What is the difference between the money multiplier and the spending (expenditure) multiplier?

The money multiplier, 1/RR, measures how much the banking system expands the money supply from new excess reserves. The spending multiplier, 1/1-MPC from Unit 3, measures how much real GDP changes from a change in autonomous spending. They use different formulas and answer different questions, so do not mix them up on the exam.

Do I multiply the whole deposit or just the excess reserves?

Multiply only the excess reserves that can actually be loaned out. For a customer cash deposit, the first bank keeps required reserves, so you multiply the excess portion. For a direct central bank reserve injection like a bond purchase, the entire amount is excess reserves and multiplies fully.

Why do deposits and reserves appear on opposite sides of a T-account?

Deposits are liabilities because the bank owes that money to depositors, so they go on the right. Reserves and loans are assets the bank owns or is owed, so they go on the left. The two sides must always be equal because every transaction affects both.

Is the money multiplier always exactly 1/RR in the real world?

No. The formula gives the theoretical maximum. Real economies fall short because the public holds some cash instead of redepositing it and banks sometimes hold excess reserves rather than lending everything. Both leakages reduce the effective multiplier below 1/RR.

AP-MACRO-4.4

U4.4 Banking and the Expansion of the Money Supply

Master fractional-reserve banking for AP Macro 4.4: compute the money multiplier (1/RR), find the max money supply expansion, and read bank T-accounts.

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What this lesson covers

When you deposit cash in a bank, that money does not just sit in a vault. Banks keep a fraction on reserve and lend the rest, and those loans become new deposits that get lent again. This chain reaction is how the banking system expands the money supply, and it is one of the most heavily tested mechanics in Unit 4.

In this lesson you will learn how fractional-reserve banking works, how to build and read a bank T-account, how to calculate the money multiplier as

\frac{1}{RR}

, and how to find the maximum possible increase in the money supply from an initial deposit or injection. You will also learn why the real-world multiplier is almost always smaller than the theoretical maximum.

Fractional-Reserve Banking and Required Reserves

In a fractional-reserve system, banks hold only a fraction of deposits as reserves and lend out the rest. The fraction they must legally hold is set by the required reserve ratio (

RR

), a decimal between 0 and 1.

Suppose

RR = 0.10

(10%). If a bank receives a 1,000 deposit, it must keep 100 in required reserves and may lend up to 900 in excess reserves. That 900 loan is spent and redeposited somewhere in the banking system, where the receiving bank keeps 10% (90) and lends 810, and so on.

Each round the new loan shrinks because a slice is siphoned off into required reserves. The deposits form a decreasing geometric series that sums to a finite total. This is the essence of the money creation process: the banking system as a whole creates far more money than the original deposit, even though no single bank lends more than its excess reserves.

A common misconception is that one bank multiplies money by itself. It does not. A single bank can only lend its excess reserves once. It is the repeated redepositing across many banks that produces the multiplier effect. The exam often gives you

RR

and asks what a single bank can initially lend (its excess reserves) versus what the whole system can ultimately create (the multiplied total). Keep those two questions separate.

Reading a Bank T-Account

A T-account is a simplified balance sheet showing assets on the left and liabilities on the right. For a bank, deposits are liabilities because the bank owes that money to depositors. Reserves (both required and excess) and loans are assets because they are things the bank owns or is owed.

The fundamental rule is that assets must equal liabilities. When a 1,000 deposit arrives with

RR = 0.20

, the T-account looks like this:

Assets	Liabilities
Required reserves 200	Demand deposits 1,000
Excess reserves 800

Both sides total 1,000, so the account balances. Once the bank lends its 800 in excess reserves, the excess reserves line becomes a loan of 800 (still an asset), and excess reserves fall to zero.

AP questions frequently show a partially filled T-account and ask you to compute a missing value: given deposits and the reserve ratio, find required reserves, or given total reserves and required reserves, find excess reserves. Remember the relationships:

\text{required reserves} = RR \times \text{deposits}

, and

\text{excess reserves} = \text{total reserves} - \text{required reserves}

. Watch the direction of transactions too. If the central bank buys bonds from a bank, the bank's securities fall and its reserves rise by the same amount, keeping the T-account balanced.

