Money and Inflation
An introduction
Introduction
• In this section we will discuss the quantity theory of money,
discuss inflation and interest rates, and the relationship
between the nominal interest rate and the demand for money.
The Quantity Equation
• This model allows us to see the effect that the quantity of
money has on the economy.
• To do this we must see how the quantity of money is
related to price and incomes.
The Quantity Equation
Consumers need money to purchase
goods and services. The quantity of
money is related to the number of
pounds exchanged in transactions. The
link between transactions and money is
expressed in the quantity equation.
On the left hand side, “M” is the
quantity of money, “V” is the
velocity of money, and “V•M” is
essentially a measure of how the
money is used to make transactions.
Rearranging the quantity equation yields
velocity to be…
Economists usually use GDP “Y” as a
proxy for “T” since data on the number of
transactions is difficult to obtain.
Money•Velocity = Price•Transactions
M V  P  T
On the right hand side, “T” is
the total number of transactions
during some period of time, “P”
is the price of a typical
transaction, and “P•T” is the
number of pounds exchanged in
a year.
V  PT / M
M V  P  Y
The Money Demand Function and the Quantity Equation
It is often useful to express the quantity of
money in terms of the quantity of good and
services it can buy. This is called the real
money balances “M/P”. We can use this to
construct a money demand function.
( M / P)d  kY
“k” is a constant that tells us how
much money people want to hold for
every unit of income.
This equation states that the
quantity of real money balances
demanded is proportional to real
income.
The Money Demand Function and the Quantity Equation
( M / P)  kY
d
The money demand function offers
another way to view the quantity
equation. If we set money supply equal
to money demand we get…
A simple rearrangement of terms
changes this equation into…
Which can be written as…
( M / P)  kY
M (1/ k )  PY
MV  PY
Where V=1/k
This shows the link between money
demand and the velocity of money.
Assuming Constant Velocity and the Quantity Theory of
Money
The quantity equation is essentially a
definition. If we make the assumption
that the velocity of money is constant,
then the quantity equation becomes a
theory of the effects of money, called
the quantity theory of money.
Because velocity is fixed, a change in
the quantity of money (M) must cause a
proportionate change in nominal GDP
(PY). So the quantity of money
determines the money value of the
economy’s output.
MV  PY
Money, Prices, and Inflation
The quantity theory of money allows us
to explain the overall level of prices.
MV  PY
The production function determines
the level of output “Y”.
Y
The money supply determines the
nominal value of output, “PY”.
PY
The price level “P” is the
ratio of the nominal value
of output “PY” to the level
of output “Y”.
PY
P
Y
So if the money supply
increases, nominal GDP will
rise as well the price level.
So, productive
capacity determines
real GDP
(numerator) and the
quantity of money
determines nominal
GDP (denominator).
Money, Prices, and Inflation
This change in prices is inflation. The
inflation rate is the percent change in
price level. So this theory of price level
is also a theory of inflation rate.
PY
P
Y
We can write the quantity equation…
MV  PY
…in percent terms:
%M + %V = %P + %Y
“M” is controlled
by the central
bank.
“%ΔV” reflects shifts in
money demand (which
are assumed constant).
“%ΔP” is the
rate of inflation.
“%ΔY” depends on
growth in the
factors of
production and on
technological
progress (we
assume this is fixed
in the short run).
Money, Prices, and Inflation
• So, the quantity theory of money states that the central bank,
which controls the money supply, has ultimate control over the
rate of inflation.
• If the central bank keeps the money supply stable, the price
level will be stable. If the central bank increases the money
supply rapidly, the price level will rise rapidly.
Inflation and the Interest Rate
Economists call the interest rate that the
bank pays the nominal interest rate “i”
and the increase in consumer purchasing
power the real interest rate “r”. If we let
“π” represent the inflation rate the
relationship among these variables is…
r  i 
i  r 
So, the real interest rate is the difference
between the nominal interest rate and the
rate of inflation.
Rearranging and solving for the nominal
interest rate yields the Fisher equation.
The Fisher equation states that the
nominal interest rate can be affected by
either the real interest rate or inflation.
Inflation and the Interest Rate
Recall that according to the quantity theory
of money a 1% increase in money growth
implies a 1% increase in the rate of
inflation. According to the Fisher equation
a 1% increase in inflation implies a 1%
increase in the nominal interest rate. This
one-to-one relationship between the
inflation rate and the nominal interest rate
is called the Fisher effect.
i  r 
i1%  r   1%
%  %i
When borrowers and lenders agree on a nominal
interest rate they do not know what the inflation rate
will be. Let “π” denote the actual future inflation and
“πe” the expectation of future inflation. This gives us
the ex ante real interest rate…
We call our original formula for real interest rate
the ex post real interest rate.
r  i 
r  i 
e
Two Real Interest Rates: Ex Ante and Ex Post
• The two real interest rates
i  r  e
differ when actual inflation
differs from expected inflation.
• This changes our fisher
equation. The nominal interest
rate now depends on expected
future inflation.
• So the nominal interest rate
r
moves one-for-one with the
expected inflation rate.
S
• The real interest rate is
determined by equilibrium in
the market for goods and
services.
r*
I(r)
S,I
The Nominal Interest Rate and the Demand for Money
• Earlier we used the quantity theory of money to explain the
effects of money on the economy. Now we will add the
nominal interest rate as another determinant of the quantity
of money demanded.
By holding money consumers are foregoing the
real return “r” that could be had by holding other
assets such as government bonds.
r 
Additionally, money
earns an expected real
return of…
e
i
The total cost of
holding money is…
The fisher equation
tells us this is equal
to the nominal
interest rate.
The Nominal Interest Rate and the Demand for Money
r 
e
i
As income “Y” rises the demand for money
rises and as the interest rate rises the
demand for money falls.
Our augmented money demand function
includes this nominal interest rate in
addition to income. Where “L” is the
liquidity of real money balances.

(M / P)  L(i, Y )
d
( M / P )  L( r   , Y )
d
Or
e
Future Money and Current Prices
• Money, prices, and interest rates are now
•
•
•
•
related.
The quantity theory of money explains that
money supply and money demand
determine price.
By definition changes in price are inflation
Inflation affects the nominal interest rate
via the fisher effect.
And the nominal interest rate affects money
demand.
i  r  e
(M / P)d  L(i, Y )
Money
Supply
Price
Level
Money
Demand
Inflation
Rate
Nominal
Interest
Rate
Conclusions
• In this section we introduced the quantity theory of money
and the relationship between money supply and inflation. Via
the fisher effect we learned that inflation affects the nominal
interest rate and finally, that the nominal interest rate affects
the demand for money.