Lecture 8 · Slides L7 · Mankiw ch. 5 · about 45 min

Money and Inflation

What money is and how it is measured, what drives the demand for it, and the quantity theory that links money growth to inflation in the long run, together with seigniorage and the Fisher effect.

By the end you can

State the three functions of money and the definitions of M0 to M3
Explain how the price level, real income and interest rates affect money demand
Use the quantity theory to predict inflation from money growth
Apply the Fisher equation and separate ex-ante from ex-post real interest rates

What money is

Money is the set of assets widely used and accepted as payment. It has three functions:

Medium of exchange: what we use to buy things.
Unit of account: how we quote prices and record debts.
Store of value: a way to carry purchasing power into the future.

Measuring money

The money supply is the amount of money in the economy. Deciding what counts is not always easy, so central banks publish several monetary aggregates. The lecture uses the Turkish definitions:

Monetary aggregates (CBRT)Formula sheet →

\begin{aligned} M0 &= \text{currency in circulation} - \text{bank vaults} = \text{banknotes} + \text{coins} - \text{bank vaults} \\ M1 &= M0 + \text{demand deposits (TL + FX)} \\ M2 &= M1 + \text{time deposits (TL + FX)} \\ M3 &= M2 + \text{repos} + \text{money market funds} + \text{debt securities} \end{aligned}

$FX$: foreign-currency deposits

Use it when a question asks which aggregate includes which assets. Each one adds less liquid assets to the one before.

Monetary policy is control over the money supply, conducted by the central bank. Its main tool is open market operations: when the central bank buys government bonds it pays with new money and the money supply rises; when it sells bonds the money supply falls.

The demand for money

The demand for money is the quantity of money people want to hold. Three things drive it:

Price level: higher prices mean more money is needed for the same transactions. The lecture’s illustration: prices are 10 times as high today as 65 years ago, so equivalent transactions take 10 times as much money. Nominal money demand is proportional to the price level.
Real income: more income means more transactions and more money demand, but less than one for one, because a country’s financial sophistication grows as its income rises.
Interest rates: a higher return on non-money assets lowers money demand; a higher interest rate on money itself raises it. People trade off liquidity against return.

Other factors: wealth (a rise raises money demand, but not by much), risk (higher economic risk raises money demand, but unpredictable inflation makes money itself risky and lowers it), and payment technology such as credit cards and ATMs. Deregulation, competition and innovation have made other assets more liquid too, so they also reduce money demand.

Money demand functionFormula sheet →

\left(\frac{M}{P}\right)^d = L(i, Y) = L(r + E\pi, Y)

$(M/P)^d$: demand for real money balances
$i$: nominal interest rate, the opportunity cost of holding money (negative effect)
$Y$: real income (positive effect)
$E\pi$: expected inflation

Use it when you need to say how money demand responds. L is used because money is the most liquid asset.

The relevant interest rate is the nominal one, $r + E\pi$ : holding cash instead of a bond costs the real return plus the loss of purchasing power from inflation. When people decide, they do not know inflation yet, so it is expected inflation that matters.

The quantity theory of money

Classical economists, who assumed that wages and prices were completely flexible, linked money to spending through velocity: how many times a unit of money changes hands in a year. The American economist Irving Fisher set the theory out clearly in his 1911 book The Purchasing Power of Money.

Equation of exchangeIdentityFormula sheet →

M \times V = P \times Y \qquad V = \frac{P \times Y}{M}

$M$: money
$V$: velocity
$P$: GDP deflator
$Y$: real GDP
$P \times Y$: nominal GDP

Use it when any quantity-theory question. As written it is an identity: it defines V.

Here $M/P$ is real money balances: the purchasing power of the money supply. Divide by $V$ to get money demand: $M^d = \frac{1}{V}PY$ , or in real terms:

Quantity-theory money demandFormula sheet →

\left(\frac{M}{P}\right)^d = kY \qquad k = \frac{1}{V}

$k$: how much money people hold per unit of income

Use it when you need money demand under the quantity theory. When k is large, money changes hands rarely and V is small.

In the lecture $k$ is exogenous: it reflects payment habits and institutions, not anything determined inside the model. The quantity theory adds one assumption: velocity is constant (Fisher thought it stable in the short run). Then nominal income moves only with money: $M\bar V = PY$ . Output is set by factors and technology, so with $Y = \bar Y$ :

P = \frac{M\bar V}{\bar Y}

In the long run, changes in money cause proportional changes in the price level. Money does not affect real variables: this is the neutrality of money.

