Jon has taught Economics and Finance and has an MBA in Finance
The Velocity of Money
Imagine an economy of exactly ten gnomes who all go by the name Namji. Each of them are completely identical in every way, and each of them is holding a giant red and yellow lollipop. The lollipops are for sale for the incredible low price of exactly $1. In addition to a lollipop, one of the ten gnomes is holding a dollar bill. This one dollar bill is the only money in the economy, so we can refer to it as 'the money supply.' This gnome, acting out of a genuine zest for life and an unwavering zeal to improve his standard of living, approaches a colleague asking to buy his lollipop. After exchanging the dollar for the lollipop, the first gnome has two lollipops. The second gnome smiles because he now has a dollar.
However, within a few seconds, he realizes that he is without a lollipop, and so he approaches another gnome asking to purchase one with his newly-acquired currency. Again, the dollar changes hands and settles in the hands of another gnome, who is temporarily happy until he realizes that he greatly desires a giant red and yellow lollipop. This scenario plays out again and again until every gnome has spent a dollar buying a lollipop, and the dollar ends up back in the hands of the original gnome. Everyone has a lollipop, and there is still only one dollar bill in this economy.
Let's take a look at how economists describe this scenario:
The velocity of money is how fast money changes hands in the economy during the year. It's defined as nominal GDP divided by the money supply. It can be thought of as the rate of turnover in the money supply: that is, the number of times that one dollar is used to purchase final goods and services included in the GDP.
In our economy, the Federal Reserve is in charge of managing the money supply, which they call monetary policy. They use monetary policy in an effort to encourage steady economic growth, stable prices and low unemployment. Estimating the velocity of money is an important part of this process and guides them in their policy decisions.
So as you can see here, in 2012, the velocity of money was approximately 7 and had fallen from a high of more than 10 just a few years earlier. In the scenario I shared with you earlier, one dollar changed hands (or in this case, gnomes), ten times, so the velocity of money was 10.
The question I want to answer in the remainder of this lesson is, 'What determines velocity?' To help us find the answer, I want you to go with me as we briefly visit two towns - the town of Ceelo and the town of Keelover.
In the town of Ceelo, a lot of people live in a small area, which means that it's densely populated. As a result, banking is easy, and business is pretty smooth. There's a bank located at nearly every corner. When you're driving about town, you'll never have to worry about getting a check cashed or withdrawing money from an ATM machine. Most banks in Ceelo have them.
Speaking of driving, the average speed limit in Ceelo is 50 miles per hour, and traffic lights are only two minutes long, so traffic keeps moving. There's a saying you can hear them use quite frequently - 'Don't let money burn a hole in your pocket!' You have plenty of opportunities to spend your money quickly because the stores in Ceelo are filled with dozens of checkout lanes, and the lines move quickly. They even have self-checkout lanes where you can check yourself out. Many residents have stopped using checks and now use debit cards instead, and that speeds up transactions even more.
Since things are so smooth, most citizens you run into are peaceful and joyful, and the economy is usually growing nicely. Interest rates are moderately high in Ceelo. Because transactions are so easy in this town, money changes hands frequently. The faster that money changes hands in an economy, the greater the economic output is.
Economists would say it this way: When the velocity of money is high, money changes hands quickly, and therefore, changes in the money supply will have a greater effect on nominal GDP.
On the other hand, in the town of Keelover, the residents are spread out over a large area. Banking is difficult, and business is slow. Banking is difficult because there are very few banks anywhere around. Whenever you would expect to pass one on the road, you end up having to drive many miles away to find one. At these banks, very few of them have ATM machines, so it's very inconvenient.
The average speed limit in Keelover is 25 miles per hour (yikes!), and traffic lights are five minutes long. In this town, there's a saying you can hear them use quite frequently - they say, 'Quality is the least of our problems.' This is very apparent when you visit the local stores because they hardly have any checkout lanes, and it takes forever to pay for your stuff. Most people whip out their checkbooks to pay for stuff at the store, which slows things down even more.
As a result of all these negatives, the general mood is fearful and anxious, and the economy here is usually in recession. Most people keep money under their mattress. When you visit this place, you literally feel like you're going to 'keel over.' Needless to say, money changes hands very slowly. The slower that money changes hands in an economy, the lower the economic output is.
Economists would say it this way: When the velocity of money is low, money changes hands slowly, and therefore, changes in the money supply will have a smaller effect on nominal GDP.
Here are some of the things that determine velocity:
- The number of financial institutions in an area
- The population density of an area
- The speed of transportation
The Equation of Exchange
Now that we've talked about what velocity is and what determines it, let's talk about how to use it.
The velocity of money is part of what economists call the equation of exchange: MV = PY
In English, this means that the money supply (M) times the velocity of money (V) equals the price level (P) times real GDP (Y).
It means that there's a direct proportional relationship between the supply of money, how fast it changes hands, the price level in the economy and the economic output. If you know three variables in an equation, you can always solve to find the missing variable that you don't know. Here's an example.
Assuming that the price level remains constant, if real GDP is $6 trillion and the money supply is $2 trillion, the velocity of money would be what?
Using the equation of exchange, we get:
$2 trillion x V = 1 x $6 trillion
And when we solve the equation, we find that the velocity V = 3.
A velocity of 3 means that each dollar in circulation changes hands three times during the year. Another way to read the equation is to say, '$2 trillion of money changed hands three times during the year, producing $6 trillion of economic output.'
Remember the illustration I started with where the ten gnomes took one dollar and completed ten transactions with the same dollar? Assuming the price level is 1, here's what the equation of exchange looks like for the scenario that we talked about:
MV = PY
Plugging in the numbers, that looks like:
$1 x 10 = 1 x $10
Based on the way things played out, the money supply in this economy was only one dollar. The economy produced ten dollars in total because the velocity of money was 10. The same one dollar bill changed hands again and again, which enabled the total spending to be greater than the amount of money in circulation.
All right, it's time to review. According to the Federal Reserve, the velocity of money is a ratio of nominal GDP to a measure of the money supply. It can be thought of as the rate of turnover in the money supply: that is, the number of times that one dollar is used to purchase final goods and services included in the GDP.
Velocity is a key element of the equation of exchange, a formula that the central bank uses when considering monetary policy. When the velocity of money is high, money changes hands quickly, and therefore, changes in the money supply will have a greater effect on real GDP. When the velocity of money is low, money changes hands slowly, and therefore, changes in the money supply will have a smaller effect on real GDP.
The determinants of velocity include:
- Financial institutions
- Population density
- Speed of transportation
Once you finish the lesson, you should be prepared to:
- Define key terms, including velocity of money, monetary policy and equation of exchange
- Identify factors that impact the velocity of money
- Describe the money supply's effect on the nominal GDP when velocity is high
- Calculate the velocity using the equation of exchange
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