The velocity equation can be used to find the effects that
changes in velocity, price level, or money supply have on
each other. When making these calculations, remember that
in the short run, output (Y), is fixed, as time is
required for the quantity of output to change.

Let's try an example. What is the effect of a 3% increase
in the money supply on the price level, given that output
and velocity remain relatively constant? The equation
used to solve this problem is (percent change in the money
supply) + (percent change in velocity) = (percent change
in the price level) + (percent change in output).
Substituting in the values from the problem we get 3% + 0%
= x% + 0%. In this case, a 3% increase in the money
supple results in a 3% increase in the price level.
Remember that a 3% increase in the price level means that
inflation was 3%.

In the long run, the equation for velocity becomes even
more useful. In fact, the equation shows that increases
in the money supply by the Fed tend to cause increases in
the price level and therefore inflation, even though the
effects of the Fed's policy is slightly dampened by
changes in velocity. This results a number of factors.
First, in the long run, velocity, V, is relatively
constant because people's spending habits are not quick to
change. Similarly, the quantity of output, Y, is not
affected by the actions of the Fed since it is based on
the amount of production, not the value of the stuff
produced. This means that the percent change in the money
supply equals the percent change in the price level since
the percent change in velocity and percent change in
output are both equal to zero. Thus, we see how an
increase in the money supply by the Fed causes inflation.

Let's try another example. What is the effect of a 5%
increase in the money supply on inflation? Again, we
being by using the equation (percent change in the money
supply) + (percent change in velocity) = (percent change
in the price level) + (percent change in output).
Remember that in the long run, output not affected by the
Fed's actions and velocity remains relatively constant.
Thus, the equation becomes 5% + 0% = x% + 0%. In this
case, a 5% increase in the money supply results in a 5%
increase in inflation.

The velocity of money equation represents the heart of the
quantity theory of money. By understanding how velocity
mitigates the actions of the Fed in the long run and in
the short run, we can gain a thorough understanding of the
value of money and inflation.