Inflation

Take growth rates of $MV = PY$ . A product’s growth rate is roughly the sum of its factors’ growth rates:

Quantity theory of inflationKey equationFormula sheet →

\%\Delta M + \%\Delta V = \%\Delta P + \%\Delta Y \quad\Rightarrow\quad \pi = \%\Delta M - \%\Delta Y

$\pi$: inflation rate
$\%\Delta V$: 0 by assumption

Use it when a question gives money growth and output growth and asks for long-run inflation.

Output growth $\%\Delta Y$ depends on growth in the factors of production and on technological progress, all of which we take as given.

Money growth %ΔM7.0Real output growth %ΔY3.0Velocity growth %ΔV0.0Real interest rate r (set by S = I)2.0

Inflation π = %ΔM + %ΔV − %ΔY: 4.0%
Nominal rate i = r + π: 6.0%

Money grows 7.0% but the economy only needs 3.0% more money for its extra transactions, so the remaining 4.0% shows up as inflation. Raise money growth by 1 point and inflation and the nominal interest rate both rise by 1 point (the Fisher effect); real output does not move (neutrality, in the long run).

Does the data agree?

The theory implies that countries with faster money growth should have higher inflation, and that a country’s long-run inflation trend should follow its money-growth trend. The lecture’s table of high-inflation episodes (the handout prints the number columns one row lower than the country names; the figures below are matched to their countries in the slide’s row order):

Country	Period	CPI inflation (% per year)	M2 growth (% per year)
Israel	1983 to 1985	338	305
Brazil	1987 to 1994	1,256	1,451
Bolivia	1983 to 1986	1,818	1,727
Ukraine	1992 to 1994	2,089	1,029
Argentina	1988 to 1990	2,671	1,583
Dem. Rep. of Congo/Zaire	1990 to 1996	3,039	2,373
Angola	1995 to 1996	4,145	4,106
Peru	1988 to 1990	5,050	3,517
Zimbabwe	2005 to 2007	5,316	9,914

Over long periods and across countries, the fit is strong. Year to year it is weak. Milton Friedman’s line, “inflation is always and everywhere a monetary phenomenon”, holds in the long run but not in the short run.

Seigniorage and the inflation tax

A government can spend without raising taxes or selling bonds: it can print money. The revenue from money creation is seigniorage. It works like a tax: the new money causes inflation, which reduces the value of everyone’s money and other nominal assets. That loss is the inflation tax, paid by holders of money and other nominal assets.

Inflation and interest rates

Fisher equationFormula sheet →

i = r + E\pi

$i$: nominal interest rate
$r$: real interest rate, set by S = I
$E\pi$: expected inflation

Use it when you convert between nominal and real interest rates.

The real rate $r$ is set by $S = I$ (Lecture 3). The Fisher effect follows from the Fisher equation together with the classical dichotomy: real variables are determined separately from nominal ones, so when expected inflation rises, the nominal interest rate rises one for one.

Money market equilibrium

Putting the pieces together in the long run: the central bank sets $M$ ; saving and investment set $r$ ; the production function sets $Y$ ; expected inflation depends on current inflation (adaptive expectations); and the price level $P$ adjusts so that $M/P = L(r + E\pi, Y)$ .

Money supply M (set by the CB)1000Expected inflation Eπ %4.0Real interest rate r %2.0

Nominal rate i = r + Eπ: 6.0%
Real money demand L(i, Y): 857
Price level P = M / L: 1.167

r comes from S = I, Y from the production function, M from the central bank. The money market then pins down P: the price level adjusts until real balances M/P equal what people want to hold. Double M and P doubles. Higher expected inflation raises i, people hold less money, and P rises today.

Exam practice

Summary and review

Functions of money: medium of exchange, unit of account, store of value.
M0 = banknotes + coins − bank vaults; M0 ⊂ M1 ⊂ M2 ⊂ M3. Buying bonds raises the money supply.
Money demand rises with $P$ and $Y$ , falls with the nominal interest rate: $(M/P)^d = L(i, Y)$ . In the quantity theory $k = 1/V$ is exogenous.
$MV = PY$ ; with constant $V$ : $\pi = \%\Delta M - \%\Delta Y$ . Money is neutral in the long run.
The link holds in the long run and across countries, not year to year.
Seigniorage: revenue from printing money; the inflation tax falls on holders of money and nominal assets.
Fisher: $i = r + E\pi$ . Ex ante $i - E\pi$ , ex post $i - \pi$ .