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Chapter 21
The Simplest
Short-Run Macro Model
Copyright © 2011 Pearson Canada Inc.
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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. …the meaning of equilibrium national income.
4. …how a change in desired expenditure affects equilibrium
income through the “simple multiplier.”
Copyright © 2011 Pearson Canada Inc.
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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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National income accountants are interested in actual GDP
and its components:
Ca, Ia , Ga, and NXa.
What actually occurred last period
Macro Economic Theory is concerned with total desired
expenditure and its components AE, C, I , G, NX
Where are the ‘a’ subscripts? They are gone because
we are referring to desired expenditure not actual!
What do economic agents intend to do in the coming period?
What plans have they made and how did they formulated
those plans?
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The sum is called desired aggregate expenditure:
AE = C + I + G + NX
Where are the ‘a’ subscripts? You absolutely need to understand
why the subscripts ‘a’ are not in the AE expression!
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We use the same
conceptual set
up to do
macroeconomic
theory
as the national
income
accountants
IM
But we are
doing
something
quite
different
C
I
G
X
C + I + G + (X - IM)
= Desired Aggregate Expenditure
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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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Two general 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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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
Slope = b
Note: the slope
of this simple
consumption
function (b) is
less than one.
YD
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A numerical example:
Work this out
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
10/20/08
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=
C
$ 4000
$ 6500
$ 8000
$ 9000
$11500
$14000
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Work this out
Picture of the Consumption Function
45º line
C= a + bYd
C
$14000
Note: the
Consumption
function is for
one period
$8000
(year) only,
so households $6000
might spend more
than they earn
during that one $4000
period (year)
Intercept
$0
Break even
$5000
$8000
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$20000
Yd
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Work this out
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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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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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 any 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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Work this out
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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C
45º line
600
C
450
300
150
•
150
300
450
600
YD
S
S
150
0
-30
-150
150
300
450
600
YD
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Since all of 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
-150
S1
150
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 entirely 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
or sales increase
Desired Investment
I
I’
200
I
150
interest rate rises
expectations worsen
or sales decrease
I’’
100
Y
0
Actual National Income
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Our Story – a simplified version
(no Government, no Trade)
We will now start to tell our story (assemble our
macroeconomic model).
Our story has two key purposes:
- to explain what determines the level of aggregate
economic activity (the size of the GDP or Y)
- to understand what might cause GDP (Y) to increase
and what might cause GDP (Y) to decrease?
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The Aggregate Expenditure Function
The AE function:
- relates desired aggregate expenditure to actual
national income
In the absence of government and international trade, desired
aggregate expenditure is:
AE = C + I
This is called a ‘closed economy with no government’
no Government, no Trade AE = C + I + G + NX
A Lou Dobbs economy (or perhaps the Fox Network economy).
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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 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 distinction between desired aggregate expenditure and actual national income
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Since
implies that
AE = C + I
AE = a + I + bY
What Canadian economic agents desire (intend or plan)
to spend on final goods and services in this period
depends on the level of actual national income (Y) this
period.
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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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The slope of the AE function is the marginal propensity to
spend:
- in this simple model, it is just MPC
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Y
30
120
150
300
450
525
600
900
desired
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
Desired Aggregate
Expenditure
actual
AE =C + I
585
600
345
510
270
300
105
75
30
75
75I
105
300
600
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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C
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Work this out
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, that 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 in our simple model)
actual output is what firms actually produce during the period (Y or GDP)
If desired aggregate expenditure exceeds actual output:
- what is happening to inventories?
falling
- there is pressure for output to rise
If desired aggregate expenditure is less than actual output:
- what is happening to inventories?
rising
- there is pressure for output to fall
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How the Economy Gets to Equilibrium
- Inventory Adjustment Mechanism
What happens if desired AE (C+I) is less than output (actual Y or GDP))?
AE < Y
(GDP)
- Firms cannot sell all that they are producing this period
- Inventories build up (this is unintended I, it is not ‘desired’)
- 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 desired AE (C+I) is greater than output (actual GDP, Y)?
AE > Y
(GDP)
- Firms are selling more than they are producing this period
- Inventories are being run down (this is an unintended decrease in I)
- This is the firms’ signal that an increase in output is
necessary
- Firms increase output until AE=Y
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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
Copyright © 2011 Pearson Canada Inc.
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21.3 Changes in Equilibrium
National Income
Shifts in the AE Function
AE1
AE
AE
AE
e
AE0
e1
e
e
e0
Y
Y0
Y1
Y
Y0
Y1
Y
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AE = Y
AE
E1
•
e1
AE1
AE0
E1
•
e2
e´1
e0
AE = Y
AE
• E0
Y0
e0
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’ but a rotation)
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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.
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
•E
0
Y0
AE1
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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What might cause GDP to increase from Y0?
What if interest rates fall?
AE
AE =Y
-Consumers borrow more (or save less)
and buy more now
- Investors borrow to buy more plant,
equipment, new housing, etc.
E1
•
- AE shifts up (both C and I have shifted up)
- Firms produce more (hire more
workers, buy more resources,
generate more profits) GDP (Y)
increases
AE1
E0
AE0
•
Y0
Y1
Same outcome for a positive change in expectations,
increase in wealth, increase in sales, etc
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Y
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What might cause GDP to decrease from Y0?
What if interest rates rise?
AE
AE =Y
-Consumers borrow less (or save more)
and buy less now
- Investors borrow less and buy less
plant, equipment, new housing, etc.
E0
•
- AE shifts down (both C and I have shifted
AE0
AE1
down)
- Firms produce less (hirer fewer
workers, buy fewer resources,
generate less profits) GDP (Y)
decrease
E1
•
Y1
Y0
Same outcome for a negative change in expectations,
decrease in wealth, decrease in sales, etc
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Y
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EXTENSIONS IN THEORY 21-2
The Algebra of the Simple Multiplier
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
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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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