Velocity of Money
What is Velocity of Money?
The velocity of money is the average number of times a unit of money is spent on final goods and services in a given period.
It measures how quickly money circulates through the economy, calculated as nominal GDP divided by the money supply. If velocity is stable, changes in the money supply lead to proportional changes in nominal GDP. It reflects how efficiently money is used in transactions.
Velocity of Money: a worked example
Start with the equation of exchange, MV = PQ. An economy has a money supply M of 180 billion dollars, real output Q of 360 billion dollars, and a price level index P of 2.0, so nominal GDP is 2.0 x 360 = 720 billion dollars. Velocity is V = 720 / 180 = 4, meaning the average dollar changes hands four times over the year. The central bank now expands the money supply by 20 percent, to 216 billion dollars, and velocity holds at 4. Nominal GDP becomes 4 x 216 = 864 billion dollars, a rise of 144 billion, or 20 percent. If the economy is already at potential and real output stays at 360 billion, the price level must climb to 864 / 360 = 2.4, also a 20 percent increase. Money growth passes straight into inflation when V and Q hold steady.
The mistake students make with velocity of money
The tempting shortcut is dividing real GDP by the money supply. The numerator of velocity is nominal GDP, P times Q, so using real output understates V whenever the price index exceeds 1. In the example above, 360 / 180 gives 2 instead of the correct 4. The other frequent slip is inverting the ratio and reporting 180 / 720 = 0.25. Use the units as a check. Velocity counts how many times each dollar gets spent, so it has to be dollars of spending divided by dollars of money, never the reverse.
Velocity of Money questions
How do you calculate the velocity of money?
Velocity equals nominal GDP divided by the money supply, or V = PQ / M. Multiply the price level by real output to get nominal GDP, then divide by the stock of money in circulation. With nominal GDP of 720 billion dollars and a money supply of 180 billion dollars, velocity is 4, so the average dollar funds four dollars of final spending during the year. The same equation rearranges to MV = PQ, which is how AP questions usually present it.
What happens to nominal GDP if the money supply doubles and velocity is constant?
Nominal GDP doubles as well. MV = PQ means that with V fixed, any percentage change in M produces the same percentage change in P times Q. Whether the increase shows up as higher prices or higher real output depends on where the economy sits. Below full employment some of it raises real Q, while at potential output the whole increase lands on the price level P. That second case is the quantity theory prediction that money growth causes inflation.
What makes the velocity of money rise or fall?
Velocity rises when people hold money for shorter stretches before spending it, which happens with faster payment technology, easier access to credit, or high expected inflation that makes holding cash costly. Velocity falls when households and firms park money idle, as in a downturn when precautionary balances build up. Because velocity moves with these habits, a central bank that expands the money supply during a slump may see nominal GDP rise by less than the quantity theory predicts.
Formula / Example
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