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Chapter 11
Spending and Output
in the Short Run
McGraw-Hill/Irwin
©2009 The McGraw-Hill Companies, All Rights Reserved
Learning Objectives
1. Identify the key assumptions of the basic Keynesian
model
2. Discuss the determination of planned investment and
planned aggregate expenditure
3. Analyze how an economy reaches short-run
equilibrium in the basic Keynesian model
4. Show how a change in planned aggregate expenditure
can cause a change in the short-run equilibrium output
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Keynesian Model
Key assumption:
 In the short run, firms meet demand at preset prices
 Firms typically set a price and meet the demand at
that price in the short run
 Eventually, firms change prices when the marginal
benefits exceed the marginal costs
 Basic Keynesian model developed here ignores
this fact.
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Planned Aggregate Expenditure
 Planned aggregate expenditure is planned spending
on final goods and services
 Four components of planned aggregate expenditure
 Consumption (C) by households
 Investment (I) is planned spending by domestic firms
on new capital goods
 Government purchases (G) are made by federal
state and local governments
 Net exports (NX) is exports minus imports
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Planned Investment Example
 Fly-by-Night Kite produces $5 million of kites per year
 Expected sales are $4.8 million and planned
inventory increase is $0.2 million
 Capital expenditure of $1 million is planned
 Planned investment is $1.2 million
 If actual sales are only $4.6 million
 Unplanned inventory investment of $0.2 million
 Actual investment is $1.4 million
 If actual sales are $5.0 million
 Unplanned inventory decrease of $0.2 million
 Actual investment is $1.0 million
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Planned Aggregate Expenditure (PAE)
 Actual spending equals planned spending for
 Consumption
 Government purchases of final goods and services
 Net exports
 Adjustments between actual and planned spending are
accomplished with changes in inventories
 The general equation for planned aggregate
expenditures is
PAE = C + IP + G + NX
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Consumption Expenditures
 Consumption (C) accounts for two-thirds of total
spending
 Powerful determinant of planned aggregate spending
 Includes purchases of goods, services, and
consumer durables, but not houses
 Rent is considered a service
 C depends on disposable income, (Y – T)
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Consumption, 1960 - 2007
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Consumption Function
 The consumption function is an equation relating
planned consumption to its determinants, notably
disposable income (Y – T)
C = C + (mpc) (Y – T)
where C is autonomous consumption spending
mpc is the change in consumption for a given
change in (Y – T)
 Autonomous consumption is spending not related to
the level of disposable income
 A change in C shifts the consumption function
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Consumption Function
C = C + (mpc) (Y – T)
 C captures wealth effect
 The effect of changes in asset prices on
consumption spending
 C also captures the effects of interest rates on
consumption
 Higher rates increase the cost of using credit to
purchase consumer durables and other items
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More Consumption Function
C = C + (mpc) (Y – T)
 Marginal propensity to consume (mpc) is the
increase in consumption spending when disposable
income increases by $1
 mpc is between 0 and 1 for the economy
 If households receive an extra $1 in income, they
spend part (mpc) and save part
 (Y – T) is disposable income
 Output minus net taxes
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Consumption spending (C)
Consumption Function
C = C + (mpc) (Y – T)
Intercept
C
slope
ΔC
C
Δ (Y – T)
Slope = Δ C / Δ (Y – T)
Disposable income (Y – T)
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Planned Spending Example
PAE = C + IP + G + NX
C = C + mpc (Y – T)
PAE = C + mpc (Y – T) + IP + G + NX
 Suppose that planned spending components have the
following values
C = 620
IP = 220
mpc = 0.8
G = 330
T = 250
NX = 20
PAE = 620 + 0.8 (Y – 250) + 220 + 330 + 20
PAE = 960 + 0.8 Y
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Planned Spending Example
C = 620 + 0.8 (Y – 250)
PAE = 960 + 0.8 Y
 If Y increases by $1, C will increase by $0.80
 PAE increases by 80 cents
 Planned aggregate expenditure has two parts
 Autonomous expenditure, the part of spending that
is independent of output
 $960 in our example
 Induced expenditure, the part of spending that
depends on output (Y)
 0.8 Y in our example
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Planned aggregate expenditure (PAE)
Planned Expenditure Graph
PAE = 960 + 0.8Y
960
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Slope = 0.8
4,800
Output (Y)
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Short-Run Equilibrium
 Short-run equilibrium is the level of output at which
planned spending is equal to output
 Our equilibrium condition can be written
Y = PAE
 Using our previous example, PAE = 960 + 0.8 Y
Y = 960 + 0.8 Y
0.2 Y = 960
Y = $4,800
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Planned aggregate expenditure (PAE)
Short-Run Equilibrium Graph
Y = PAE
PAE = 960 + 0.8Y
Slope = 0.8
960
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45o
4,800
Output (Y)
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Output Greater than Equilibrium
Y = PAE
PAE = 960 +
0.8Y
PAE
 Suppose output
reaches 5,000
 Planned spending is
less than total output
 Unplanned inventory
increases
 Businesses slow
down production
 Output goes down
96
0
45o
4,800
5,000
Output (Y)
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Output Less than Equilibrium
Y = PAE
PAE = 960 +
0.8Y
PAE
 Suppose output is only
4,500
 Planned spending is
more than total output
 Unplanned inventory
decreases
 Businesses speed up
production
 Output goes up
96
0
4,700 4,800
