Session 10 · Money, Banking and Inflation
In the previous session we measured inflation. What is missing is explaining where it comes from.
The answer forces us to understand what money is and, above all, who creates it. 🏦
And it ends where the next session begins: with the Eurosystem. 🇪🇺
Imagine trading directly: you give bread to whoever cuts your hair.
You need to find someone who wants bread and cuts hair. This is the “double coincidence of wants”. Hard. 😬
Money solves this. That is why it appeared in almost every civilization.
Why does money exist? It solves the problems of direct barter.
🛒 Medium of exchange: accepted in all transactions, it avoids direct barter.
📏 Unit of account: we measure prices in the same unit.
🏦 Store of value: it carries purchasing power into the future.
Not all “money” is the same. We measure it in decreasing order of liquidity.
M1: the most liquid. Notes, coins and overnight deposits.
M2: M1 plus time and savings deposits. Less liquid, but near money.
In the euro area, it is the Eurosystem that defines and monitors these aggregates. 🇪🇺
Here is the idea that surprises everyone: banks create money when they lend.
You deposit €1000. The bank keeps a reserve and lends out the rest.
Whoever receives the loan deposits it at another bank, which keeps a reserve and lends again. And so on. 🔄
With a reserve ratio \(rr\), an initial deposit \(D\) generates total deposits of:
\[ D \times \frac{1}{rr}. \]
Money multiplier: \(1/rr\). With 10% reserves, each euro of base money can become 10 euros of deposits.
Each round generates a smaller deposit (here, with 10% reserves). The sum converges to €10,000.
Treat \(1/rr\) as an upper bound, not a description of what banks do.
The story above has causality running from reserves to loans. In practice a bank makes the loan first, creating the deposit as it does so, and finds the reserves afterward.
So what actually binds is not the reserve ratio. It is capital requirements, the bank’s own risk appetite, and above all the demand for credit.
Since 2008 euro area banks have held reserves far above any requirement, and the multiplier has been nowhere near its bound. Money did not multiply, because nobody wanted to borrow. 📉
Keep the arithmetic, drop the mechanism. It is a ceiling on money creation, not an engine. 🧠
Banks do not keep all the money: they lend most of it out.
This works as long as depositors trust the system and do not withdraw everything at once.
When trust breaks down, there is a bank run. This is where the central bank comes in. 🏛️
Two multiple choice questions and one exercise. ✍️
Which function of money allows purchasing power to be carried into the future?
A. Medium of exchange.
B. Unit of account.
C. Store of value.
D. Multiplier.
✅ C. Money as a store of value preserves purchasing power over time.
A central bank injects reserves into the banking system. Deposits barely move. The best explanation is:
A. The reserve ratio must have risen to exactly offset it.
B. Banknotes were printed instead of deposits being created.
C. The quantity theory has been refuted.
D. The multiplier is a ceiling, and the binding constraint was demand for credit, not reserves.
✅ D. Reserves permit lending; they do not cause it. If firms and households do not want to borrow, or banks lack capital to lend, extra reserves simply sit on the balance sheet. This is the euro area after 2008.
The reserve ratio is 20 percent and the monetary base is 500 euros.
a) Compute the multiplier and the maximum total deposits.
b) Banks voluntarily hold an extra 5 percent in excess reserves. Recompute.
c) Which of the two is closer to the euro area since 2008?
d) What does the central bank control directly, and what does it not?
a) Multiplier \(= 1/0.20 = 5\), so deposits reach at most \(500 \times 5 = 2{,}500\) euros.
b) The effective ratio is 0.25, so the multiplier falls to 4 and deposits to 2,000 euros. Voluntary reserves cut money creation just as required ones do.
c) (b), and by a wide margin. Excess reserves have dwarfed required ones for over a decade.
d) It controls the monetary base and the rate paid on reserves. It does not control how much banks choose to lend, nor how much anyone wants to borrow. ✅
An identity linking money and prices:
\[ M \cdot V = P \cdot Y. \]
\(M\) money, \(V\) velocity, \(P\) the price level, \(Y\) real output.
As written this is an identity: \(V\) is defined as \(PY/M\), so it cannot be false. It becomes a theory only once you assume \(V\) is stable and \(Y\) is set by real factors. ⚠️
Over decades, and at high inflation, it holds well. Over a few quarters \(V\) moves a lot, which is why no central bank now targets money growth. 📉
If \(V\) and \(Y\) are stable, in percentage changes:
\[ \frac{\Delta M}{M} \approx \frac{\Delta P}{P} = \pi. \]
Too much money chasing the same goods generates inflation. “Inflation is always and everywhere a monetary phenomenon” (Friedman). 💸
This is why the ECB controls money to keep inflation low and stable.
The target is 2% over the medium term. Neither high inflation (which erodes savings) nor deflation (which paralyzes the economy).
A clear anchor helps keep expectations anchored. ⚓
For finance, what matters is the real return. The Fisher equation links the two:
\[ i \approx r + \pi. \]
The nominal rate \(i\) is the real rate \(r\) plus expected inflation \(\pi\). If inflation rises, nominal rates tend to rise. 📊
Exactly, it is \((1 + i) = (1 + r)(1 + \pi)\), so \(i = r + \pi + r\pi\). The cross term is negligible at 2 percent and very much not at 20. 🧮
And mind which \(\pi\): ex ante the relevant one is expected inflation, which is what you contract on. Ex post it is realized inflation, which is what you actually earned. The gap between them is session 9’s redistribution. ⚠️
A bond pays fixed nominal flows. If inflation erodes their real value, its price falls.
