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Chapter 21
The Simplest
Short-Run Macro Model
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In this chapter you will learn
1. the difference between desired expenditure and actual
expenditure.
2. the determinants of desired consumption and desired
investment expenditures.
3. how to define equilibrium national income.
4. how a change in desired expenditure affects equilibrium
income, and how this change is reflected by the multiplier.
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21.1 DESIRED AGGREGATE EXPENDITURE
The national accounts divide actual GDP into its components:
- Ca, Ia , Ga, and NXa.
Total desired expenditure is divided into the same categories:
• desired consumption, C
• desired investment, I
• desired government purchases, G
• desired net exports, NX
Where are the ‘a’
subscripts?
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The sum is called desired aggregate expenditure:
AE = C + I + G + NX
Where are the ‘a’
subscripts?
Two types of expenditures:
- autonomous expenditures do not depend on the level
of national income
- induced expenditures do depend on the level of
national income
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What Does “Desired” Really Mean?
“Desired” expenditure is not just a list of what consumers and firms
would buy if they had no constraints on their spending — it is
much more realistic than that.
Desired expenditure is what consumers and firms would like to
purchase, given their real-world constraints of income and market
prices.
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Desired Consumption Expenditure
Two possible uses of disposable income:
- consumption (C) or saving (S)
What about taxes and imports?
In the simplest theory, consumption is determined primarily by
current disposable income (YD).
Recall: disposable income (YD) is national income (Y) less taxes (T).
In more advanced theories, individuals are forward looking,
and so consumption depends more on “lifetime” income.
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An Important Tool: the 45º line - our reference line
Properties of the 45º line
- bisects the quadrant
- intercept of zero
- slope of 1
45º line
C
200
100
100
200
YD
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The simple consumption function is written as:
C = a + bYD
where a represents autonomous consumption expenditure
and bYD represents induced consumption expenditure.
C
45º line
C = a +bYD
intercept (a)
a
slope (b)
YD
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Note: the slope
of this simple
consumption
function (b) is
less than one.
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A numerical example:
Consider C = a + bYd where a = 4000 and b =0.5
Yd
=
a
+ bYd
$
0
$4000
$
0
$ 5000
$4000
$ 2500
$ 8000
$4000
$ 4000
$10000
$4000
$ 5000
$15000
$4000
$ 7500
$20000
$4000
$10000
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=
C
$ 4000
$ 6500
$ 8000
$ 9000
$11500
$14000
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Picture of the Consumption Function
C= a + bYd
C
$14000
Break even
$8000
$6000
$4000
Intercept
$0
$5000 $8000
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$20000
Yd
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Exercise: repeat the previous calculations and
draw the graph using the following
parameter values
a
b
you should find
1)
$5000
0.5
intercept shifts up
2)
$3000
0.5
intercept shifts down
3)
$4000
0.7
slope rotates upwards
4)
$4000
0.3
slope rotates downwards
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Changes in the slope of the consumption function
C = a + bYD
C = a + b’YD
versus
where b’ > b
C = a + b’YD
C
C = a + bYD
A change in slope
causes a rotation of the line
a
YD
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Changes in the intercept of the consumption function
C = a + bYD
versus
C = a’ + bYD
where a’ > a
C = a’ + bYD
C
C = a + bYD
a’
A change in the intercept
causes a shift in the line
a
YD
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Shifts in the Consumption Function
What might cause a shift in the consumption function
(the amount of consumption desired by all
households at all levels of income)?
- change in wealth
- change in interest rates
- change in expectations
- change in population size or age distribution
- change in taste
- ?
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What about savings?
If C = a + bYd and Yd = C + S then S= -a +(1-b)Yd
Yd
$
0
$ 5000
$ 8000
$10000
$15000
$20000
C
$ 4000
$ 6500
$ 8000
$ 9000
$11500
$14000
Calculate APS = S/YD
Savings = Yd - C
-$4000
-$1500
$
0
$1000
$3500
$6000
MPS = S/YD
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The marginal propensity to consume (MPC) relates the
change in desired consumption to the change in disposable
income that brings it about.
