# The Quantity Theory of Money

The Quantity Theory of Money

Department of Economics

University X

The Quantity Theory of Money

The quantity theory of money can be described by the following quantity equation

P × T = M ×V

where P is the general level of prices, T is the level of transactions (= number of times in a given period that goods and services are exchanged for money), M is the stock of money and V is the velocity of money.

The Quantity Theory of Money

In any given time period, the value of all goods sold must equal the number of transactions in the time period, T, times the average price of transactions, P.

The value of money is equal to the nominal quantity of money in circulation, M times the average number of times that the quantity of money in circulation turns over the period, V.

This accounting identity is expressed symbolically as MV=PT, which is the quantity theory of money.

Velocity

Velocity is defined as the speed at which money circulates or as the number of transactions that each unit of money is used in per period.

In other words, Velocity is the number of times the average dollar bill changes hands in a given time

Period.

In practice it represents the rate at which money circulates.

Velocity

Suppose that in 2007: \$500 billion in transactions and money supply = \$100 billion

The average dollar is used in five transactions in 2007

So, velocity = 5

This is because in order for \$500 billion in transactions to occur when the money supply is only \$100b, each dollar must be used, on average, in five transactions.

The Quantity Theory of Money

In general the number of transactions is difficult to measure we can replace with the total output produced in the economy in a given period of time. This is just an approximation, however, when total output produced increases, there are more goods and services to be sold and therefore transactions also increase. Therefore the two concepts are proportional.

The Quantity Theory of Money

Denote with Y the total output produced in an economy (in terms of quantity not in terms of value). Then, Y can represent the Real GDP, and therefore PY represents the nominal GDP (and so P is the GDP deflator).

Then, the quantity theory of money becomes:

P × Y = M ×Y

This is the standard way of writing the quantity theory of money.

It is an identity: it holds by definition of the variables.

Velocity

Velocity is measured as the ratio of current dollar GDP to the money supply.

The quantity equation and the link between Money and Inflation

The quantity equation gives us a simple relationship between the aggregate level of prices and the stock of money in the economy.

Starts with quantity equation and assumes V is constant and exogenous: V=V?

With this assumption, the quantity equation can be written as:

M X V?=P X Y

The implication of this is that with V constant, changes in the money supply must cause a proportionate change in nominal GDP (P ×Y ).

The Link between Money and Inflation

We can also see the quantity theory as a theory that tells us what determines inflation in the long-run.

To see this we need to rewrite the quantity equation in terms of growth rate. For example, suppose two periods of time: t and t+1. The rate of inflation between t and t+1 is given by:

?t+1=Pt+1-Pt /Pt=?Pt+1/Pt

The quantity equation in growth rates:

?M/M + ?V/V= ?P/P + ?Y/Y

The quantity theory assumes that the velocity V is a constant and therefore ?V/V=0

The Link between Money and Inflation

Then the quantity equation in growth rates implies that:

Denote the inflation rate as:?M/M = ?P/P + ?Y/Y

?= ?P/P

Then we have that: ?= ?M/M – ?Y/Y

Normal economic growth requires a certain amount of money supply growth to facilitate the growth in transactions.

Money growth in excess of this amount leads to inflation.

The Link between Money and Inflation

Suppose real GDP is growing by 3% per year over the long run. Thus, production, income, and spending are all growing by 3%. This means that the volume of transactions will be growing as well.

The central bank can achieve zero inflation (on average over the long run) simply by setting the growth rate of the money supply at 3%, in which case exactly enough new money is being supplied to facilitate the growth in transactions.

The Quantity Theory predicts a one-for-one relation between changes in the money growth rate and changes in the inflation rate. It does predict that a change in the money growth rate will cause an equal change in the inflation rate.

The Quantity Theory of Money

To summarize:

The quantity theory of money implies:

1. countries with higher money growth rates should have higher inflation rates.

2. the long-run trend behaviour of a country’s inflation should be similar to the long-run trend in the country’s money growth rate.

Inflation and interest rates

We define two interest rates:

– Nominal interest rate, i, not adjusted for inflation.

– Real interest rate, r, adjusted for inflation: r = i ? ?

The basic idea is the following: suppose that at the beginning of the year you deposit some money in a bank that pays an annual interest rate of 5%. After one year you withdraw the money from the bank and so you have 5% more money in your hand.

Are you 5% richer then?

Inflation and interest rates

The answer depends on how much the price level has increased over the year. If the prices are now 3% higher, you are only 2% richer than before, meaning that the amount of goods you can purchase now has increased by only 2%.

The relationship between nominal interest rate and inflation is called the Fisher equation : i = r + ?

Hence, an increase in ? causes an equal increase in i. This is known as the Fisher effect.