Required Reserves and the Deposit Multiplier - Video Tutorials & Practice Problems
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Bank Balance Sheet and Money Supply
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Alright, so let's see how checking account deposits can have a multiple effect on the money supply, meaning that the amount of money being saved in a bank rather than saved under your mattress can actually increase the money supply by a multiple amount. So, remember when we defined M1, we included the currency in circulation and checking account deposits, right? That was the significant portion of M1 was the currency in circulation. And the amount in checking deposits. So that's how we define the money supply. So now we're gonna think about from the bank's perspective, we're gonna be looking from a bank perspective and see how the money supply is affected. So reserves are deposits that the banks have received but not loaned out. Okay, So what we're gonna see is that banks, when they hold deposits, they're not going to have all of that money just sitting in the bank. If you go to the bank and you deposit $1000 well, they're going to take that $1000 and they're gonna loan some of it out and they're gonna keep some of it as reserves just in case you go and make a withdrawal and the rest of it, they're gonna loan out. So the idea here is that they're not expecting you when you put the money in the bank to just withdraw all your money at once. And if you did, well, they have other people's reserves to help maintain that now. Um So in general, what they're gonna have is a certain portion of each checking account deposit on reserve and that's what's called the reserve ratio. The amount of deposits that the banks have to keep in cash. And this is usually mandated by the government what that reserve ratio is. So generally they're only gonna keep a fraction of their deposits as cash. And let's go ahead and go through this this example and see how the money supply is affected by this reserve ratio. So let's start here where clutch Topia originally has no banks. And the total amount of currency in circulation is equal to $1000. So what is the money supply in this case the money supply is gonna be the currency in circulation? The $1000 plus zero in banks, right? The deposits are zero. So I'll say currency in circulation CC for 1000 and zero in deposits. So there's 1000 there in our money supply. Now let's go on where first bank of clutch opens and clutch tokens are so excited that they deposit all $1000 in the bank. They deposit all $1000 in the bank. So we're gonna go through a banks kind of balance here. So over here we're gonna have the assets of the bank, what they own and the liabilities of the bank over here, what they what they owe, Right? So we're gonna say um how much money they have in liabilities and how much they own. So generally what we're gonna see Is that the liabilities when people deposit the money into the bank. Well, they're gonna have deposits, right, these are liabilities that they have, that they go to to the people who deposited, they're gonna have $1,000 as deposits that they owe to their people. And they're gonna have assets, they're gonna have cash Of $1,000, right? So they have this $1000 in cash, but they owe it to somebody. It all belongs to someone else as a liability there. So, what is the money supply in this case? Right now? How much currency in circulation is there? There's none. Right? Everyone deposited their money in the bank and the bank is holding all 1000 as checkable deposits. So the currency in circulation is zero, and the deposits are now 1000. Cool. So let's go through a few definitions of Of related to these these reserves and how we're gonna start seeing the money supply multiply based on these deposits. So, the first system that we've seen so far is 100% reserve banking system, a system where all deposits are held as reserves. So in this case, the reserve ratio would be equal to one, right? one. When we, when we define the reserve ratio, we're talking about reserves over deposits. So, if everything is held, if everything is held as reserves, all $1000 that were deposited in the bank are being held as reserves. Well 1000 divided by 1000 gives us a reserve ratio of one, all 100% of deposits are held. But now we're going to get into a system of fractional reserve banking, a system where the bank holds only a fraction of deposits as reserves. So the rest of it, they're going to loan out. And this is going to be a system where a reserve ratio is less than one. Okay, It's gonna be some some number less than one where the reserves are less than the deposits. Right? So we're gonna have $1000 of deposits and say $600 of reserves. Right? That would be a 60% reserve ratio. 600 divided by 1000 something like that. So required reserves. These are reserves that a bank is legally required to hold. And this is based on some mandated reserve ratio from the government. The government's going to say, Hey, you have to keep 10% of your reserve of your deposits as reserves, whatever that might be. So, excess reserves are reserves held over the legal requirement. So if you hold more, if the legal requirements, 10%, but you're holding 20% as reserves, that's excess reserves. Everything above the legal requirement. Alright, so let's go ahead and pause here. And then we're gonna see how this reserve ratio, uh less than one. When we have a fractional system, how it affects the money supply. Cool. Let's do