MPC = C/YD
denoted b in
our expression
and diagram
The MPC is the slope of the consumption function.
In the previous diagram, the MPC is the same at every level
of income.
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The average propensity to consume (APC) is equal to total
consumption divided by total disposable income.
APC = C/YD
In the previous diagram, the APC falls as the level of
income rises.
EXTENSIONS IN THEORY 21-1
The Theory of the Consumption Function
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C
45º line
600
C
450
300
150
•
150
300
450
600
YD
S
S
150
0
-30
150
-150
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300
450
600
YD
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Since all disposable income is either consumed or saved, we
have:
• APC + APS = 1
• MPC + MPS = 1
Is our simple theory of the consumption function supported by
empirical evidence? For some Canadian data on aggregate
consumption and disposable income, look for “The Consumption
Function in Canada” in the Additional Topics section of this
book’s MyEconLab.
www.myeconlab.com
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Shifts in the
Consumption Function?
C
600
45º line
C1
•
450
If consumption function
shifts upward, the
saving function must
shift downward.
C0
300
150
•
30
150
What causes a shift?
-  wealth
-  interest rate
-  expectations
300
450
600
YD
S
S0
150
0
-30
S1
150
-150
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300
450
600
YD
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Desired Investment Expenditure
Recall: Investment refers to purchases of
- capital stock (plant & equipment)
- residential building
- business inventories
Investment expenditure is the most volatile component of
GDP:
 changes in investment expenditure are strongly
associated with short-run fluctuations
Three important determinants of aggregate investment
expenditure are:
• the real interest rate
• changes in the level of sales
• business confidence
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The Real Interest Rate
The real interest rate is the opportunity cost for:
- investment in new plants and equipment
- investment in inventories
- investment in residential construction
Thus, all three components of desired investment
expenditure are negatively related to the real interest rate,
other things being equal.
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Changes in Sales
The higher the level of production and sales, the larger the
desired stock of inventories:
 changes in the rate of sales cause temporary bouts
of investment in inventories
Business Confidence
When business confidence improves, firms want to invest now
so as to reap future profits.
Business confidence and consumer confidence may feed off
of one another.
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The Investment Function
Desired investment is treated as autonomous
– completely unrelated to the current level of Y
We can write I = I
Were I is determined by - real interest rates
- expectations
(confidence)
- changes in sales
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Investment Function (the picture)
interest rate falls
expectations improve
sales increase
Desired Investment
I
I’
200
I
150
I’’
100
interest rate rises
expectations worsen
sales decrease
Y
0
Actual National Income
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Our Story – a simplified version
We will now start to tell our story (build our
macroeconomic model).
Our story has one key purpose: to explain what
determines the level of aggregate economic activity
(the size of the GDP or Y)
– and to understand what might cause Y to increase
and what might cause Y to decrease?
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The Aggregate Expenditure Function
Desired aggregate expenditure, or more simply Aggregate
Expenditure (AE).
AE = C+I+G+(X-IM)
Now what if we get rid of the Government and foreign
economies?
A Lou Dobbs economy (or perhaps the Fox Network economy).
This is termed a closed economy with no government
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A closed economy with no government
Domestic Households
Savings
Consumption
Financial
markets
Investment
Factor income:
wages, rents profits
Domestic Firms
YD = Y
Revenue from
sales of final G & S
=C+I
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The Aggregate Expenditure Function becomes
In the absence of government and international trade, desired
aggregate expenditure is just equal to C + I.
AE = C + I
The aggregate expenditure function relates the level of
desired aggregate expenditure to the level of actual national
income (through actual national income’s influence on C)
(Note the distinction between desired aggregate expenditure
and actual national income.)
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The aggregate expenditure function relates the level of
desired aggregate expenditure to the level of actual national
income.
