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Lesson summary: banking and the expansion of the money supply

In this lesson summary review and remind yourself of the key terms and calculations related to fractional reserve banking, required reserves, excess reserves, and the money multiplier.


Money is created when the government prints it, right? That’s only partially true because banks create money too. Banks don’t literally print their own currency (save for a few banks in Scotland, who do just that). So how does a bank “create” money?
Recall that the narrowest definition of the money supply is M1, which includes money in circulation (not held in a bank) and demand deposits held inside banks. In the United States, less than half of M1 is in the form of currency—much of the rest of M1 is in the form of bank accounts.
Every time a dollar is deposited into a bank account, a bank’s total reserves increases. The bank will keep some of it on hand as required reserves, but it will loan the excess reserves out. When that loan is made, it increases the money supply.
This is how banks “create” money and increase the money supply. When a bank makes loans out of excess reserves, the money supply increases. We can predict the maximum change in the money supply with the money multiplier.

Kluczowe terminy

Key termDefinition
Bank(sometimes called a commercial bank) A financial institution that accepts deposits and makes loans; banks are sometimes referred to as “depository institutions.”
Central bank(sometimes called a reserve bank or banking authority) an institution that manages a country’s money supply and monetary policy
Financial intermediarya middle-person in a financial transaction; a bank is an intermediary that coordinates borrowing and lending by combining the deposits of many agents into loans.
Assetssomething of value to the agent that holds it; a bank’s assets include real assets owned by the bank (such as a building), the money they hold, and financial assets such as bonds and loans.
Liabilitiesobligations to pay back; to a bank, your savings account is a liability because you might show up one day and want the money you deposited back.
Fractional reservesthe practice of keeping a percentage of deposits on hand but loaning out the rest
Reserve requirementa legal obligation to keep a minimum amount of reserves; if the reserve requirement is 20, percent and you deposit dollar sign, 100 in a bank, the bank must keep dollar sign, 20 of that in its vaults, but it can loan out the rest.
Excess reservesthe remainder of the deposited money that banks are not required to keep on hand; banks can make loans out of excess reserves or choose to keep excess reserves in their vaults.
Fully loaned outa situation in which a bank has only required reserves and keeps no excess reserves; when a bank is fully loaned out it cannot make any additional loans.
T-accounta tool for describing the financial position of a business by showing assets (on the left) and liabilities (on the right) in a table; each side of the table must equal the other side.
Money multiplierthe ratio of the money supply to the monetary base (money in bank vaults and money in circulation); the money multiplier tells us how many additional dollars will be created with each addition to the monetary base, such as when there is a dollar sign, 1 increase in a bank’s reserves.

Key Takeaways

Assets and Liabilities

Banks, like any other business, need to keep track of their assets and liabilities. T-accounts are tables that banks use to keep track of assets and liabilities.
Let’s create a T-account for a bank that has just opened for business, First Bank of Pulitzer. Nobody has deposited any money yet, so other than its obligations to the bank owners and the real assets that the bank has (like the bank building itself), the bank’s T-account is empty:
dollar sign, 0dollar sign, 0
Now suppose you win dollar sign, 100 in a poetry writing competition. Congratulations! You deposit your winnings in a First Bank of Pulitzer checking account. That deposit creates two entries on the bank’s balance sheet. The dollar sign, 100 in cash creates an entry on the asset side because the money is an asset for the bank (because they can put that money to use by loaning it out). But, the bank must give you back that money as well. That obligation is a liability, so there is a dollar sign, 100 entry on the liabilities side as well.
The bank’s balance sheet now looks like this:
Cash dollar sign, 100dollar sign, 100 Your Deposit

Fractional reserve banking

Banks are more than just a vault to keep money in. If banks just acted as a storage facility for money, that wouldn’t be a very profitable business. The dollar sign, 100 you deposited from your groundbreaking verses will be used to make loans. Banks profit from making loans by charging interest.
But the new First Bank of Pulitzer has a problem. They want to make loans (because that is how they earn a profit). But at some point, they also need to pay back the money that people have deposited into the bank. This is where reserves come in.
Reserves are the amount of money that banks keep in vaults, and they are a fraction of all deposits made. In most countries, banks are heavily regulated and are required to keep a minimum percentage of all deposits, just in case someone wants to withdraw some money. This minimum percent is the reserve requirement.
For example, suppose the reserve requirement is 20, percent. The bank would need to keep dollar sign, 20 of your dollar sign, 100 on hand. We can break this down in our T-account:
Required reserves dollar sign, 20dollar sign, 100 Your Deposit
The rest of the cash dollar sign, 80

