So, a cool thing happens here if we hold the velocity of money constant. So the quantity theory of money argues that the velocity is constant, and it kind of makes sense. If you think about the average times a dollar is spent, remember, that's what the velocity is talking about. How often is that money spent? How often is it changing hands? Well, it depends on things that do not change that often. A lot of times when money changes hands, it's on things that are kind of regularly scheduled. How often you get paid, right? Every time you get paid, well, that's pretty consistent regardless of the price levels, what's happening in the economy. You're generally going to be paid every 2 weeks, every Friday. However, your schedule is, that's not going to change based on macroeconomic events. How often you go to the grocery store, right? How often you make these general purchases, how often you pay your bills, these things are pretty constant, right? From person to person, they're going to be constant in how often they're doing that. So the velocity of money more or less doesn't change too much. It's not like you start spending a lot of cash at one point and then slow down how much money you spend. You kind of have this average rate that you're spending cash.

A mathematical rule allows us to take the equation we've been using, \( m \cdot v = p \cdot y \) to analyze inflation. So without getting too much into the math, we can make this relationship where if we analyze the changes in these variables, well, we can set up the same calculation as additions here. So, the change in the money supply, plus the change in the velocity. So notice, we've changed from multiplication to addition, okay? Now, I don't want to get into the details of the mathematics. We don't need all of that. We just can know that equation that's set up like this with the multiplication. Well, if we want to analyze the differences, the changes in the variables, well, we can add them together like this. Okay? So this is a mathematical identity that we can do here. So the change in the money supply plus the change in velocity is equal to the change in prices plus the change in GDP.

We just said that we're going to hold velocity constant, right? Velocity is going to be constant. So the change in the velocity of money is going to be the same from year to year. If there was 6, 6 was the velocity of money last year, 6 will be the velocity of this year. So the change in the velocity is 0. There's no change in velocity. So that leaves us with the other three variables. The change in the money supply equals the change in the price level plus the change in GDP. Okay?

So let's go ahead and let's get the price level by itself. Let's move the change in GDP to the other side of the equation here and we'll have the change in the money supply minus the change in GDP equals the change in prices. And what is the change in prices? This is inflation, right? The change in prices is inflation. If that's a positive number, if prices are higher this year than they were last year, well, that's an increase in the prices. It's inflation there.

So what does this tell us? Look down here where we can make our conclusions. I'll get out of the way. If the money supply grows faster than real GDP so in this situation, we have something going on where we've got the change in money supply minus the change in GDP equals the change in price level. So in this case, the money supply is growing faster. Right, the money supply is growing faster than real GDP, well, we're going to see inflation. Right? There's more money available and it's going to increase the prices in the economy.

So this is the connection we're making from the quantity theory of money. These are the conclusions we can make: this balance between the money supply and the price level. So if the money supply grows slower than real GDP, so in this case, we've got the same equation, change in money supply, change in y, change in prices. Well, now there's the same amount of money, but there are more goods available leading to lower prices, which is what we call deflation. There's going to be a decrease in the prices in this case.

And finally, if they grow at a constant rate, money supply growing at the same rate as GDP. So they're growing equally. Well, if those changes are growing equally, there's not going to be a change in the price level. What's going to then there will be, what are we going to call this? We're going to call this stable prices. Right? There's not going to be a change in the prices. There will be stable prices in the economy. Okay.

So we can use that quantity theory of money equation two ways. We can use it as that multiplication, and we can solve for one of the variables or we can use the changes in the variables to describe how the money supply and GDP affect inflation. Alright? Let's go ahead and move on to.