But how? Through actual national income’s influence on C
AE = C + I
But, C= a + bYD
and YD = Y
(the consumption function)
(no government – no taxes)
Therefore AE = a + bY + I
AE = a + I + bY
(Note the distinction between desired aggregate expenditure
and actual national income.)
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Consider the following example.
The consumption function is:
C = 30 + (0.8)Y
The investment function is:
I = 75
The AE function is then given by:
AE = C + I = 30 + (0.8)Y + 75
==> AE = 105 + (0.8)Y
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C
54
126
150
270
390
450
510
750
I
75
75
75
75
75
75
75
75
AE
129
201
225
345
465
525
585
825
AE =C + I
900
Desired Aggregate
Expenditure
Y
30
120
150
300
450
525
600
900
C
600
300
105
75
30
I
300
600
900
Actual National Income
The slope of the AE function is the marginal propensity to
spend. In the simplest model with no taxes and no
international trade, this is just the MPC.
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Exercise
Repeat the above calculations and graphing for the
following economies
1) C = 30 + (0.8)Y
and
I = 125
2) C = 60 + (0.8)Y
and
I = 75
3) C = 30 + (0.6)Y
and
I = 75
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Summary
The AE function combines the spending plans of households
and firms. It shows, for any level of actual national income, the
level of desired aggregate spending.
What happens to AE if the consumption function shifts up or
down?
What happens to AE if the slope of the consumption function
increases or decrease?
What happens to AE if the investment function shifts up or
down?
What happens to AE if the slope of the investment function
increases or decrease? (We will assume that it is always zero?)
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21.2 EQUILIBRIUM NATIONAL INCOME
Recall:
desired aggregate expenditure is what buyers want to buy
during the period (C+I)
actual output is what firms actually produce during the period (Y)
If desired aggregate expenditure exceeds actual output:
- what is happening to inventories?
- there is pressure for output to rise
If desired aggregate expenditure is less than actual output:
- what is happening to inventories?
- there is pressure for output to fall
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National
Income (Y)
OUTPUT
30
120
150
300
450
525
600
900
Desired
Aggregate
Expenditure
(AE = C + I)
129
201
225
345
465
525
585
825
Effect
Pressure
On output
to rise


Equilibrium income

Pressure on output
to fall
Equilibrium occurs where aggregate desired expenditure
equals actual national income (output).
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How the Economy Gets to Equilibrium – Inventory
Adjustment Mechanism
What happens if output (GDP) is greater than
desired AE?
AE < Y
- Firms cannot sell all that they are producing
- Inventories build up (this is unintended I)
- This is the firms’ signal that a decrease in output is
necessary
- Firms decrease output until AE=Y
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How the Economy Gets to Equilibrium – Inventory
Adjustment Mechanism
What happens if output (GDP) is less than desired AE?
AE > Y
- Firms are selling more than they are producing
- Inventories are being run down (this is unintended I)
- This is the firms’ signal that an increase in output is
necessary
- Firms increase output until AE=Y
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Equilibrium Mechanism Illustrated
45º line
AE
Equilibrium national
income is that level of
national income at which
desired aggregate
expenditure equals
actual national income.
At an actual national
income of 300, AE > Y
(How do you know?)
therefore inventories are
falling and firms expand
output.
Desired Aggregate
Expenditure
900
600
•
300
105
300
600
900
Actual National Income
At an actual national
income of 900, AE <Y
(How do you know?)
therefore inventories are
increasing and firms
decrease output.
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In this model, output is
said to be demand
determined.
The equilibrium condition
is:
Y = AE(Y)
Desired A.E.
45º line
AE
900
600
•
300
105
300
600
900
Actual National Income
In words: Equilibrium national income is that level of
national income where desired aggregate expenditure
equals actual national income.
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Remember!
INVENTORIES!
INVENTORIES!
INVENTORIES!
