The Spending Multiplier
• What effect does a change in spending (AE =
C+Ig+G+Xn) have on income and output in the
economy?
small changes in spending  _______
larger changes in income/output
_______
AE = Aggregate Expenditures = C + I + G + Xn = AD
The Multiplier Effect
A little change in spending gives rise to a
larger change in income/output (Y) --initial spending creates additional income
that results in additional spending.
This may also work in reverse. A small
decrease in spending gives rise to much
larger decreases in income and output.
Spending by Alex  income earned by Rosaura who spends
some and saves some. Rosaura’s spending leads to income
for Jovan who spends some and saves some. Jovan’s
spending becomes income for Kara who spends some and …
Read: “Squaring the Economic
Circle” on p. 199 in your text book
for a
humorous explanation of the
multiplier in reverse.
The Multiplier Effect
A little change in spending gives rise to a larger change
in income/output (Y) --- initial spending creates
additional income that results in additional spending.
Price Level
LRAS
SRAS
PL1
AD
YF Real GDP
How much spending is needed to
close the GDP gap?
• In a recession,
Price Level
spending is insufficient
to reach full
employment
• The shortfall in
PL1
spending is called a
recessionary gap.
• Because there is a
recessionary gap, a
GDP gap exists (short
fall between actual
(Y1) and potential
GDP (YF).
LRAS
SRAS
AD
Y1
YF Real GDP
GDP Gap
How much spending is needed to
close the gap?
• If the GDP gap is $100 Price Level
billion due to a
recessionary gap in
spending, should spending
be increased $100 billion
to close the gap?
PL1
• Does a certain amount of
spending result in an equal
amount of GDP (income
and output)?
LRAS
SRAS
AD
Y1
YF Real GDP
Due to the multiplier effect, a $100 billion increase in spending
would be far too much spending to close the GDP gap. A smaller,
not equal change in AE leads to a desired larger change in GDP.)
How much should spending be
reduced?
• An inflationary gap Price Level LRAS
occurs if spending
SRAS
exceeds the amount
necessary to purchase
the full employment
PL1
level of output (YF).
AD
• Does a reduction in
spending (AE) result
YF Y1 Real GDP
in an equal decrease in
GDP (income and
output)? WHY?
Actual output > potential output
No – due to the multiplier effect.
Tuesday
• Need multiplier handout, pen, and paper at table.
• Tutorials: 6:30 a.m. Study sessions for AP Gov: 2:45
p.m.
• Record make-up scores for the following quizzes:
exchange rates, net exports, balance of payments (see Unit
3)
• AP Gov Study session Saturday: 10-12 noon
• AP macro study sessions --- next week
• If you want AP gov study guide materials, please ask.
• Wednesday: Rm 112 (2-4th); Thursday Rm 207 (2-4th)
How much of an increase or
decrease in spending is needed to
close these gaps and return to YF?
Price Level
Price Level
LRAS
SRAS
PL1
LRAS
SRAS
PL1
AD
Y1
YF Real GDP
A recessionary gap (shortfall) in
spending leads to a GDP gap
(income/output less than potential).
AD
YF Y1 Real GDP
An inflation gap in spending
means spending exceeds the
YF level of income/output.
Too Much!
The Multiplier Effect
• A change in a component of aggregate
expenditures (C, I, G, or Xn) gives rise to a
LARGER change in equilibrium GDPR.
• A GDPR gap of $100 billion could be closed
less than $100
by a change in AE of _____
billion.
 AE x Multiplier =  GDPR
small
larger
___________
’s in spending  ___________
’s in income/GDPR
Key Assumptions of the
Spending Multiplier:
• The economy supports repetitive, continuous
flows of expenditures and income through which
dollars spent by Smith are received as income by
Chin, then spent by Chin and received as income
by Gonzales, and so on.
• Any change in income will cause both
consumption and saving to vary in the same
direction.
Yd  __C and __ S
A larger disposable income means more is available to spend and save.
Assume that all consumers spend 80% (MPC = .80)
and save 20% (MPS = .20) of any change in income.
$100 expenditure  Yd of $100   $80 in C and  $20 in S
$80 expenditure   Yd of $80   $64 in C and  $16 in S
$64 expenditure   Yd of $64   $51.20 in C and  $12.80 in S
$51.20 expenditure  . . .
