDITURE
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
THE AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
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)
THE AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
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
THE AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
OUTPUT
X and M
0
OUTPUT
AGGREGATE EXPENDITURE
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 AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL
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]]
THE AGGREGATE THE AGGREGATE EXPENDITURE MODELEXPENDITURE MODEL