c h a p t e r c h e c k l i s t

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

C H A P T E R C H E C K L I S T

Distinguish between autonomous expenditure and induced expenditure and explain how real GDP influences expenditure plans.

1

Explain how real GDP adjusts to achieve equilibrium expenditure.2

Describe and explain the expenditure multiplier.3

Derive the AD curve from equilibrium expenditure.4

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The Economy at Full EmploymentAt full employment, real GDP equals potential GDP and the unemployment rate equals the natural unemployment.

Potential GDP and the natural unemployment rate are determined by real factors and are independent of the price level.

A QUICK REVIEW AND PREVIEW

4

The quantity of money and money equilibrium determine nominal GDP.

Nominal GDP and potential GDP determine the price level.

So changes in the quantity of money change nominal GDP and change the price level but have no effect on potential GDP.

• Since 1959, unit money supply (M2/Y) has risen by 3.7% per year while the price level (P) has risen by 3.8% per year.


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Departures from Full EmploymentAggregate supply and aggregate demand determine equilibrium real GDP and the price level.

Fluctuations in aggregate supply and aggregate demand bring fluctuations around full employment.


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Fixed Price Level

• In the aggregate expenditure model, the price level is fixed.

• Keynes wrote the model to explain an economy in a deep recession, when firms could produce more without raising prices.

• It explains the forces that determine real GDP at a given price level.


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15.1 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 purchases of goods and services, G• Net exports, NX = X - M

Aggregate expenditure = C + I + G + X - M.

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Planned and Unplanned ExpendituresMotorola decides to produce 11 million cell phones, planning to sell 10 million phones and to put 1 million into inventory.

People plan to and buy 9 million phones from Motorola.

Planned expenditure is 10 million phones (9 million + 1 million), which is less than production of 11 million.

Motorola’s inventories rise by 2 million phones, 1 million more than planned, so Motorola cuts production.

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

Notice that actual expenditure, which equals planned expenditure plus the unplanned change in firms’ inventories, always equals GDP and aggregate income.

But aggregate planned expenditure might not equal real GDP because firms might end up with up more or less inventories than planned.

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If aggregate planned expenditure (AE) equals real GDP (Y), firms’ inventories are as planned – this is expenditure equilibrium.

If AE > Y, firms’ inventories are smaller than planned; firms increase production.

If AE < Y, firms’ inventories are larger than planned; firms reduce production.

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Unplanned changes in firms’ inventories lead to changes in production and incomes.

• When firms have unwanted inventories, they decrease production. Real GDP falls.

• When inventories fall below planned levels, firms increase production. Real GDP rises.

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Induced Expenditure and Autonomous Expenditure

Autonomous expenditure, AThe components of aggregate expenditure that do not change when real GDP changes. A = I + G + X + C0 + M0, where C0 and M0 are the portions of consumption expenditure and imports that are independent of real GDP.

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Induced expenditureThe components of aggregate expenditure that change when real GDP changes. Induced expenditure equals consumption expenditure minus imports (excluding C0 + M0).

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The Consumption FunctionConsumption functionThe relationship between consumption expenditure and disposable income, other things remaining the same.

Disposable income is aggregate income (GDP) minus net taxes. YD = Y - T

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

T = Ta + tY - Tr

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Figure 15.1 shows the consumption as a function of disposable income C = a + bYD

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

When YD = 0, C = a = $1.5 trillion. This portion of C is independent of YD, hence autonomous.

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Along the 45° line, y = x.At D, 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 (MPC) is the fraction of a change in disposable income that is spent on consumption. It is the slope of C = a + b YD.

MPC = b.

MPC = Change in consumption expenditure

Change in disposable income

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15.1 EXPENDITURE PLANS AND REAL GDPFigure 15.2 shows how to calculate the marginal propensity to consume.

1. A $2 trillion change in disposable income brings

2. A $1.5 trillion change in consumption expenditure, so...

3. The MPC is $1.5 trillion ÷ $2.0 = 0.75.

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Other Influences on Consumption

The factors that influence planned consumption are:

• Disposable income

• Real interest rate

• The buying power of net assets (e.g., money)

• Expected future disposable income

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A change in disposable income leads to a change in consumption expenditure and a movement along the consumption function.A change in any other influence on planned consumption shifts the consumption function, C.For example, C shifts upward when

• The real interest rate decreases• The buying power of net assets increases• Expected future income increases

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15.1 EXPENDITURE PLANS AND REAL GDPFigure 15.3 shows shifts in the consumption function.

1. A fall in the real interest rate or an increase in either the buying power of money or expected future income increases consumption expenditure and shifts the consumption function upward from CF0 to CF1.

