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In the last video, we learned the quantity theory of money and its corresponding identity equation: M x V = P x Y For a quick refresher: - M is the money supply. -

In the last video, we learned the quantity theory of money and its corresponding identity equation: M x V = P x Y

For a quick refresher:

- M is the money supply.

- V is the velocity of money.

- P is the price level.

- And Y is the real GDP.

In this video, we’re rewriting the equation slightly to divide both sides by Y and explore the causes behind inflation. What we discover is that a change in P has three possible causes – changes in M, V, or Y.

You probably know that prices can change a lot, even over a short period of time.

Y, or real GDP, tends to change rather slowly. Even a seemingly small jump or fall in Y, such as 10% in a year, would signal astonishing economic growth or a great depression. Y probably isn’t our usual culprit for inflation.

V, or the velocity of money, also tends to be rather stable for an economy. The average dollar in the United States has a velocity of about 7. That may fall or rise slightly, but not enough to influence prices.

That leaves us with M. Changes in the money supply are the driving factor behind inflation. Put simply, when more money chases the same amount of goods and services, prices must rise.

Can we put this theory to the test? Let’s look at some real-world examples and see if the quantity theory of money holds up.

In Peru in 1990, hyperinflation came into full swing. If we track the growth rate of the money supply to the growth rate of prices, we can see that they align almost perfectly on a graph with both clocking in around 6,000% that year.

If we plot the growth rates of the money supply along with the growth rates of prices for a many countries over a long stretch of time, we can see the same relationship.

We’ll wrap-up the causes of inflation with three principles to keep in mind as we continue exploring this topic:

- Money is neutral in the long run: a doubling of the money supply will eventually mean a doubling of the price level.

- “Inflation is always and everywhere a monetary phenomena.” – Milton Friedman

- Central banks have significant control over a nation’s money supply and inflation rate.

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**Transcript**

Today, we're going to explain the primary cause of inflation. And we're going to do so using the quantity theory of money. Let's start by rewriting our equation slightly. We'll divide both sides by Y, so we get this. What this equation tells us is that if prices are changing, 42,007 there are three possible causes -- changes in M, V, or Y.

Now remember that P -- prices -- they can change quite a bit in a short period of time. There are many times and places, for example, when prices have doubled or tripled in a year. On the other hand, V and Y are pretty stable. Consider Y -- that's real GDP. Real GDP -- it doesn't vary that much within a year. An increase of 10% in a single year -- that would be astonishing growth. And a fall of 10% -- that would be a very unusual, great depression.

So, changes in real GDP -- they don't seem like a plausible candidate for explaining large and sustained changes in prices. What about V -- the velocity of money? The velocity of money is the average number of times that the dollar is used to purchase final goods and services in a year. In the U.S. economy in recent years, V -- it's been about seven. And it's determined by the same kinds of factors that might determine your personal V, factors like whether you're paid weekly or biweekly, or how long it takes to clear a check. As we'll discuss later, V can change in the short run, but it might go up to eight or down to six. Usually, usually not much more than that.

So, again, V doesn't seem like it can change enough to explain large and sustained changes in prices. So, if Y and V are relatively stable, which we'll note by adding a bar over top, then it follows immediately that the only thing that can cause an increase in P is an increase in M. In other words, increases in prices are caused by increases in the money supply. It's changes in the money supply that are driving the speed and the height of our inflation elevator. We can summarize this by writing the quantity theory of money in a nutshell.

Here's our equation written in the earlier form. Now what this equation says is very simple and intuitive. When more money chases the same amount of goods and services, prices must rise. Okay. How well does the theory hold up? In this figure, we plot the price level and the money supply from Peru during its hyperinflation. A product with a price of one Peruvian intis in 1980 -- it would have cost 10 million intis by 1995.

Now what caused this massive increase in prices? Well, just as the quantity theory would predict, we also see at this time a massive increase in the money supply. M skyrocketed and so did P. We can also write the quantity theory in terms of growth rates, which we'll indicate with a little arrow above the variable. What the growth form of the quantity theory tells us is that if V and Y, if they're not growing too much, then the growth rate of M should be equal to the growth rate of prices. And remember, the growth rate of prices is the inflation rate.

Here's the same data from Peru as before, except now we're looking at the growth rate of the money supply and the growth rate of prices. As the growth rate of the money supply increased, so did the inflation rate. Amazingly, the money supply was growing at a rate of 6,000% per year in 1990. And as the quantity theory predicts, the inflation rate -- it was about 6,000% per year in 1990. Okay -- so the theory works pretty well for Peru in 1990.

