Money creation in a fractional reserve system | Financial sector | AP Macroeconomics | Khan Academy

Let's say for some reason you had lent the government one thousand dollars, and so the government has given you a formally issued piece of paper that says, "Hey, we the government owe you one thousand dollars." This is issued by the treasury. This could be a treasury bond; it could be a T-bill of some kind.

And let's say that the Federal Reserve, the central bank, is interested in inserting money into our system. So let's say this is the Federal Reserve right over here. Federal Reserve. And so what they do is they create one thousand dollars of Federal Reserve notes, what we associate as paper money, and they pay it to you, and they buy the treasury. So that treasury goes to the Federal Reserve from you, and so in exchange, you get this newly created money that the Federal Reserve just created. So there you go, you have this is one thousand dollars.

Now what would you likely do with that one thousand dollars? Well, it might not be safe to walk around town with your pockets bulging like that, so a lot of folks would deposit it into a bank. So let's think about what would happen to the bank's balance sheet.

So you go to Bank A, and I'm just going to think about—I'm not going to think about what was the balance sheet, the pre-existing balance sheet for the bank, but let's just think about what happens to its assets and its liabilities when you make that deposit. A for assets, L for liabilities. If you deposit those thousand dollars, then your assets for the bank is going to get one thousand dollars in reserves.

But you didn't just give them the money; they have a liability to you. You should have a checkable deposit account now. So we could say checking account. So now you have a one thousand dollar checking account, which you would view as an asset for yourself, but it's a liability for the bank. At any time you could come and ask for that one thousand dollars—one thousand dollar checking account—and this would be for you.

Now we've already spent several videos talking about fractional reserve lending, and there are two ways we can conceptualize it, as we've seen in those videos. But I'm going to go with the simpler version of fractional reserve lending. And so this bank says, "Look, we are in a world where our reserve requirement—" I will do a reserve requirement. This actually is a typical reserve requirement. The reserve requirement in this country is 10%, which says that the bank only has to keep 10 percent of these cash reserves, and then it can loan out the rest. And so it does that—that's its business model or a significant part of its business model.

And so what it does is instead of having one thousand dollars in reserves, it keeps ten percent. So it keeps one hundred dollars, and it loans out the rest. So it loans out nine hundred dollars. So it's lending out now nine hundred dollars to someone else, hopefully someone who is good for the money, who maybe they're going to invest in their business or they're going to buy a house or whatever else.

Now once again, the bank just didn't give them the money in exchange; they get an asset, which is an IOU from that person. That person owes the bank money—they owe them nine hundred. So we could say that in exchange for giving them that cash, they're going to have a nine hundred dollar loan on their balance sheet as an asset.

Now once again, the person that they lent the money to—the loan would be a liability—they owe the money, but for the bank, that's an asset. "Hey, someone owes me, the bank, nine hundred." But then what's this person going to do? Well, once again, their pockets aren't going to bulge quite as much, but they still might not want to walk around town with nine hundred in their pockets.

So they are likely to deposit it in a bank. And they could deposit it in Bank A, or they could deposit it in another bank. Let's call it very creatively Bank B.

All right, so Bank B—same exercise. I think you might see where this is going. So it's assets, it's liabilities. And so they go and they deposit this nine hundred. So you have nine hundred right over there, and the corresponding liability— that person didn't give the money to the bank; the bank owes them. That person can demand that money at any point from the bank, and so you have a nine hundred dollar checking account.

And that person would draw on that checking account to buy the machinery for their business or whatever else. But once again, we have a 10% reserve requirement, which says that the bank only has to keep 10 percent of that. And so their business model is they do only keep 10% of it, and then the rest of it they loan out.

So they loan out eight hundred and ten dollars. It could be a loan or it could be multiple loans altogether, and I think you see where this is going. And so this is lent out to someone else. So now we have eight hundred and ten dollars, which can then be deposited in another bank, Bank C. They can lend out ninety percent of that, and that process keeps going on and on and on and on.

So an interesting question is, given this infusion of one thousand dollars and given this reserve requirement, how much total money has been created? Well, in other videos, we talk about the multiple measures of the money supply. When the Federal Reserve put this one thousand dollars of Federal Reserve notes into circulation, they increased the monetary base by one thousand dollars.

But one measure of the monetary supply is, well, what are the Federal Reserve notes, the coins, and the paper money that's in circulation, plus the amount of checkable deposits? And we talk about that in other videos as M1.

And so our M1 over here—what's it going to be? Well, this person has a one thousand dollar checking account—a one thousand dollar checking account. They think they have one thousand dollars that they can write checks against, and they do. And this person has a nine hundred dollar checking account—a nine hundred dollar checking account.

And then this person right over here, when they deposit their money, they're going to think they have an eight hundred and ten dollar checking account. They have that. And then that process is going to go on and on and on.

Someone else, when this eight hundred and ten gets deposited, the bank's going to lend out ninety percent of that. That person is going to think they have that amount of money. And so what we do is we're just multiplying by 0.9 every time. We're multiplying by one minus the reserve requirement every time.

And we've done the mathematics on this multiple times. This is going to be equal to one thousand dollars—the initial amount that was put into the monetary base—times one over one minus zero point nine. And that is just going to be equal to one thousand dollars times one over 0.1.

Or you could just view this as one over the reserve requirement. It just happened to be 0.1 in this example, reserve requirement. And you could do the math on what that's going to be. One divided by one tenth is going to be ten, and so our M1 money supply that has been created in this very simple example is going to be equal to—is going to be equal to ten times one thousand dollars, so it's going to be equal to ten thousand.

So big picture: when the monetary base is increased by a certain amount, if you know the reserve requirement and if you assume that all of the banks minimize their reserves, that keep only the 10%, they don't keep 11% or 12% or 20%, then what this calculation is going to show you is what is going to be the maximum effect on M1, given that infusion into the monetary base. And all it is is the amount that was infused times one over the reserve requirement.