© 2013 Pearson EYE Ons 30 Aggregate Expenditure Multiplier

© 2013 Pearson

EYE Ons

30Aggregate ExpenditureMultiplier

© 2013 Pearson

How big is the government

expenditure multiplier?

© 2013 Pearson

30When you have completed your study of this chapter, you will be able to

1 Explain how real GDP influences expenditure plans.

2 Explain how real GDP adjusts to achieve equilibrium expenditure.

3 Explain the expenditure multiplier.

4 Derive the AD curve from equilibrium expenditure.

CHAPTER CHECKLIST

Aggregate Expenditure Multiplier

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30.1 EXPENDITURE PLANS AND REAL GDP

From the circular flow of expenditure and income, aggregate expenditure is the sum of

• Consumption expenditure, C• Investment, I• Government expenditure on goods and services, G• Net exports, NX

Aggregate expenditure = C + I + G + NX.

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Aggregate planned expenditure is the sum of the spending plans of households, firms, and governments.

Aggregate planned expenditure is planned consumption expenditure, plus planned investment, plus planned government expenditure, plus planned exports, minus planned imports.

We divide aggregate expenditure plans into autonomous expenditure and induced expenditure.

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Autonomous expenditure is the components of aggregate expenditure that do not change when real GDP changes.

Autonomous expenditure equals investment, plus government expenditure, plus exports, plus the components of consumption expenditure and imports that are not influenced by real GDP.

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Induced expenditure is the components of aggregate expenditure that change when real GDP changes.

Induced expenditure equals consumption expenditure minus imports (excluding the elements of consumption expenditure and imports that are part of autonomous expenditure).

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The Consumption Function

Consumption function is the relationship between consumption expenditure and disposable income, other things remaining the same.

Disposable income is aggregate income (GDP) minus net taxes.

Net taxes are taxes paid to the government minus transfer payments received from the government.

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Figure 30.1 shows the consumption function.

As disposable income increases, consumption expenditure increases—induced consumption.

Each dot corresponds to a column of the table.

Point A shows that autonomous consumption is $2 trillion.

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Along the 45° line, consumption expenditure equals disposable income.

1. When the consumption function is above the 45° line, saving is negative (dissaving occurs).

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3. At the point where the consumption function intersects the 45° line, all disposable income is consumed and saving is zero.

2. When the consumption function is below the 45° line, saving is positive.

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Marginal Propensity to Consume

Marginal propensity to consume (MPC) is the fraction of a change in disposable income that is spent on consumption.

MPC = Change in consumption expenditure

Change in disposable income

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Figure 30.2 shows how to calculate the marginal propensity to consume.

1. A $3 trillion change in disposable income brings

2. A $2 trillion change in consumption expenditure, so...

3. The MPC is $2 trillion ÷ $3 trillion = 2/3.

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Other Influences on Consumption Expenditure

The factors that influence consumption plans are

• Real interest rate

• Wealth

• Expected future income

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Real Interest Rate

When the real interest rate falls, consumption expenditure increases and saving decreases.

When the real interest rate rises, consumption expenditure decreases and saving increases

Wealth and Expected Future Income

When wealth or expected future income increases, consumption expenditure increases.

When wealth or expected future income decreases, consumption expenditure decreases.

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Figure 30.3 shows shifts in the consumption function.

1. Consumption expenditure increases and the consumption function shifts upward if• The real interest rate falls• Wealth increases• Expected future income

increases

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2. Consumption expenditure decreases and the consumption function shifts downward if• The real interest rate rises• Wealth decreases• Expected future income

decreases

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Imports and Real GDP

Consumption expenditure is one major component of induced expenditure, imports are the other.

In the short run, the factor influencing imports is U.S. real GDP.

Marginal propensity to import is the fraction of an increase in real GDP that is spent on imports.

The marginal propensity to import equals the change in imports divided by the change in real GDP that brought it about.

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30.2 EQUILIBRIUM EXPENDITURE

Aggregate Planned Expenditure and Real GDP

Consumption expenditure increases when disposable income increases.

Disposable income equals aggregate income—real GDP—minus net taxes, so disposable income and consumption expenditure increase when real GDP increases.

We use this link between consumption expenditure and real GDP to determine equilibrium expenditure.

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Investment (I),

Exports (X),

Figure 30.4 shows the AE curve.

Aggregate expenditure is the sum of

Government expenditure (G),

Consumption expenditure (C)

minus Imports (M).

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Equilibrium Expenditure

Equilibrium expenditure is the level of aggregate expenditure when aggregate planned expenditure equals real GDP.

