Macro11 Money and Inflation

8/7/2019 Macro11 Money and Inflation

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Money and InflationAn introduction


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Introduction

In this section we will discuss the quantity theory of money,discuss inflation and interest rates, and the relationshipbetween the nominal interest rate and the demand for money.


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The Quantity Equation

This model allows us to see the effect that the quantity ofmoney has on the economy.

To do this we must see how the quantity of money isrelated to price and incomes.


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The Quantity Equation

M V P T y ! y

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.

MoneyVelocity = PriceTransactions

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 PT is the

number of pounds exchanged ina year.

On the left hand side, M is the

quantity of money, V is the

velocity of money, and VM is

essentially a measure of how the

money is used to make transactions.

/V PT M !

M V P Y y ! y

Rearranging the quantity equation yields

velocity to be

Economists usually use GDP Y as a

proxy forT since data on the number of

transactions is difficult to obtain.


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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 thereal

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.


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The Money Demand Function and the Quantity Equation

( / )dM P kY!

The 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 PY!A simple rearrangement of termschanges this equation into

Which can be written as MV PY!

Where V=1/k

This shows the link between money

demand and the velocity of money.


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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 moneydetermines the money value of the

economys output.

MV PY!


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Money, Prices, and Inflation

PY

P Y!

The quantity theory of money allows usto 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 Pis the

ratio of the nominal value

of output PY to the levelof 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.


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PYP

Y!

This change in prices is inflation. Theinflation 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 centralbank.

%V reflects shifts in

money demand (which

are assumed constant).

%P 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).


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So, the quantity theory of money states that the central bank,which controls the money supply, has ultimate control over therate of inflation.

If the central bank keeps the money supply stable, the price

level will be stable. If the central bank increases the moneysupply rapidly, the price level will rise rapidly.


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Inflation and the Interest Rate

r i T! Economists call the interest rate that thebank pays the nominal interest rate i

and the increase in consumer purchasing

power the real interest rate r. If we let

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 rT!


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Inflation and the Interest Rate

1% 1%i rT

o o!

i rT!

% % iTo o

Recall that according to the quantity theoryof 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 theinflation 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 denote the actual future inflation and

e the expectation of future inflation. This gives us

the ex ante real interest rate

er i T!

We call our original formula for real interest rate

the ex post real interest rate.

r i T!


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Two Real Interest Rates: Ex Ante and Ex Post

The two real interest ratesdiffer when actual inflationdiffers from expected inflation.

This changes our fisherequation. The nominal interestrate now depends on expectedfuture inflation.

So the nominal interest ratemoves one-for-one with theexpected inflation rate.

T

he real interest rate isdetermined by equilibrium inthe market for goods andservices. r*

S

I(r)

ei rT!

r

S,I


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The Nominal Interest Rate and the Demand for Money

Earlier we used the quantity theory of money to explain theeffects of money on the economy. Now we will add thenominal interest rate as another determinant of the quantityof money demanded.

r

By holding money consumers are foregoing the

real return rthat could be had by holding other

assets such as government bonds.

Additionally, money

earns an expected real

return ofThe total cost of

holding money is

eT i!

The fisher equation

tells us this is equal

to the nominal

interest rate.


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The Nominal Interest Rate and the Demand for Money

r

( / ) ( , )dM P L i Y!

eT i!

Our augmented money demand function

includes this nominal interest rate in

addition to income. WhereL is theliquidity 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 YT!


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Future Money and Current Prices

Money, prices, and interest rates are nowrelated.

The quantity theory of money explains thatmoney supply and money demanddetermine price.

Money

Supply

NominalInterest

Rate

Inflation

Rate

Price

Level

Money

Demand

ei r T!

( / ) ( , )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.


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Conclusions

In this section we introduced the quantity theory of moneyand the relationship between money supply and inflation. Viathe fisher effect we learned that inflation affects the nominalinterest rate and finally, that the nominal interest rate affectsthe demand for money.

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Macro11 Money and Inflation

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