Hi. Say a person deposits $100,000 into his checking accounts at a bank. Can we use this and multiply by the MM to get total change in M1? Or this will not change money supply as in question 1, part 3a. Thanks.

As stated in the article, no money is created or destroyed when money is withdrawn from or deposited in a bank. Thus, when a person deposits $100,000 into his checking accounts, there will be no change in M1. M1 will be changed if loan is made. Before that, no new money is created.

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Course: AP®︎/College Macroeconomics > Unit 4

Lesson 4: Banking and the expansion of the money supply

Lesson summary: banking and the expansion of the money supply

Google Classroom

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.

Lesson Summary

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.

Key Terms

Key term	Definition
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 intermediary	a 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.
Assets	something 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.
Liabilities	obligations 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 reserves	the practice of keeping a percentage of deposits on hand but loaning out the rest
Reserve requirement	a legal obligation to keep a minimum amount of reserves; if the reserve requirement is $20 %$ ‍ and you deposit $$ 100$ ‍ in a bank, the bank must keep $$ 20$ ‍ of that in its vaults, but it can loan out the rest.
Excess reserves	the 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 out	a 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-account	a 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 multiplier	the 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 $$ 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:

Assets	Liabilities
$$ 0$ ‍	$$ 0$ ‍

Now suppose you win

$ 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

$ 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

$ 100

entry on the liabilities side as well.

The bank’s balance sheet now looks like this:

Assets	Liabilities
Cash $$ 100$ ‍	$$ 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

$ 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 %

. The bank would need to keep

$ 20

of your

$ 100

on hand. We can break this down in our T-account:

Assets	Liabilities
Required reserves $$ 20$ ‍	$$ 100$ ‍ Your Deposit
The rest of the cash $$ 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:

\begin{aligned} M 1 & = currency in circulation + 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 = $ 0 + $ 100

How does the First Bank of Pulitzer bank create more money out of this

$ 100

? Our bank now has

$ 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 $$ 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

$ 50

. Let’s see how the bank’s loan to Sylvia impacts their T-account and the money supply:

Assets	Liabilities
Required reserves $$ 20$ ‍	$$ 100$ ‍ Your Deposit
Loan to Sylvia $$ 50$ ‍
Excess reserves $$ 30$ ‍

M1 has changed as well. Remember, your

$ 100

deposit is still your money. If you check your account balance, it still says you have

$ 100

. But Sylvia now has

$ 50

in cash in her pocket, too:

\begin{aligned} M 1 & = cash in circulation + 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

Sure! Let’s take another look at the bank. Right now, they still have

$ 30

sitting around. Suppose they lend that out to Ted. Now, the bank’s T-account looks like this:

Assets	Liabilities
Required reserves $$ 20$ ‍	$$ 100$ ‍ Your Deposit
Loan to Sylvia $$ 50$ ‍
Loan to Ted $$ 30$ ‍

What impact does that have on the money supply? Well, now Ted also has some money in his pocket:

\begin{aligned} M 1 & = cash in circulation + deposits \\ = ($ 50 + $ 30) + $ 100 \\ = $ 180 \end{aligned}

Sylvia and Ted take the money they borrowed and decide to take a trip to Seamus’s House of Donuts and spend their combined

$ 80

on chocolate donuts. Seamus takes that money and deposits it into the bank. Now the bank has

$ 80

in its vaults (an asset) and a new liability (the money the bank owes Seamus). We can note these changes in the bank’s T-account:

Assets	Liabilities
Required reserves $$ 20$ ‍	$$ 100$ ‍ Your Deposit
Loan to Sylvia $$ 50$ ‍	$$ 80$ ‍ Seamus's deposit
Loan to Ted $$ 30$ ‍
Cash $$ 80$ ‍

We can also track the changes in the money supply:

\begin{aligned} M 1 & = cash in circulation + deposits \\ = $ 0 + $ 180 \\ = $ 180 \end{aligned}

Notice that the money supply hasn’t changed. But, the bank must keep

20 %

of that

$ 80

on hand. So it stores

$ 16

(

20 %

$ 80

) and has

$ 64

in excess reserves. Gwendolyn borrows that money to spend on writing journals. When the loan is issued, the money supply increases again:

\begin{aligned} M 1 & = cash in circulation + deposits \\ = $ 64 + $ 180 \\ = $ 244 \end{aligned}

Each time money is deposited, the reserve requirement (rr) is kept, but the rest can be loaned out.

$ 100 + $ 80 + $ 64 + . . . = $ 100 + $ 100 (1 - r r) + $ 100 (1 - r r)^{2} + . . .