There is an end point or maximum by which income and expenditures
are generated by the initial expenditure. The amount by which the
change in Yd is spent (MPC) ensures the expansion and the leakage
of saving (MPS) ensures that the expansion diminishes over time.
Key Relationships:
GDP = Yd
$370
$390
410
430
450
470
490
510
530
C
$375
390
405
420
435
450
465
480
495
S
-$5
0
5
10
15
20
25
30
35
APC
1.01
1.00
.99
.98
.97
.96
.95
.94
.93
APS
-.01
.00
.01
.02
.03
.04
.05
.06
.07
MPC
.75
.75
.75
.75
.75
.75
.75
.75
.75
MPS
.25
.25
.25
.25
.25
.25
.25
.25
.25
• YD ____ C ____ S ____ APC ____ APS
• MPC and MPS are relatively stable as income
increases.
Key Definitions and Formulas:
C/Yd
• APC = Average Propensity to Consume = _____
• (fraction of any income spent)
S/Yd
• APS = Average Propensity to Save = _______
• (fraction of any income that is saved)
1
• C/Yd + S/Yd = _____
• If income is $100 billion and the APS is .20, then the
average amount of consumption = ??
$80 Billion
Key Definitions and Formulas:
ΔC / ΔYd
• MPC = Marginal Propensity to Consume = _________
• (fraction of any change in income that is spent)
ΔS / ΔYd
• MPS = Marginal Propensity to Save = _________
• (fraction of any change in income that is saved)
1
• C/ Yd +  S/ Yd = _____
• If income increases by $100 billion and the MPC is .75,
.25 and the change in saving =
then the MPS = ____
______?
$25
B
Spending Multiplier Formulas:
M = 1/MPS or 1/1-MPC or GDPE/ AE
.80
5
If the MPS = .20 the MPC = ____
M = ____
.25
4
If the MPC = .75 the MPS = ____ M = ____
.10
10
If the MPC = .90 the MPS = ____ M = ____
If the change in GDPE = $20 billion and the change in
4
AE = $5 billion, then the multiplier = ____
and the
.75 and the MPS = _____.
.25
MPC = _____
Key Formula:  AE x M =  GDPE
M = 1/MPS or 1/1-MPC or GDPE/ AE
• If the GDP gap is $100 billion, how much
must AE (C, I, G, or Xn) increase to return
the economy to YF if the MPC = .80?
5
M = 1/1-MPC = 1/1-.80 = 1/.20 = _____
 AE x M =  GDPE
20
______
X
5
______
= 100 Billion
Key Formula:  AE x M =  GDPE
M = 1/MPS or 1/1-MPC or GDPE/ AE
• If the GDP gap is $40 billion and the MPS = .25,
what amount must AE increase to close the GDP
gap?
4
M = 1/MPS = 1/.25 = _____
 AE x M =  GDPE
10
______
X
4
______
= 40 Billion
Key Formula:  AE x M =  GDPE
M = 1/MPS or 1/1-MPC or GDPE/ AE
• If the economy is experiencing an inflationary
gap and actual GDP exceeds potential GDP by
$50 billion, how much must government decrease
G to close the inflationary gap and return to full
employment, assuming an MPS of .20?
5
M = 1/MPS = 1/.20 = _____
 AE x M =  GDPE
10
______
X
5
______
= 50 Billion
Does a change in G have the
same effect on GDP as a change
in T? No – G has a greater effect!
A change in G affects GDP directly by a
multiple of the change in G.
A change in T affects GDP by a multiple of
less than the change in T.
A change in T results in a change in Yd. Yd can
be either spent (C) or saved (S); therefore, a
change in T only affects GDP by a multiple of the
change in C. The initial change in C is less than
the change in T.
Determine the effect on GDP of an increase in
G of $20 billion and the effect of a decrease in
T of $20 billion. Assume the MPC = .80
Remember:  AE x M =  GDP
1/1-.80 = _____
5
Multiplier = _________
• Effect of the the increase in G:
G
20
5
100 increase
_____
X ______
= ______
• Effect of the decrease in T:
20   _____
16 C _____
4 S
 T of $20 billion   Yd _____
C
16 X ______
5
80 increase which is less than
_____
= ______
the increase of 100 from G.
