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Velocity

While the relationship between money supply, money demand,
the price level, and the value of money presented above is
accurate, it is a bit simplistic. In the real world
economy, these factors are not connected as neatly as the
quantity theory of money and the basic money market
diagram present. Rather, a number of variables mediate
the effects of changes in the money supply and money
demand on the value of money and the price level.

The most important variable that mediates the effects of
changes in the money supply is the velocity of money.
Imagine that you purchase a hamburger. The waiter then
takes the money that you spent and uses it to pay for his
dry cleaning. The dry cleaner then takes that money and
pays to have his car washed. This process continues until
the bill is eventually taken out of circulation. In many
cases, bills are not removed from circulation until many
decades of service. In the end, a single bill will have
facilitated many times its face value in purchases.

Velocity of money is defined simply as the rate at which
money changes hands. If velocity is high, money is
changing hands quickly, and a relatively small money
supply can fund a relatively large amount of purchases.
On the other hand, if velocity is low, then money is
changing hands slowly, and it takes a much larger money
supply to fund the same number of purchases.

As you might expect, the velocity of money is not
constant. Instead, velocity changes as consumers'
preferences change. It also changes as the value of money
and the price level change. If the value of money is low,
then the price level is high, and a larger number of bills
must be used to fund purchases. Given a constant money
supply, the velocity of money must increase to fund all of
these purchases. Similarly, when the money supply shifts
due to Fed policy, velocity can change. This change makes
the value of money and the price level remain constant.

The relationship between velocity, the money supply, the
price level, and output is represented by the equation
M * V = P * Y where M is the money supply, V is the
velocity, P is the price level, and Y is the quantity of
output. P * Y, the price level multiplied by the quantity
of output, gives the nominal GDP. This equation can
thus be rearranged as V = (nominal GDP) / M.
Conceptually, this equation means that for a given level
of nominal GDP, a smaller money supply will result in
money needing to change hands more quickly to facilitate
the total purchases, which causes increased velocity.

The equation for the velocity of money, while useful in
its original form, can be converted to a percentage change
formula for easier calculations. In this case, the
equation becomes (percent change in the money supply) +
(percent change in velocity) = (percent change in the
price level) + (percent change in output). The percentage
change formula aids calculations that involve this
equation by ensuring that all variables are in common
units.