Money Multiplier

Macroeconomics Banking
The ratio linking the monetary base to broader money in simplified banking models.
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The money multiplier is a ratio that connects the monetary base (currency plus bank reserves) to a broader measure of money (like deposits). In simplified models of fractional-reserve banking, an injection of base money can support a larger stock of deposits through repeated lending and redepositing.

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The Textbook Multiplier

In the most stripped-down version:

\[ m = \frac{1}{rr} \]

where rr is the required reserve ratio. If rr = 0.10, then m = 10. In that same simplified model:

\[ M = m \times MB \]

where M is a broad money measure (often deposits plus currency) and MB is the monetary base.

A More Realistic Version (Currency Drain And Excess Reserves)

Banks and the public do not behave as if only required reserves exist. A common extension adds:

  • c: currency-to-deposit ratio (how much cash the public holds relative to deposits)
  • er: excess reserves-to-deposit ratio (extra reserves banks choose to hold)

Then the multiplier becomes:

\[ m = \frac{1 + c}{c + rr + er} \]

This makes the intuition clear:

  • More cash held by the public (c up) reduces deposit creation.
  • Banks holding more excess reserves (er up) reduces deposit creation.
  • Higher required reserves (rr up) reduces deposit creation.

Example: if rr = 0.10, c = 0.20, and er = 0.05, then:

\[ m = \frac{1.2}{0.35} \approx 3.43 \]

Why The Multiplier Is Not A Policy “Dial”

The money multiplier is useful as a teaching tool, but it is often unstable in practice because:

  • Most modern central banks target an interest rate, not a quantity of reserves. Reserves are then supplied as needed to keep the payment system stable and the policy rate on target.
  • Bank lending depends on credit demand, borrower quality, bank capital and regulation, and risk appetite, not just reserves.
  • In “floor” systems with abundant reserves, an increase in the monetary base (for example via quantitative easing) does not mechanically force a proportional increase in deposits.

In short, the multiplier is better thought of as an outcome of banking behavior and policy regimes, not a constant.

Knowledge Check

### In the simplest textbook model, if the required reserve ratio is 10%, what is the money multiplier? - [ ] 2 - [ ] 5 - [x] 10 - [ ] 20 > **Explanation:** In the basic model, `m = 1/rr = 1/0.10 = 10`. ### In the extended multiplier formula, what happens when the public holds more cash relative to deposits (a higher `c`)? - [x] The multiplier tends to fall - [ ] The multiplier tends to rise - [ ] The multiplier is unchanged by `c` - [ ] The multiplier becomes negative > **Explanation:** If more money stays as currency instead of bank deposits, there is less deposit expansion through the banking system. ### Why can the money multiplier be unstable in modern monetary systems? - [x] Banks may hold large excess reserves and central banks often target interest rates, not reserve quantities - [ ] Reserve requirements are always 100% - [ ] Currency is illegal - [ ] Deposit-taking banks no longer exist > **Explanation:** The central bank can expand the monetary base, but whether deposits expand depends on bank behavior, regulation, and credit demand.
money supply
Money Market