How this calculator works
The quantity equation says the money supply times its velocity equals the price level times real output. Velocity is the average number of times each unit of money is used to buy final goods and services in a period. A velocity of 2 with a $1,000 money supply and $2,000 of nominal output means each dollar supports $2 of spending over the year. Measured velocity depends on which money definition is used: broader measures such as M2 move more slowly than narrow measures, and the ratio can fall sharply when people hold cash balances during a crisis. Velocity is not stable in the short run, which is why central banks do not target money growth directly.
Formula
Velocity = price level × real output / money supply, where the price index is divided by 100. Rearranged, money supply = price level × real output / velocity and real output = money supply × velocity / price level. Nominal output is price level × real output.
Worked example
A price index of 100, real output of $2,000 and a money supply of $1,000 give nominal output of $2,000 and a velocity of 2. If velocity fell to 1.5, the same $2,000 of nominal output would require $1,333.33 of money.
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Frequently asked questions
Income velocity or transactions velocity?
Income velocity divides nominal GDP by the money stock and counts only final goods. Transactions velocity divides the value of all transactions, including intermediate and financial ones, by money, so it is much larger and harder to measure.
Which money supply should I use?
Use the measure that matches your purpose, and keep it consistent over time. M1 velocity is more volatile than M2 velocity, and the two series are not interchangeable.
Why does velocity change?
Interest rates, uncertainty, payment technology and the availability of close money substitutes all affect how much money people hold relative to their spending. During a financial crisis, precautionary balances can lower velocity sharply.