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.

Planned Disposable consumption Planned

income expenditure saving

(trillions of 1992 dollars per year)

a 0 0.75 -0.75b 1 1.50 -0.50c 2 2.25 -0.25d 3 3.00 0e 4 3.75 0.25f 5 4.5 0.50

Consumption and Saving Plans

Disposable income is either spent on consumption (C)

or saved (S), so

YD = C + SThe relationship between consumption expenditure anddisposable income, with other things remaining the same, iscalled the consumption function.

The amount of consumption expenditure that takes place whenpeople have zero income is called autonomous consumptionexpenditure.

Consumption and Saving PlansC

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200

300

400

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0

ab

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fSaving

Dissaving

100 200 300 400 500Disposable income (billions of 1995 pounds per year)

Consumptionfunction

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

Consumption and Saving Plans

0

-100

100

100 300 400 500

Dissaving

Saving

Savingfunction

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Disposable income(billions of 1995 pounds per year)

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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

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100

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100 200 300 400 500

100$YD billion

MPC= 0.75

75$C billion

Consumptionfunction

45o line

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 = ΔYdDividing both sides by DYD

ΔC + ΔS = ΔYd

ΔYd ΔYd ΔYd

MPC + MPS = 1

The Aggregate Expenditure Model

Aggregate planned expenditure is planned consumptionexpenditure plus planned investment plus plannedgovernment expenditures plus planned exports minusplanned imports.Planned consumption expenditure and planned importsare 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 aggregateexpenditure that are not influenced by real GDP.

(trillions of 1992 dollars)

Planned expenditure

AggregateConsumption Government planned

Real GDP expenditure Investment purchases Exports Imports expenditure(Y) (C) (I) (G) (X) (M) (AE=C+I+G+X–M)

0 0.75 0.5 0.55 1.2 0.0 3

2 2.25 0.5 0.55 1.2 0.5 4

4 3.75 0.5 0.55 1.2 1.0 5

6 5.25 0.5 0.55 1.2 1.5 6

8 6.75 0.5 0.55 1.2 2.0 7

10 8.25 0.5 0.55 1.2 2.5 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.

Multiplier =Change in equilibrium expenditure

Change in autonomous expenditure

= = 4£200 billion

£50 billion

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 = 1

ΔA 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 amountsof consumption expenditure, investment, governmentexpenditures, and exports minus the planned amount ofimports:

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, wesolve the equation for the AE curve and the 45º line forAE and Y:

AE = A + [b(1 – t) – m]YAE = Y

Equilibrium Expenditure

Replace AE with Y in the AE equation to obtain:Y = A + [b(1 – t) – m]Y

or

Amtb

Y] - ) - (1[ - 1

1