Without banks, there would be no checkable deposits, and so the quantity of currency in circulation would equal the money supply. In that case, the money supply would be determined solely by whoever controls government minting and printing presses. But banks do exist, and through their creation of checkable bank deposits, they affect the money supply in two ways. First, banks remove some currency from circulation: dollar bills that are sitting in bank vaults, as opposed to sitting in people’s wallets, aren’t part of the money supply. Second, and much more importantly, banks create money by accepting deposits and making loans—that is, they make the money supply larger than just the value of currency in circulation. Our next topic is how banks create money and what determines the amount of money they create.

To see how banks create money, let’s examine what happens when someone decides to deposit currency in a bank. Consider the example of Silas, a miser, who keeps a shoebox full of cash under his bed. Suppose Silas realizes that it would be safer, as well as more convenient, to deposit that cash in the bank and to use his debit card when shopping. Assume that he deposits $1,000 into a checkable account at First Street Bank. What effect will Silas’s actions have on the money supply?

Panel (a) of Figure 25.3 shows the initial effect of his deposit. First Street Bank credits Silas with $1,000 in his account, so the economy’s checkable bank deposits rise by $1,000. Meanwhile, Silas’s cash goes into the vault, raising First Street’s reserves by $1,000 as well.

This initial transaction has no effect on the money supply. Currency in circulation, part of the money supply, falls by $1,000; checkable bank deposits, also part of the money supply, rise by the same amount.

But this is not the end of the story because First Street Bank can now lend out part of Silas’s deposit. Assume that it holds 10% of Silas’s deposit—$100—in reserves and lends the rest out in cash to Silas’s neighbor, Mary. The effect of this second stage is shown in panel (b) of Figure 25.3. First Street’s deposits remain unchanged, and so does the value of its assets. But the composition of its assets changes: by making the loan, it reduces its reserves by $900, so that they are only $100 larger than they were before Silas made his deposit. In the place of the $900 reduction in reserves, the bank has acquired an IOU, its $900 cash loan to Mary. So by putting $900 of Silas’s cash back into circulation by lending it to Mary, First Street Bank has, in fact, increased the money supply. That is, the sum of currency in circulation and checkable bank deposits has risen by $900 compared to what it had been when Silas’s cash was still under his bed. Although Silas is still the owner of $1,000, now in the form of a checkable deposit, Mary has the use of $900 in cash from her borrowings.

This may not be the end of the story either. Suppose that Mary uses her cash to buy a television and a Blu-ray player from Acme Merchandise. What does Anne Acme, the store’s owner, do with the cash? If she holds on to it, the money supply doesn’t increase any further. But suppose she deposits the $900 into a checkable bank deposit—say, at Second Street Bank. Second Street Bank, in turn, will keep only part of that deposit in reserves, lending out the rest, creating still more money.

Assume that Second Street Bank, like First Street Bank, keeps 10% of any bank deposit in reserves and lends out the rest. Then it will keep $90 in reserves and lend out $810 of Anne’s deposit to another borrower, further increasing the money supply.

Table 25.1 shows the process of money creation we have described so far. At first the money supply consists only of Silas’s $1,000. After he deposits the cash into a checkable bank deposit and the bank makes a loan, the money supply rises to $1,900. After the second deposit and the second loan, the money supply rises to $2,710. And the process will, of course, continue from there. (Although we have considered the case in which Silas places his cash in a checkable bank deposit, the results would be the same if he put it into any type of near-money.)

This process of money creation may sound familiar. Recall the spending multiplier process that we described in Module 16: an initial increase in spending leads to a rise in real GDP, which leads to a further rise in spending, which leads to a further rise in real GDP, and so on. What we have here is another kind of multiplier—the money multiplier. Next, we’ll learn what determines the size of this multiplier.

In tracing out the effect of Silas’s deposit in Table 25.1, we assumed that the funds a bank lends out always end up being deposited either in the same bank or in another bank—so funds disbursed as loans come back to the banking system, even if not to the lending bank itself. In reality, some of these loaned funds may be held by borrowers in their wallets and not deposited in a bank, meaning that some of the loaned amount “leaks” out of the banking system. Such leaks reduce the size of the money multiplier, just as leaks of real income into savings reduce the size of the real GDP multiplier. (Bear in mind, however, that the “leak” here comes from the fact that borrowers keep some of their funds in currency, rather than the fact that consumers save some of their income.) But let’s set that complication aside for a moment and consider how the money supply is determined in a “checkable-deposits-only” monetary system, in which funds are always deposited in bank accounts and none are held in wallets as currency. That is, in our checkable-deposits-only monetary system, any and all funds borrowed from a bank are immediately deposited into a checkable bank account. We’ll assume that banks are required to satisfy a minimum reserve ratio of 10% and that every bank lends out all of its excess reserves, reserves over and above the amount needed to satisfy the minimum reserve ratio.