As we have seen before with other multipliers (like the expenditure multiplier and tax multiplier), this kind of expansion can be simplified to

Total increase in money supply = $ 100 \times \frac{1}{r r}

So, if the bank never keeps any excess reserves on hand, and all money is always deposited into banks, your

$ 100

prize will turn into a money supply of

$ 500

$ 100 \times \frac{1}{0.2} = $ 500

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:

\begin{aligned} M M & = \frac{1}{r r}, where \\ M M & = money multiplier \\ r r & = reserve requirement \end{aligned}

For example, if the reserve requirement is 25%, the money multiplier is

4

\begin{aligned} M M & = \frac{1}{r r} \\ = \frac{1}{0.25} \\ = 4 \end{aligned}

So, if I know that the money multiplier is

4

, then if the central bank creates

$ 100

in money, the money supply will increase by

$ 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 $$ 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 = \frac{M S}{M B}

Where:

\begin{aligned} A M M & = actual money multiplier \\ M S & = money supply \\ M B & = monetary base \end{aligned}

For example, if M1 is

$ 100

million, and there is

$ 40

million in circulation and

$ 10

million in reserves at banks, then the actual money multiplier is:

\begin{aligned} A M M & = \frac{$ 100}{($ 40 + $ 10)} \\ = \frac{$ 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

Total change in M S = change in M B \times M M

For example, suppose the First Bank of Pulitzer bank buys a bond from Langston for

$ 200

. They deposit

$ 200

into his bank account. The reserve requirement is

25 %

. 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

\begin{aligned} Maximum total change in M S & = change in M B \times M M \\ = $ 200 \times 4 \\ = $ 800 \end{aligned}

Calculating excess reserves

Excess reserves = Deposits - (Deposits \times reserve requirement)

For example, if Maya deposits

$ 4000

into the bank, and the reserve requirement is 10%, the bank must keep

$ 400

in reserves but has excess reserves of

\begin{aligned} Excess reserves & = $ 4000 - ($ 4000 \times 10 %) \\ = $ 4000 - $ 400 \\ = $ 3600 \end{aligned}

Maximum new loans possible from a deposit

Maximum increase in loans = (Deposit - reserves) \times Money multiplier

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

($ 4000 - $ 400) \times 4 = $ 14, 400

Common Misperceptions

Some learners get confused about what the simple money multiplier represents. The simple multiplier $\frac{1}{r r}$ ‍ 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

$ 100,000

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.

Assets	Liabilities
Required reserves $$ 20,000$ ‍	Demand deposits $$ 200,000$ ‍
Excess reserves $$ 50,000$ ‍
Loans $$$ ‍ _

Assume that this bank has no assets other than cash and loans.

What is the value of the loans that this bank has made? Explain how you know this.
What is the reserve requirement?
If Ted withdraws $$ 10,000$ ‍ 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?

The bank has $$ 130,000$ ‍ in loans outstanding. The asset and liabilities sides must equal each other on the balance sheet. Required reserves and excess reserves are worth $$ 70,000$ ‍ total, so:

$ 200,000 - $ 70,000 = $ 130,000

The reserve requirement is $10 %$ ‍. From the equation to calculate the amount of reserves required:

\begin{aligned} Deposits \times reserve requirement & = required reserves \\ $ 200,000 \times r r & = $ 20,000 \\ r r & = \frac{$ 20,000}{$ 200,000} \\ r r & = 10 % \end{aligned}

3a. M1 will not change. Before the withdrawal:

\begin{aligned} M 1 & = cash in circulation + demand deposits \\ M 1 & = $ 100,000 + $ 200,000 \end{aligned}

After the withdrawal:

M 1 = $ 110,000 + $ 190,000

Only the composition of the money supply changes, not the quantity of money. No money is created or destroyed when money is withdrawn from or deposited in a bank

3b. Before the withdrawal, the bank has

$ 70, 000

in total reserves:

$ 20,000 (required) + $ 50,000 (excess)

When he withdraws

$ 10,000

, total reserves decrease by

$ 10,000

$ 60,000

. The bank only needs

$ 19,000

in reserves, so excess reserves are:

$ 60, 000 - $ 19, 000 = $ 41, 000

Question 2

The balance sheet for The First Bank of Pulitzer is shown below. Assume the reserve requirement is 5%.

Assets	Liabilities
Total reserves $$ 35,000$ ‍	Demand deposits $$ 500,000$ ‍
Home loans $$ 445,000$ ‍
Government bonds $$ 20,000$ ‍

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

$ 5, 000

of the government bonds from The First Bank of Pulitzer. Will the money supply increase, decrease, or stay the same? Explain.

a. This bank can make

$ 10,000

in additional loans. The required reserves for

$ 500,000

are:

.05 \times $ 500, 000 = $ 25, 000

They have

$ 35,000

in total reserves, so excess reserves are:

\begin{aligned} = $ 35,000 - $ 25,000 \\ = $ 10,000 \end{aligned}

b. To find the total change in demand deposits:

\begin{aligned} Total change in demand deposits & = excess reserves \times money multiplier \\ = $ 10, 000 \times \frac{1}{r r} \\ = $ 10,000 \times \frac{1}{0.5} \\ = $ 10,000 \times 20 \\ = $ 200, 000 \end{aligned}

c. The total change in reserves will be

$ 0

. The monetary base is money in circulation plus money in banks. The monetary base does not change when loans are made. If all money is redeposited into banks, and all excess reserves are fully loaned out, all of the monetary base will be in the form of currency in bank vaults.

d. The money supply will increase. When the central bank buys the bonds, it pays

$ 5,000

in exchange for the bonds. The bank now has

$ 5,000

in excess reserves that can be loaned out. By loaning that out, money will be created.

