Money creation in a fractional reserve system

- [Instructor] Let's say, for some reason, you had lent the government $1,000, and so the government has given you a formally issued piece of paper that says, "Hey, we, the government, owe you $1,000." 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 $1,000 of Federal Reserve Notes, what we associate as paper money, and they pay it to you and they buy the Treasury, so the Treasury goes to the Federal Reserve from you. And so, in an exchange, you get this newly created money that the Federal Reserve just created. So, there you go. You have, this is $1,000. Now, what would you likely do with that $1,000? 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 the Bank A and I'm just gonna 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 the deposit. A for assets, L for liabilities. If you deposit those thousand dollars, then your assets for the bank is going to get $1,000 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 $1,000 checking account which you would use an asset for yourself but it's a liability for the bank. At any time, you could come and ask for that thousand dollars. $1,000 checking account and this would be for you. Now, we've already spent several videos talking about fractional-reserve lending and there's two ways we can conceptualize it as we've seen in those videos but I'm gonna 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% of these cash reserves and then it could 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 $1,000 in reserves, it keeps 10%, so it keeps $100, and it loans out the rest. And so, it loans out $900. So, it's loaning out now $900 to someone else, hopefully someone who is good for the money, who maybe they're gonna invest it into 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 $900. So, we could say that in exchange for giving 'em that cash, they're going to have a $900 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, $900." But then what's this person going to do? Well once again, their pocket's are gonna bulge quite as much but they still might not wanna walk around town with $900 in their pocket, so they are likely to deposit 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 (chuckles). So, Bank B, same exercise. I think you might see where this is going, so its assets, its liabilities. And so they go and they deposit this $900, so you have $900 right over there. And the corresponding liability, that person then give the money to the bank, that person can demand that money at any point from the bank, and so you have a $900 checking account, checking account. And that person would drop 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% 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 $810. It could be a loan or it could be multiple loans altogether. And I think you see where this is going. So, this is lent out to someone else, so now we have $810, which can then be deposited in another bank, Bank C. They can lend out 90% of that and that process keeps going on and on and on and on. So, an interesting question is given this infusion of a thousand dollars and given this reserve requirement, how much total money has been created? Well, in one other videos, we talk about the multiple measures of the money supply. When the Federal Reserve put this $1,000, a Federal Reserve Notes into circulation, they increased the monetary base by $1,000, 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 gonna be? Well, this person has a thousand dollar checking account, $1,000 checking out, they think they have $1,000 that they can write checks against and they do. And this person has a $900 checking account, $900 checking out. And then this person right over here that when they deposit their money, they're gonna think they have an $810 checking account. They have that. And then that process, they're gonna go on and on and on and on. Someone else, when this $810 gets deposited, the bank's gonna lend out 90% of that. That person's gonna think they have that amount of money. And so what we do is we're just multiplying by .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 $1,000, the initial amount that was put into the monetary base, times one over one minus 0.9 and that is just going to be equal to $1,000 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 1/10 is going to be 10, and so our M1 money supply that has been created in this very simple example is going to be equal to 10 times the thousand dollars, so it's gonna be equal to $10,000. 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 the banks minimize their reserves, that they keep only the 10%, they don't keep 11% or 12% or 20%, then what this calculation is gonna 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.