Money Multiplier: Definition, Formula, Examples (2024)

Money multiplier and the reserve ratio

To fully understand the concept of the Money Multiplier, we first need to understand a key concept in banking called the Reserve Ratio. Think of the Reserve Ratio as the ratio, or percentage, of cash deposits that a bank is required to keep in its reserves, or in its vault at any given time.

For example, if Country A decides that all banks in the country have to adhere to a Reserve Ratio of 1/10th or 10%, then for every $100 deposited into a bank, that bank is only required to keep $10 from that deposit in its reserves, or its vault.

The Reserve Ratio is the minimum ratio or percentage of deposits that a bank is required to keep in its reserves as cash.

Now you might wonder why a country, say Country A, wouldn't require its banks to keep all of the money they receive in deposits in their reserves or vaults? That's a good question.

The reason for this is that generally speaking when people deposit money into a bank, they don't turn around and take it all out again the next day or the next week. The majority of people leave that money in the bank for some time to have it for a rainy day, or maybe a large future purchase like a trip or a car.

In addition, since the bank pays a little bit of interest on the money people deposit, it makes more sense to deposit their money than to keep it under their mattress. In other words, by incentivizing people to deposit their money through interest earnings, the banks are actually creating the process of increasing the money supply and facilitating investment.

Money multiplier equation

Now that we understand what the Reserve Ratio is, we can provide another formula for how to calculate the Money Multiplier:

\(\text{Money Multiplier}=\frac{1}{\text{Reserve Ratio}}\)

We're finally at the fun part now.

The best way to fully understand how these concepts work together to create the Money Multiplier is through a numerical example.

Money Multiplier Example

Assume Country A printed $100 worth of money and decided to give it all to you. As a smart budding economist, you would know that the smart thing to do would be to deposit that $100 into your savings account so that it could earn interest while you studied for your degree.

Now assume that the Reserve Ratio in Country A is 10%. This means that your bank - Bank 1 - will be required to keep $10 of your $100 deposit in its reserves as cash.

However, what do you suppose your bank does with the other $90 they're not required to keep in their reserves?

If you guessed that Bank 1 would loan that $90 to someone else like a person or business, then you guessed right!

In addition, the bank will lend that $90 out, and at a higher interest rate than what they have to pay you for your initial $100 deposit into your savings account so that the bank is actually making money from this loan.

Now we can define the Monetary Supply as $100, consisting of the $90 in circulation through the Bank 1 loan, plus the $10 Bank 1 has in its reserves.

Now let's discuss the person who accepted the loan from Bank 1.

The person who borrows the $90 from Bank 1 will then deposit that $90 into their bank - Bank 2 - until they need it.

As a result, Bank 2 now has $90 in cash. And what do you suppose Bank 2 does with that $90?

As you might have guessed, they put 1/10th, or 10% of the $90 into its cash reserves, and lend out the rest. Since 10% of $90 is $9, the bank keeps $9 in its reserves and lends out the remaining $81.

If this process continues, as it does in real life, you can start to see that your initial deposit of $100 has actually begun to increase the amount of money circulating in your economy due to the banking system. This is what Economists call money creation through Credit Creation, where credit is defined as the loans the banks are making.

Let's look at Table 1 below to see what the total impact of this process will end up being, rounding to the nearest whole dollar for simplicity.

Table 1. Money Multiplier Numerical Example - StudySmarter

We can see that the sum of all the deposits in the economy is $1,000.

Since we identified the Monetary Base as $100, the Money Multiplier can be calculated as:

\(\text{Money Multiplier}=\frac{\text{Money Supply}}{\text{Monetary Base}}=\frac{\$1,000}{\$100}=10\)

However, we now also know that the Money Multiplier can be calculated in a simpler way, a theoretical shortcut, as follows:

\(\text{Money Multiplier}=\frac{1}{\text{Reserve Ratio}}=\frac{1}{\%10}=10\)

Money Multiplier Effects

The Money Multiplier Effect is that it significantly increases the total money available in the economy, which Economists call the Money Supply.

Most importantly, however, the Money Multiplier measures the number of dollars created in the banking system by each $1 addition to the monetary base.

Moreover, if you take this idea to the next level, you can see that Country A could use the required Reserve Ratio to increase the total Money Supply if it wanted to.

For example, if Country A has a current reserve ratio of 10% and it wanted to double the Money Supply, all it would have to do is change the Reserve Ratio to 5%, as follows:

\(\text{Initial Money Multiplier}=\frac{1}{\text{Reserve Ratio}}=\frac{1}{\%10}=10\)

\(\text{New Money Multiplier}=\frac{1}{\text{Reserve Ratio}}=\frac{1}{\%5}=10\)

So the effect of the Money Multiplier is to increase the Money Supply in an economy.

But why is increasing the Money Supply in an economy so important?

Increasing the Money Supply through the Money Multiplier matters because when an economy receives an injection of money through loans, that money goes towards consumer purchases and business investment. These are good things when it comes to stimulating a positive change in an economy's Gross Domestic Product - a key indicator of how well the economy, and its people, are doing.

Factors affecting Money Multiplier

Let's talk about the factors that could affect the Money Multiplier in real life.

If everyone takes their money and deposits it into their savings account, the multiplier effect will be in full effect!

However, that doesn't happen in real life.

For example, let's say someone takes their money, deposits some of it into their savings account, but decides to purchase a book at their local book store with the remainder. In this situation, it's very likely that they'll have to pay some form of tax on their purchase, and that tax money will not go into a savings account.

In another example, it's possible that, instead of buying a book from the book store, a person may buy something online that was manufactured in another country. In this case, the money for that purchase will leave the country, and therefore the economy altogether.

Yet another factor that would affect the money multiplier is the simple fact that some people like to keep a certain amount of cash in hand, and never deposit it, or even spend it.

Finally, another factor that affects the Money Multiplier is a bank’s desire to hold excess reserves, or reserves greater than required by the Reserve Ratio. Why would a bank hold excess reserves? Banks will generally hold excess reserves to allow for the possibility of increases in the Reserve Ratio, to protect themselves from bad loans, or to provide a buffer in the event of significant cash withdrawals by customers.

So as you can see from these examples, the effect of the Money Multiplier in real life is influenced by a number of possible factors.