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.
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.
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.
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.
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.
This equation states that the quantity of real money balances demanded is proportional to real income.
“k” is a constant that tells us how much money people want to hold for every unit of income.
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…
This shows the link between money demand and the velocity 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.
The quantity theory of money allows us to explain the overall level of prices.
The production function determines the level of output “Y”.
The money supply determines the nominal value of output, “PY”.
So, productive capacity determines real GDP (numerator) and the quantity of money determines nominal GDP (denominator).
The price level “P” is the ratio of the nominal value of output “PY” to the level of output “Y”.
So if the money supply increases, nominal GDP will rise as well the price level.
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.
We can write the quantity equation…
…in percent terms:
“M” is controlled by the central bank.
“%ΔY” depends on growth in the factors of production and on technological progress (we assume this is fixed in the short run).
“%ΔP” is the rate of inflation.
“%ΔV” reflects shifts in money demand (which are assumed constant).
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.
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…
We call our original formula for real interest rate the ex post real interest rate.
By holding money consumers are foregoing the real return “r” that could be had by holding other assets such as government bonds.
The fisher equation tells us this is equal to the nominal interest rate.
Additionally, money earns an expected real return of…
The total cost of holding money is…
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.