Output (Y)
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Planned aggregate expenditure
(PAE)
Lower Equilibrium
Y = PAE
PAE = 960 + 0.8Y
PAE = 950 + 0.8Y
E
F
960
950
45o
Recessionary gap
4,750 4,800
Y* Output Y
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New Equilibrium
–
 Autonomous consumption, C, decreases by 10
 Causes a downward shift in the planned aggregate
expenditures curve
 The economy eventually adjusts to a new lower level
of equilibrium spending an output, $4,750
 Suppose that the original equilibrium level, $4,800,
represented potential output, Y*
 A recessionary gap develops
 Size of the recessionary gap is 4,800 – 4,750 = $50
 Entire decrease is in Consumption spending
 Same process applies to a decrease in IP, G, or NX
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Japan's Recession and East Asia
 Japanese recession in 1990s reduced Japanese
imports
 East Asian economies developed by promoting exports
 The decrease in exports to Japan decreased planned
aggregate expenditures in these countries
 The decrease in planned spending caused the
economies to contract to a new, lower level of
planned spending and output
 Japan exported its recession to its neighbors
 US recessions have similar effects on our major trading
partners
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Income-Expenditure Multiplier
 The income – expenditure multiplier shows the effect of
a one-unit increase in autonomous expenditure on
short-run equilibrium output
 Previous example
 Initial planned expenditure = 960 + 0.8 Y
 New planned expenditure = 950 + 0.8 Y
 Equilibrium changed from $4,800 to $4,750
 A $10 change in autonomous expenditures caused
a $50 change in output
 Multiplier = 5
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Stabilization Policy
 Stabilization policies are government actions to affect
planned spending with the intention of eliminating
output gaps
 Expansionary policies increase planned spending
 Contractionary policies decrease planned spending
 Two major stabilization tools are fiscal policy and
monetary policy
 Fiscal policy uses changes in government
spending, transfers, or taxes
 Monetary policy uses changes in the money
supply
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Government Spending
 Government spending is part of planned spending
 Changes in government spending will directly affect
planned aggregate expenditures
 Suppose planned spending decreases $ 10 from
Y = 960 + 0.8 Y
to
Y = 950 + 0.8 Y
 Equilibrium Y decreases from $4,800 to $4,750
 Recessionary gap is $50
 Stabilization policy indicates a $10 increase in
government spending will restore the economy to Y* at
$4,800
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Planned aggregate expenditure
(PAE)
$10 Fiscal Stimulus
Y = PAE
PAE = 960 + 0.8Y
PAE = 950 + 0.8Y
E
F
960
950
45o
4,750 4,800
Y* Output Y
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Japanese Spending
 In the 1990s Japan spent over $1 trillion on public
works
 Highways, subways, and transportation projects
 Concert halls
 Re-laying cobblestone sidewalks
 Projects did not end the recession
 Prevented larger decrease in income
 Eroded consumer confidence because there was
little demand
 Consumers reduced spending in anticipation of
higher taxes in the future
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Taxes and Transfers
 Planned aggregate expenditures are affected by taxes
and transfers
 The effect is indirect, channeled through the effects
on disposable income
 Lower taxes or higher transfers increase disposable
income
 Increases in disposable income lead to higher C
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Tax Cuts Stimulate – An Example
 Original planned spending PAE = 960 + 0.8 Y
 Autonomous consumption, C, decreases by 10.
Recessionary gap is $50.
PAE = C + 0.8 (Y – T) + IP + G + NX
 Tax cut to close the gap must be bigger than $10
 Increase disposable income to cause initial increase
in spending to be $10
 Taxes will have to go down by $12.5
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Chapter 23
Appendix A
An Algebraic Solution
of the Basic Keynesian Model
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The Basic Keynesian Model
PAE = C + IP + G + NX
–
C = C + mpc (Y – T)
 The consumption function is defined by
 C, autonomous consumption
 mpc, the marginal propensity to consume, a number
between 0 and 1
 IP, G, T and NX are given
–
I=I
planned investment
–
G=G
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government purchases
–
T=T
net taxes
–
NX = NX
–
net exports
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Find Short-Run Equilibrium Output
–
– – – ––
PAE = C + mpc (Y – T) + I + G + NX
–
– – – ––
PAE = C – mpc T + I + G + NX + mpc Y
 Equilibrium condition is PAE = Y
–
– – – ––
Y = C – mpc T + I + G + NX + mpc Y
–
– – – ––
Y – mpc Y = C – mpc T + I + G + NX
–
– – – ––
(1 – mpc) Y = C – mpc T + I + G + NX
–
– – – ––
C – mpc T + I + G + NX
Y=
(1 – mpc)
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Short-Run Equilibrium Example
–
– – – ––
C – mpc T + I + G + NX
Y=
(1 – mpc)
–
C = 620
–
G = 300
–
T = 250
Y=
–
I = 220
––
NX = 20
mpc = 0.8
620 – 0.8 (250) + 220 + 300 +20
(1 – 0.8)
Y = 960 / 0.2 = 4,800
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Chapter 23
Appendix B
The Multiplier in
the Basic Keynesian Model
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The Income and Expenditure Multiplier
 Suppose autonomous spending decreases $10 and
mpc is 0.8
 First decrease in spending is $10
 Leads to a decrease in output of $10
 Second decrease in spending is $8
 Third decrease is $6.40, etc.
 Sum of the decreases in spending
10 + 8 + 6.4 + 5.12 + …
= 10 [1 + 0.8 + (0.8)2 + (0.8)3…]
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Income and Expenditure Multiplier
 To find the sum of the series, we need a relationship
when x is between 0 and 1
1
2
3
4
1+x+x +x +x +…=
= multiplier
(1 – x)
 In our case, x = 0.8
10 [1 + 0.8 + (0.8)2 + (0.8)3…]
= 10
1
1
= 10
(1 – 0.8)
(1 – x)
= 10 (1 / 0.2) = 10 (5) = 50
 In this case, the multiplier is 5
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