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A different, but equivalent, way of thinking about the equilibrium
level of national income involves comparing desired saving with
desired investment. For more details, look for “Investment,
Saving, and Equilibrium GDP” in the Additional Topics section
of this book’s MyEconLab.
www.myeconlab.com
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21.3 CHANGES IN EQUILIBRIUM
NATIONAL INCOME
‘Movement along’ vs. ‘shifts’ in the AE Function
AE1
AE
AE
e1
AE
e´´
e´
e
e0
AE0
Y
Y0
Y1
Y
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Y0
Y1
Y
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AE =Y
AE
E1
•
e1
AE1
AE0
E1
•
e2
e´1
e0
AE =Y
AE
•E
e0
0
Y0
Y1
Y
AE1
AE0
•E
0
Y0
Y1
Y
Two types of ‘shifts’ can occur with the AE function:
1. The AE function can shift parallel to itself
2. The slope of the AE function can change (should not
really be called a ‘shift’)
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The Multiplier
The multiplier is a measure of the size of the change in
equilibrium Y that results from a change in autonomous
expenditure.
For example, a $1 billion increase in desired investment
expenditure will increase the equilibrium level of national
income by more than $1 billion.
In our simplest of macro models, the multiplier exceeds
one.
APPLYING ECONOMIC CONCEPTS 21-1
The Multiplier: A Numerical Example
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Simple multiplier =
Y
1
=
A
1-z
AE
AE =Y
E1
•
e1
•
e´1
Where z is the
marginal propensity to
spend out of national
income and A is the
change in autonomous
expenditure.
AE0
A
e0
AE1
•E
0
Y0
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Y
Y1
Y
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AE
AE =Y
AE
E1
AE =Y
E1
•
A
0
Y
Y0
Y1
Y
AE1
AE0
AE1
AE0
•E
•
A •
E0
Y0
Y
Y1
Y
The larger is z, the steeper is the AE curve and the larger is
the simple multiplier.
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Example of the multiplier and its use
AE
AE =Y
E1
•
If we know that the multiplier e1
is 4 and we know that the
e´1
•
A is $500 million, then we
A
can calculate that the Y
•E
is going to be $2,000 million e0
0
Y
Y0
Y
AE1
AE0
Y1
= multiplier x A
What is the value of the multiplier in the real world?
Canada = 1.20 or so
Windsor = ? Maybe 1.06
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Y
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Another example of the multiplier and its use
What if the marginal
AE
propensity to spend (z) is
0.75 and GM decides to build e
1
a new auto plant for $500
million, what would the
e´1
change in equilibrium Y be?
AE =Y
E1
•
•
AE0
A
e0
•E
Simple multiplier =
0
Y
Y
1
=
Y0
A
1-z
So the multiplier is 1 / (1-0.75) = 1 / 0.25 = 4
AE1
Y1
Y
The change in equilibrium Y will be 4 x $500 million =
$2,000 million ($2 billion). A = $500 million and Y=$2,000 million
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EXTENSIONS IN THEORY 21-2
The Algebra of the Simple Multiplier
Politicians in Canada and elsewhere are often heard “talking
up” their economies. This can be understood by examining
the role that expectations play in booms and recessions. For
more on this topic, look for “Recessions and Booms as SelfFulfilling Prophecies” in the Additional Topics section of this
book’s MyEconLab.
www.myeconlab.com
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Economic Fluctuations as Self-Fulfilling
Prophecies
Households and firms base their desired investment and
consumption partly on their expectations of the future:
 changes in expectations can lead to real changes
in the current state of the economy
Example:
- imagine that firms feel optimistic about the future
- this increases their desired investment, shifting up the
AE curve
- this increases Y, justifying the initial optimism
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Now imagine the opposite scenario. It should be clear that if
firms and households are pessimistic about the future in large
numbers, the ensuing change in their behaviour will lead to a
self-fulfilling prophecy of reduced national income.
Could the Prime Minister (or the Governor of the
Bank of Canada) ever announce to the country
that they might have made a ‘big’ mistake?
For example: suppose that government analysts
report to the Prime Minister that having signed
the Kyoto Accord might result in a recession.
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