What would be the effect on the economy (GDPE) of a
decrease of $100 billion in G. Assume the MPS =.25
100 X 4 = $400 billion decrease in GDP
• What would be the effect of an increase in taxes of
$100 billion?
Increase T of $100 billion decreases income (Yd) by
100 billion. That means consumers will decrease spending
by $75 billion (.75 x100) and decrease saving by $25 bill.
The $75 billion decrease in C X the multiplier of 4 = a $300
billion decrease in GDP.
Effect of EQUAL increases or
decreases in G and T?
Effect on Budget? no change / balanced
Effect on Economy?
Expansionary or contractionary
depends on increase or decrease.
Determine the effect on GDP of equal
increases (balanced budget) in both G and T
of $50 billion. Assume an MPC of .80.
• Effect on Budget? balanced
• Effect on GDP (economy)?
$40 billion
(.80x50)
5
• Multiplier = _____
 C = _____
Effect on GDP?
Effect of G: 5 x 50 = 250 billion increase in GDP
Effect of T: decrease income by $50 billion; therefore,
C decreases by $40 billion and S decreases by $10 billion.
Therefore, $40 billion X 5 = 200 billion decrease in GDP
Net effect: 250 – 200 = $50 billion increase in GDP
Key Idea: The balanced budget
multiplier is 1 x G
• An increase in G and T of $50 billion would
50 billion
increase GDPE by how much? ________
• A decrease in G and T of $30 billion would
$30 billion
decrease GDPE by how much? _______
• Conclusion: A balanced budget increase in G and
T (spending and taxes are equal) has an
expansionary
____________
effect on the economy.
• A balanced budget decrease in spending and taxes
contractionary effect on the budget.
has a ______________
Disequilibrium in the Keynesian
AE Model.
• Equilibrium occurs when AE = GDPE
• Expenditure = output
decreasing
• If AE > GDP then inventories are ______
 output.
and businesses will ____
increasing
• If AE < GDP then inventories are ______
and businesses will ____ output.

AP Questions
The Multiplier
AE = Aggregate expenditures = C, I, G, Xn
If $500 billion in AE  $1000 billion in
GDPE, then how much would G have to
 to reach a YF of $2000 billion?
•
•
•
•
•
$2000B
$1000B
$500B
$200B
$100B
Key Formula:  AE x M =  GDPE
M = 1/MPS or 1/1-MPC or GDPE/ AE
The value of the spending multiplier
decreases when?
A.
B.
C.
D.
Tax rates are decreased
Exports decrease
Imports decrease
Government
expenditures decrease
E. The MPS increases
Key Formula:  AE x M =  GDPE
M = 1/MPS or 1/1-MPC or GDPE/ AE
Which of the following best explains why
equilibrium income will rise by more than
$100 in response to a $100 increase in G?
A. Incomes will  which leads to  taxes
B. Incomes will  which leads to C which leads
to additional increases in income . . .
C. AE  PL
D. Aggregate expenditures  MS   I
E. budget deficit  Aggregate Expenditures
small
larger
___________
’s in spending  ___________
’s in income/GDPR
Key Formula:  AE x M =  GDPE
M = 1/MPS or 1/1-MPC or GDPE/ AE
In a closed economy with no taxes in which
the APC is 0.75, which of the following is
true?
A.
B.
C.
D.
E.
If income is $100, then saving is $75
If income is $100, then C is $50
If income is $200, then saving is $50
If income is 200, then C is $75
If income is $500, then S is $100
C/YD
APC = Average Propensity to Consume = _____
(fraction of any income spent)
Suppose that Yd is $1000, C is $700, and
the MPC is 0.60. If Yd increases by $100,
C and S will equal which of the following?
A.
B.
C.
D.
E.
C
S
420
600
660
660
760
280
400
320
440
340
MPC = Marginal Propensity to Consume = ΔC/ Δ Yd
(fraction of any change in income that is spent)
MPS = Marginal Propensity to Save = ΔS/ Δ Yd
(fraction of any change in income that is saved)
C/ Yd +  S/ Yd = __1___
If at YF, government wants to increase its
spending by $100 billion without inflation
in the short run, it must do which of the
following?
A.
B.
C.
D.
E.
