The Simplest ShortRun Macro Model

1
The Simplest Short-Run Macro Model
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Overview

• Components of Aggregate Expenditure
• The Aggregate Expenditure Function in a closed
  economy without government
• Equilibrium National Income and the Multiplier
• Introducing Government

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Desired Aggregate Expenditure
Recall that total desired expenditure on
domestically produced goods and services can be
divided into similar categories desired
consumption (C), desired investment (I),
desired government purchases (G), and desired
net exports (NX).
The sum of these components is called desired
aggregate expenditure, or more simply Aggregate
Expenditure (AE).
AE CIG(X-IM)
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Components of aggregate expenditure that do not
depend on national income are called autonomous
expenditures.
Components of aggregate expenditure that do
change in response to changes in national income
are called induced expenditures.
There are only two possible uses of disposable
income (YD). consumption (C) or saving (S).
In the simplest theory, consumption is determined
primarily by current disposable income
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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.
The simple savings function is written as
S -a (1-b)YD
APC C/YD
MPC ?C/?YD
APS S/YD
MPS ?S/?YD
APC APS 1 MPC MPS 1
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C1
Shifts in Consumption Functions
45º line
600
Desired Consumption
C0
450

Suppose there is an unexpected increase in
wealth.
300
150

The consumption function will shift upward, and
the saving function downward.
30
150
300
450
600
Real Disposable Income
Desired Saving
Other reasons the consumption function might
shift include changes in interest rates or
expectations.
S0
150
S1
0
150
450
600
-30
300
-150
Real Disposable Income
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Desired Investment Expenditure
Investment expenditure is the most volatile
component of GDP. Changes in investment
expenditure are strongly associated with economic
fluctuations.
Three important determinants of aggregate
investment expenditure are

• the real interest rate,
• changes in the level of sales, and
• business confidence.

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The Aggregate Expenditure Function
The aggregate expenditure function relates the
level of desired aggregate expenditure to the
level of actual national income.
(Note the distinction between desired aggregate
expenditure and actual national income.)
In the absence of government and international
trade, desired aggregate expenditure is just
equal to C I.
AE C I
G 0, X 0 and IM 0
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Consider the following example.
The consumption function is C 300 (0.8)Y
The investment function is I 750
The AE function is then given by AE C I

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9000
Desired Aggregate Expenditure
6000
3000
1050
3000
6000
9000
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 (0.8).
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Equilibrium National Income
Desired Expenditure and Actual Output
If desired aggregate expenditure exceeds actual
output, there will be pressure for output to rise.
If desired aggregate expenditure is less than
actual output, there will be pressure for output
to fall.
Why? Think about what happens to inventories when
AE gt Y, and why this leads to more production.
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Equilibrium occurs where aggregate desired
expenditure equals actual national income
(output).
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AE Y
AE
9000
Desired Aggregate Expenditure
6000
3000
1050
45º
Y
3000
6000
9000
Actual National Income
AE Y Short-Run Macroeconomic Equilibrium
Condition
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Desired Saving and Desired Investment
We can view the equilibrium differently by
considering desired saving and desired investment.
The difference between desired investment and
desired saving is exactly equal to the difference
between desired aggregate expenditure and actual
national income.
To see this, suppose the difference between
desired saving and desired investment is equal to
some number, W. Thus,
S - I W
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Now, recall that S Y - C. We can therefore
write
Y - C - I W
Since AE C I, we can rewrite the equation
again as
Y - (C I) W ? Y - AE W
Thus defining the equilibrium as the level of
output where AE Y is exactly the same as
defining the equilibrium as the level of output
where S I.
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Equilibrium Illustrated
45º line
AE
900
Desired Aggregate Expenditure
Equilibrium national income is that level of
national income where desired aggregate
expenditure equals actual national income.
600

300
105
300
600
900
Saving, Investment
Actual National Income
Or, equivalently, it is the level of national
income where desired saving equals desired
investment.
S
I
75