What about other times and places? Here we show inflation rates on the vertical axis and money growth rates on the horizontal axis. This is for about 110 countries between 1960 and 1990. You can see that, on average, the relationship is close to perfectly linear, with a one percentage point increase in the money supply growth rate leading to a one percentage point increase in the inflation rate.

Now what this tells us is three very important principles. First, in the long run, money is neutral. A doubling of the money supply will, in the long run, lead to a doubling of prices. Second, if we're thinking about a significant and sustained inflation rate, then Milton Friedman had it exactly right when he said, "Inflation is always and everywhere a monetary phenomena." Third, since central banks often have significant control over a nation's money supply, they also often have significant control over a nation's inflation rate.

Okay. Keep those three principles in mind. We'll be referring to them in future videos.

## Ask a Question

I realized that you do change the signs from M + v = P + r ---(1) to M x v = P x r ---(2). Indeed in equation (2) you said you were looking at the growth rate. So my question is that why does the growth rate change the Quatity Theory of Money formula/identity from addition to multiplication?

Imagine a small economy, with just 2 dollars in it. The first dollar changes hands three times, so it is used in three transactions (John gives the dollar to Jane, Jane to Mary, Mary to Mark), sequentially. The second dollar is itself used in three transactions. M is the money supply. In our case this is 2. V is velocity, which is the number of times one dollar (the "average dollar" so to say) changes hands. In our case this is 3.

In each transaction there is some good exchanged for that dollar. The value of that good in that transaction is one dollar. So 1 is the price of the average good exchanged in this economy. How about Y. Y is the total number of goods. Since there is a good like this exchanged in each of the six transactions, the total amount (the total quantity or number of goods) in this economy is 6.

If we plug in the numbers in our minieconomy, we get MV=PY, or 2x3=1x6.

Now let's think about the growth rates.

We add the growth rates: growth of M plus growth of V = growth of P plus growth of Y.

In short: gM+gV=gP+gY.

MV=PY is about levels.

gM+gV=gP+gY is about growth rates.

Imagine our minieconomy after one year. Assume Y has not changed. So the growth of Y is zero. (The number of goods is the same, 6. Say, 6 apples. So Y is still 6.)

Assume V hasn't changed either. So the growth of V is zero as well.

But the Central Bank has printed one more dollar. So M=3 now. From 2 to 3 there is a 50% growth.

Let's plug in the numbers describing the minieconomy in the second year:

gM+gV=gP+gY is now 50%+0%=___+0%.

The blank space is gP, the growth of the price level, which is inflation. Clearly, P, the price level must have gone up by 50 percent too. (And this was the result of the growth in the money supply.)

The average price in a transaction is now 1.5 dollars.

Now we can use this to see the levels in the second year:

MV=PY is now 3x3=1.5x6

We now have an intuition why the equation about growth rates needs to use addition.

(If you like math, you can also check Khan Academy's lesson on logarithms. We see there that we can derive the equation about growth rates starting from the equation about levels, by "taking the logarithm of the equation, and then taking the derivative of the logarithmic equation". So we only need one basic equation, to start from, the one about levels, which is with multiplication. The rest is mathematical derivation.)

I still have a question like Eric. Start with the quantity o money equation for year 1: m1 x v1 = p1 x y1. Then assume a 30% inflation rate over the following year, with no increase in actual GDP. Also assume a growth in money supply of 15%. Then according to the rate of change (growth) equation, the velocity of money must also increase by 15%, since gm + gv = gp + gy or 15% + 15% = 30% +0%. So for year 2, we can write:

m2 = m1x1.15

v2 = v1x1.15

p2=p1x1.30

y2=y1.

We should then be able to write the quantity of money equation for year 2 as m2 x v2 = p2 x y2 , which the "rate" form of the equation told us should be equal to: m1x1.15 x v1x1.15 = p1x1.30 x y1. This can be rearranged to give: m1 x v1 x 1.15^2 = p1 x y1 x1.30. But if, as we said in the beginning,

m1 x v1 = p1 x y1, then the equation for year 2 cannot be correct, since 1.15^2 does not equal 1.30! (in fact, 1.15^2 = 1.323). Admittedly there is not much difference here, but the basic equality does not hold.