 T by greater than $100 B
 T by $100B
 T by less than $100 B
 T by $100 B
 by less than $100 B
ΔG x Multiplier = Δ GDP
ΔT → Δ Yd → Δ C and Δ S
Δ C x multiplier = Δ GDP
If AE  from 200 to 300 solely due to a
change in G which leads to a change in
GDPe of 1000 to 1500, which of the
following is true?
A.
B.
C.
D.
E.
G is 300 and the multiplier is 5
G is 100 and the multiplier is 5
G is 100 and C increases by 500
G and GDP increase by 500 each
C and GDP increase by 500 each
Key Formula:  AE x M =  GDPE
M = 1/MPS or 1/1-MPC or GDPE/ AE
If G and T are simultaneously
increased by $100 billion and the
MPS = .20, what is the impact on
GDP?
A.
B.
C.
D.
E.
Increase $500 billion
Decrease $500 billion
Increase $100 billion
Decrease $100 billion
increase $80 billion
Key Idea: The balanced budget multiplier is 1 x G
Unit 3 Website
• Multiplier Online Quiz
• Record actual score earned.
• If you retake the quiz for homework, you may
change your score; however, you may not retake
the quiz in class immediately after taking it the
first time.
• Do not submit your answers until you are finished
with the quiz.
• Thank you.
Tuesday
• See board for study sessions/info on
practice tests
• Need pen/handouts on spending multiplier;
FED/Money; Balance Sheets; Long-run
Growth
Have a nice day!
The FED and Monetary Policy
Banks play an important role in
determining changes in the money
supply.
a) Assume that a bank receives a cash deposit of
$9000 from a customer. What is the immediate
impact of this transaction on the money supply?
Explain.
b) Since the cash was already a part of the
money supply (M1), depositing it in a
checking account does not increase the money
supply --- it only changes its composition
from $9000 in cash to $9000 in checkable
deposits.
The FED and Monetary Policy
Key Ideas
Banks can create money!
• When you deposit money in a checking
account at the bank, does the bank have to
keep all your money in the bank vault?
• The FED requires that banks keep only a
certain percentage of your money in the
bank vault or on deposit at the FED.
Reserve Ratio (Requirement)
• The percent that must be kept in the bank vault or
on deposit at the FED is the required reserve ratio
or reserve requirement.
• The actual amount is called the required or legal
reserves.
• For example, if the RR is 20%, the bank must
keep $200 of your $1000 deposit in the bank vault.
• What can the bank do with the other $800 (excess
reserves)?
So – how do banks create $?
Bank
A
B
C
D
E
F
…
Deposit
$1000
$800
$640
$588.80
$471.04
…
…
RR
ER
Loan
$200
$800
$800
$160
$640
$640
$51.20 $588.80 $588.80
$117.76 $471.04 $471.04
…
…
…
…
…
…
…
…
…
Total Amount of $ created by banking system: $4000
Money Creation Formula
• A single bank can create $ by the amount of its excess
reserves.
• The banking system as a whole can create $ by a multiple
of the excess reserves.
• Money Multiplier = 1/RR
• $ created by Banking System = DM x ER
• Ex. If RR = 20% MM = 1/.20 = 5
• If $1000 is deposited in bank, required reserves are $200;
excess reserves are $800. A single bank can create money
(loan) by this amount)
• The banking system as a whole can create:
• 5 X $800 = $4000.
New vs Existing $
•
•
•
•
•
•
Out of circulation  into circulation
Not currently counted until put into
circulation (added)
Bank Reserves (out) --- loans made
(in/added as new)
Bank Reserves (out) – bonds
purchased from public (in/added as
new)
FED reserves (out) – bonds purchased
from public (in/added as new)
Buried treasure (out) – deposited in
bank checking account (new/added)
•
•
•
•
In Circulation
Counted as part of M1
M1 = currency + checkable
deposits (demand deposits)
Changing coins to checkable
deposits changes only the
COMPOSITION of the money
supply but does not add to it.
To determine total change in MS:
•Include (add) deposit if NEW $ + banking system created $
•Shortcut: New deposit X DM = Total change in money supply
•If initial deposit not new --- total change is ONLY banking system
created money (if coins to checks --- changes composition of MS)
Tools of the FED used to control
the money supply:
• Reserve Requirement
– Percent the bank must keep of your deposit in the bank
vault or on deposit at the FED
• Discount Rate
– Interest rate the FED charges banks to borrow money
• Open Market Operation
– The buying and selling of government securities
(bonds) by the New York FED.
