Money: created on a balance sheet
Introduced| English | Meaning |
|---|---|
| reserve ratio/rɪˈzɜːv ˈreɪʃɪəʊ/ | the share of deposits a bank must hold rather than lend |
| money multiplier/ˈmʌni ˌmʌltɪˈplaɪə/ | In a stylised reserve-constrained banking model, the maximum deposit expansion per extra unit of reserves, equal to one divided by the reserve ratio under its simplifying assumptions. |
Banks do not store money
- A deposit is not a claim on a vault of notes. It is the bank's liability — and the raw material of lending. When a bank lends, it CREATES a deposit: money is born on a balance sheet.
- This lesson follows one injection of £100 of reserves through the system, to the last pound.
The chain, round by round
- Bank receives 100, keeps a tenth as reserves (a 10% reserve ratio 存款准备金率), lends 90. The borrower spends; the seller deposits 90. Round 2: keep 9, lend 81. Round 3: lend 72.9…
- After three rounds deposits are $100 + 90 + 81 = 271$; the chain runs to $100 \times \tfrac{1}{1-0.9} = 1{,}000$ ✓.
Reserves 100, reserve ratio 10%. After the first three rounds of lending, total new deposits (one decimal)?
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$100 + 90 + 81 = 271$. The chain continues: 72.9, 65.61... towards 1,000.
With no cash drain and rr = 10%, what total deposits does 100 of reserves support?
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Multiplier $1/0.1 = 10$, so $100 \times 10 = 1{,}000$.
The leak that shrinks the multiplier
- Households hold cash: 30 pence per deposit pound ($c = 0.3$). The money multiplier 货币乘数 becomes $(1+c)/(r_d + c) = 1.3/0.4 = 3.25$.
- The same 100 of reserves then supports $325$ of money, not 1,000 — which is why real-economy multipliers are 3-ish.
Money or not, and which layer moves it?
Sort instruments into M1 money, broader money and non-money, and match each central-bank tool to its channel.
Cash drain c = 0.3, rr = 0.1. The multiplier (two decimals)?
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$m = (1+0.3)/(0.1+0.3) = 3.25$ - the same 100 of reserves supports 325 of money.
The central bank's four tools
- The policy rate (the floor system's anchor), open-market operations, reserve requirements, and the lending facility.
- The tools interlock: with $m = 3.25$, a £10 open-market SALE drains $32.5$ of money ✓ — a rate decision and a quantity decision are the same decision in different units.
With m = 3.25, a 10 open-market sale drains how much money?
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A sale of bonds takes reserves out; multiplied by 3.25 the money stock falls 32.5. Rate and quantity tools interlock.
Match each tool to its main channel.
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Four tools, one system - each names the channel it works through.
Nominal today, real tomorrow
- The central bank moves the NOMINAL short rate; spending responds to the REAL rate — the Fisher link from lesson 0403.
- Rate 5% with expected inflation 4%: real $1.05/1.04 - 1 = 0.96$%. Raise to 6%: real $1.92$% — transmission begins as arithmetic.
Policy rate 6% with expected inflation 4%. The ex-ante real rate (two decimals)?
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$1.06/1.04 - 1 = 1.92$%. At a 5% rate it was 0.96% - the tightening doubled the real cost of borrowing.
The channel, with its lags
- Rate ↑ → bank funding costs ↑ → lending rates ↑ → real rate ↑ → investment and durables fall → output gap turns negative → inflation drifts down.
- Every arrow is a mechanism with a delay: policy acts on forecasts, not readings — the theme lesson 0405 makes a discipline.
Why does the transmission chain end at "inflation drifts down" rather than "inflation falls on arrival"?
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Transmission is a chain of mechanisms with delays. That is why central banks act on forecasts - the reading arrives after the decision point.
Three money slips
- "Banks lend out reserves." Lending creates deposits; reserves settle payments BETWEEN banks.
- Reading the multiplier as behaviour. Banks lend when profitable loans exist; the arithmetic is a ceiling, not an engine.
- Quoting nominal rates as the cost of borrowing. The real rate is what the economy hears.
Banks lend out the reserves customers deposit with them.
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Lending creates a new deposit - money is born. Reserves exist to settle payments between banks; the loan does not hand them to anyone.
Recap
- $m = (1+c)/(r_d+c)$; deposits are created by lending, not stored.
- Four interlocking tools steer one system.
- Nominal rates move first; real rates do the work, with lags all the way down.