The Simplest ShortRun Macro Model

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The Simplest Short-Run Macro Model

• Lecture 7-B

Part II
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Overview

• The Multiplier
• Government Spending and Net Tax Revenue
• Net Exports
• Short-run Equilibrium National Income for an Open
  Economy with Government

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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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Example

• If our aggregate expenditure function is AE
  1050 0.8Y
• Then our Marginal Propensity to Spend (z) is 0.8.
• Therefore the multiplier is
• So a 1 increase in autonomous expenditure (A),
  increases equilibrium national income by 5.

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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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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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Government Spending and Net Tax Revenue
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.
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.
When measuring the overall contribution of
government to desired aggregate expenditure and
to public saving, all levels of government must
be included federal, provincial and municipal.
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Public Saving
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.
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 tY - G
T - G (0.1)Y - 51
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The Public Saving Function
As national income rises, the budget surplus
(public saving) increases.
Public Saving
T - G
0
300
600
900
The slope of the public saving function is equal
to the net tax rate.
National Income
51
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Disposable Income vs. 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
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
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Net Exports
Canadas exports are autonomous with respect to
Canadian national income. In contrast, desired
imports rise as Canadian national income
increases.
The marginal propensity to import is the change
in imports that results from a 1 change in
national income. Denoted m.
Overall net exports, X IM, falls as national
income rises. This relationship is called the net
export function.
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Suppose that X 72 and IM (0.1)Y. That is, the
marginal propensity to import, m, is 0.1.
Net Exports NX X IM NX X - mY NX 72
(0.1)Y
Notice that the slope of the net exports function
is negative. Net exports is decreasing in
national income.
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Imports and Exports
Net Exports Function
96
IM 0.1Y
72
X 72
48

• The NX function is drawn holding constant
• foreign national income,
• domestic and foreign prices,
• and the exchange rate.

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0 300 600 900
Y
72
Net Exports
NX 72 - 0.1Y
48
24
0 300 600 900
Y
-24
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Shifts in the Net Exports Function
Foreign Income An increase in foreign income,
ceteris paribus, will lead to an increase in the
quantity of Canadian goods demanded by foreign
countries. This increases X and shifts up the NX
function.
Relative International PricesA rise in Canadian
relative to foreign prices reduces Canadian
exports, decreasing X. The IM function also
rotates up since Canadians now spend a higher
fraction of income on foreign goods. The NX
function shifts down and also gets steeper.
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This diagram illustrates the case of an increase
in Canadian prices relative to foreign prices.
IM
IM
X
X
Imports and Exports
An important source of such relative prices
changes is change in exchange rates.
Actual National Income
(X - IM)
Net Exports
An appreciation of the Canadian dollar will
increase Canadian prices relative to foreign
prices.
(X - IM)
Actual National Income
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The Aggregate Expenditure Function
We can now expand the AE function to include net
exports.
AE C I G NX
Recall that the slope of the AE function is the
marginal propensity to spend out of national
income we call this z.
Suppose Y rises by 1. Then an additional 72
cents is spent on consumption, but 10 cents of
the extra consumption is on imports. Therefore,
desired spending on domestic production rises by
only 62 cents z is 0.62.
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In general form, C a bYD a b(1-t)Y T
tY IM mY G, I, X are autonomous
So AE C I G (X IM) AE a
b(1-t)Y I G (X mY)
AE a I G X b(1-t) mY
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Autonomous Expenditure (A) a I G X
Induced Expenditure b(1-t) mY
Marginal Propensity to Spend (z) b(1-t) m
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Equilibrium National Income
As before, equilibrium occurs where desired
aggregate expenditure equals actual national
income.
What happens if AE gt Y? When households, firms,
and governments try to spend their desired
amounts, they will find that production is
insufficient to meet their demand. This will
deplete inventories and lead domestic firms to
increase production.
If AE lt Y, then desired aggregate spending is
less than current production. Inventories will
build up, and firms will reduce their production.
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Exercise
C 50 0.7YD T 0.2Y I 75 X 50 G
100 IM 0.15Y
The AE function AE C I G (X - IM)
AE 50 0.7(0.8)Y 75 100 50 0.15Y AE
275 0.41Y
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AE 275 0.41Y
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• Y AE at equilibrium
• YE 275 0.41 YE
• YE 0.41 YE 275
• 0.59Y 275
• YE (275/0.59) 466.1

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• The multiplier 1 1/0.59 1.69
• 1 z
• This means that a 1 increase in autonomous
  expenditure (a, G, I, or X) will increase
  equilibrium national income by 1.69.

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Summary

• Net Tax function T tY
• Public Saving T G tY G
• Disposable income YD (1 - t)Y
• Consumption function with government
• C a b(1 - t)Y
• Import function IM mY
• Net Exports X IM X mY

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• Aggregate Expenditure in an open economy with
  government
• AE C I G NX
• AE a I G X b(1 t) mY
• The marginal propensity to spend
• z b(1 t) m
• The multiplier
• 1
• 1 - z