 Reserve Requirement
• More money kept in bank vault – less
money can be loaned out
$ Available for
Loans
Vault
 Reserve Requirement
• Less money kept in bank vault – More
money can be loaned out
$ Available for Loans
Vault
 Discount Rate
• Higher interest rate makes it more difficult
for banks to borrow $ from the FED.
Loans to banks
 $ for banks to loan
FED -- High Rates
 Discount Rate
• Lower interest rate makes it more easier for
banks to borrow $ from the FED.
Loans to banks
 $ for banks to loan
FED -- Low Rates
Buy Bonds:
Open Market Operation
Assume purchase is from the public and the public
deposits its payment into bank accounts.
FED
Banks
Money Supply?
Sell Bonds:
Open Market Operation
Assume the sell is to the public and the payment for the
bonds reduces the checking accounts of the public.
FED
Banks
Money Supply?
Expansionary (Easy)
Monetary Policy
• _____ discount rate
• _____ reserve requirement
• _____ open market operations
• ____ Money Supply
• ____ Aggregate Demand
Contractionary (Tight)
Monetary Policy
• _____ discount rate
• _____ reserve requirement
• _____ open market operations
• ____ Money Supply
• ____ Aggregate Demand
The FED Funds Rate
• The interest rate banks charge each other for
temporary loans.
• This is what the FED usually targets with its
OMO. It cannot directly change an interest rate
set by a bank, but by changing the reserves of the
bank, it pressures the bank to change its interest
rates.
• The FED can directly change only the
DISCOUNT rate (relatively ineffective)
Demand for Money
• Transactions demand – to purchase output –
varies directly with nominal GDP (vertical)
–  GDPN →  DM to purchase output
–  GDPN →  DM to purchase output
• Asset or speculative demand varies inversely
with interest rates (downward-sloping)
–  interest rates →  OC of holding money balances →
 asset demand for money
–  interest rates →  OC of holding money balances →
 asset demand for money
The Transmission Mechanism
PL
LRAS
(i)
SM1
SRAS
i1
PL1
DM
AD
Y1 YF
GDPR
QM1
QM
The Transmission Mechanism
PL
LRAS
SRAS
5th
(i)
SM1
PL1
i1
DM
AD
YF Y1
GDPR
QM1
QM
Bank Balance Sheets (T- Accounts)
• A T-account shows
– changes in a bank’s assets (amounts owed the bank or
the bank has a claim on)
– And a bank’s liabilities (claims against the bank --such as checking account deposits)
• Basic relationship: Assets – liabilities = net
worth.
• Simplified: Assets should equal liabilities (that’s
why they call it a “balance” sheet)
Suppose Justin deposits in Bank A $1000 in quarters he
received from a relative for graduation. Bank A’s balance
sheet (T-Account) looks like this:
Assets
Liabilities
+1000 actual reserves
+$1000 checkable deposit
Does the money supply change when Justin deposits his quarters?
The quarters were already counted in M1. The
deposit does not increase the money supply; it
just changes its composition from quarters to
checkable deposit.
Assuming the required reserve ratio (reserve requirement) is
10%, the bank’s balance sheet should look like this: BANK
A
Assets
+ $100 required reserves
+ $900 excess reserves
Liabilities
+$1000 checkable deposit
Assuming that for the sake of convenience, Bank A keeps all of its
reserves (required and excess) on deposit at the FED and keeps zero
in vault cash. The FED’s balance sheet should look like this as a result
of Justin’s deposit of coins: THE FED:
Assets
Securities
Liabilities
+1000 Reserves of Bank
A
Assume that Bank A decides to loan out its excess reserves of
$900 to Sarah. The loan is deposited in Sarah’s account in
Bank A.
New
Assets
Liabilities
$
+ $100 required reserves
+ $900 excess reserves
+ $900 loans
+$1000 checkable deposit
+ 900 checkable deposits
Assume the Sarah writes a $900 check to Allie who
deposits the check in his bank (Bank B). Assume that Bank B also keeps
All of its reserves on deposit at the FED. After the check clears, the
Balance sheet of Bank A, should look like this
Assets
+100 required reserves (Justin’s deposit)
$0 excess reserves
$900 loans (Sarah)
Liabilities
+1000 checkable deposit (Justin)
$0 checkable deposit (Sarah)
Bank B (Allie’s bank)
Assets
+ $90 required reserves
+ $810 excess reserves
Liabilities
+$900 checkable deposit (Allie’s)
FED Bank
Assets
+Securities
Liabilities
+$100 reserves of Bank A (1000-900)
$900 reserves of Bank B
Conclusions: Reserves lost by one bank are gained by other banks.