Excess reserves allow expansion of the money supply

To understand how banks create money, let’s take a step back. What if that poetry competition money was the only money that existed in the economy. Before you deposit the money in the bank, let’s calculate the money supply:
M1=currency in circulation+deposits=$100+$0\begin{aligned} M1&=\text{currency in circulation} + \text{deposits}\\\\ &=\$100 + \$0\end{aligned}
Once you deposit your money in the bank, M1 doesn’t change; only the composition of the money supply changes:
M, 1, equals, dollar sign, 0, plus, dollar sign, 100
How does the First Bank of Pulitzer bank create more money out of this dollar sign, 100? Our bank now has dollar sign, 80 just sitting around. This is the bank’s excess reserves - the extra money beyond what they must keep in required reserves. The bank can do one of two things with that money:
  • Keep it in the bank (just in case you want to withdraw more than dollar sign, 20)
  • Loan it out
In the real world, your deposit wouldn’t be the only deposit in the bank. Usually, only a small number of people want to withdraw their money on a given day. So, the bank might want to loan out that money to earn a profit.
Now, suppose Sylvia shows up at the bank and wants to borrow dollar sign, 50. Let’s see how the bank’s loan to Sylvia impacts their T-account and the money supply:
Required reserves dollar sign, 20dollar sign, 100 Your Deposit
Loan to Sylvia dollar sign, 50
Excess reserves dollar sign, 30
M1 has changed as well. Remember, your dollar sign, 100 deposit is still your money. If you check your account balance, it still says you have dollar sign, 100. But Sylvia now has dollar sign, 50 in cash in her pocket, too:
M1=cash in circulation+deposits=$50+$100=$150\begin{aligned} M1 &= \text{cash in circulation} + \text{deposits}\\\\ &=\$50 + \$100\\\\ &=\$150\end{aligned}
By loaning out from excess reserves, the bank has added to the money supply.

The money multiplier determines the size of the expansion

Banks can’t create an unlimited amount of money. The money multiplier determines the limit of how much money a bank can create. The money multiplier is how much the money supply will change if there is a change in the monetary base.
There are several reasons that the actual increase in the money supply will be smaller than the simple money multiplier predicts, including: People decide not to deposit money into banks, so money “leaks” out of the banking system Banks decide not to loan out everything and keep some excess reserves

Key equations

The money multiplier

The money multiplier determines the maximum expansion of the money supply that will occur when new money is introduced into the banking system. If you know the size of the reserve requirement, you can use this to figure out the largest change in the money supply that is possible if the central bank creates new money. The money multiplier (M, M) is calculated as follows:
MM=1rr,whereMM=money multiplierrr=reserve requirement\begin{aligned}MM&=\dfrac{1}{rr}, \text{where}\\\\ MM & = \text{money multiplier}\\\\ rr &= \text{reserve requirement}\end{aligned}
For example, if the reserve requirement is 25%, the money multiplier is 4:
MM=1rr=10.25=4\begin{aligned}MM&=\dfrac{1}{rr}\\\\ &=\dfrac{1}{0.25}\\\\ &=4\end{aligned}
So, if I know that the money multiplier is 4, then if the central bank creates dollar sign, 100 in money, the money supply will increase by dollar sign, 400 at most.
In reality, however, the money multiplier is more complicated than this, which is why it is sometimes called the simple money multiplier. The simple money multiplier assumes that:
  • Banks never keep any excess reserves, and
  • People keep all money in banks (in other words, if you get dollar sign, 20, you immediately deposit it).
Now suppose instead that you know the actual change in the money supply from a change in the monetary base. With this information, you can find the actual money multiplier, rather than the theoretical maximum change. To find the actual money multiplier, you divide the money supply by the monetary base:
A, M, M, equals, start fraction, M, S, divided by, M, B, end fraction
AMM=actual money multiplierMS=money supplyMB=monetary base\begin{aligned}AMM &= \text{actual money multiplier}\\\\ MS &= \text{money supply}\\\\ MB&= \text{monetary base}\end{aligned}
For example, if M1 is dollar sign, 100 million, and there is dollar sign, 40 million in circulation and dollar sign, 10 million in reserves at banks, then the actual money multiplier is:
AMM=$100($40+$10)=$100$50=2\begin{aligned}AMM &= \dfrac{\$100}{(\$40+\$10)}\\\\ &=\dfrac{\$100}{\$50}\\\\ &=2\end{aligned}
In this case, the more realistic money multiplier is only 2, rather than the simple money multiplier that is predicted using the reserve requirement.