0
300
600
-30
900
Actual National Income
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Changes in Equilibrium National Income
Shifts in the AE Function
AE1
AE
AE
AE
?e
AE0
e1
?e
?e
e0
?Y
Y0
Y1
Y0
Y1
Y
Y
A movement along the AE function occurs in
response to a change in Y a shift of the AE
function indicates a change in desired
expenditure for any given level of Y.
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AE Y
AE Y
AE
AE
AE1
AE1
E1
e1

AE0
AE0
E1

e2
e1
e0


e0
E0
E0
Y
Y
Y0
Y1
Y0
Y1

• Two types of shifts can occur with the AE
  function
• First, the AE function can shift parallel to
  itself.
• Second, the slope of the AE function can change.

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The Multiplier
What is the Multiplier? The multiplier is a
measure of the size of the change in equilibrium
national income that results from a change in
autonomous expenditure.
In the simplest of macro models, the multiplier
is greater than one.
For example, a 1 billion increase in desired
investment expenditure will increase the
equilibrium level of national income by more than
1 billion.
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Suppose there is an increase in autonomous
desired expenditure equal to ?A.
AE
AE Y
E1
e1

AE1
We can derive the precise value of the simple
multiplier
e1

AE0
?A
e0

Simple multiplier
E0
?Y
?Y
1

Y
Y0
Y1
?A
1-z
where z is the marginal propensity to spend out
of national income.
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Example

• If our aggregate expenditure function is AE
  1050 0.8Y
• Then our Marginal Propensity to Spend (z) is
  ____.
• Therefore the multiplier is

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AE Y
AE
AE
E1
AE Y
AE1

E1
AE0
AE1

?A
AE0


?A
E0
E0
?Y
?Y
Y0
Y1
Y0
Y1
Y
Y
The larger the marginal propensity to spend out
of national income (z), the steeper the AE curve
and the larger the multiplier.
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Economic Fluctuations as Self-Fulfilling
Prophecies
Households and firms base their desired
investment and consumption partly on their
expectations for the future.
As a result, changes in expectations about the
future can lead to real changes in the current
state of the economy.
To see this, imagine that many firms feel
optimistic about future economic prospects. This
increased optimism will increase their desired
investment, shifting up the AE curve.
As we have seen, this shift will increase
national income, justifying the firms 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.
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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.
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Introducing Government
Government Spending
Government purchases of goods and services, G,
are part of desired aggregate expenditures.
Transfer payments are not government purchases
they only affect aggregate expenditure through
their effect on disposable income.
Tax Revenues
Net tax revenue is defined as total tax revenue
received by the government minus total transfer
payments made by the government it is denoted T.
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The Budget Balance
The budget balance is the difference between
government revenue and government expenditures T
- G.
When revenues exceed expenditures, there is a
budget surplus. When expenditure exceeds
revenues, there is a budget deficit.
The Public Saving Function
We assume that G is autonomous with respect to
national income, Y. However, as Y increases, net
taxes rise tax revenues rise and transfers
payments fall.
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Suppose that the net tax rate is 10, that is t
0.1 and that G 51
Then, T (0.1)Y and YD (0.9)Y
The Public Saving Function T - G
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Public Saving
The Public Saving Function
T - G
0
300
600
900
As national income rises, the budget surplus
(public saving) increases.
Actual National Income
51
The slope of the public saving function is equal
to the net tax rate.
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Provincial and Municipal Governments
When measuring the overall contribution of
government to desired aggregate expenditure and
to public saving, all levels of government must
be included.
This is particularly important in Canada, where
the combined purchases of provincial and
municipal governments are larger than those of
the federal government.
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Desired Consumption and National Income
When taxes are included, disposable income (YD)
is less than national income (Y).
Suppose T (0.1)Y. Then, YD Y - T Y 0.1Y
1Y - 0.1Y (1 0.1)Y So, YD (0.9)Y. How
does this alter the simple consumption function?
C 30 (0.8)YD
With income taxes, the MPC out of national income
(0.72) is less than the MPC out of disposable
income (0.8).
C 30 (0.8)(0.9)Y
C 30 (0.72)Y