Aggregate Expenditure
and Equilibrium Output
The Core of Macroeconomic Theory
Aggregate Output and
Aggregate Income (Y)
• Aggregate output is the total
quantity of goods and services
produced (or supplied) in an
economy in a given period.
• Aggregate income is the total
income received by all factors of
production in a given period.
Aggregate Output and
Aggregate Income (Y)
• Aggregate output (income) (Y) is a
combined term used to remind you of
the exact equality between aggregate
output and aggregate income.
• When we talk about output (Y), we
mean real output, or the quantities of
goods and services produced, not the
dollars in circulation.
Explaining Spending Behavior
• All income is either spent on consumption or saved
in an economy in which there are no taxes.
Saving / Aggregate Income - Consumption
Household Consumption and Saving
•
Some determinants of aggregate consumption include:
1.
2.
3.
4.
•
Household income
Household wealth
Interest rates
Households’ expectations about the future
In The General Theory, Keynes argued that household
consumption is directly related to its income.
Household Consumption and Saving
C = a  bY
• The slope of the
consumption function (b) is
called the marginal
propensity to consume
(MPC), or the fraction of a
change in income that is
consumed, or spent.
0  b<1
Household Consumption and Saving
• The fraction of a change in income that is saved is
called the marginal propensity to save (MPS).
MPC+MPS  1
• Once we know how much consumption will
result from a given level of income, we
know how much saving there will be.
Therefore,
S Y-C
An Aggregate Consumption Function
Derived from the Equation C = 100 + .75Y
C  100 .75Y
• At a national income of
zero, consumption is
$100 billion (a).
• For every $100 billion
increase in income (DY),
consumption rises by
$75 billion (DC).
Consumption Function (alternative formulation)
C  c  c(Y - T )
c
c
(Y - T )
-Autonomous consumption
-Marginal Propensity to Consume (MPC)
-Disposable Income (DI) (Income - Net Taxes)
The Determinants of Consumption
•
Wealth
– Affects consumption
expenditures
•
The price level
– Affects real purchasing power
of financial assets
•
$
C’’
C
C’
The interest rate
– Causes consumers to
postpone consumption
•
Expectations (of income or
prices)
– A more optimistic outlook on
the economy will raise
consumers’ expenditures
Y
Deriving a Saving Function
from a Consumption Function
C  100 .75Y
S Y-C
Y
AGGREGATE
INCOME
(Billions of
Dollars)
-
C
=
AGGREGATE
CONSUMPTION
(Billions of
Dollars)
S
AGGREGATE
SAVING
(Billions of
Dollars)
0
100
-100
80
160
-80
100
175
-75
200
250
-50
400
400
0
600
550
50
800
700
100
1,000
850
150
Planned Investment (I)
• Investment refers to purchases by firms of new
buildings and equipment and additions to
inventories, all of which add to firms’ capital stock.
• One component of investment—inventory change—
is partly determined by how much households
decide to buy, which is not under the complete
control of firms.
change in inventory = production – sales
Actual versus Planned Investment
• Desired or planned investment refers to the
additions to capital stock and inventory that
are planned by firms.
• Actual investment is the actual amount of
investment that takes place; it includes items
such as unplanned changes in inventories.
The Planned Investment Function
• For now, we will assume that
planned investment is fixed.
It does not change when
income changes.
• When a variable, such as
planned investment, is
assumed not to depend on
the state of the economy, it is
said to be an autonomous
variable.
Investment Function
I I
Investment is autonomous (independent of income)
Present Value
Internal Rate of Return
$n
$1
$2
PV 