The maximum predicted change in the money supply from an increase in the monetary base

start text, T, o, t, a, l, space, c, h, a, n, g, e, space, i, n, space, end text, M, S, equals, start text, c, h, a, n, g, e, space, i, n, space, end text, M, B, times, M, M
For example, suppose the First Bank of Pulitzer bank buys a bond from Langston for dollar sign, 200. They deposit dollar sign, 200 into his bank account. The reserve requirement is 25, percent. If there are no leakages from the banking system (banks fully loan out, and everyone keeps all of their money in the bank), the maximum total change in the money supply from the central bank buying a bond is
Maximum total change in MS=change in MB×MM=$200×4=$800\begin{aligned}\text{Maximum total change in } MS & = \text{change in }MB \times MM\\\\ &= \$200 \times 4\\\\ &=\$800\end{aligned}

Calculating excess reserves

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For example, if Maya deposits dollar sign, 4000 into the bank, and the reserve requirement is 10%, the bank must keep dollar sign, 400 in reserves but has excess reserves of
Excess reserves=$4000($4000×10%)=$4000$400=$3600\begin{aligned} \text{Excess reserves} &= \$4000 - (\$4000\times 10\%)\\\\ &=\$4000 - \$400\\\\ &= \$3600\end{aligned}

Maximum new loans possible from a deposit

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For example, if the money multiplier is 4, banks fully loan out, and all money is deposited into banks, then the total amount of new loans that can be made from Maya’s deposit is
left parenthesis, dollar sign, 4000, minus, dollar sign, 400, right parenthesis, times, 4, equals, dollar sign, 14, comma, 400

Częste błędne wyobrażenia

  • Some learners get confused about what the simple money multiplier represents. The simple multiplier start fraction, 1, divided by, r, r, end fraction is the maximum change in the money supply. In all probability, the final increase in the money supply will be far smaller due to leakages from the financial system.
  • Printing money and creating money is not the same thing. Printing money creates currency, but the amount of money that exists at any point in time (in other words, the money supply) is cash and deposits. The pivotal moment in the creation of money is lending: when loans are made, money is created.
  • It might seem strange that a bank account is a liability. To you, the owner of the account, the account is an asset. But to the bank, who has to return that money to you on demand, it is a liability.
  • As a new learner, it might be confusing about which stage in this process creates money. It is the loan. If a bank does not loan out from a deposit, no new money is created.

Discussion questions

Question 1

There is currently dollar sign, 100, comma, 000 in circulation outside of banks in the nation of Rhyme. The following is a simplified balance sheet for the Bank of Rhyme. However, some of the data on the balance sheet is missing.
Required reserves dollar sign, 20, comma, 000Demand deposits dollar sign, 200, comma, 000
Excess reserves dollar sign, 50, comma, 000
Loans dollar sign _
Assume that this bank has no assets other than cash and loans.
  1. What is the value of the loans that this bank has made? Explain how you know this.
  2. What is the reserve requirement?
  3. If Ted withdraws dollar sign, 10, comma, 000 from his checking account at the Bank of Rhyme:
    a. What is the initial effect of the withdrawal on M1?
    b. What effect will this have on the bank’s total reserves, required reserves, and excess reserves?

Question 2

The balance sheet for The First Bank of Pulitzer is shown below. Assume the reserve requirement is 5%.
Total reserves dollar sign, 35, comma, 000Demand deposits dollar sign, 500, comma, 000
Home loans dollar sign, 445, comma, 000
Government bonds dollar sign, 20, comma, 000
a. What is the total amount of new loans that this bank can make? Explain.
b. Now, suppose that the First Bank of Pulitzer, and all other banks in the financial system, loan out all excess reserves. Calculate the maximum total change in deposits throughout the banking system. Show all work.
c. Assume that there are no leakages from the financial system. What will be the change in total reserves throughout the banking system? Explain.
d. Suppose the central bank in this country buys dollar sign, 5, comma, 000 of the government bonds from The First Bank of Pulitzer. Will the money supply increase, decrease, or stay the same? Explain.

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