A rise in expected inflation, a rise in nominal rates, a fall in bond prices. This is interest rate risk. 📉
Two multiple choice questions and one exercise. ✍️
\(M\) grows sharply and inflation does not follow. This shows that:
A. \(V\) fell, which the identity \(MV = PY\) permits but the quantity theory assumes away.
B. The identity \(MV = PY\) is false.
C. Real output must have fallen.
D. The money supply was mismeasured.
✅ A. \(MV = PY\) cannot fail, because \(V\) is defined as \(PY/M\). What can fail is the extra assumption that \(V\) is stable. Distinguishing the identity from the theory is the whole point of the slide.
A bank offers 5 percent nominal for one year, and you expect 3 percent inflation. If inflation turns out to be 6 percent, your ex post real return is roughly:
A. Plus 2 percent, as you expected.
B. Minus 1 percent.
C. Plus 5 percent, since the rate was fixed.
D. Minus 6 percent.
✅ B. \(r \approx i - \pi = 5 - 6 = -1\) percent. Ex ante you contracted for plus 2; ex post you got minus 1. The 3 point surprise moved value from you to the bank’s borrowers.
Money grows 7 percent a year, real output grows 2 percent, and velocity is stable.
a) Find approximate inflation.
b) With a real rate of 1 percent, what nominal rate does Fisher imply?
c) Compute the exact Fisher nominal rate and compare.
d) Velocity in fact falls 3 percent. Redo (a).
a) From \(\Delta M/M + \Delta V/V = \pi + \Delta Y/Y\): \(\pi \approx 7 - 2 = 5\) percent.
b) \(i \approx r + \pi = 1 + 5 = 6\) percent.
c) \((1.01)(1.05) = 1.0605\), so \(i = 6.05\) percent. The cross term is worth 5 basis points here, and would be worth 200 at 20 percent inflation.
d) \(\pi \approx 7 + (-3) - 2 = 2\) percent. Money grew just as fast and inflation is far lower, which is question 3 in numbers. ✅
The central bank is the “bank of banks”. Its main functions:
💶 Issues currency and manages the monetary base.
🎯 Conducts monetary policy to maintain price stability.
🛡️ Supervises banks and acts as lender of last resort in crises.
In a bank run, a solvent bank can run out of liquidity.
The central bank lends to it at that moment, stopping the panic before it spreads.
This was crucial in the 2008 crisis and in the euro debt crisis. 🔥
The classic rule (Bagehot): lend freely, against good collateral, at a penalty rate.
Every clause is doing work. Freely, to stop the panic. Against collateral and at a penalty, so that only banks genuinely short of liquidity come forward.
Because if the central bank rescues insolvent banks too, it has just written free insurance against bad lending. Which is session 6’s moral hazard, at the scale of a banking system. 🎭
And in a panic the distinction is close to impossible to make in real time. That is the genuinely hard part of the job, not the theory. ⏱️
In the euro area, monetary policy is single across 20 countries.
Eurosystem: the European Central Bank (ECB) plus the national central banks (such as the Banco de Portugal).
Decisions are taken in Frankfurt, at the ECB, and carried out by each national central bank. 🏛️
The ECB is independent of political power.
The reason: to avoid the temptation of printing money to finance governments, which would generate inflation.
Its primary mandate is clear: maintain price stability (inflation close to 2%). 🎯
Two multiple choice questions and one exercise. ✍️
Bagehot’s rule says to lend at a penalty rate. The reason is:
A. To make a profit for the central bank during a crisis.
B. To punish the bank’s management for poor decisions.
C. So that only banks genuinely short of liquidity come forward, limiting moral hazard.
D. To keep inflation on target while lending.
✅ C. A cheap standing rescue is free insurance against bad lending, and banks would price it in. The penalty makes the facility unattractive to anyone who does not truly need it: exactly the deductible logic from session 6.
The Eurosystem is made up of:
A. The ECB and the national central banks of the euro area countries.
B. The ECB alone.
C. All commercial banks operating in the euro area.
D. The ECB together with the International Monetary Fund.
✅ A. Decisions are taken in Frankfurt and executed by each national central bank, such as the Banco de Portugal. Note it is not the same as the European System of Central Banks, which also includes non euro EU members.
A bank faces heavy withdrawals and runs out of liquidity overnight.
a) What can the central bank do, and under what conditions?
b) Why does the answer depend on whether the bank is solvent?
c) Why is that distinction so hard to make during a panic?
d) What does the ECB’s independence have to do with any of this?
a) Lend as lender of last resort: freely, against good collateral, at a penalty rate.
b) Lending to a solvent bank stops a panic and gets repaid. Lending to an insolvent one converts a private loss into a public one, and teaches every other bank that risk is subsidized. 🎭
c) Solvency depends on asset values, and in a panic those are exactly the prices collapsing. The test you need is the one the crisis has made unreadable. ⏱️
d) An independent central bank can refuse. One that answers to a government facing bank failures in an election year cannot credibly say no. ✅
💶 Money is a medium of exchange, a unit of account and a store of value; it is measured by aggregates (M1, M2).
🔁 Banks create money when they extend credit: the multiplier is \(1/r\) with reserves \(r\).
🧮 By the quantity theory (\(MV = PY\)), sustained inflation is a monetary phenomenon.
📈 Distinguish nominal from real interest: that difference determines the return on a bond.
Monetary Policy.
We know what the ECB is. Now we see what it does, and how that reaches the economy and portfolios. 🎯
See you next week. 🙌