AP® Macroeconomics review sheet from Aim for Five (aimforfive.com/macro/units/4/4-4)
Unit 4 · Topic 4.4
4.4 Banking and the Expansion of the Money Supply
Banks keep only part of their deposits as reserves and lend out the rest. When those loans are spent and deposited again, the banking system creates new money. The money multiplier tells you the most the money supply can grow from new excess reserves, and real-world leaks make the actual growth smaller.
Key terms
- fractional reserve banking
- balance sheet (T-account)
- required reserves
- excess reserves
- required reserve ratio
- money multiplier
Fractional reserve banking and the balance sheet
Banks don't keep every dollar you deposit in a vault. In fractional reserve banking, a bank holds only a fraction of its deposits as reserves and lends out much of the rest, earning interest on the loans.
A bank's balance sheet, drawn as a T-account, lists assets on the left and liabilities on the right. Total assets always equal total liabilities plus owners' equity, so every transaction changes at least two entries.
- Assets (what the bank owns or is owed): reserves (vault cash plus deposits at the central bank), loans it has made, and securities such as government bonds.
- Liabilities (what the bank owes): demand deposits, which depositors can withdraw at any time.
- Owners' equity (the owners' stake): whatever is left, which keeps the two sides equal. AP problems often set it at $0.
Required and excess reserves
Required reserves are the share of deposits a bank must hold, set by the required reserve ratio (rr). Excess reserves are any reserves above that, and they are what a single bank can safely lend. If a bank has $100,000 in demand deposits and the required reserve ratio is 10%, it must hold $10,000. If it actually holds $25,000, it has $15,000 in excess reserves to lend.
In March 2020 the Fed cut the U.S. required reserve ratio to 0%. AP questions about required reserves describe an economy that uses a reserve requirement, so use whatever ratio the question gives.
- Required reserves = demand deposits × required reserve ratio (rr).
- Excess reserves = total reserves − required reserves.
How lending creates money
Suppose rr = 10% and $1,000 of new reserves is deposited at Bank A. Bank A keeps $100 and lends $900. The borrower spends it, and the seller deposits the $900 at Bank B. Bank B keeps $90 and lends $810, and so on. Each round is smaller than the last.
Total new deposits add up to $1,000 × 10 = $10,000. The loans made along the way total $9,000, and those loans are newly created money.
| Bank | New deposit | Required reserves (10%) | New loan |
|---|---|---|---|
| Bank A | $1,000 | $100 | $900 |
| Bank B | $900 | $90 | $810 |
| Bank C | $810 | $81 | $729 |
| All banks together | $10,000 | $1,000 | $9,000 |
The money multiplier and its limits
The money multiplier tells you the most the money supply can grow from new excess reserves (the formulas are below). The real increase is usually smaller, for two reasons. Banks may choose to keep some excess reserves instead of lending them, and people may hold some of the money as cash instead of depositing it. Either one is a leak that stops part of the chain.
The multiplier story describes a banking system with limited reserves, where banks lend out every spare dollar. In an ample-reserves system like the U.S. today, banks hold far more reserves than they need, so the simple multiplier isn't a good guide to how the money supply changes (4.6).
- Simple money multiplier = 1 ÷ rr. With rr = 10%, it's 10; with rr = 20%, it's 5.
- Maximum change in the money supply = new excess reserves × money multiplier.
- Put another way, the money multiplier compares the money supply with the monetary base: money supply ÷ monetary base. 1 ÷ rr is the largest value it can reach.
Worked examples
Try each one yourself first, then open the solution.
- Example 1Calculator allowed
Reading a T-account
First Bank's balance sheet shows assets of $12,000 in reserves and $38,000 in loans, and liabilities of $50,000 in demand deposits. The required reserve ratio is 20%. (a) What are its required and excess reserves? (b) How much can First Bank lend right now? (c) What's the maximum change in the money supply the banking system can create from these excess reserves?
Show the solutionHide the solution
- Step 1: (a) Required reserves = $50,000 × 0.20 = $10,000. Excess reserves = $12,000 − $10,000 = $2,000.
