Download ° Money and Inflation Introduction Quantity Equation elQuantity

Introduction
° Money and Inflation
An introduction
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.
• 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.
elQuantity 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.111" 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.
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•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 IM
M•V=P•Y
The Money Demand Function and the Quantity
Equation
(M I P) d = kY
The money demand function offers
another way to view the quantity
equation. If we set money supply equal
to money demand we get...
Asimple rearrangement of terms
changes this equation into...
owl . = w
A4onerVelocity = Price •Transactions
(M I 11= kY
--M(11k)=PY
Which can be written as...
"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.
This shows the link between money
demand and the velocity of money.
1
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.
MV = PY
Money, Prices, and Inflation
he quantity theory of money allows us
to explain the overall level of prices.
= PY
e production function determines .\
the level of output "Y".
Y
The money supply determines the
nominal value of output, "PY".
PY
Because velocity is fixed, a change
in
So,
productive
ductive
price level "P" is the
the quantity of money (M) must cause a
py
capacity determines
proportionate change in nominal GDP
ratio of the nominal value real GDP
P=
of output "PY" to the level
(PY). So the quantity of money
Y
(numerator) and the
of output "Y"
determines the money value of the
quantity of money
economy's output.
determines nominal
So if the money supply
GDP (denominator).
increases, nominal GDP will
..../
, rise as well the price level. i
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.
Money, Prices, and Inflation
P=
PY
Y
, the quantity theory of money states that the central bank,
ich controls the money supply, has ultimate control over the
r • te of inflation.
• Iflthe central bank keeps the money supply stable, the price
level will be stable. If the central bank increases the money
s mply rapidly, the price level will rise rapidly.
We can write the quantity equation...
...in percent terms:
%AlVii4-,PAAV = %AP + %AY
"M" is controlled
by the central
bank.
"%fiN" reflects shifts in
money demand (which
are assumed constant).
"%AP" is the
rate of inflation.
"%&Y" depends on
growth in the
factors of
production and on
technological
progress (we
\,assume this is fixed}
in the short run).
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
"n" represent the inflation rate the
relationship among these variables is...
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
n„ either the real interest rate or inflation.
a ion 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 +2T
% T Ir
i
When borrowers and lenders agree on a nominal
r=i—Tce
interest rate they do not know what the inflation rate
will be. Let "Tr" denote the actual future inflation and
"Tr." the expectation of future inflation. This gives us
Jr = i — 7r
the ex ante real interest rate...
We call our original formula for real interest rate
the ex post real interest rate.
2
mina! Interest Rate and the Demand for Money
al Interest Rates: Ex Ante and Ex Post
The two real interest rates differ
n actual inflation differs from
cted inflation.
• Thi changes our fisher equation.
The nominal interest rate now
depnds on expected future
inflation.
• So he nominal interest rate moves
one for-one with the expected
inflation rate.
rlier we used the quantity theory of money to explain the effects of
oney on the economy. Now we will add the nominal interest rate
another determinant of the quantity of money demanded.
i=r-For e
1
By holding money consumers are foregoing the .\
real return "r" that could be had by holding other
assets such as government bonds.
1
1
1
r
• The real interest rate is determined
by equilibrium in the market for
gods and services.
The fisher equation
tells us this is equal
to the nominal
interest rate.
+ e
Additionally, money
earns an expected real
return of...
The total cost of
holding money is...
s,I
mina! Interest Rate and the Demand for Money
Future Money and Current Prices
es prices, and interest rates are now related.
r +
= i
Th. quantity theory of money explains that money
suply and money demand determine price.
•
•
By definition changes in price are inflation
Inflation affects the nominal interest rate
i=r-F ge
xis the fisher effect.
• dens
Ardnd
thenominal interest rate affects money ( m p)d = L(i, Y)
As income "V° 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.
[ Or
wipy =47,P)
Money
Supply
Price
Level
= L(Y 7r e
Y)
0
Inflation
Rate
0
Nominal
Interest
Rate
Money
41
Demand
Conclusions
1 this section we introduced the quantity theory of money and the
lationship between money supply and inflation. Via the fisher effect we
..arned that inflation affects the nominal interest rate and finally, that the
ominal interest rate affects the demand for money.
3