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2. A rise in the real interest rate or a decrease in either the buying power of money or expected future income decreases consumption expenditure and shifts the consumption function downward from CF0 to CF2.

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Imports and GDP

Short run changes in imports are directly related to, or induced by, changes in real GDP.

Marginal propensity to import, m, 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.

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15.2 EQUILIBRIUM EXPENDITURE Writing consumption as a function of real GDP

YD = Y – T; definition of disposable income

T = Ta + tY – Tr ; definition of net taxes

C = a + b YD ; consumption as a function of YD. Substitute for YD

C = a + b (Y – T); substitute for T

C = a + b (Y – (Ta + tY –Tr )); multiply through by -1

C = a + b (Y – Ta – tY + Tr ); multiply through by b

C = a + b Y – bTa – btY + bTr ; rearrange to group like terms

C = (a – bTa + bTr )+ b Y – btY; Let C0 = a – bTa + bTr

C = C0 + b Y – btY; factor out b and Y

C = C0 + b (1 – t) Y; Result is C as a function of Y.

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15.2 EQUILIBRIUM EXPENDITURE

Aggregate Planned Expenditure and GDPM = M0 + mY, but let’s assume M0 = 0, so M = mY

AE = C + I + G + X – M; substitute for C and M.

AE = C0 + b (1 – t) Y + I + G + X – mY; rearrangeAE = C0 + I + G + X + b (1 – t) Y – mY

Let A = C0 + I + G + X; factor out YAE = A + (b (1 – t) – m)Y; Let g = b (1 – t) – mAE = A + gY

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• In equilibrium, Y = AE. To find equilibrium expenditure, substitute for AE and solve for Y

• Y = A + gY; subtract gY from both sides• Y – gY = A; factor out Y• Y(1 – g) = A; divide both sides by 1 – g

Ag

Yeq

11

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• The Autonomous Expenditure Multiplier

… equals the change in real GDP divided by the change in autonomous expenditure:

gAY

Ag

Y

11

11

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• The Lump-sum Tax Multiplier

… equals the change in real GDP divided by the change in lump-sum taxes.

gb

TY

gTbY

TbA

a

a

a

1

11

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• The Lump-sum Transfer Payments Multiplier

… equals the change in real GDP divided by the change in lump-sum transfers.

gb

TY

gTbY

TbA

r

r

r

1

11

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Figure 15.4 shows the AE curve.

Aggregate expenditure (AE) is the sum of investment (I), government purchases (G), exports (X), 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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15.2 EQUILIBRIUM EXPENDITUREFigure 15.5 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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15.2 EQUILIBRIUM EXPENDITUREFigure 15.5 shows equilibrium expenditure.

3. When aggregate planned expenditure equals real GDP, there are no unplanned changes in inventories and real GDP remains at 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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Back at Motorola

Recall that Motorola has unwanted inventories.

So, Motorola cuts production.

Where does the process end?

The process ends when expenditure equilibrium is reached.

Equilibrium expenditure is reached because when real GDP changes by $1 aggregate planned expenditure changes by less than $1.

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When aggregate planned expenditure is less than real GDP, firms cut production and 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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Similarly, when aggregate planned expenditure exceeds real GDP, firms increase production and 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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15.3 THE EXPENDITURE MULTIPLIER

When 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 investment is multiplied to determine the change that it generates in equilibrium expenditure and real GDP.

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The Basic Idea of the MultiplierThe initial increase in investment brought an even bigger increase in aggregate expenditure because it induced 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.

The leakages, savings, imports, and income taxes, open a gap between expenditure decisions and real GDP. Each reduces the size of the multiplier.

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Figure 15.6 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 $9 trillion to $11 trillion.

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


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The Size of the Multiplier

The multiplier• 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 expenditureChange 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 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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Imports and Income TaxesThe multiplier depends, in general, not only on consumption decisions but also on imports and income taxes.

Imports make the multiplier smaller that 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 15.7 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 autonomous expenditure 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 autonomous expenditure 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.

15.4 THE AD CURVE AND EQUILIBRIUM

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

The quantity of real GDP demanded at the price level of 110 is $10 trillion—one point on the AD curve.

Equilibrium expenditure is $10 trillion at point B.


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When the price level falls to 90, the AE curve is AE1.

The quantity of real GDP demanded at the price level of 90 is $11 trillion—a movement along the AD curve to point C.

Equilibrium expenditure increases to $11 trillion at point C.


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When the price level rises to 130, the AE curve is AE2.

The quantity of real GDP demanded at the price level of 130 is $9 trillion—a movement along the AD curve to point A.

Equilibrium expenditure decreases to $9 trillion at point A.


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