Expenditures Multipliers: The Keynesian Model
Lecture notes 9
Instructor: MELTEM INCE
Expenditure Plans
The aggregate expenditure model explains
fluctuations in aggregate demand by identifying the
forces that determine expenditure plans.
The components of aggregate expenditure are:
1) Consumption expenditure
2) Investment
3) Government purchases of goods and services
4) Net exports (exports minus imports)
Expenditure Plans
The main factors that influence consumption and saving
are:
1) Real interest rate
2) Disposable income
3) Purchasing power of net assets
4) Expected future income
Expenditure Plans
 The
consumption function shows the
relationship between consumption
expenditure and disposable income.
 The saving function shows the relationship
between saving and disposable income.
Disposable
income
Planned
consumption
expenditure
Planned
saving
(trillions of 1992 dollars per year)
a
b
c
d
e
f
0
1
2
3
4
5
0.75
1.50
2.25
3.00
3.75
4.5
-0.75
-0.50
-0.25
0
0.25
0.50
Consumption and Saving Plans
Disposable income is either spent on consumption (C)
or saved (S), so
YD = C + S
The relationship between consumption expenditure and
disposable income, with other things remaining the same, is
called the consumption function.
The amount of consumption expenditure that takes place when
people have zero income is called autonomous consumption
expenditure.
Consumption expenditure
(billions of 1995 pounds per year)
Consumption and Saving Plans
500
Consumption
f
function
Saving
400
e
Dissaving
c
300
200
100
0
d
b
a
100
200
300
400
500
Disposable income
(billions of 1995 pounds per year)
Consumption and Saving Plans
The relationship between saving and disposable income,
with other things remaining the same, is called the
saving function.
Negative saving is called dissaving
Saving
(billions of 1995 pounds per year)
Consumption and Saving Plans
100
Saving
e
Dissaving
0
-100 a
Saving
f function
d
100
200
c
b
300
400
500
Disposable income
(billions of 1995 pounds per year)
Marginal Propensity to Consume
The marginal propensity to consume (MPC) is the
fraction of a change in disposable income that is
consumed.
MPC= ΔC
ΔYd
Consumption expenditure
(billions of 1992 pounds per year)
o
45 line
500
Consumption
f function
MPC= 0.75
400
e
300
c
200
100
0
b
C  $75 billion
YD  $100 billion
a
100
d
200
300
400
500
Disposable income
(billions of 1992 pounds per year)
Marginal Propensity to Save
The marginal propensity to save (MPS) is the fraction of
a change in disposable income that is saved.
MPS= ΔS
ΔYd
MPC AND MPS
Because consumption expenditure and saving exhaust disposable
income, the marginal propensity to consume plus the marginal
propensity to save always equals 1.
ΔC + ΔS = ΔYd
Dividing both sides by DYD
ΔC + ΔS = ΔYd
ΔYd ΔYd ΔYd
MPC + MPS = 1
The Aggregate Expenditure Model
Aggregate planned expenditure is planned consumption
expenditure plus planned investment plus planned
government expenditures plus planned exports minus
planned imports.
Planned consumption expenditure and planned imports
are influenced — and influence — real GDP
The Aggregate Expenditure Model
The aggregate expenditure schedule lists aggregate planned expenditure
generated at each level of real GDP.
Aggregate planned expenditure increases as real GDP increases.
However, only consumption expenditure and imports increase with real
GDP.
Induced expenditure is the sum of the components of aggregate
expenditure that vary with real GDP.
Autonomous expenditure is the sum of the components of aggregate
expenditure that are not influenced by real GDP.
Planned expenditure
Consumption
Real GDP expenditure
(Y)
(C)
Investment
(I)
Government
purchases Exports
(G)
(X)
Aggregate
planned
Imports
expenditure
(M) (AE=C+I+G+X–M)
(trillions of 1992 dollars)
0
2
4
6
8
10
0.75
2.25
3.75
5.25
6.75
8.25
0.5
0.5
0.5
0.5
0.5
0.5
0.55
0.55
0.55
0.55
0.55
0.55
1.2
1.2
1.2
1.2
1.2
1.2
0.0
0.5
1.0
1.5
2.0
2.5
3
4
5
6
7
8
The Size of the Multiplier
The multiplier is the amount by which a change in
autonomous expenditure is multiplied to determine the
change in equilibrium expenditure that it generates.
Change in equilibrium expenditure
Multiplier =
=
Change in autonomous expenditure
£200 billion
£50 billion
= 4
The Multiplier and the Slope of the AE Curve
The slope of the AE curve determines the magnitude of the multiplier.
The steeper the AE curve, the greater is the increase in induced expenditure
that results from a given increase in real GDP.
Multiplier = ΔY
ΔA
=
1
1- Slope of AE curve
If the slope of the AE curve is 0.75:
Multiplier =
1
= 1 = 4
1- 0.75 0.25
The Algebra of the Multiplier
Symbols:
 Aggregate planned expenditure, AE
 Real GDP, Y
 Consumption expenditure, C
 Investment, I
 Government expenditures, G
 Exports, X
 Imports, M
 Net taxes, NT
 Disposable income, YD
 Autonomous consumption expenditure, a
 Marginal propensity to consume, b
 Marginal propensity to import, m
 Marginal tax rate, t
 Autonomous expenditure expenditures, A
Aggregate Expenditure
Aggregate expenditure is the sum of planned amounts
of consumption expenditure, investment, government
expenditures, and exports minus the planned amount of
imports:
AE = C + I + G + X – M
We write the consumption function as:
C = a + bYd
Equilibrium Expenditure
Grouping together terms that involve Y we obtain:
AE = [a + I + G + X] + [b(1 – t) – m]Y
Autonomous
expenditure
(A)
Slope of the
AE curve
Equilibrium Expenditure
Equilibrium expenditure occurs when aggregate planned
expenditure equals real GDP:
AE = Y
To calculate equilibrium expenditure and real GDP, we
solve the equation for the AE curve and the 45º line for
AE and Y:
AE = A + [b(1 – t) – m]Y
AE = Y
Equilibrium Expenditure
Replace AE with Y in the AE equation to obtain:
Y = A + [b(1 – t) – m]Y
or
Y
1
A
1 - [b(1 - t ) - m]