• What could Bank B do with its $810 in excess reserves?
• If the deposit expansion continues through the banking system, what is the
potential new money the banking system could create from the quarters?
• What is the total change in the money supply from the deposit?
FED Open Market Purchase of Government Securities
FED
Banks
FED Buys Bonds from Commercial Banks
Balance Sheet of Federal Reserve Bank
Assets
Liabilities
+ Securities
+ reserves of commercial banks
Balance Sheet of Commercial Banks
Assets
Liabilities
- Securites
+reserves
FED Buys Bonds from the Public
Balance Sheet of Federal Reserve Bank
Assets
Liabilities
+ Securities
+reserves of commercial banks
Balance Sheet of Commercial Banks
Assets
Liabilities
+ reserves
+checkable deposits
FED Open Market Sale of Government Securities
FED
Banks
FED Sells Bonds to Commercial Banks
Balance Sheet of Federal Reserve Bank
Assets
Liabilities
- Securities
- reserves of commercial banks
Balance Sheet of Commercial Banks
Assets
Liabilities
+ Securites
- reserves
FED Sells Bonds to the Public
Balance Sheet of Federal Reserve Bank
Assets
Liabilities
- Securities
- reserves of commercial banks
Balance Sheet of Commercial Banks
Assets
Liabilities
- reserves
- checkable deposits
Impact on the Economy
Fed Purchase of government securities:
FED
Banks
___ Sm  ___ i  ___ I, C  ___ AD __ 0 __PL __U
FED
Banks
___ Sm  ___ i  ___ I, C  ___ AD __ 0 __PL __U
Name two factors that weaken the
money (deposit) multiplier:
• Banks do not loan out all of their excess
reserves
• Loans are taken in cash rather than
checkable deposits (cash drain)
Janet Smith deposits $1000 of her cash holdings in
her checking account at the bank. The reserve
requirement is 20% and the bank has no excess
reserves.
• A) what is the immediate effect of her deposit on
the money supply? Explain why.
• B) What is the maximum amount of money the
bank can initially loan out? Explain.
• C) What is the maximum amount of money the
entire banking system can create? Explain.
• D) Give one reason why the money supply may
not increase by the amount you identified in (C)
Janet Smith deposits $1000 of her cash holdings in
her checking account at the bank. The reserve
requirement is 20% and the bank has no excess
reserves.
• A) what is the immediate effect of her deposit on
the money supply? Explain why.
There is no increase in the money
supply because the cash was already
counted as part of M1.
Only the composition of the money supply
changes from $1000 cash to $1000
checkable deposit.
Janet Smith deposits $1000 of her cash holdings in
her checking account at the bank. The reserve
requirement is 20% and the bank has no excess
reserves.
• B) What is the maximum amount of money the
bank can initially loan out? Explain.
• A single bank can loan the amount of its excess
reserves.
• If 20% of $1000 ($200) is set aside in the bank
vault or on deposit at the FED, this leaves
excess reserves ($1000 - $200) of $800 for the
bank to loan out.
Janet Smith deposits $1000 of her cash holdings in
her checking account at the bank. The reserve
requirement is 20% and the bank has no excess
reserves.
• C) What is the maximum amount of money the
entire banking system can create? Explain.
• The banking system as a whole can create
money by a multiple of the initial excess
reserves of a deposit (DM x ER = BS created
money)
• DM = 1/RR = 1/.20 = 5
5 x 800 = $4000
Janet Smith deposits $1000 of her cash holdings in
her checking account at the bank. The reserve
requirement is 20% and the bank has no excess
reserves.
• D) Give one reason why the money supply may
not increase by the amount you identified in (C)
• If banks do not loan out all excess reserves, the
potential to create money by the system is
reduced.
• If customers take loans in cash rather than
checkable deposits, the potential to create more
loans from deposits is reduced.