- Step 2: (b) A single bank can lend only its own excess reserves: $2,000.
- Step 3: (c) Money multiplier = 1 ÷ 0.20 = 5. Maximum change in the money supply = $2,000 × 5 = $10,000.
Answer: (a) $10,000 required, $2,000 excess. (b) $2,000. (c) A $10,000 increase.
- Example 2Calculator allowed
A cash deposit (classic trap)
Sam deposits $1,000 in cash, which had been sitting in a drawer at home, into a checking account. The required reserve ratio is 10%. Banks lend all excess reserves and all loans are redeposited. (a) What's the immediate change in the money supply? (b) What's the maximum change in demand deposits in the banking system? (c) What's the maximum change in the money supply?
Show the solutionHide the solution
- Step 1: (a) Currency in circulation falls $1,000 and checkable deposits rise $1,000. The money supply doesn't change; the money just changed form.
- Step 2: The bank must keep $1,000 × 0.10 = $100, so its new excess reserves are $900.
- Step 3: (b) Demand deposits include Sam's $1,000 plus the deposits created by lending: $1,000 + $900 × 10 = $10,000.
- Step 4: (c) Only the lending creates new money: $900 × 10 = $9,000. The trap is answering $10,000, which counts Sam's deposit as new money.
Answer: (a) $0. (b) $10,000. (c) $9,000.
- Example 3Calculator allowed
An open market purchase from a bank
The central bank buys $5,000 of government bonds from a commercial bank. The required reserve ratio is 10%. What's the maximum change in the money supply?
Show the solutionHide the solution
- Step 1: The bank's securities fall by $5,000 and its reserves rise by $5,000. Its deposits don't change, so its required reserves don't change either.
- Step 2: All $5,000 of new reserves are excess reserves.
- Step 3: Money multiplier = 1 ÷ 0.10 = 10. Maximum change = $5,000 × 10 = $50,000.
- Step 4: Compare: if the central bank had bought the bonds from a household that deposited the $5,000 check, the deposit itself would be new money ($5,000), excess reserves would be $4,500, and lending could add $45,000. The total is the same $50,000.
Answer: The money supply can rise by up to $50,000.
Common mistakes
- Multiplying total reserves, or the whole deposit, by the money multiplier. Multiply only the new excess reserves.
- Counting a cash deposit as new money. Moving currency into a checking account doesn't change the money supply; only the loans made from the new excess reserves do.
- Saying one bank can lend its excess reserves times the multiplier. A single bank can lend only its own excess reserves; the multiplier describes the whole banking system.
- Putting loans on the liabilities side. Loans are assets to the bank, because borrowers owe the bank money; demand deposits are liabilities.
On the exam
- Free-response questions often give a T-account and ask for required reserves, excess reserves, the most one bank can lend, and the maximum change in the money supply. Show each calculation.
- When a question asks why the actual change could be smaller than the maximum, name a leak: banks keep excess reserves, or the public holds more cash.
Connected topics
Videos
Check yourself
5 questions on 4.4 Banking and the Expansion of the Money Supply. Pick an answer to see if you got it, and why.
| Assets | Amount | Liabilities and owner's equity | Amount |
|---|---|---|---|
| Reserves | $50,000 | Demand deposits | $400,000 |
| Loans | $300,000 | Owner's equity | $100,000 |
| Government bonds | $150,000 | — | — |
Hypothetical data. The required reserve ratio is 10 percent, and the bank has no other assets or liabilities.
What are First Coastal Bank's excess reserves?
What is the largest amount First Coastal Bank can lend right now?
If First Coastal Bank lends out all of its excess reserves, what is the maximum possible increase in the money supply for the banking system as a whole?
Suppose a customer deposits $10,000 in cash into a checking account at First Coastal Bank. Immediately after the deposit, which of the following is true?
After the $10,000 cash deposit, what is the maximum amount by which the money supply can eventually increase?
0 of 5 answered