# Quantity theory of money

## Video transcript

- [Instructor] 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 and 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 price level, and we'll try to make
this tangible in a second, and then it also introduces this idea of the velocity of money which is a measure of how
much that money supply is how quickly is it circulating. If there's a dollar out
there, how many times per year is it actually changing hands? Velocity of money. And the equation of exchange that is used in the quantity theory of money relates these as following, that the money supply times the velocity of money is equal to your price level times your real GDP. And we can 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,
that is our money supply. And let's say that our real
GDP in this economy this year is going to be a 100 billion, I'll just call it per year, and let's say the price level, and this is usually some
type of index, this 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 gonna
give you your 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. And 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 a 100 is a
110 divided by 10 is 11. So we are going to get, this
is going to be equal to 11. The dollar units would actually cancel out and all you're left with if you tried to look at the units is 11 times per year. And so, 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, and 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, or 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 hand once. So the velocity of
money in this situation, it would be just one time per year. But imagine another scenario where instead of M being equal
to a 100 billion dollars, imagine a situation
where M is equal to $1, where there's only $1 there. You could still have a
GDP of 100 billion dollars because that $1 could just switch hands a 100 billion times. It would have to happen quite rapidly for a dollar happened 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 and services from that person and it would go back and
forth 100 billions times. And so, in this situation
where you still have the same real, and actually nominal, GDP, if your amount of money is
one-one hundred billionth, then your velocity would have to be a 100 billion times higher. Now, the folks who like to think about this equation of exchange and
the quantity theory of money, they're often known as monetarists, and monetarists believe that inflation is fundamentally a monetary phenomenon, that if you increase the money supply, that 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. So 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. And 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 wanna 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. And 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, well 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've 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 of
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
increase the price level. You would have more money
chasing the same output.