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Fractional Reserve Banking
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Alright, so let's keep going with this example. And let's see how the fractional reserve system is going to increase the money supply. The government in clutch. Topia mandates that the banks must hold 10% of deposits in reserve. So the required reserves here are 10% right, This is the required reserve ratio, 10% of deposits. So first bank of clutch decides to loan all excess reserves to johnny clutch. Okay, so what's what's happening in this situation? They had $1000 of deposits, right? And they have to hold 10% of it. So times 10%,, There's gonna be $100, 1000 times 10% is $100 required reserves, right? They need to hold 10% of it just in case uh the people who deposited the money come to grab it, they'll have some money on hand now, the rest of it, they're gonna loan out. So, what's gonna happen here in their bank balance sheet? So if they're if they're holding 900 excuse me, 100 as reserves, 1000 minus 100 right, 1000 deposits minus 100 reserves. Well, that tells us that he loaned out our first Bank of clutch loaned The excess reserves of 900 to Johnny Clutch, right? It's his first bank of clutch, decides to loan all excess reserves to Johnny Clutch and that's going to be this 900, everything above that 10% ratio. So now let's go to first Banks um First bank's balance sheet again. So remember they had their liabilities, the liabilities are here on the right hand side, let me get out of the way, are on the right hand side. They had the $1000 of deposits that don't belong to them, right? These deposits, they owe to other people. If people came to get the money, they would owe them $1000. However, now their cash is no longer $1000 because they've loaned out 900 to johnny clutch. So they're only sitting on $100 in cash, right? Those reserves, and I'm gonna put that here as reserves. So, those reserves are cash that they're holding, right, that's the cash that they're holding related to those deposits. And then finally, we're going to think about um the loan. So the other 900 belongs to the bank, but they loaned it out to johnny clutch johnny clutch. Alright, so that loan of 900 is an asset of the bank as well. So here we go. We're still balanced out here where the $1000 of deposits is being reconciled here with the $100 in reserves and 900 as a loan? But now, what's happened to the money supply? What's our currency in circulation? And what's our deposits over here? So our deposits are still the $1000 right, $1000 has been deposited at clutch bank at the first bank of clutch. However, $900 is now in Johnny Clutches, hands as a loan. So Johnny Clutches sitting on $900 in cash, right? He received that as a loan of 900. So our money supply is now 1900 Right? Our money supply has increased to 1900 based on this lower required reserve ratio because the bank was able to take that, that extra reserves and loan it out to Johnny Clutch. So let's go ahead here on the next page. Let's continue this example. And let's see what johnny clutch here does with the money. So I'm coming back in here, johnny clutch buys his dream car a 1971 ford pinto from Fast Eddie. Fast Eddie deposits the money at second bank of clutch in his checking account. And second bank of clutch loans out there, excess reserves. So now we've got to banks and there's the money that johnny clutch had, The $900 has now been deposited by Fast Eddie. So now we're at 2nd bank. And now let's think about the deposits at second bank. So at second bank, they received the $900. Right, john johnny clutch bought his dream car for $900 for uh, the loan he got from first bank. So now the deposits at second bank, that Fast Eddie made our $900 right, $900. And what does it tell us? Second bank loans out their excess reserves. So second bank has taken their excess reserves and loan them out And they have the same reserve ratio, 900 times 10%. That's gonna give us $90 in reserves And the rest of it, 900 - the 90 Is going to be loaned out. $810 loaned out. Okay, so this is what's gonna happen here now, the $90 is gonna be the reserves that second bank is holding And $810 are being loaned out. So notice this time the loan got smaller because there's a smaller deposit, so it's gonna keep getting smaller and smaller as we go on, but it's still increasing our money supply. Because in the previous example, We had $1900 in the money supply, right? We had uh 1000 in so before we had $900 plus $1000 Right? We had 900 in circulation plus $1000. Well that 900 in circulation has now been deposited, right, johnny clutch paid it too fast. Eddie and fast. Eddie deposited it. So we've got 1900 in deposits now plus what second bank loaned out now. Second bank loaned out $810. So that $810 is in circulation now leading us to have an even bigger money supply, pull out my calculator. I'm not trying to do math in my head right now, 1900 plus 8 10 that comes out, 2 27 10, 2710. Did I Do