Macroeconomics 7: Quantity Theory of Money

Question 1

Describe & explain the quantity theory of money

Answer 1

In the long-run, changes in money will influence the general price level but not real wages, real interest
rate and real exchange rate that determine resource allocation. The Quantity Theory of Money is the
theoretical device for modelling this idea
The first version of the Quantity Theory was based on money being used for transactions. MV = PT
where M is Money in circulation, V is the (Transactions) Velocity of Circulation, P is the general Price
level, T is the volume of Transactions
The monetary value of transaction being undertaken (PT) in a given period of time must equal the flow
of money to make those transactions happen (MV) during the same time period
In order to make this identity interesting for Macroeconomics we need to introduce output rather than
use transactions. This is straightforward since we can associate the production and sale of output during
a period of time with a volume of transactions.
We write MV=PY where Y is the level of output and V is the (income) velocity of money.
Assuming long-run equilibrium so that Y=Y, and also imposing constant V=V we obtain
M= λP where λ=Y/V
There is a proportional relationship between the general level of prices and the money supply
Is the assumption of constant velocity of money reasonable? Over long periods of time, we would expect
transactions technology to change and hence so will V. For example:
- credit cards
- mobile payments
Other factors influence money demand
- individuals hold more cash during bad times e.g. the global financial crisis
- interest rates
So we need to think about the quantity theory in terms of money market equilibrium

Question 2

Describe the demand for money and the quantity theory

Answer 2

We can write the demand for (nominal) money as
M^D=kPY
Or, real terms M^D/P=kY
where M^D/P is the demand for REAL money balances and k is a constant reflecting the (constant) transaction technology and the
cost of holding money. Money market equilibrium implies that the real supply of, and demand for, money, are equal
M/P=M^D/P.
Hence we have
M/P=kY or M(1/k)=PY
which is the Quantity Theory equation if we set V=(1/k)
We observe that the Velocity of Money is inversely related to the Demand for Money. If individuals hold large money balances for
given PY (k is large) then V is small. Alternatively, if the demand for money is relatively low (k is small) then V is large.
The value of k is dependent on the cost of holding money (interest rate). If the interest rate is high, we observe low k and V is high

Question 3

Describe & explain Money and Inflation

Answer 3

Using our M=λP relation we have, by taking logs lnM=lnλ+lnP and differentiating with respect to time with λ being assumed constant gives
us
dM/dt 1/M = dP/dt 1/P
This tells us that % changes in the general price level are dependent on %changes in the money supply (assuming constant velocity of
Money and real output). It is the foundation of the statement ‘inflation is always and everywhere a monetary phenomenon’
Now suppose that Y and V (and hence λ) are not constant but change over time. We take logs of the equation MV=PY so
ln(M)+ln(V)=ln(P)+ln(Y)
Differentiate with respect to t gives us 1/M dM/dt + 1/V dV/dt =1/P dP/dt +1/Y dY/dt
Hence 1/P dP/dt = 1/M dM/dt + 1/V dV/dt − 1/Y dY/dt
% change in price (inflation) = % change in money supply + %change in velocity - % change in output
So how money and inflation interact depends on real economic growth and the development of transactions technology, and other factors which influence the demand for money (and hence V). The data graphs in the following two slides illustrate this.
There’s a chart that shows how
money and inflation are related in the
US, over decades from 1870-2010 witha correlation of 0.79.
That the correlation is not 1 reflects
that real output (Y) grows at different
rates, and that transaction technology
is changing over time, and also that
changes in interest rates impact on V
This chart reflects Milton Friedman’s
work with Anna Schwartz and the
famous statement alluded to on the
previous slide. Mankiw and Reis
(other reading) provide a perspective
on the importance of this and other
work by Friedman