Equilibrium expenditure equals the real GDP at which the AE curve intersects the 45° line.

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Figure 30.5 shows equilibrium expenditure.

1. When aggregate planned expenditure exceeds real GDP, an unplanned decrease in inventories occurs.

2. When aggregate planned expenditure is less than real GDP, an unplanned increase in inventories occurs.

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3. When aggregate planned expenditure equals real GDP, there are no unplanned inventories and real GDP remains at equilibrium expenditure.

Part (b) shows the unplanned changes in inventories that bring about equilibrium expenditure.

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Convergence to Equilibrium

At equilibrium expenditure, production plans and spending plans agree, and there is no reason to change production or spending.

But when aggregate planned expenditure and actual aggregate expenditure are unequal, production plans and spending plans are misaligned, and a process of convergence toward equilibrium expenditure occurs.

Throughout this convergence process, real GDP adjusts.

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Convergence from Below Equilibrium

When aggregate planned expenditure is less than real GDP, firms cut production. Real GDP decreases.

When real GDP decreases, aggregate planned expenditure decreases.

But real GDP decreases by more than planned expenditure, so eventually the gap between planned expenditure and actual expenditure closes.

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Convergence from Above Equilibrium

When aggregate planned expenditure exceeds real GDP, firms increase production. Real GDP increases.

But real GDP increases by more than the increase in planned expenditure.

Eventually, the gap between planned expenditure and actual expenditure is closed.

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30.3 EXPENDITURE MULTIPLIERS

When autonomous expenditure (e.g. investment) increases, aggregate expenditure and real GDP also increase.

But the increase in real GDP is larger than the increase in investment.

The multiplier is the amount by which a change in any component of autonomous expenditure is magnified or multiplied to determine the change that it generates in equilibrium expenditure and real GDP.

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The Basic Idea of the Multiplier

The initial increase in investment brings an even bigger increase in aggregate expenditure because it induces an increase in consumption expenditure.

The multiplier determines the magnitude of the increase in aggregate expenditure that results from an increase in investment or another component of autonomous expenditure.

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Figure 30.6 illustrates the multiplier.


1. A $0.5 trillion increase in investment shifts the AE curve upward by $0.5 trillion from AE0 to AE1.

2. Equilibrium expenditure increases by $2 trillion from$13 trillion to $15 trillion.

3. The increase in equilibrium expenditure is 4 times the increase in investment, so the multiplier is 4.

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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.

That is,

Multiplier =Change in equilibrium expenditure

Change in autonomous expenditure

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Why Is the Multiplier Greater Than 1?

The multiplier is greater than 1 because an increase in autonomous expenditure induces an increase in aggregate expenditure in addition to the increase in autonomous expenditure.

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The Multiplier and the MPC

The greater the marginal propensity to consume, the larger is the multiplier.

Ignoring imports and income taxes, the change in real GDP (Y) equals the change in consumption expenditure (C) plus the change in investment (I).

That is,

Y = C + I

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Y = C + I

But the change in consumption expenditure is determined by the change in real GDP and the marginal propensity to consume.

It is

C = MPC Y

Now substitute MPC Y for C in the equation at the top of the screen

Y = MPC Y + I

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Now solve for Y as

(1 – MPC) Y = I

Rearrange to get

Y = I

(1 – MPC)

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Now, divide both sides of the equation by the I to give

(1 – MPC)

1YI

=

When MPC is 0.75, so the multiplier is

Y = I

(1 – MPC)

(1 – 0.75)

1YI

= =0.25

1= 4.

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The Multiplier, Imports, and Income Taxes

The size of the multiplier depends not only on consumption decisions but also on imports and income taxes.

Imports make the multiplier smaller than it otherwise would be because only expenditure on U.S.-made goods and services increases U.S. real GDP.

The larger the marginal propensity to import, the smaller is the change in U.S. real GDP that results from a change in autonomous expenditure.

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Income taxes make the multiplier smaller than it would otherwise be.

With increased incomes, income tax payments increase and disposable income increases by less than the increase in real GDP.

Because disposable income influences consumption expenditure, the increase in consumption expenditure is less than it would if income tax payments had not changed.

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The marginal tax rate determines the extent to which income tax payments change when real GDP changes.

The marginal tax rate is the fraction of a change in real GDP that is paid in income taxes—the change in tax payments divided by the change in real GDP.

The larger the marginal tax rate, the smaller is the change in disposable income and real GDP that results from a given change in autonomous expenditure.

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The marginal propensity to import and the marginal tax rate together with the marginal propensity to consume determine the multiplier.

Their combined influence determines the slope of the AE curve.

