4. The monetary policy rule and the velocity of money

The quantity equation, also known as the equation of exchange, shows that the product of the money supply (MM) and the velocity of money (VV) is equal to the product of the price level (PP) and real GDP (QQ): MV=PQMV=PQ. Observe that when the left-hand side of the quantity equation, MVMV, changes by a given percentage, the right-hand side, PQPQ, must change by the same percentage:

PercentageChangein(MV)PercentageChangein(MV)

==

PercentageChangein(PQ)PercentageChangein(PQ)

You can use the rule that the percentage change in the product of two variables is approximately equal to the sum of the percentage changes in each of the variables (as long as the percentage changes are fairly small) to further analyze changes in the variables of the quantity equation. In the following equation, let "%" stand for "percentage change in":

%M+%V%M+%V

==

%P+%Q%P+%Q

For example, if you know that the money supply grows at a rate of 8% per year, velocity grows at a rate of 1% per year, and real GDP grows at a rate of 5% per year, you can use this rule to determine that the percentage change in the price level is equal to 4% (%M+%V%Y=%P).(%M+%V%Y=%P).

Suppose the central bank believes that the velocity of money grows at a predictable rate of 2% per year and that potential real GDP grows at a rate of 2% per year. If the central bank follows a monetary policy rule that stipulates money supply growth of 4% per year, it will expect an inflation rate of

per year and nominal GDP growth of

per year.

Suppose that actual growth in the velocity of money unexpectedly rises to 2.5%. If the central bank continues to adhere to money supply growth of 4% per year and real GDP is unchanged, the inflation rate will be than anticipated, and nominal GDP growth will be than anticipated.