Money is what money does — and what it does depends on how banks and central banks create it. The money supply, the money multiplier, and central bank balance sheets form the institutional backbone of monetary economics. If you are studying intermediate macro in a UK or US university, this is the material your exam questions draw from. It is also the framework a money and banking tutor builds your understanding around.
1 · What counts as money
Money has three functions: medium of exchange, unit of account, store of value. But for macroeconomics, the relevant question is measurement. Central banks publish several monetary aggregates.
In the UK, the Bank of England reports M0 (notes and coin in circulation plus banks’ operational deposits at the central bank) and M4 (broad money, which includes bank deposits held by the private sector). In the US, the Federal Reserve reports M1 (currency, demand deposits, traveller’s cheques, other checkable deposits) and M2 (M1 plus savings deposits, money market mutual funds, small time deposits).
The distinction matters because different aggregates behave differently. M0 is narrow and tightly controlled by the central bank. M2 is broad and responds to bank lending decisions. The money multiplier connects them.
2 · The money multiplier — a first pass
The simplest model of money creation starts with two assumptions. First, the public holds a fixed fraction c of its money as currency and the rest as deposits. Second, banks hold a fixed fraction r of deposits as reserves and lend out the rest.
Define the monetary base B (also called high-powered money) as currency in circulation plus bank reserves. Define the money supply M as currency in circulation plus deposits. Then:
M = C + D
B = C + R
where C is currency held by the public, D is deposits, and R is bank reserves. The currency-deposit ratio is c = C/D. The reserve-deposit ratio is r = R/D.
Substitute and rearrange. M = cD + D = (1 + c)D. And B = cD + rD = (c + r)D. So:
M = [(1 + c)/(c + r)] × B
The term in brackets is the money multiplier. It tells you how much the money supply expands for each unit of monetary base. If c = 0.2 and r = 0.1, the multiplier is (1.2)/(0.3) = 4. Each pound of base money supports four pounds of broad money.
The multiplier is larger when c is small (people use deposits more than cash) and when r is small (banks lend out more of their deposits). Both ratios are behavioural. The central bank controls B directly, but c and r depend on the public and the banks.
3 · The central bank balance sheet — where base money comes from
The monetary base is a liability of the central bank. To understand how it changes, you need the central bank’s balance sheet.
On the asset side: government bonds, foreign exchange reserves, and loans to commercial banks (discount window lending, repos). On the liability side: currency in circulation and commercial bank reserves.
When the central bank buys a government bond from a commercial bank, it pays by crediting the bank’s reserve account. Reserves rise by the amount of the purchase. The monetary base rises by the same amount. This is an open-market purchase, and it is the standard tool for expanding the monetary base.
When the central bank sells a bond, reserves are debited and the monetary base falls. Open-market sales contract the base.
The balance sheet identity is strict: assets = liabilities. Every change on one side must be matched on the other. If the central bank buys foreign currency, it pays with newly created reserves. If it lends to a bank at the discount window, it creates reserves. If the government withdraws currency from circulation (say, by collecting taxes), the monetary base shrinks.
4 · Deposit creation — the T-account mechanics
The money multiplier is an algebraic shortcut. The actual process runs through bank balance sheets. A single round of deposit creation shows the mechanism.
Start with a central bank open-market purchase of £100 in bonds from Bank A. Bank A’s reserves rise by £100. Its balance sheet changes:
Bank A: reserves +£100, bonds −£100. Net worth unchanged.
Now Bank A wants to lend. With a reserve requirement of 10%, it can lend out £90 of its new reserves. It makes a loan of £90 to a customer, who deposits the proceeds in Bank B. Bank A’s balance sheet now shows loans +£90, reserves −£90 (the loan is paid out of reserves). Bank A’s reserves are back to the required level.
Bank B receives a deposit of £90. Its reserves rise by £90, and its deposits rise by £90. It must hold 10% of £90 = £9 as reserves. It can lend out £81. It makes a loan, the borrower deposits in Bank C, and the process continues.
Each round creates new deposits and new loans. The total deposit creation from the initial £100 injection is £100 + £90 + £81 + … = £100 × (1/0.1) = £1,000. The money supply rises by £1,000. The monetary base rose by £100. The multiplier is 10 — but only if the public holds no currency and banks hold no excess reserves.
