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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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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.)