The Fisher equation of exchange and the quantity theory of money

Overview

Fisher equation of exchange and define each term, velocity of circulation measure and why the velocity of circulation is not constant in practice.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   State the Fisher equation of exchange and define each term.

   Model answer

   The equation of exchange is written MV = PT. M is the quantity of money in circulation. V is the velocity of circulation, the average number of times each unit of money is used in transactions over a period. P is the average price at which transactions take place, and T is the volume of transactions over the same period. A common variant replaces T with Y, the real output of the economy, so that PY is nominal national income and V becomes the income velocity of money, the number of times each unit of money is used to buy final output.

2. 2

   Why is the equation of exchange described as an identity rather than a theory?

   Model answer

   The left-hand side measures total spending as the quantity of money multiplied by the number of times each unit is spent, and the right-hand side measures the value of what was bought as the average price multiplied by the quantity of transactions. Those are two ways of counting the same flow of expenditure, so they must be equal by construction, and velocity is in practice calculated as whatever number makes the two sides balance. Because it cannot be false, it explains nothing on its own. It becomes a theory only when assumptions are added about how the variables behave, in particular that velocity and real output are determined independently of the quantity of money.

3. 3

   What does the velocity of circulation measure, and what determines it?

   Model answer

   Velocity measures how intensively the money stock is used: it is nominal spending divided by the quantity of money, so a velocity of four means each pound financed four pounds' worth of transactions over the year. It reflects how long people hold money before passing it on, and so it depends on payment habits and technology, on how frequently people are paid, on the availability of credit and cards, on the interest forgone by holding money rather than interest-bearing assets, and on confidence, since people hold larger precautionary balances when they are anxious. Anything that makes holding money more attractive lowers velocity, and anything that makes it costlier to hold raises it.

4. 4

   Nominal national income is £2,400 billion and the money stock is £600 billion. Calculate the income velocity of circulation.

   Model answer

   Velocity is nominal income divided by the money stock, so V equals 2,400 divided by 600, which is 4. Each pound of the money stock therefore financed four pounds of final expenditure over the year, meaning it changed hands four times on average.

5. 5

   The money supply is £800 billion, velocity is 5 and real output is 2,000 billion units. Calculate the price level, then find the new price level if the money supply rises by 10% while velocity and real output are unchanged.

   Model answer

   Rearranging MV = PT gives P equal to MV divided by T. Initially that is 800 multiplied by 5, which is 4,000, divided by 2,000, giving a price level of 2.0. After a 10% rise the money supply is 880, so MV is 880 multiplied by 5, which is 4,400, and dividing by 2,000 gives a price level of 2.2. The price level has risen from 2.0 to 2.2, a rise of 10%, exactly matching the rise in the money supply. The result depends entirely on the assumption that velocity and real output did not change.

6. 6

   What assumptions turn the equation of exchange into the quantity theory of money?

   Model answer

   Two assumptions are needed. First, velocity is taken to be stable, because it is determined by payment habits and institutions that change only slowly. Second, real output is taken to be determined by the supply side of the economy, meaning the labour force, the capital stock and technology, and therefore to be independent of the quantity of money, at least in the long run. If both hold, the only variable free to adjust when M changes is P, so a given percentage increase in the money supply produces the same percentage increase in the price level. The conclusion is the classical proposition that inflation is caused by money growing faster than output.

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