5 · Why the multiplier is smaller in practice
The textbook multiplier of 10 assumes c = 0 and r = 0.1. In reality, both ratios are positive and variable.
The public holds currency for everyday transactions. In the UK, the currency-deposit ratio is roughly 0.04 (about 4% of broad money is notes and coin). In the US, it is around 0.08. A positive c reduces the multiplier because currency drains out of the banking system and cannot be lent.
Banks also hold excess reserves — reserves above the required minimum. After the 2008 financial crisis, excess reserves in the US exploded. The reserve-deposit ratio rose from about 0.01 to over 0.20. The money multiplier collapsed. The Fed expanded the monetary base massively through quantitative easing, but broad money grew much less. The multiplier fell because banks sat on their reserves instead of lending them.
The multiplier is not a mechanical constant. It is an equilibrium outcome of choices by the public and the banks. Central banks control the base, but the money supply depends on behaviour.
6 · The central bank balance sheet in crisis times
Quantitative easing (QE) changes the central bank balance sheet in scale and composition. The central bank buys long-term government bonds and sometimes private-sector assets. It pays by creating reserves. The asset side grows, and the liability side grows by an equal amount.
Before QE, the Fed’s balance sheet was about $900 billion. After several rounds of QE, it peaked at over $4.5 trillion. The Bank of England’s balance sheet grew from about £200 billion to over £800 billion.
The standard money multiplier framework breaks down here. With massive excess reserves, the reserve-deposit ratio is no longer stable. The link between base money and broad money becomes loose. Central banks now use interest on reserves as their main policy tool, not the quantity of reserves. The old model of money creation — where the central bank controls the money supply by controlling the base — no longer describes how policy works.
Examiners know this. A good answer on the money multiplier should acknowledge its limits and explain why QE did not cause inflation in the way a simple multiplier model would predict.
Worked example — deposit creation from an open-market purchase
The central bank buys £200 in government bonds from Bank A. The reserve requirement is 10%. The public holds no currency (c = 0). Banks hold no excess reserves beyond the requirement.
Step 1 — The open-market purchase. The central bank buys £200 in bonds from Bank A. It credits Bank A’s reserve account by £200. Bank A’s balance sheet: reserves +£200, bonds −£200. The monetary base rises by £200.
Step 2 — Bank A lends. Bank A now has £200 in new reserves. It must hold 10% of its deposits as reserves, but its deposits have not changed yet. The new reserves are excess. Bank A lends £200 to a customer. The customer deposits the £200 in Bank B. Bank A’s balance sheet: loans +£200, reserves −£200. Bank A’s reserves return to the original level.
Step 3 — Bank B receives the deposit. Bank B’s deposits rise by £200. Its reserves rise by £200. It must hold 10% × £200 = £20 as required reserves. The remaining £180 is excess. Bank B lends £180 to a customer, who deposits in Bank C.
Step 4 — The process continues. Bank C receives £180 in deposits. It holds £18 as required reserves and lends £162. The next bank receives £162, holds £16.20, lends £145.80. And so on.
Step 5 — Total deposit creation. The initial injection of £200 in reserves generates a geometric series of deposits: £200 + £180 + £162 + £145.80 + … = £200 × (1/0.1) = £2,000. Total deposits rise by £2,000. The money supply (all deposits, since c = 0) rises by £2,000.
Step 6 — Check the balance sheet identity. The monetary base rose by £200 (the initial reserve injection). The money supply rose by £2,000. The multiplier is 2,000/200 = 10, which equals 1/r = 1/0.1 = 10. ✓
Step 7 — Interpretation. The banking system as a whole creates money. No single bank lends out more than its excess reserves, but the system multiplies the initial injection through successive rounds of lending and deposit. The reserve requirement is the binding constraint. A lower requirement means a larger multiplier. A higher requirement means a smaller one.
Struggling to track the T-account flows through multiple rounds? That is exactly the skill a one-on-one money and banking tutor drills with you, working through central bank balance sheets and deposit creation until the mechanics become automatic. Book a trial session.
Practice
Q1. The monetary base is £500 billion. The currency-deposit ratio is 0.05. The reserve-deposit ratio is 0.12.
