Short on time? This page is the recap. For explanations and worked examples, use the full study guide.
Recap
- Banks record their position on a balance sheet (T-account): assets = liabilities + owners’ equity.
- Fractional reserve banking: banks keep only a fraction of deposits as reserves and lend the rest.
- Reserves split into required reserves (set by the required reserve ratio) and excess reserves (the rest).
- Excess reserves are the basis of money creation. When a bank lends, it creates a new demand deposit: new money.
- Each loan is spent and redeposited, so the process repeats in ever-smaller rounds.
- The money multiplier is the money supply ÷ the monetary base. Its maximum is 1 ÷ rr.
- The simple multiplier overstates expansion if banks hold excess reserves or the public holds more currency.
Key relationships
| Relationship | Formula | Use it to |
|---|---|---|
| Balance sheet | Assets = liabilities + owners’ equity | check a T-account |
| Required reserves | rr × demand deposits | find what must be held |
| Excess reserves | total reserves − required reserves | find what one bank can lend |
| Excess reserves from a new cash deposit | (1 − rr) × deposit | the quick route |
| Maximum money multiplier | 1 ÷ rr | size the expansion |
| Maximum change in money supply (and loans) | initial excess reserves × multiplier | system-wide effect |
| Maximum change in demand deposits | new reserves × multiplier | system-wide effect on deposits |
Assumptions behind the numbers
- Banks lend all their excess reserves.
- Every loan is spent and fully redeposited: no one holds extra cash.
- The required reserve ratio is positive and given. (Some real central banks, including the US Federal Reserve since 2020, set it at zero.)
Mistakes to avoid
- Putting deposits on the assets side. They are liabilities.
- Calculating required reserves from total reserves. Use demand deposits.
- Letting one bank lend the whole deposit. It lends only excess reserves.
- Using the deposit, not the excess reserves, for the money supply change after a cash deposit.
- Saying a cash deposit itself changes M1. It only changes the form of money.
- Thinking a higher rr raises the multiplier. It lowers it.
Quick self-check
All figures are fictional, in millions of valdas (VD).
- What is the maximum money multiplier when rr = 5%? (20)
- A bank has demand deposits of 2,500 and reserves of 300; rr = 10%. What are its excess reserves? (VD 50 million)
- With rr = 10%, what is the maximum change in the money supply from VD 50 million of new excess reserves? (VD 500 million)
Next: practice questions.