Velocity of money

The velocity of money is the average frequency with which a unit of money is spent in a specific period of time. Velocity affects the amount of economic activity associated with a given money supply. When the period is understood, the velocity may be present as a pure number; otherwise it should be given as a pure number over time. In the equation of exchange, velocity of money is one of the key variables determining inflation.

If, for example, in a very small economy, a farmer and a mechanic, with just $50 between them, buy goods and services from each other in just three transactions over the course of a year

• Mechanic buys $40 of corn from farmer.
• Farmer spends $50 on tractor repair.
• Mechanic spends $10 on barn cats from farmer

then $100 changed hands in course of a year, even though there is only $50 in this little economy. That $100 level is possible because each dollar was spent an average of twice a year, which is to say that the velocity was $2/yr$.

In practice, attempts to measure the velocity of money are usually indirect:

$V\_T\; =frac\{nT\}\{M\}$

where

$V\_T,$ is the velocity of money for all transactions.

$nT,$ is the nominal value of aggregate transactions.

$M,$ is the total amount of money in circulation on average in the economy.

(be it M0, M1, M2, or M3; see money supply for details). (Given the classical dichotomy, $nT$ may be factored into a product $Pcdot\; T$ of a price level $P$ and a “real” aggregate value of transactions $T$.)

Values of $nT$ and $M$ permit calculation of $V\_T$.

A rise or fall in the velocity of money usually follows a rise or fall in the interest rate.

As applied to an economy expenditures on final output are of interest, the relation may be written:

$V\; =frac\{nQ\}\{M\}$

where

$V,$ is the velocity for transactions counting towards national or domestic product.

$nQ,$ is nominal national or domestic product.

(Analogously with $nT$, given the classical dichotomy, $nQ$ may be factored into a product $Pcdot\; Q$.)

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.

See also

• Equation of exchange
• Quantity theory of money

References

• J.S. Cramer (1987). “velocity of circulation”, The New Palgrave: A Dictionary of Economics, v. 4, pp. 601-02.
• Milton Friedman (1987). “quantity theory of money”, in The New Palgrave: A Dictionary of Economics, v. 4, pp. 3-20.