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Subha Satapathy
Posted 3 years ago. Direct link to Subha Satapathy's post “For the question: b. Now,...”
For the question:
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.
Doubt: Given the reserve requirement of 5%,the money multiplier should be 1/(1-0.95) = 1/0.05 = 20

The answer mistakenly mentions it as 1/0.5 in an intermediary step while writing the correct answer later on as 20.
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(3 votes)
Answer
Rubytranhcm
Posted 4 years ago. Direct link to Rubytranhcm's post “Hi. Say a person deposits...”
Hi. Say a person deposits $100,000 into his checking accounts
at a bank. Can we use this and multiply by the MM to get total change in M1? Or this will not change money supply as in question 1, part 3a. Thanks.
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(2 votes)
Answer
- Qing Sun
  Posted 4 years ago. Direct link to Qing Sun's post “As stated in the article,...”
  As stated in the article, no money is created or destroyed when money is withdrawn from or deposited in a bank. Thus, when a person deposits $100,000 into his checking accounts, there will be no change in M1.
  
  M1 will be changed if loan is made. Before that, no new money is created.
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  (3 votes)
Ethan Lin
Posted 4 years ago. Direct link to Ethan Lin's post “So what if someone decide...”
So what if someone decides to withdraw the more than the maximum amount in excess reserves, and the bank doesn't call in the loans?
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(2 votes)
Answer
- 23dzhao
  Posted 4 years ago. Direct link to 23dzhao's post “You take the total money ...”
  You take the total money withdrawn and subtract it with your total reserves. The leftover reserves will be your required reserves. The demand deposit will decrease and the bank needs to borrow money to reach the reserve requirement.
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  (1 vote)
banrif4213
Posted 4 years ago. Direct link to banrif4213's post “Can someone explain the c...”
Can someone explain the combined quantity of money all the banks in multibank banking system will be capable of creating, if one bank is capable of creating money?
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shaoxin.enactustfsu
Posted 4 years ago. Direct link to shaoxin.enactustfsu's post “In "calculating excess re...”
In "calculating excess reserve" part, the money multiplier still uses the one from the previous part, which is 4, while in this part since the RRR is 10%, the MM should be 10, as it's stated that all money loaned will be deposited, and all deposited will be loaned out. Following this line, the final amount of increased loan should be 4000*10-4000=3600
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Answer
- Tony Zheng
  Posted 3 years ago. Direct link to Tony Zheng's post “The final result of 14400...”
  The final result of 14400 is wrong.
  
  Reserve requirement is 10%:
  4000*0.9=3600 is available to be loaned at first, and
  4000*(10-1)=36000 is the maximum amount which can be loaned.
  
  Reserve requirement is 25%:
  4000*0.75=3000 is available to be loaned at first, and
  4000*(4-1)=12000 is the maximum amount which can be loaned.
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jasmine.delgadoramirez
Posted 5 months ago. Direct link to jasmine.delgadoramirez's post “So if the government lend...”
So if the government lends more money to the banks than the amount of money they have, they can't print more?
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- DrCurieuse
  Posted 4 months ago. Direct link to DrCurieuse's post “In reality, the money sup...”
  In reality, the money supply is endogenous, private banks own the private money printing press and are not constrained by the limitations set by central banks, they can print as much money as they wish, although in reality, this is limited by the demand for credit by households and companies, with their access depending on the contraction of interest rates influenced by the central bank. The bank's willingness to make a profit and extend credit to people it trusts must also be taken into account.
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Jack Hora
Posted 4 years ago. Direct link to Jack Hora's post “Asset loans coming from d...”
Asset loans coming from deposits seems like a virtual transaction from the banks liability source. How does this create hard cash to lend?
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(1 vote)
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Miracle Guy
Posted 4 years ago. Direct link to Miracle Guy's post “I had want to know what i...”
I had want to know what is the total amount of new loans
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- Davoid Coinners
  Posted 4 years ago. Direct link to Davoid Coinners's post “If you're looking to find...”
  If you're looking to find the total amount of new loans, find the Required Reserves for a bank's demand deposit. Once you have that, subtract the demand deposit's worth minus the (demand deposit times the reserve requirement)
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  (1 vote)
Vikram Chandramouli
Posted 3 years ago. Direct link to Vikram Chandramouli's post “For part b of the last qu...”
For part b of the last question, I believe there is a typo. It says the money multiplier is 1/rr, and rr= 5% or 0.05. In part B it says it multiplies it by 1/.5 instead of 1/.05
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joyceye.nyc
Posted 3 years ago. Direct link to joyceye.nyc's post “Can someone explain when ...”
Can someone explain when to use RR versus RRR for the money multiplier?
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