The Money Multiplier and Maximum Expansion

The money multiplier (also called the simple deposit multiplier) tells you the maximum amount of new money the banking system can create per dollar of new excess reserves. It equals the reciprocal of the required reserve ratio:

\text{money multiplier} = \frac{1}{RR}

RR = 0.10

, the multiplier is

\frac{1}{0.10} = 10

. To find the maximum change in the money supply, multiply the initial excess reserves (the amount that can actually be loaned out) by the multiplier:

\Delta MS_{max} = \text{excess reserves} \times \frac{1}{RR}

Be careful with the starting point. If new cash is deposited into a checking account, the first bank must set aside required reserves, so only the excess portion multiplies. If instead the central bank injects reserves directly (for example, buying bonds from a bank), the entire injection counts as new excess reserves and multiplies fully.

Example distinction with

RR = 0.20

(multiplier 5): a 1,000 cash deposit creates 800 in excess reserves, so maximum new loans equal

800 \times 5 = 4{,}000

, but total change in the money supply from the checking deposit is complicated because the original 1,000 was already money if it came from currency in circulation. On the exam, read carefully whether the question asks for total new loans, the change in checking deposits, or the total change in the money supply, and state your assumption when currency source matters.

Central Bank Injections Versus Simple Deposits

The most exam-relevant application connects to open market operations, previewed here and developed in U4.6. When the central bank buys government bonds from banks, it pays by crediting the banks' reserves. Because those reserves are brand new to the system, the full amount is excess reserves and multiplies by

\frac{1}{RR}

Scenario	Initial excess reserves	Max money creation
Central bank buys 1,000 in bonds, $RR=0.10$	1,000	$1{,}000\times10=10{,}000$
Customer deposits 1,000 cash, $RR=0.10$	900	$900\times10=9{,}000$ in new loans

Notice the difference. A direct reserve injection multiplies fully, while a cash deposit loses the first required-reserve slice before multiplication begins. This is a classic trap: students apply the multiplier to the whole deposit instead of to excess reserves.

When the central bank sells bonds, the process runs in reverse: bank reserves fall, loans contract, and the money supply shrinks by up to the injection times the multiplier. The maximum contraction uses the same

\frac{1}{RR}

formula with a negative sign. Always identify who is on which side of the transaction and whether reserves are rising or falling before you calculate.

Why the Real Multiplier Is Smaller

The formula

\frac{1}{RR}

gives the theoretical maximum, but real economies never reach it because money leaks out of the lending chain at every step. Two leakages matter most.

First, cash leakages (or currency drains): if people hold some of their loans as cash rather than redepositing all of it, less money returns to banks to be lent again, so each round shrinks faster.

Second, excess reserve holding: if banks choose to keep excess reserves rather than lend every available dollar, fewer loans are created. Banks may do this during recessions when lending is risky or when reserves earn interest.

Factor	Effect on multiplier
Higher required reserve ratio	Smaller multiplier
Public holds more cash	Smaller effective multiplier
Banks hold excess reserves	Smaller effective multiplier
Lower required reserve ratio	Larger multiplier

On the exam, if asked why the actual increase in the money supply is less than the maximum, cite that some borrowers hold cash instead of depositing it, or that banks hold excess reserves and do not loan out all available funds. Both reasons break the assumption that every dollar of excess reserves is fully loaned and fully redeposited. Understanding these leakages shows you grasp the mechanism rather than just plugging into a formula, and free-response rubrics reward that reasoning explicitly.

Key terms

Fractional-reserve banking.: A system in which banks hold only a portion of deposits as reserves and lend out the remainder, enabling money creation.
Required reserve ratio (RR).: The fraction of deposits a bank must legally hold as reserves, expressed as a decimal used to compute the money multiplier.
Excess reserves.: Reserves a bank holds beyond its required amount; equal to total reserves minus required reserves and available for lending.
Money multiplier.: The maximum amount of new money the banking system can create per dollar of new excess reserves, equal to $\frac{1}{RR}$ .
T-account.: A simplified balance sheet listing a bank's assets (reserves and loans) on the left and liabilities (deposits) on the right, which must balance.
Demand deposits.: Funds held in checking accounts that are counted as a bank liability because the bank owes them to depositors.
Cash leakage.: Money the public holds as currency rather than redepositing, which reduces the effective size of the money multiplier.