Now suppose that for some reason a bank suddenly finds itself with $1,000 in excess reserves. What happens? The answer is that the bank will lend out that $1,000, which will end up as a checkable bank deposit somewhere in the banking system, launching a money multiplier process very similar to the process shown in Table 25.1. In the first stage, the bank lends out its excess reserves of $1,000, which becomes a checkable bank deposit somewhere. The bank that receives the $1,000 deposit keeps 10%, or $100, as reserves and lends out the remaining 90%, or $900, which again becomes a checkable bank deposit somewhere. The bank receiving this $900 deposit again keeps 10%, which is $90, as reserves and lends out the remaining $810. The bank receiving this $810 keeps $81 in reserves and lends out the remaining $729, and so on. As a result of this process, the total increase in checkable bank deposits is equal to a sum that looks like:

$1,000 + $900 + $810 + $729 + . . .

We’ll use the symbol rr for the reserve ratio. More generally, the total increase in checkable bank deposits that is generated when a bank lends out $1,000 in excess reserves is:

(25-1) $1,000 + $1,000 × (1 − rr) + $1,000 × (1 − rr)² + $1,000 × (1 − rr)³ + . . .

As we have seen, an infinite series of this form can be simplified to $1,000/rr. We must introduce another term before formally defining the money multiplier, but we can now see its usefulness: it is the factor by which we multiply an initial increase in excess reserves to find the total resulting increase in checkable bank deposits:

Given a reserve ratio of 10%, or 0.1, a $1,000 increase in excess reserves will increase the total value of checkable bank deposits by $1,000 × 1/rr = $1,000/0.1 = $10,000. In fact, in a checkable-deposits-only monetary system, the total value of checkable bank deposits will be equal to the value of bank reserves divided by the reserve ratio. Or to put it a different way, if the reserve ratio is 10%, each $1 of reserves held by a bank supports $1/rr = $1/0.1 = $10 of checkable bank deposits.

In reality, the determination of the money supply is more complicated than our simple model suggests because it depends not only on the ratio of reserves to bank deposits but also on the fraction of the money supply that individuals choose to hold in the form of currency. In fact, we already saw this in our example of Silas depositing the cash instead of holding it under his bed: when he chose to hold a checkable bank deposit instead of currency, he set in motion an increase in the money supply.

To define the money multiplier in practice, we need to understand that the Federal Reserve controls the monetary base, the sum of currency in circulation and the reserves held by banks. The Federal Reserve does not determine how that sum is allocated between bank reserves and currency in circulation. Consider Silas and his deposit one more time: by taking the cash from under his bed and depositing it in a bank, he reduced the quantity of currency in circulation but increased bank reserves by an equal amount. So while the allocation of the monetary base changes—the amount in reserves grows and the amount in circulation shrinks—the total of these two, the monetary base, remains unchanged.

The monetary base is different from the money supply in two ways. First, bank reserves, which are part of the monetary base, aren’t considered part of the money supply. A $1 bill in someone’s wallet is considered money because it’s available for an individual to spend, but a $1 bill held as bank reserves in a bank vault or deposited at the Federal Reserve isn’t considered part of the money supply because it’s not available for spending. Second, checkable bank deposits, which are part of the money supply because they are available for spending, aren’t part of the monetary base.

Figure 25.4 shows the two concepts schematically. The circle on the left represents the monetary base, consisting of bank reserves plus currency in circulation. The circle on the right represents the money supply, consisting mainly of currency in circulation plus checkable or near-checkable bank deposits. As the figure indicates, currency in circulation is part of both the monetary base and the money supply. But bank reserves aren’t part of the money supply, and checkable or near-checkable bank deposits aren’t part of the monetary base. In normal times, most of the monetary base actually consists of currency in circulation, which also makes up about half of the money supply.

Now we can formally define the money multiplier: it’s the ratio of the money supply to the monetary base. Most importantly, this tells us the total number of dollars created in the banking system by each $1 addition to the monetary base. We have seen that in a simple situation in which banks hold no excess reserves and all cash is deposited in banks, the money multiplier is 1/rr. So if the reserve requirement is 0.1 (the minimum required ratio for most checkable deposits in the United States), the money multiplier is 1/0.1 = 10; if the Federal Reserve adds $100 to the monetary base, the money supply will increase by 10 × $100 = $1,000. During normal times, the actual money multiplier in the United States, using M1 as our measure of money, is about 1.9. That’s a lot smaller than 10. Normally, the reason the actual money multiplier is so small arises from the fact that people hold significant amounts of cash, and a dollar of currency in circulation, unlike a dollar in reserves, doesn’t support multiple dollars of the money supply. In fact, currency in circulation normally accounts for more than 90% of the monetary base.