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.