1. Module 16D-The Magic of the Multiplier
J.A.Sacco

2. The Multiplier Multiplier
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.

3. and Investment per Year Real National Income per Year
The Multiplier
6.0
C + I
45o
C + I = Y C
5.0
4.0
and Investment per Year
Planned Consumption
($ trillions)
3.0
-Without I -- equilibrium = $1.5
-With I -- equilibrium = $5
-The change in Y (3.5) was
5 times the change in I (.7)
2.0
1.0
0.3
WHY?
1.0
1.5
2.0
3.0
4.0
5.0
6.0
Real National Income per Year
($ trillions)

4. The Multiplier Question Answer
How can $.7 trillion of I generate $3.5 trillion of Y
Answer
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.

5. The Multiplier Process
Assumption: MPC = .8 or 4/5
Annual Increase Annual Increase Annual Increase
in Real in Planned in Planned
National Income Consumption Saving
Round ($ billions per year) ($ billions per year) ($ billions per year)
1 ($100 billion per year increase in I
All later rounds
Totals
Multiplier is “5”

6. The Multiplier The Multiplier Formula
Sacco Tip- The multiplier is the reciprocal of the MPS.

7. The Multiplier
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?

8. The Multiplier
Examples

9. The Multiplier Question Answer
How does the size of the MPC influence the value of the multiplier?
Answer
The smaller the MPS, the larger the multiplier.
The larger the MPC, the larger the multiplier.

10. The Multiplier
Question- What would happen to the multiplier if people saved more of their additional income? Less of their income?
Answer- Multiplier smaller/larger.

11. The Multiplier
Measuring the Change in Equilibrium Income from a Change in Autonomous Spending
Multiplier x Change in autonomous spending =
Change in Equilibrium Income (Output)

12. The Multiplier
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?

13. The Multiplier
Answer 1- $500B
Answer 2- $250M
Answer 3- $1B

14. The Multiplier Question
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?

15. Changes in Investment and the Great Depression
What does the Investment Schedule and Business Cycle suggest?

16. Tax Multiplier
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

17. Tax Multiplier 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 always smaller by 1. The savings acts as a leakage.

18. 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!

19. Spending Multiplier vs.Tax Multiplier
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.

20. The Multiplier Effect When the Price Level Can Change
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.

21. Multiplier Effect on Equilibrium of Real National Income
LRAS
AD2
With $100 billion
increase in autonomous
spending
SRAS
AD1
Price Level
120
5.0
Real National Income per Year
($ trillions)

22. Multiplier Effect on Equilibrium of Real National Income
LRAS
AD2
SRAS
AD1
125
5.3
With price adjustment,
the multiplier effect is less.
Price Level
What is the point
being made here?
120
SRAS
5.5
With constant prices,
real national income
increases to 5.5 trill.
5.0
Real National Income per Year
($ trillions)