Quantity Theory of Money - Online Tutor, Practice Problems & Exam Prep

The quantity theory of money connects the money supply (M) to price levels (P) and real GDP (Y) through the equation $M^v=P^Y$. The velocity of money (v) measures how often a dollar is spent. If the money supply grows faster than real GDP, inflation occurs; if it grows slower, deflation happens. Holding velocity constant allows analysis of inflation through changes in money supply and GDP, emphasizing the balance between these economic factors.

Quantity Theory of Money

Alright. So now let's look into the quantity theory of money. The quantity theory of money connects the money supply, the amount of money available in the economy, with the level of prices. There has to be a connection between the amount of money available and how the price level is going to be in the economy. And that's what this theory tries to connect. It's a very simple equation: m∙v=p∙y. Let's go ahead and define all of these variables. M is our money supply, and remember, we're trying to connect the money supply to the level of prices in the economy. So let's see what these variables do.

Our money supply, the amount of money available in the economy set by the Fed, and then the velocity of money. The velocity of money is the average number of times each dollar in the money supply is spent. Think about when you go to the store and you spend a dollar, you bring a dollar and you buy a candy bar, and then the store goes and they take that money and they pay their employees, and the employee goes and buys some groceries at the store, and then that dollar goes from the store and gets spent somewhere else, right? This same dollar doesn't just get spent once and retire. No, it keeps circulating. It goes from one hand to another and keeps getting spent. So the velocity of money is the average number of times each dollar is going to be spent, generally, in a year. How many times will this dollar that I have in my pocket be spent, someone else spends it, how many times will it change hands during one year? That's the velocity of money.

Next, we have P, which is the price level in the economy. And remember, we're trying to connect the money supply to the level of prices. And finally, y is going to be our GDP, real GDP, because remember, real GDP keeps prices constant and then we'll multiply it by the price level to get to the current prices in the economy. Alright. So let's go through this example together real quick and we'll see how this money supply works, and then we'll go into more detail in the next video.

In 2014, the money supply equaled 2.8 trillion dollars while the real GDP totaled 16 trillion dollars. The price deflator was 1.09. Calculate the velocity of money. Remember, we have m∙v=p∙y. The money supply times the velocity equals the price level times the level of real GDP. Let's go ahead and put in what we know. They told us the money supply is 2.8 trillion. We're calculating the velocity of money. They told us the price level is 1.09. That means that prices are 1.09 times what they were in the original year, in our base year. If something cost us a dollar in the base year, this year, that same product would cost a dollar and nine cents. So, the prices have gone up since the base year. Real GDP, it also told us, is 16 trillion.

Let's go ahead and solve for the velocity here. If we divide both sides by 2.8, we'll have solved for the velocity. So let's go ahead and snag our calculators. Now, let's do some quick math here. 1.09∙162.8. So that tells us the velocity. I'm going to round it off to 6 here. I'm just going to say it's approximately 6. It was like 6.1 something and it comes out to approximately 6. So that says, each dollar changes hands approximately 6 times per year. So, each time you spend a dollar, it's going to be spent on average 6 times each dollar in the economy. Right? So that's how the theory works. You'll be given some variables and you can solve for the last variable.

Quantity Theory of Money and Inflation

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.

Here’s what students ask on this topic:

What is the Quantity Theory of Money?

The Quantity Theory of Money connects the money supply (M) to price levels (P) and real GDP (Y) through the equation $Mv=PY$. Here, $v$ represents the velocity of money, which measures how often a dollar is spent in a year. The theory suggests that if the money supply grows faster than real GDP, inflation occurs; if it grows slower, deflation happens. By holding the velocity constant, we can analyze inflation through changes in the money supply and GDP, emphasizing the balance between these economic factors.

How does the Quantity Theory of Money explain inflation?

The Quantity Theory of Money explains inflation through the equation $Mv=PY$. If the money supply (M) grows faster than real GDP (Y), the price level (P) increases, leading to inflation. This is because more money is chasing the same amount of goods and services, driving prices up. Conversely, if the money supply grows slower than real GDP, deflation occurs as there is less money available relative to goods and services, causing prices to fall. Holding the velocity of money (v) constant simplifies this analysis.

What is the velocity of money in the Quantity Theory of Money?

The velocity of money (v) in the Quantity Theory of Money is the average number of times each dollar is spent in a year. It measures how frequently money circulates in the economy. For example, if a dollar is spent six times in a year, the velocity of money is 6. The equation $Mv=PY$ uses this concept to link the money supply (M) to the price level (P) and real GDP (Y). The theory often assumes that the velocity of money is constant over time.

How do changes in money supply and GDP affect inflation according to the Quantity Theory of Money?

According to the Quantity Theory of Money, changes in the money supply (M) and real GDP (Y) directly affect inflation. The equation $Mv=PY$ shows that if the money supply grows faster than real GDP, the price level (P) increases, leading to inflation. Conversely, if the money supply grows slower than real GDP, deflation occurs as prices decrease. If both grow at the same rate, prices remain stable. This relationship helps economists understand and predict inflationary trends based on monetary and economic growth.

What happens if the money supply grows at the same rate as real GDP?

If the money supply (M) grows at the same rate as real GDP (Y), the price level (P) remains stable, resulting in no inflation or deflation. This is because the increase in money supply is perfectly balanced by the increase in goods and services available in the economy. The equation $Mv=PY$ shows that when both M and Y grow at the same rate, P does not change, leading to stable prices. This scenario is ideal for maintaining economic stability and avoiding the negative effects of inflation or deflation.