 ... 
1
2
n
1  i  1  i 
1  i 
The Present Value of a stream of payments
Where I can be interpreted as the internal rate of return
Present Value
Internal Rate of Return
5mil
5mil
PV  5mil 
 ... 
1
19
1  i 
1  i 
The Present Value of a 100 million Lotto pay off
Interest Rate
6.0%
7.0%
8.0%
9.0%
10.0%
15.0%
20.0%
Present Value
($60,790,582.46)
($56,677,976.21)
($53,017,996.00)
($49,750,573.90)
($46,824,600.46)
($35,991,155.97)
($29,217,478.40)
Investment and the Investment
Function
Nominal
• At this point investment is
interest rate
planned investment
expenditures (I)
• Investment is closely linked
to the interest rate, since
interest represents the
opportunity cost of
investing in capital
• The investment function
will shift with changes in
expectations for business
profits
D’
D
Investment spending (I)
Autonomous Investment
• Although investment is related
to the interest rate and
business expectations,
investment does not depend in
any significant way on
disposable income
– As such, investment is
“autonomous”
• However, changes in the
interest rate or expectations for
profits will still shift
autonomous investment
$
I”
I
I’
Real disposable income
Determinants of Investment
• Below are all the things that can cause a shift
in the investment function
– The interest rate
– Expectations of future profits
– Technology
Planned Aggregate Expenditure (AE)
• Planned aggregate
expenditure is the total
amount the economy
plans to spend in a
given period. It is
equal to consumption
plus planned
investment.
AE  C  I
Equilibrium Aggregate
Output (Income)
• Equilibrium occurs when there is no
tendency for change. In the
macroeconomic goods market,
equilibrium occurs when planned
aggregate expenditure is equal to
aggregate output.
Equilibrium Aggregate
Output (Income)
aggregate output / Y
planned aggregate expenditure / AE / C
+I
equilibrium: Y = AE, or Y = C + I
Disequilibria:
Y>C+I
aggregate output > planned aggregate expenditure
inventory investment is greater than planned
actual investment is greater than planned investment
C+I>Y
planned aggregate expenditure > aggregate output
inventory investment is smaller than planned
actual investment is less than planned investment
Equilibrium Aggregate
Output (Income)
Equilibrium Aggregate
Output (Income)
C  100 .75Y
I  25
Deriving the Planned Aggregate Expenditure Schedule and Finding Equilibrium (All Figures in
Billions of Dollars) The Figures in Column 2 are Based on the Equation C = 100 + .75Y.
(1)
(2)
(3)
AGGREGATE
OUTPUT
AGGREGATE
PLANNED
(INCOME) (Y) CONSUMPTION (C) INVESTMENT (I)
(4)
(5)
(6)
PLANNED
AGGREGATE
EXPENDITURE (AE)
C+I
UNPLANNED
INVENTORY
CHANGE
Y - (C + I)
EQUILIBRIUM?
(Y = AE?)
100
175
25
200
- 100
No
200
250
25
275
- 75
No
400
400
25
425
- 25
No
500
475
25
500
0
Yes
600
550
25
575
+ 25
No
800
700
25
725
+ 75
No
1,000
850
25
875
+ 125
No
Equilibrium Aggregate
Output (Income)
(2)
Y  C I
C  100 .75Y
(3)
I  25
(1)
By substituting (2) and
(3) into (1) we get:
Y  100 .75Y  25
There is only one value of Y
for which this statement is
true. We can find it by
rearranging terms:
Y - .75Y  100  25
Y  100 .75Y  25 Y - .75Y  125
.25Y  125
125
Y
 500
.25
The Saving/Investment
Approach to Equilibrium
If planned investment is exactly equal to saving, then
planned aggregate expenditure is exactly equal to
aggregate output, and there is equilibrium.
The S = I Approach to Equilibrium
• Aggregate output will be equal to
planned aggregate expenditure only
when saving equals planned investment
(S = I).
The Multiplier
• The multiplier is the ratio of the change in the
equilibrium level of output to a change in some
autonomous variable.
– An autonomous variable is a variable that is assumed not
to depend on the state of the economy—that is, it does
not change when the economy changes.
• In this chapter, for example, we consider planned
investment to be autonomous.
The Multiplier
• The multiplier of autonomous investment
describes the impact of an initial increase in
planned investment on production, income,
consumption spending, and equilibrium
income.
• The size of the multiplier depends on the
slope of the planned aggregate expenditure
line.
The Multiplier Equation
• The marginal propensity to save may be
expressed as:
DS
MPS 
DY
• Because DS must be equal to DI for
equilibrium to be restored, we can
substitute DI for DS and solve:
