Quantity theory of money | AP Macroeconomics | Khan Academy

In this video, we're going to talk about the quantity theory of money, which is based on what is known as the equation of exchange. It tries to relate the money supply ( M ) (so this is some measure of the money supply) with the real GDP ( Y ) (so that is real GDP) and the price level ( P ) (so this is the price level). We'll try to make this tangible in a second.

It also introduces this idea of the velocity of money, which is a measure of how much that money supply is circulating. If there's a dollar out there, how many times per year is it actually changing hands? The velocity of money and the equation of exchange that is used in the quantity theory of money relates these as follows: the money supply times the velocity of money is equal to your price level times your real GDP.

We could view this on a per year basis. So let's make this a little bit tangible, and actually, let's try to make it tangible by making velocity tangible. Let's say we are in a world where we have whatever we're using for ( M ), whatever measure of our money supply; let’s say it says that we have 10 billion—it’s a relatively small economy, right? Over that is our money supply, and let’s say that our real GDP in this economy this year is going to be 100 billion—100 billion I'll just call it per year.

Let’s say the price level, and this is usually some type of index, is 1.1. So, one way to think about it: if you take your price level times your real GDP—so if you take this product right over here—that's going to give you your nominal GDP. Nominal GDP, where if this was 1.0, that would be in reference to some year that you consider your base year; so this would be your real GDP in terms of that base year, and then you would multiply it times this right over here to get your nominal GDP.

But given this information, pause this video and try to figure out what the velocity of money would be for that year. Well, this is relatively straightforward algebra to solve for ( V ). We just divide both sides by ( M ), and we would get that our velocity of money in this year is equal to our price level times our real GDP divided by our amount of money.

So this is going to be equal to—we have 1.1 times 100 billion (100 billion dollars per year) divided by 10 billion dollars. So what is this going to be? 1.1 times 100 is 110, divided by 10 is 11. So we are going to get that this is going to be equal to 11. The dollar units would actually cancel out, and all you're left with, if you try to look at the units, is 11 times per year.

One way of interpreting this is: for these numbers, your average dollar is going to circulate 11 times per year. If this idea still seems too abstract to you, think of it this way: let’s have an extreme economy where we only have two parties, and let’s assume that our price level is just a simple one, in which case our real GDP would be the same as our nominal GDP.

Let’s say that our GDP this year is 100 billion dollars—100 billion dollars per year—and let’s take an extreme situation where the amount of money that we have is also 100 billion. Well, this would be a world—if there's only two people in this economy—where maybe this person just pays that person 100 billion dollars in order to get that much worth of output, and so every dollar has just switched hands once.

So the velocity of money in this situation would be just one time per year. But imagine another scenario where instead of ( M ) being equal to 100 billion dollars, imagine a situation where ( M ) is equal to one dollar. Where there's only one dollar, you could still have a GDP of a hundred billion dollars because that one dollar could just switch hands a hundred billion times.

It would have to happen quite rapidly for it to all happen in the year, but this person could buy a dollar's worth of goods and services from this person, and that person buys a dollar's worth of goods from that person, and it would go back and forth 100 billion times. And so in this situation where you still have the same real—and actually nominal—GDP, if your amount of money is 1 billion, then your velocity would have to be 100 billion times higher.

Now, the folks who like to think about this equation of exchange and the quantity theory of money are often known as monetarists. Monetarists believe that inflation is fundamentally a monetary phenomenon—that if you increase the money supply, that’s going to lead to increased inflation, and if you decrease the money supply, that might slow inflation or even result in deflation.

So if you want to think about inflation in terms of money, we could solve for ( P ) from this equation. To solve for ( P ), we would just divide both sides by our real GDP, and so you would get your price level is equal to the amount of money times your velocity divided by real GDP.

These monetarists will assume that velocity is constant, although folks theorize that maybe it's not constant, that technology, for example, might make it a little bit easier to transact, which might make velocity increase. There could also be a world where just people's mindsets make them want to transact more or less, which could change velocity.

But monetarists tend to assume that this is constant because it frankly allows you to make conclusions from this equation of exchange. Monetarists also assume that changes in the money supply will not have an impact on real output in the long run—so not impacted by ( M ) in the long run.

Well, if you assume that these two things are relatively constant, then you will see this direct relationship between your price level and the quantity of money. Now, in practice, this is likely to be an oversimplification—like most of our economics models.

For example, coming out of the last recession of 2008-2009, the Federal Reserve practiced quantitative easing, where they dramatically increased the money supply right over here. But we did not see a commensurate dramatic increase in inflation in the price level.

Now, some folks could argue that when the Federal Reserve in 2008 dramatically increased the money supply without a dramatic increase in price levels, it might have been because the velocity of money went down—that people weren't actually transacting with all of that money that was being injected into the system. Who knows?

And if you're always able to use velocity as a bit of a fudge factor, well then it puts into debate how useful this might be. But needless to say, it is an interesting model to at least think about: that if the money supply were to increase dramatically and people transact at roughly the same rate, but the actual output that the economy is producing isn't changing, it makes some level of common sense that maybe that would increase the price level. You'd have more money chasing the same output.