Transcript The Multiplier

Module 16D-The Magic of the Multiplier
J.A.Sacco
The Multiplier
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Multiplier
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The ratio of the change in the equilibrium level of
real national income to the change in any
autonomous expenditures.
It is the number by which a permanent change in
autonomous expenditures is multiplied to get the
change in the equilibrium level of real national
income.
Think of the multiplier as an amplifier of
autonomous expenditures leading to a change in
real national income.
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The Multiplier
6.0
C+I
Planned Consumption
and Investment per Year
($ trillions)
C
5.0
4.0
C+I=Y
3.0
-Without I -- equilibrium = $1.5
-With I -- equilibrium = $5
-The change in Y (3.5) was
5 times the change in I (.7)
2.0
1.0
0.3
0
45o
1.0 1.5 2.0
3.0
4.0
5.0
Real National Income per Year
($ trillions)
6.0
WHY?
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The Multiplier
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Question
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How can $.7 trillion of I generate $3.5 trillion of
Y
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Answer
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The autonomous spending multiplier
Note- Any permanent decrease in autonomous spending will
cause a larger decrease in the equilibrium level of real national
income. Here the multiplier works in reverse.
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The Multiplier Process
Assumption: MPC = .8 or 4/5
Annual Increase
in Real
National Income
($ billions per year)
Annual Increase
in Planned
Consumption
($ billions per year)
1 ($100 billion per
year increase in I
2
3
4
5
.
.
.
All later rounds
100.00
80.00
64.00
51.20
40.96
.
.
.
163.84
80.000
64.00
51.200
40.960
32.768
.
.
.
131.072
20.000
16.000
12.800
10.240
8.192
.
.
.
32.768
Totals
500.00
400.00
100.000
Round
Multiplier is “5”
Annual Increase
in Planned
Saving
($ billions per year)
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The Multiplier
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The Multiplier Formula
1
1
Multiplier 

1-MPC MPS
Sacco Tip- The multiplier is the reciprocal of the MPS.
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The Multiplier
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Example- If MPC is 4/5, then MPS is
___. What is the multiplier?
Example- If the MPC is .50, then the
MPS is___. What is the multiplier?
The Multiplier
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Examples
4
5
3
MPC 
4
2
MPC 
3
3
MPC 
5
7
MPC 
9
MPC 
1
5
1
MPS 
4
1
MPS 
3
2
MPS 
5
MPS 
2
MPS 
9
1
5
15
1
Mult . 
4
14
1
Mult . 
3
13
1
Mult . 
 2.5
52
1
Mult . 
 4 .5
92
Mult . 
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The Multiplier
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Question
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How does the size of the MPC influence the
value of the multiplier?
Answer
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The smaller the MPS, the larger the
multiplier.
The larger the MPC, the larger the
multiplier.
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The Multiplier
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Question- What would happen to the
multiplier if people saved more of their
additional income? Less of their
income?
Answer- Multiplier smaller/larger.
The Multiplier
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Measuring the Change in Equilibrium
Income from a Change in Autonomous
Spending
Multiplier x Change in autonomous spending =
Change in Equilibrium Income (Output)
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The Multiplier
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Q1- MPC=0.8. Change in autonomous
spending is $100B. What is the change in
real national income?
Q2- If the multiplier is 4, how much additional
gov’t spending would be necessary to
increase the economy by $1B?
Q3- If the multiplier is 4, how much would
the gov’t have to cut spending to lower
demand by $4B?
The Multiplier
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Answer 1- $500B
Answer 2- $250M
Answer 3- $1B
The Multiplier
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Question
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What does the multiplier tell us about the
potential impact on the economy from a
change in autonomous spending?
When is the multiplier most important?
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Changes in Investment
and the Great Depression
What does the Investment Schedule and Business Cycle suggest?
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Tax Multiplier
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Up to this point have looked at the
spending/expenditure multiplier on autonomous
expenditures.
What about a decrease or increase in taxes?
It’s important to know that the typical household will
treat a decrease in taxes as in increase in disposable
income. Most will increase consumption by a factor of
the MPC and save based on the MPS. It is important
to know that less than 100% of this increase in
disposable income will circulate throughout the
economy because most households will save a
portion of it
Tax Multiplier
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Example of the tax multiplier
1) MPC is .90, tax refund=$200.
2) Tax multiplier process begins but not on the entire
$200, only on the consumed portion of $180 because
$20 is saved
3) Therefore with an MPC of .90 the autonomous
spending multiplier is 10, but the tax multiplier Tm,
which is 9, is smaller.
4) Tax multiplier is smaller by 1. The savings acts as
a leakage.
Tax Multiplier
So for our example:
Tm=MPC x (Spending multiplier)=.90x(1/.10)= 9
*the tax multiplier is always smaller than the
spending multiplier by 1. Always!!!
Try This!- MPC is .80 and the government decides to
impose a $50 decrease in taxes. How does this effect
real national income? Explain your reasoning.
Answer- Since the tax multiplier is 4, real national
income would increase by $200 not by $250 as with
the autonomous spending multiplier/
Note- Tax multiplier is negative with an increase in taxes!
Spending Multiplier vs.Tax Multiplier
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Scenario- The nation is in a recession.
What would be more effective to help
end the recession, a $500 B tax refund
to the entire population or a $500B
autonomous government expenditure?
Explain your answer.
The Multiplier Effect When
the Price Level Can Change
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The multiplier effect on equilibrium real
national income will not be as great if
part of the increase in nominal national
income occurs because of increases in
the price level.
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Multiplier Effect on
Equilibrium of Real National Income
LRAS
Price Level
SRAS
With $100 billion
increase in autonomous
spending
120
AD2
AD1
0
5.0
Real National Income per Year
($ trillions)
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Multiplier Effect on
Equilibrium of Real National Income
LRAS
Price Level
SRAS
With price adjustment,
the multiplier effect is less.
125
120
SRAS
What is the point
being made here?
AD2
AD1
0
5.0 5.3 5.5
Real National Income per Year
($ trillions)
With constant prices,
real national income
increases to 5.5 trill.
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