(a) Calculate the money multiplier and the money supply.
(b) If the central bank conducts an open-market purchase of £50 billion in bonds, what is the new money supply? Assume c and r are unchanged.
Q2. A central bank buys £100 in government bonds from a commercial bank. The reserve requirement is 8%. The public holds no currency. Banks hold no excess reserves.
(a) Show the first three rounds of deposit creation in T-account form.
(b) What is the total increase in the money supply?
Q3. In an economy, the currency-deposit ratio rises from 0.04 to 0.10. The reserve-deposit ratio is constant at 0.10.
(a) Calculate the money multiplier before and after the change.
(b) By what percentage does the money supply fall if the monetary base is unchanged?
Answers: Q1 (a) multiplier = (1.05)/(0.17) ≈ 6.18, M ≈ £3,088 billion; (b) new B = £550 billion, new M ≈ £3,397 billion. Q2 (a) Round 1: Bank A reserves +£100, bonds −£100; Bank A lends £100 → Bank B deposits +£100, reserves +£100. Round 2: Bank B holds £8 required, lends £92 → Bank C deposits +£92, reserves +£92. Round 3: Bank C holds £7.36 required, lends £84.64 → Bank D deposits +£84.64. (b) Total M increase = £100/0.08 = £1,250. Q3 (a) Before: (1.04)/(0.14) ≈ 7.43; After: (1.10)/(0.20) = 5.50. (b) M falls by (7.43 − 5.50)/7.43 ≈ 26.0%.
Key takeaways
- The money supply is currency plus deposits. The monetary base is currency plus bank reserves. The money multiplier connects them: M = [(1 + c)/(c + r)] × B.
- The central bank controls the monetary base through open-market operations. Buying bonds expands the base; selling bonds contracts it.
- Deposit creation is a geometric process. Each round of lending creates new deposits, which support further lending. The reserve requirement limits the expansion.
- The money multiplier is not a constant. It depends on the public’s currency-deposit ratio and banks’ reserve-deposit ratio. Both are behavioural and can change rapidly.
- Quantitative easing broke the simple multiplier relationship. With massive excess reserves, the link between base money and broad money became loose. Central banks now rely on interest on reserves as their main policy tool.
Why UK and US students choose our money and banking tutoring
- One-on-one format: every session is private and built around your course, from your lecture notes to your problem sets and your university’s notation for the money multiplier.
- Institutional detail: our tutors teach the mechanics of central bank balance sheets, open-market operations, and deposit creation as they actually work — including the post-crisis changes that exam questions now test.
- Exam-first preparation: sessions work through past papers with marking schemes in view, because the T-account flows and the multiplier algebra are where intermediate marks are won and lost.
FAQ
Q: What is the money multiplier?
A: The ratio of the money supply to the monetary base. It shows how much broad money the banking system creates from each unit of central bank money. The formula is (1 + c)/(c + r), where c is the currency-deposit ratio and r is the reserve-deposit ratio.
Q: How do open-market operations affect the money supply?
A: When the central bank buys bonds, it pays by creating reserves. The monetary base rises. Banks then lend out the excess reserves, creating deposits through the multiplier process. The money supply expands. Selling bonds has the opposite effect.
Q: Why did the money multiplier fall after 2008?
A: Banks chose to hold massive excess reserves instead of lending them out. The reserve-deposit ratio rose sharply. Even though the central bank expanded the monetary base through QE, the multiplier fell, so broad money grew much less than the base.
Q: What is the difference between M0 and M4?
A: M0 is narrow money — notes and coin in circulation plus banks’ operational deposits at the central bank. M4 is broad money — M0 plus all bank deposits held by the private sector. M4 is what households and firms actually use for transactions.
Q: Do banks create money out of nothing?
A: In a sense, yes. When a bank makes a loan, it creates a new deposit in the borrower’s account. That deposit is money. But the bank is constrained by reserve requirements and by the need to settle payments with other banks. The system as a whole is constrained by the monetary base.
Q: Does the central bank control the money supply?
A: Directly, it controls only the monetary base. The money supply depends on the multiplier, which reflects choices by the public and banks. In normal times, the multiplier is stable enough that the central bank can target the money supply. In crisis times, the link breaks.
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