The general formula for the multiplier is

(1 – Slope of AE curve)YI

=1

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Figure 30.7 shows the multiplier and the slope of the AE curve.

With no imports and income taxes, the slope of the AE curve equals the marginal propensity to consume, which in this example is 0.75.

A $0.5 trillion increase in investment increases real GDP by $2 trillion. The multiplier is 4.

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With imports and income taxes, the slope of the AE curve is less than the marginal propensity to consume.

A $0.5 trillion increase in investment increases real GDP by $1 trillion. The multiplier is 2.

In this example, the slope of the AE curve is 0.5.

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Business Cycle Turning Points

The forces that bring business-cycle turning points are the swings in autonomous expenditure such as investment and exports.

The mechanism that gives momentum to the economy’s new direction is the multiplier.

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An expansion is triggered by an increase in autonomous expenditure that increases aggregate planned expenditure.

At the moment the economy turns the corner into expansion, aggregate planned expenditure exceeds real GDP.

In this situation, firms see their inventories taking an unplanned dive.

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The expansion now begins.

To meet their inventory targets, firms increase production, and real GDP begins to increase.

This initial increase in real GDP brings higher incomes, which stimulate consumption expenditure.

The multiplier process kicks in, and the expansion picks up speed.

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The process works in reverse at a business cycle peak.

A recession is triggered by a decrease in autonomous expenditure that decreases aggregate planned expenditure.

At the moment the economy turns the corner into recession, real GDP exceeds aggregate planned expenditure.

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In this situation, firms see unplanned inventories piling up.

The recession now begins.

To reduce their inventories, firms cut production, and real GDP begins to decrease.

This initial decrease in real GDP brings lower incomes, which cut consumption expenditure.

The multiplier process reinforces the initial cut in autonomous expenditure, and the recession takes hold.

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Deriving the AD Curve from Equilibrium Expenditure

The AE curve is the relationship between aggregate planned expenditure and real GDP when all other influences on expenditure plans remain the same.

A movement along the AE curve arises from a change in real GDP.

30.4 THE AD CURVE AND EQUILIBRIUM EXPENDITURE

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The AD curve is the relationship between the quantity of real GDP demanded and the price level when all other influences on expenditure plans remain the same.

A movement along the AD curve arises from a change in the price level.


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Equilibrium expenditure depends on the price level.

When the price level changes, other things remaining the same, aggregate planned expenditure changes and equilibrium expenditure changes.

Aggregate planned expenditure changes because a change in the price level changes the buying power of net assets, the real interest rate, and the real prices of exports and imports.

So when the price level changes, the AE curve shifts.


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1. When the price level is 110, the AE curve is AE0.

The quantity of real GDP demanded at the price level of 110 is $14 trillion—one point on the AD curve.

Equilibrium expenditure is $14 trillion at point B.

Figure 30.8 shows the connection between the AE curve and the AD curve.


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2. When the price level rises to 130, the AE curve shifts downward

to AE1.

The quantity of real GDP demanded at the price level of 130 is $13 trillion—a

movement along the AD curve to point A.

Equilibrium expenditure decreases to $13 trillion at point A.


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3. When the price level falls to 90, the AE curve shifts upward

to AE2.

The quantity of real GDP demanded at the price level of 90 is $15 trillion—a

movement along the AD curve to point C.

Equilibrium expenditure increases to $15 trillion at

point C.


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Christina Romer, Chair of the President’s Council of Economic Advisers (CEA), has estimated the government expenditure multiplier to be 1.6.

This number led administration economists to predict that the stimulus plan that increased government expenditure would prevent the unemployment rate from rising much above 8 percent.

This prediction turned out to be optimistic.

One reason might be that the multiplier assumption was also too optimistic.

How Big Is the Government Expenditure Multiplier?

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Robert Barro, a leading macroeconomist at Harvard University, has studied the effects of very large increases in government expenditure during wars.

Barro finds that the multiplier is only 0.8.

Barro’s multiplier means that real GDP increases by less than the increase in government expenditure.

The reason is that some private expenditure, mainly investment, gets “crowded out” and real GDP falls.


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John Taylor of Stanford University, another leading macroeconomist, agrees with Barro that the government expenditure multiplier is less than 1.

Taylor says that crowding out gets more severe as time passes.

So Taylor says that the multiplier gets smaller after two years and smaller still after three years.

The figure on the next slide shows the range on estimates of the expenditure multiplier.


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A big multiplier can occur only if there is substantial slack in the economy—when the recessionary gap is large.


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© 2013 Pearson EYE Ons 30 Aggregate Expenditure Multiplier