DI
1
MPS 
therefore, D Y  D I 
DY
MPS
1
1
,
or
multiplier 
multiplier 
1 - MPC
MPS
The Multiplier
• After an increase in
planned investment,
equilibrium output is
four times the
amount of the
increase in planned
investment.
The Size of the Multiplier
in the Real World
• The size of the multiplier in the
U.S. economy is about 1.4. For
example, a sustained increase in
autonomous spending of $10
billion into the U.S. economy can
be expected to raise real GDP over
time by $14 billion.
The Paradox of Thrift
• When households become
concerned about the
future and decide to save
more, the corresponding
decrease in consumption
leads to a drop in spending
and income.
• Households end up consuming less, but
they have not saved any more.
Government Expenditures and
Autonomous Net Taxes
• We will assume that
government expenditures
(G) and net taxes (T) are
autonomous
– This assumption will keep
our models from becoming
overly complex
– It will also allow us to
easily analyze fiscal policy
as both G and T change
• It would be possible to
consider taxes that vary
with GDP (income taxes)
$
T T
G G
G
T
Real income
Autonomous Net Exports (X - M)
• If both exports (X) and
imports (M) are
autonomous, then net
exports are
autonomous
$
X’’-M’’
X-M
X -M  X -M
X’-M’
Real disposable income
Determinants of X-M
• The following will cause a shift in the net export function.
– The Exchange Rate
• If the Dollar appreciates, then exports fall and imports rise, both
causing net exports to fall, or shift down.
– Foreign GDP (Income)
• As foreign income rises, they import more goods from around the
world including the US. So our exports will rise as we satisfy their
demand for our goods.
Variable Imports
• Imports may very well $
be related to income
• This makes net exports
decrease with income
M  m  m(Y - T )
X-M
Real disposable income
Aggregate Expenditure and
Income
Planned Expenditures
• What about the behavior (the “plans”) of our economic
actors?
– Consumption (C) is “planned” on the basis of disposable income
– Investment (I) is “planned” based on the interest rate and business
expectations (although it is autonomous with respect to GDP, or
income)
– G and (X-M) are simply autonomous
• According to Keynes, aggregate planned expenditures
(demand) determine output and income, even in the long
run
The Income-Expenditure Model
• A relationship between aggregate income and planned
aggregate expenditures that determines, for a given price
level, where income (and GDP) equals planned
expenditures
• The aggregate expenditure function is a relationship
showing the amount of planned spending for each level of
income
• Equilibrium occurs in the model where planned aggregate
expenditures equal income (GDP)
– Unintended changes in inventories play a key role
Planned Aggregate Expenditure (trillions of dollars)
Real Net
Dis.
Planned
Gov't
Net Planned
GDP Taxes Income Cons. Saving
Inv.
Purchases Export
Exp.
$6.0
$1.0
$5.0 $4.7
$0.3
$0.6
$1.0 -$0.1
$6.2
$6.5
$1.0
$5.5 $5.1
$0.4
$0.6
$1.0 -$0.1
$6.6
$7.0
$1.0
$6.0 $5.5
$0.5
$0.6
$1.0 -$0.1
$7.0
$7.5
$1.0
$6.5 $5.9
$0.6
$0.6
$1.0 -$0.1
$7.4
$8.0
$1.0
$7.0 $6.3
$0.7
$0.6
$1.0 -$0.1
$7.8
Deriving Equilibrium Income and
Output
$
45o
C+I+G+(X-M)
Equilibrium Real GDP
Real GDP
The Simple Spending Multipliers
$
45o
C+I’+G+(X-M)
C+I+G+(X-M)
DI
Simple spending multiplier =
DGDP/DI = 1/(1-MPC) = 1/MPS
DGDP
Real GDP
The Spending Multiplier and the Circular Flow
(MPC = .8)
Round
1
2
3
4
.
.
.
New
Spending
$100.00
$80.00
$64.00
$51.20
.
.
.
$0.00
Cumulative
Cumulative
New
New
New
Spending Saving
Saving
$100.00
$180.00 $20.00
$20.00
$244.00 $16.00
$16.00
$295.20 $12.80
$12.80
.
.
.
.
.
.
.
.
.
$500.00
$0.00
$100.00
Keynes and the Great Depression
• John Maynard Keynes argued that prices and wages are not sufficiently
flexible to ensure the full employment of resources
• Furthermore, Keynes argued that when resources (especially labor) are
not fully employed (due to a lack of private investment expenditures),
the government could provide offsetting expenditures as a means of
stabilizing the economy
• Thus, Keynesian economics places emphasis on planned expenditures
and all its components
Appendix B--The Algebra of the Income and
Expenditure Model
Y  C  I  G  (X - M )
 c  cY - T   I  G  ( X - M )
144444244443
C
Y 1 - c  c - cT  I  G  ( X - M )


