# Velocity of money

Chart showing the log of US M2[1][2] money velocity (green), calculated by dividing nominal GDP by M2 stock, M1 plus time deposits 1959–2010. Employment-to-population ratio is displayed in blue, and periods of recession are represented with gray bars).
Similar chart showing the velocity of a slightly narrower measure of money consisting of currency and liquid deposits M1 1959–2010.
Similar chart showing the velocity of a broader measure of money that covers M2 plus large institutional deposits, M3. The US no longer publishes official M3 measures, so the chart only runs through 2005.

The term "velocity of money" (also "The velocity of circulation of money") refers to how fast money passes from one holder to the next. It can refer to the income velocity of money, which is the frequency at which the average same unit of currency is used to purchase newly domestically-produced goods and services within a given time period.[3] In other words, it is the number of times one unit of money is spent to buy goods and services per unit of time.[3] Alternatively and less frequently, it can refer to the transactions velocity of money, which is the frequency with which the average unit of currency is used in any kind of transaction in which it changes possession—not only the purchase of newly produced goods, but also the purchase of financial assets and other items."

If the velocity of money is increasing, then transactions are occurring between individuals more frequently.[3] Although once thought to be constant,[citation needed] it is now understood that the velocity of money changes over time and is influenced by a variety of factors.[4]

## Illustration

If, for example, in a very small economy, a farmer and a mechanic, with just $50 between them, buy new goods and services from each other in just three transactions over the course of a year • Farmer spends$50 on tractor repair from mechanic.
• Mechanic buys $40 of corn from farmer. • Mechanic spends$10 on barn cats from farmer.

then $100 changed hands in the course of a year, even though there is only$50 in this little economy. That \$100 level is possible because each dollar was spent on new goods and services an average of twice a year, which is to say that the velocity was ${\displaystyle 2/{\text{year}}}$. Note that if the farmer bought a used tractor from the mechanic or made a gift to the mechanic, it would not go into the numerator of velocity because that transaction would not be part of this tiny economy's gross domestic product (GDP).

## Relation to money demand

The velocity of money provides another perspective on money demand. Given the nominal flow of transactions using money, if the interest rate on alternative financial assets is high, people will not want to hold much money relative to the quantity of their transactions—they try to exchange it fast for goods or other financial assets, and money is said to "burn a hole in their pocket" and velocity is high. This situation is precisely one of money demand being low. Conversely, with a low opportunity cost velocity is low and money demand is high. In money market equilibrium, some economic variables (interest rates, income, or the price level) have adjusted to equate money demand and money supply.[citation needed]

## Indirect measurement

In practice, attempts to measure the velocity of money are usually indirect. The transactions velocity can be computed as

${\displaystyle V_{T}={\frac {PT}{M}}}$

where

${\displaystyle V_{T}\,}$ is the velocity of money for all transactions in a given time frame;
${\displaystyle P\,}$ is the price level;
${\displaystyle T\,}$ is the aggregate real value of transactions in a given time frame; and
${\displaystyle M\,}$ is the total nominal amount of money in circulation on average in the economy (see “Money supply” for details).

Thus ${\displaystyle PT}$ is the total nominal amount of transactions per period.

Values of ${\displaystyle PT}$ and ${\displaystyle M}$ permit calculation of ${\displaystyle V_{T}}$.

Similarly, the income velocity of money may be written as

${\displaystyle V={\frac {PQ}{M}}}$

where

${\displaystyle V\,}$ is the velocity for transactions counting towards national or domestic product; and
${\displaystyle PQ\,}$ is nominal national or domestic product.

## Determination

The determinants and consequent stability of the velocity of money are a subject of controversy across and within schools of economic thought. Those favoring a quantity theory of money have tended to believe that, in the absence of inflationary or deflationary expectations, velocity will be technologically determined and stable, and that such expectations will not generally arise without a signal that overall prices have changed or will change.

## Criticism

Ludwig von Mises said "The main deficiency of the velocity of circulation concept is that it does not start from the actions of individuals but looks at the problem from the angle of the whole economic system. This concept in itself is a vicious mode of approaching the problem of prices and purchasing power. It is assumed that, other things being equal, prices must change in proportion to the changes occurring in the total supply of money available. This is not true."[5]

## References

### Notes

1. ^ M2 Definition – Investopedia
2. ^ M2 Money Stock – Federal Reserve Bank of St Louis
3. ^ a b c "Money Velocity". Federal Reserve Bank of St. Louis. Retrieved October 28, 2013.
4. ^ Mishkin, Frederic S. The Economics of Money, Banking, and Financial Markets. Seventh Edition. Addison–Wesley. 2004. p. 520.
5. ^ Ludwig von Mises, Human Action (New Haven: Yale University Press, 1949), and The Theory of Money and Credit (London: Jonathan Cape, Limited, 1934, and New Haven: Yale University Press, 1953).