Money and InflationAn 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

M V P T

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.

Money•Velocity = Price•Transactions

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.

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.

/V PT M

M V P Y

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

( / )dM P kY

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.

“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

( / )dM P kYThe money demand function offers

another way to view the quantity equation. If we set money supply equal to money demand we get…

( / )M P kY

(1/ )M k PYA simple rearrangement of terms changes this equation into…

Which can be written as… MV PYWhere 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

PYP

Y

The quantity theory of money allows us to explain the overall level of prices.

Y

PY

The production function determines the level of output “Y”.

MV PY

The money supply determines the nominal value of output, “PY”.

The price level “P” is the ratio of the nominal value of output “PY” to the level

of output “Y”.

So, productive capacity determines

real GDP (numerator) and the quantity of money

determines nominal GDP (denominator).So if the money supply

increases, nominal GDP will rise as well the price level.

Money, Prices, and Inflation

PYP

Y

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.

% M + % V = % P + % Y

We can write the quantity equation… MV PY…in percent terms:

“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

r i 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…

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.

i r

Inflation and the Interest Rate

1% 1%i r i r

% % i

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.

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…

er i

We call our original formula for real interest rate the ex post real interest rate.

r i

Two Real Interest Rates: Ex Ante and Ex Post

• The two real interest rates 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 moves one-for-one with the expected inflation rate.

• The real interest rate is determined by equilibrium in the market for goods and services. r*

S

I(r)

ei r

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.

r

By holding money consumers are foregoing the real return “r” that could be had by

holding other assets such as government bonds.

Additionally, money earns an expected

real return of…The total cost of

holding money is…

e i The fisher equation tells us this is equal

to the nominal interest rate.

The Nominal Interest Rate and the Demand for Money

r

( / ) ( , )dM P L i Y

e i

Our augmented money demand function includes this nominal interest rate in addition to income. Where “L” is the liquidity of real money balances.

As income “Y” rises the demand for money rises and as the interest rate rises the

demand for money falls.

Or( / ) ( , )d eM P L r Y

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.

Money Supply

NominalInterest

Rate

InflationRate

Price Level

Money Demand

ei r ( / ) ( , )dM P L i Y

• 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.

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.