1
Y 
c - cT  I  G  ( X - M )
1 - c 1444444444442444444444443
Autonomous
{
*
Simple
Multiplier
Spending
Appendix B--Introducing Variable Imports
Y  C  I  G  (X - M )
 c
cY
- T   I  G  ( X - (m  m(Y - T ))


C
Y 1 - c  m  c - cT  I  G  X - m  mT
M
1

Y 
c - cT  I  G  X - m  mT ) 



 

1-c
m

Autonomous
*
Open
Economy
Multiplier
Spending
Appendix
• Slides after this point will most likely not be covered in
class. However they may contain useful definitions, or
further elaborate on important concepts, particularly
materials covered in the text book.
• They may contain examples I’ve used in the past, or slides I
just don’t want to delete as I may use them in the future.
Household Consumption and Saving
• The relationship between
consumption and income is called
the consumption function.
• For an individual
household, the consumption
function shows the level of
consumption at each level
of household income.
Income, Consumption,
and Saving (Y, C, and S)
• A household can do two, and only two, things with its
income: It can buy goods and services—that is, it can
consume—or it can save.
• Saving (S) is the part of its income that a household does
not consume in a given period. Distinguished from
savings, which is the current stock of accumulated
saving.
S Y -C
An Aggregate Consumption Function
Derived from the Equation C = 100 + .75Y
C  100 .75Y
AGGREGATE
INCOME, Y
(BILLIONS OF
DOLLARS)
AGGREGATE
CONSUMPTION, C
(BILLIONS OF
DOLLARS)
0
100
80
160
100
175
200
250
400
400
400
550
800
700
1,000
850
Aggregate Demand and Changes in the
Price Level
• An increase in the price level has a negative impact on real
GDP for three reasons
– As the price level increases the real value of fixed financial assets is
diminished. This reduces consumption demand and GDP.
– An increase in the price level puts upward pressure on interest
rates and downward pressure on investment
– As the price level increases, foreign goods become more attractive
• Of course all of these effects are reversed for a decrease in
the price level
The Aggregate Demand Curve
P
AE’’ (P’’)
AE (P)
AE’ (P’)
45o
Y
P
P’
P
P’’
AD
Y
Shifts in the Aggregate Demand Curve
P
C+I’+G+(X-M)
C+I+G+(X-M)
45o
Y
P
AD
AD’
Y
Appendix A--Variable Net Exports
P
X-M
Real GDP
P
C+I+G
C+I+G+(X-M)
Real GDP
The Circular Flow of Income and
Expenditure
X-M
consumption (C)
Investment (I)
S
Financial
markets
Gov’t (G)
transfer payments
Disposable income
taxes
C+I+G+X-M
aggregate income
= GDP
Review Terms and Concepts
actual investment
identity
aggregate income
investment
aggregate output
marginal propensity to consume (MPC)
aggregate output (income) (Y)
marginal propensity to save (MPS)
autonomous variable
multiplier
change in inventory
paradox of thrift
consumption function
planned aggregate expenditure (AE)
desired, or planned, investment (I)
saving (S)
equilibrium
Consumption and Aggregate
Expenditure
Classical Economists
• A group of 18th- and 19th-century economists
who believed that recessions and depressions
were short-run phenomena that corrected
themselves through natural market forces;
thus the economy was self-adjusting
Consumption
• Consumption is the portion of disposable
income that is spent and not saved
• Consumption spending bears a close
relationship to disposable income
• Consumption makes up the largest share of
aggregate planned expenditures
• Approximately 2/3 of GDP
The Consumption and Savings
Functions
$
C
DC
DDI
$
MPC = DC/DDI
real disposable income
MPS = DS/DDI
S
real disposable income
The Marginal Propensity to Consume
and Save
• The marginal propensity to consume (MPC) is
the fraction of a change in income that is
spent on added consumption
• The marginal propensity to save (MPS) is the
fraction of a change in income that is devoted
to added savings
• 0 < MPC < 1
• MPS = 1 - MPC
Planned Versus Actual Investment
• Planned investment is the amount of
investment firms plan to undertake during a
year
• Actual investment is the amount of
investment actually undertaken during a year
• Actual investment equals planned investment
plus unplanned changes in inventories
The Income Half of the Circular Flow
• Since profits (the difference between expenditures on
output and production-related costs) are paid to firms’
owners, GDP equals income:
GDP = Aggregate Income
• Since disposable income is aggregate income minus taxes
(less transfer payments), GDP must equal disposable
income (DI) plus net taxes (T):
GDP = Aggregate income = DI + T
The Expenditure Half of the Circular
Flow
• Disposable income is either spent on
consumption (C) or put into savings (S): DI = C
+S
• From an earlier chapter, aggregate
expenditure has four components
– Consumption (C), Investment (I), Government
Purchases (G) , Net Exports (X - M)
• As a result,
C + I + G + ( X - M ) = GDP
Leakages Equal Injections
• The two equalities for GDP written together give,
GDP = Y=DI + T = C + I + G + ( X - M )
• Since S = DI - C
S+T+M=I+G+X
(leakages = injections)
Leakages and Injections
• A leakage is any
diversion of income
from the domestic
spending stream
• An injection is any
payment of income
other than by firms, or
any spending other
than by domestic
households