that, right? Yeah, 1900 plus 8 10, 27 10 is the new money supply. So notice the money supply keeps growing as as these loans are happening, right? The loans that are going out are being deposited again and the new loans are being made. So that initial $1000 is being multiplied into several times into the money supply. So let's go through one more rotation of this with the third bank of clutch. So third bank of clutch receives the deposit from the second bank of clutch loans. So those loans that were made up here, the $810 that were loaned out. Well now third bank of clutch Is going to receive those $810 as deposits. Now of course, it doesn't always have to be a new bank. It could have gone back to the first bank, but I'm kind of trying to keep it separate so we can can see everything as it's moving. So $810 in deposits, that means they have to keep 10 $81 As their reserves and they're going to loan out the rest of it. So the 810 - the $81 in reserves, definitely not doing that one in my head right now. 8 10 minus 81 $729. They're gonna Loan out. So they're gonna loan $729. So $81 is their reserves and they're gonna loan the other $729. Okay, so now our money supply is again gonna grow by 7 29. Why? Because this 8 10 that was in circulation up here. This 8 10 was in circulation from this loan? Well, now it's been deposited here, so that's going to be included in our deposits. So, our deposits are now 27 10. That's the 1000 at the first bank. The 900 at the second bank. 810 at the third bank. That comes out to 2027 10 in deposits. And now they've made a loan and there's $729 in the hands of the people from these loans that they made. Okay, so what's our total money supply now? 7 29 plus 27 10 30 for 39. So, you can see that this process would continue and continue right. The next bank would receive that as a deposit the 729, and then loan out the their excess reserves and it would keep going and keep going as those and it would keep getting smaller as we've seen. Cool. So, let's pause here, and let's make a final conclusion about the deposit. The multiplier. We see from the deposits. And what happens with the money
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Required Reserves and the Deposit Multiplier
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Alright, so, let's go ahead and wrap up our example here and see what happens with the money multiplier. So, the money multiplier is the amount of money the bank generate for each dollar of deposits. So, every time there's a deposit, Well, they can loan out a portion of it because of the excess reserves and they keep getting more and more out of it. All right. So, what did we see in our example? We saw an initial deposit of $1000. Right? And then second bank of clutch. Well, they first bank of clutch held 10% of it and the other 90% went to second bank of clutch. Right? We saw the $1000. So, let me write the 1000. Actually, I'm gonna write them over here. 1000 and then second bank of clutch got 90% of it because 10% was held as reserves at first bank of clutch. The other 90% went to second bank of clutch. And then they loaned out that excess reserves. So the 900 Time 0.9 went to 3rd Bank of Clutch 810 and so on. 810 times 0.9 gave us the 7 29. And this would keep going. The 7 29 times 10%. Right? And then that times 10%. That times 10%. And there's a mathematical equation that we can use that we're not gonna get into the mathematical details about because we don't need to. But what it tells us is that it comes out to a total change Of $10,000. So that 1st $1,000 deposit gets multiplied 10 times. So how does the reserve ratio get involved in that? Because think about if the reserve ratio had been higher and they had to hold say 20% as deposits. Well, they wouldn't have been able to make such a big loan. Right? The second bank wouldn't have received $900, they would have received $800. And there would've been less of a multiplier. So the more reserves you have to hold, the less the multiplier is gonna be right because more reserves means there's less available to be loaned out and be multiplied. So the lower the reserve goes, the more we can get out of these loans. So the money multiplier ends up being save us the mathematical uh mumbo jumbo comes out to be one divided by the reserve ratio, easy as that. So in this case we had one divided by our reserve ratio of 10% 100.10 and that came out to be 10. So our initial deposit of $1000 Got multiplied 10 times to a total increase of $10,000. So our money supply would be $10,000 in this case, from that initial $1000 deposit. That's pretty crazy. Right? We started with just $1000 and through this series of loans and deposits, it came out to be worth $10,000 of money supply available. Okay, so just to reiterate here, we've got a reserve ratio right next to it. Reserve ratio is defined as the amount of reserves you hold divided by the deposits. Generally when you see a question, they're going to tell you the reserve ratio straight up, they'll tell you the reserve ratio is 10% 5% 20% whatever it might be. Okay, So there we go, the money multiplier is going to take one checkable deposit and turn it into a significant increase in the money supply. Alright, let's go ahead and move on to the next uh
