01 / 20
$

Banking & the
Money Multiplier

How banks create money through lending, the role of reserve requirements, and the money multiplier that expands the money supply.

AP Macroeconomics

What Is the Money Supply?

The money supply is the total amount of money available in an economy at a given time. Economists measure it using categories called monetary aggregates.

M1
Currency in circulation, demand deposits (checking accounts), and other checkable deposits: the most liquid forms of money.
M2
M1 plus savings deposits, small time deposits, and money market funds: near-money that is slightly less liquid.

How Fractional Reserve Banking Works

Banks are only required to keep a fraction of each deposit on reserve. The rest can be loaned out, which is how banks create new money in the economy.

Deposit $1,000 Bank Splits deposit into: Reserves + Loans Required Reserves $100 (10%) Excess Reserves $900 (Loanable) Borrower $900 Deposited at Bank B: $900 Cycle repeats: Bank B keeps 10%, lends 90%...

Key Banking Terms to Know

Reserve Ratio (\(rr\))
The fraction of deposits a bank must hold as reserves, set by the central bank.
Excess Reserves
Reserves held above the required amount: the funds available for lending.
Money Multiplier
The factor by which total deposits can expand from an initial injection of reserves.

The Money Multiplier Formula

$$ \text{Money Multiplier} = \frac{1}{rr} $$

where \( rr \) is the required reserve ratio (as a decimal).

Visualizing Deposit Expansion

With \( rr = 10\% \), a $1,000 initial deposit creates up to $10,000 in total deposits.

Round 1 $1,000.00 Round 2 $900.00 Round 3 $810.00 Round 4 $729.00 . . . Total $10,000.00 Multiplier at work:
\( rr = 10\% = 0.10 \)
\( \text{Multiplier} = \frac{1}{0.10} = 10 \)
\( \$1{,}000 \times 10 = \$10{,}000 \)
Each round = 90% of previous

Excess Reserves vs. New Deposits

A critical distinction on the AP exam: the multiplier applies to excess reserves, not to the total deposit. The initial deposit itself is already counted in the money supply.

New Deposit
Someone deposits $1,000 from under their mattress. The initial deposit is new money entering the banking system. Excess reserves = \( \$1{,}000 \times (1 - rr) \).
Fed Bond Purchase
The Fed buys $1,000 in bonds from a bank. The entire $1,000 is new excess reserves: the multiplier applies to the full amount.

Reading a Bank T-Account

A T-account is a simplified balance sheet showing a bank's assets and liabilities.

First National Bank Assets Required Reserves $100 Excess Reserves $900 Total Assets $1,000 Liabilities Demand Deposits $1,000 Total Liabilities $1,000
After a $1,000 deposit with \( rr = 10\% \)

How to Apply the Money Multiplier

1
Identify the source. Is the new money from a cash deposit, a Fed open market operation, or a change in reserve requirements?
2
Calculate excess reserves. For a new deposit: \( \text{Excess} = \text{Deposit} \times (1 - rr) \). For a Fed purchase: the entire amount is excess reserves.
3
Find the multiplier. \( \text{Money Multiplier} = \frac{1}{rr} \)
4
Compute maximum expansion. \( \Delta M_s = \text{Multiplier} \times \text{Excess Reserves} \)
5
State the result. Specify "maximum" change: actual expansion may be less if banks hold extra reserves or borrowers don't re-deposit.

Example 1: Cash Deposit

Maria deposits $5,000 in cash at her bank. The required reserve ratio is 20%. What is the maximum increase in the money supply?

1
Excess reserves: \( \$5{,}000 \times (1 - 0.20) = \$5{,}000 \times 0.80 = \) \( \$4{,}000 \)
2
Money multiplier: \( \frac{1}{0.20} = \) \( 5 \)
3
Maximum expansion: \( 5 \times \$4{,}000 = \) \( \$20{,}000 \)

Example 2: Fed Open Market Purchase

The Federal Reserve buys $2,000 in government bonds from a commercial bank. The reserve ratio is 10%. What is the maximum increase in the money supply?

1
Excess reserves: The entire \( \$2{,}000 \) is new excess reserves (the bank traded a bond for cash reserves).
2
Money multiplier: \( \frac{1}{0.10} = \) \( 10 \)
3
Maximum expansion: \( 10 \times \$2{,}000 = \) \( \$20{,}000 \)

Example 3: Changing the Reserve Ratio

The Fed lowers the reserve ratio from 20% to 10%. A bank currently holds $50,000 in deposits. How much new lending capacity is created?

1
Old required reserves: \( \$50{,}000 \times 0.20 = \$10{,}000 \)
2
New required reserves: \( \$50{,}000 \times 0.10 = \$5{,}000 \)
3
Freed excess reserves: \( \$10{,}000 - \$5{,}000 = \) \( \$5{,}000 \)
4
Max new money: \( \frac{1}{0.10} \times \$5{,}000 = 10 \times \$5{,}000 = \) \( \$50{,}000 \)

Why "Maximum" Expansion?

The simple multiplier gives the theoretical maximum. In practice, the actual money creation is often less due to leakages in the system.

Cash Drains
Borrowers may keep some cash instead of depositing it, removing money from the multiplier cycle.
Excess Reserves Held
Banks may choose to hold reserves above the requirement, especially during uncertain times.
Low Loan Demand
If few creditworthy borrowers want loans, banks cannot lend out all excess reserves.

Common Mistakes to Avoid

✕ Multiplying the Full Deposit
For a cash deposit, the multiplier applies to excess reserves, not the total deposit. Required reserves cannot be lent out.
✕ Confusing rr with Multiplier
The multiplier is \( \frac{1}{rr} \), not \( rr \) itself. A 20% reserve ratio gives a multiplier of 5, not 0.20.
✕ Forgetting "Maximum"
The multiplier gives the maximum possible expansion. Actual expansion is typically less due to leakages.

Comparing Money Creation Scenarios

Cash Deposit Fed Bond Purchase Lower rr
Source of funds Public deposits cash Fed buys bonds Policy change
Excess reserves \( \text{Deposit} \times (1 - rr) \) Full purchase amount Freed from existing deposits
Multiplier applies to Excess reserves only Full amount Freed reserves
Fed tool? No Yes: Open Market Ops Yes: Reserve Requirements

Question 1 of 5

If the required reserve ratio is 25%, what is the simple money multiplier?

Question 2 of 5

A customer deposits $8,000 in cash at a bank with a reserve ratio of 10%. What is the maximum increase in the money supply from this deposit?

Question 3 of 5

The Federal Reserve purchases $10,000 in government bonds from a commercial bank. With a reserve ratio of 20%, the maximum increase in the money supply is:

Question 4 of 5

Which of the following would decrease the money supply?

Question 5 of 5

A bank has $500,000 in deposits and a reserve ratio of 10%. It currently holds $80,000 in total reserves. How much can this bank individually lend?