Worked example

The required reserve ratio is 0.25. A customer deposits 2,000 in currency into a bank. Assuming banks lend all excess reserves and all loans are redeposited, find (a) the initial required reserves, (b) the initial excess reserves, (c) the money multiplier, and (d) the maximum increase in loans for the banking system.

Start with the reserve ratio

RR = 0.25

.

Step (a): Required reserves equal

RR

times the deposit:

0.25 \times 2{,}000 = 500

. The first bank must hold 500 as required reserves.

Step (b): Excess reserves equal total reserves minus required reserves. Since the full 2,000 arrived as reserves, excess reserves

= 2{,}000 - 500 = 1{,}500

. Only this 1,500 can be loaned out.

Step (c): The money multiplier is the reciprocal of the reserve ratio:

\frac{1}{RR} = \frac{1}{0.25} = 4

.

Step (d): Maximum new loans equal initial excess reserves times the multiplier:

1{,}500 \times 4 = 6{,}000

.

So the banking system can create up to 6,000 in new loans. Note the trap: multiplying the full 2,000 by 4 gives 8,000, which is wrong because the first bank cannot lend its required reserves. Always multiply excess reserves, not the whole deposit, when the injection is a customer cash deposit.

Practice questions

If the required reserve ratio is 0.20 and the central bank purchases 5,000 in bonds from a commercial bank, what is the maximum possible increase in the money supply?

1,000
4,000
20,000
25,000

Answer: 25,000

A central bank bond purchase credits the bank's reserves directly, so the entire 5,000 is new excess reserves. The money multiplier is

\frac{1}{0.20} = 5

. Maximum expansion is

5{,}000 \times 5 = 25{,}000

. Because reserves were injected directly rather than deposited as cash by a customer, no required-reserve slice is removed before multiplying.

A bank has demand deposits of 10,000 and total reserves of 3,000. The required reserve ratio is 0.10. Explain how much this single bank can lend and why the whole banking system can create more than that amount.

Answer: The bank can initially lend 2,000, and the system can ultimately create up to 20,000 in new money because loans are redeposited and re-lent across many banks.

Required reserves are

0.10 \times 10{,}000 = 1{,}000

. Excess reserves are

3{,}000 - 1{,}000 = 2{,}000

, so this single bank can lend 2,000. When that 2,000 is spent and redeposited, the next bank keeps 10% and lends the rest, continuing the chain. With a multiplier of

\frac{1}{0.10} = 10

, the system can create up to

2{,}000 \times 10 = 20{,}000

. The distinction is that one bank lends only its excess reserves once, while the system multiplies through repeated redepositing.

Which of the following would cause the actual increase in the money supply to fall short of the maximum predicted by the money multiplier?

Banks lend every dollar of excess reserves
The public redeposits all loaned funds
Banks choose to hold excess reserves
The central bank lowers the reserve ratio

Answer: Banks choose to hold excess reserves

The maximum assumes banks loan out all excess reserves and all funds are redeposited. If banks hold excess reserves instead of lending them, fewer loans are created and the effective multiplier shrinks. Lending every dollar and full redepositing would achieve the maximum, and lowering the reserve ratio actually raises the multiplier.

FAQ

What is the difference between the money multiplier and the spending (expenditure) multiplier?: The money multiplier, $\frac{1}{RR}$ , measures how much the banking system expands the money supply from new excess reserves. The spending multiplier, $\frac{1}{1-MPC}$ from Unit 3, measures how much real GDP changes from a change in autonomous spending. They use different formulas and answer different questions, so do not mix them up on the exam.
Do I multiply the whole deposit or just the excess reserves?: Multiply only the excess reserves that can actually be loaned out. For a customer cash deposit, the first bank keeps required reserves, so you multiply the excess portion. For a direct central bank reserve injection like a bond purchase, the entire amount is excess reserves and multiplies fully.
Why do deposits and reserves appear on opposite sides of a T-account?: Deposits are liabilities because the bank owes that money to depositors, so they go on the right. Reserves and loans are assets the bank owns or is owed, so they go on the left. The two sides must always be equal because every transaction affects both.
Is the money multiplier always exactly 1/RR in the real world?: No. The formula gives the theoretical maximum. Real economies fall short because the public holds some cash instead of redepositing it and banks sometimes hold excess reserves rather than lending everything. Both leakages reduce the effective multiplier below $\frac{1}{RR}$ .

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