Required Reserves and the Deposit Multiplier: Videos & Practice Problems

Depositing money in a bank can significantly increase the money supply through the money multiplier effect. In a fractional reserve banking system, banks hold a fraction of deposits as reserves, allowing them to loan out the rest. The money multiplier is calculated as $1/r$, where r is the reserve ratio. A lower reserve ratio leads to a higher money multiplier, amplifying the initial deposit's impact on the overall money supply.

Bank Balance Sheet and Money Supply

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 say, under your mattress, can actually increase the money you supply by a multiple amount. So remember when we defined M1, we included the currency in circulation and checking account deposits. Right? That was a significant portion of M1, the currency in circulation, and the amount in checking deposits. So that's how we define the money supply.

So now we're going to think about it from the bank's perspective. We're going to 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 going to see is that when banks 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 $1,000, well, they're going to take that $1,000 and they're going to loan some of it out and they're going to keep some of it as reserves, just in case you go and make a withdrawal. And the rest of it, they're going to 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, in general, what they're going to 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 going to keep a fraction of their deposits as cash. Let's go ahead and go through this example and see how the money supply is affected by this reserve ratio.

So let's start here where Clutchtopia originally has no banks and the total amount of currency in circulation is equal to $1,000.

So what is the money supply in this case? The money supply is going to be the currency in circulation, the $1,000 plus 0 in banks. Right? The deposits are 0. So I'll say currency in circulation (cc) for a 1,000 and 0 in deposits. So there's a 1,000 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 $1,000 in the bank. They deposit all $1,000 in the bank.

So we're going to go through a bank's kind of balance here. So over here, we're going to have the assets of the bank, what they own, and the liabilities of the bank over here, what they owe. Right? So we're going to say, how much money they have in liabilities and how much they own. So generally, what we're going to see is that the liabilities when people deposit money into the bank, well, they're going to have deposits. These are liabilities that they have that they owe to the people who deposited. They're going to have $1,000 as deposits that they owe to their people and they're going to have assets. They're going to have cash of $1,000, right? So they have this $1,000 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 1,000 as checkable deposits. So the currency in circulation is 0 and the deposits are now 1,000. Cool?

So let's go through a few definitions related to these reserves and how we're going to start seeing the money supply multiply based on these deposits.

The first system that we've seen so far is a 100% Reserve Banking System. A system where all deposits are held as reserves. So in this case, the reserve ratio would be equal to 1. Right? 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 $1,000 that were deposited in the bank are being held as reserves. Well, a 1,000 divided by a 1,000 gives us a reserve ratio of 1. 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 1. Okay? It's going to be some number less than 1 where the reserves are less than the deposits. Right? So we're going to have $1,000 of deposits and say $600 of reserves. Right?

That would be a 60% reserve ratio, 600 divided by 1,000, 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 is going to say: Hey, you have to keep 10% 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 requirement is 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 going to see how this reserve ratio, less than 1 when we have a fractional system, how it affects the money supply. Cool? Let's do

Required Reserves and the Deposit Multiplier

Alright. So let's go ahead and wrap up our example here and see what happens with the money multiplier. The money multiplier is the amount of money the bank generates 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. Alright? So what did we see in our example? We saw an initial deposit of $1,000. Right? And then 2nd Bank of Clutch, well, they 1st Bank of Clutch held 10% of it, and the other 90% went to 2nd Bank of Clutch. Right? We saw the $1,000. So let me write the 1,000, actually. I'm gonna write them over here. 1,000 and then 2nd Bank of Clutch got 90% of it because 10% was held as reserves at 1st Bank of Clutch. The other 90% went to Second Bank of Clutch, and then they loaned out those excess reserves. So the 900 times 0.9 went to 3rd Bank of Clutch, 810 and so on. 810 times 0.9 gave us 729, and this would keep going. The 729 times 10%, right? And then that times 10%, that times 10%.

M S = 1 r

And there's a mathematical equation that we can use, that we're not going to get into the mathematical details. A $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 have been less of a multiplier. So the more reserves you have to hold, the less the multiplier is going to be, right? Because more reserves mean there's less available to be loaned out and 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 mumbo jumbo, it comes out to be 1 divided by the reserve ratio. Easy as that. So in this case, we had 1 divided by our reserve ratio of 10% or 0.10, and that came out to be 10. So our initial deposit of $1,000 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 $1,000 deposit. That's pretty crazy, right? We started with just $1,000 and through the 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. The 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.

Here’s what students ask on this topic:

What is the money multiplier and how is it calculated?

The money multiplier is the amount of money that banks generate with each dollar of reserves. It is calculated using the formula:

$\frac{1}{r}$

where r is the reserve ratio. For example, if the reserve ratio is 10% (or 0.10), the money multiplier would be:

$\frac{1}{0.10}=\; 10$

This means that an initial deposit of $1,000 can increase the money supply by $10,000 through the process of loans and deposits.

How does the reserve ratio affect the money supply?

The reserve ratio directly impacts the money supply through the money multiplier effect. A lower reserve ratio allows banks to loan out a larger portion of deposits, leading to a higher money multiplier. Conversely, a higher reserve ratio means banks must hold more reserves, reducing the amount available for loans and thus decreasing the money multiplier. For example, with a reserve ratio of 10% (0.10), the money multiplier is 10, but if the reserve ratio is 20% (0.20), the money multiplier drops to 5.

What are required reserves and excess reserves?

Required reserves are the minimum amount of reserves that a bank is legally required to hold, as mandated by the government. This is based on a specified reserve ratio. Excess reserves are any reserves held by the bank over and above the required minimum. For example, if the reserve ratio is 10% and a bank has $1,000 in deposits, it must hold $100 as required reserves. If the bank holds $200 in reserves, the additional $100 is considered excess reserves.

What is fractional reserve banking?

Fractional reserve banking is a system in which banks hold only a fraction of their deposits as reserves and loan out the rest. This system allows banks to create money through the lending process. For example, if a bank receives a $1,000 deposit and the reserve ratio is 10%, it must hold $100 in reserves but can loan out $900. This $900 can then be deposited in another bank, which will hold 10% ($90) in reserves and loan out $810, continuing the cycle and increasing the money supply.

How does the money supply increase through the deposit multiplier effect?

The money supply increases through the deposit multiplier effect when banks loan out a portion of deposits, which are then redeposited and loaned out again. This process continues, multiplying the initial deposit. For example, with a reserve ratio of 10%, an initial deposit of $1,000 can lead to a total increase in the money supply of $10,000. This is because each round of deposits and loans adds more money to the economy, as calculated by the money multiplier formula:

$\frac{1}{r}$

where r is the reserve ratio.