# The Money Multiplier

Instructor: Alex Tabarrok, George Mason University

When you deposit money into a bank, do you know what happens to it? It doesn’t simply sit there. Banks are actually allowed to loan out up to 90% of their deposits

When you deposit money into a bank, do you know what happens to it? It doesn’t simply sit there. Banks are actually allowed to loan out up to 90% of their deposits. For every \$10 that you deposit, only \$1 is required to stay put.

This practice is known as fractional reserve banking. Now, it’s fairly rare for a bank to only have 10% in reserves, and the number fluctuates. Since checkable deposits are part of the U.S. money supplies, fractional reserve banking, as you might have guessed, can have a big impact on these supplies.

This is where the money multiplier comes into play. The money multiplier itself is straightforward: it equals 1 divided by the reserve ratio. If reserves are at 10%, the minimum amount required by the Fed, then the money multiplier is 10. So if a bank has \$1 million in checkable deposits, it has \$10 million to work with for stuff like loans and reserves.

Now, typically, the money multiplier is more like 3, because banks can always hold more in reserves than the minimum 10%. When the money multiplier is higher, like during a boom, this gives the Fed more leverage to move M1 and M2 with a small change in reserves. But when the multiplier is lower, such as during a recession, the Fed has less leverage and must push harder to wield its indirect influence over M1 and M2.

Next up, we’ll take a closer look at how the Fed controls the money supply and how that has changed since the Great Recession.

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## Transcript

Now that we know how money is defined, we'll learn how banks can affect the supply of money through fractional reserve banking. Let's imagine that you graduate from college and your grandma gives you \$1,000 in cash -- that she's been saving under her mattress since the 1970s. And you deposit this cash in your checking account. What does the bank do with your money? Does it sit in a vault with your name on it? No.

Banks lend most of your money to people who want to borrow. Banks keep in reserve only a fraction of your money -- money they keep in cash for the ATM or to meet withdrawal demands. This is why this system is known as "fractional reserve banking." So what fraction of your deposit do banks keep in reserve? Well, large banks in the United States must keep in reserve at least \$1 for every \$10 in deposits. Or we say, large banks are required to have a reserve ratio of at least 10%. But banks often have higher reserve ratios depending upon how liquid that they want to be. If a bank is worried that its customers might withdraw most of their money or if bank loans are just not that profitable, banks will hold more reserves.

So, the reserve ratio can be greater than 10% and it can change over time. Because of fractional reserve banking, the banking system has a big effect on the supply of money. Let's see how. Suppose that your bank keeps 10% of your \$1,000 deposit, or \$100, as reserve. And suppose it lends out 90%, or \$900, say to Tyler, who's interested in starting a business. That \$900 loan is credited to Tyler's checking account. So now there's \$1,900 in new deposits. And since checkable deposits are part of the money supply, the money supply has increased. And it doesn't stop there.

Suppose that the bank holds 10% of Tyler's deposit in reserve and it lends out 90%, or \$810, say, to Janet. Now deposits have increased by \$2,710. And suppose that 10% of Janet's money is held in reserve and the rest is lent out. And so, this process continues. And as the banks make more loans -- that increases the number of deposits, which increases the number of loans, which increases the number of deposits.

So how much money do we ultimately end up with? You can figure that out using what's called the "money multiplier." The money multiplier tells us how many dollars' worth of deposits are created with each additional dollar of reserves. And the money multiplier is simple. It's just 1 divided by the reserve ratio. So, if the reserve ratio is 10%, the money multiplier is 1 divided by 0.1, or 10. And what that means is that \$1 in new reserves will ultimately lead, through the multiplier process, to \$10 in additional money, as measured by, say, M1 or M2.

Now let's clarify our previous example and why it was key that Grandma was pulling cash from under her mattress. If Grandma had instead given you a check for \$1,000, she'd simply be transferring money from her account to yours, which would not be creating new reserves -- and so we wouldn't see this multiplier effect. And, actually, the key player here isn't Grandma -- it's Uncle Sam. The Federal Reserve can, with the click of a computer button, create new money, new money, which it can use to buy financial assets, thus injecting new reserves into the banking system. But the Fed's control over the money-supply process is indirect. If banks hold the minimum amount of required reserves -- 10%, as we assumed earlier -- then the money multiplier will be close to 10. And if this is the case, the Fed will have a lot of leverage to move M1 and M2 with a small change in reserves.

But in normal circumstances, the actual money multiplier is closer to 3. How come? Well, remember, banks can't hold less than 10% in reserve. They can always hold more. And the more banks hold in reserve, the lower the money multiplier. So, it's important to understand that the money multiplier isn't a fixed number. And the multiplier process isn't a mechanical relation. Here's another factor. If Tyler had stashed some of his loan under his mattress instead of depositing it into a bank, then his bank -- it wouldn't have had the money to lend out his deposit, and the money multiplier would have been lower.

And during a recession, both of these things can happen at the same time. Banks may be reluctant to lend, and they'll maybe put more cash in reserve. Plus, people tend to hold more cash and not deposit their money in banks during a recession. Both of these factors cause the money multiplier to fall. So, the Federal Reserve may have to push harder to increase the money supply during a recession than during a boom.

We're going to dive further into how the Fed controls the money supply, and how that's changed since the Great Recession in our next video.