In this lesson, explore the concept of the multiplier effect and the money multiplier. Then, learn the formula for calculating changes in the money supply.

## The Multiplier Effect

Go with me to the town of Ceelo, where Margie has just inherited \$1,000,000 from a long-lost relative. Once she returns to her bakery, she decides to eat an entire chocolate cake, which comforts her during this difficult time, and then she heads to the First National Bank of Ceelo with a small entourage of bulletproof vehicles.

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When Margie deposits \$1,000,000 into the banking system, she doesn’t realize it, but this one activity has a big effect on the town of Ceelo. Economists call it ‘the multiplier effect.’ Her single deposit leads to a series of loans and other deposits throughout the banking system that stimulates economic activity on a much greater level than she ever imagined. Because of the fortunate position that she found herself in, Lydia the factory worker is able to borrow money to attend college. Many other businesspeople in Ceelo are able to start new businesses, and this single increase of \$1,000,000 that started at one bank turns into a much larger increase in the money supply within the economy.

The multiplier effect describes how an increase in one economic activity leads to a much greater increase in economic output. In the banking system, money that gets deposited multiplies as it filters through the economy, going from depositor to borrower multiple times. For any change in bank reserves, the money supply will ultimately change by a multiple of that amount.

Just think about a bicycle. On a bicycle, when you pedal with your feet, a very small rotation leads to a much bigger turn of the wheels. Very small changes in the banking system can lead to much larger changes in the money supply of the economy.

Let’s take a look at the multiplier effect as it unfolds using Margie’s \$1,000,000 deposit as an example. When Margie deposits \$1,000,000 into the banking system, the total reserves in the banking system immediately go up by \$1,000,000. However, the bank will separate this money into two different kinds of reserves: required reserves and excess reserves. Eventually, this \$1,000,000 will turn into a much larger money supply because of the multiplier effect.

Now, the reserve ratio represents the fraction of a customer’s deposits that a bank is required to withhold on reserve in their vault or on deposit with the central bank. For example, when the reserve ratio is ten percent, that means ten percent of all new total reserves are required to be reserved by the bank. The reserve ratio is set by the Federal Reserve and gives the central bank power to influence and change the money supply.

Whatever is not required reserves is called excess reserves. Excess reserves represent the fraction of a customer’s deposits a bank is able to loan out to borrowers so they can earn a profit. Banks make a profit by loaning out excess reserves. In the process, they play an important role in the economy by increasing the money supply through their lending. Here’s the formula that economists use to describe this. Total reserves = required reserves + excess reserves.

## Example of the Multiplier Effect

So let’s talk about the multiplier effect for a little bit. Suppose that the reserve ratio is currently ten percent. When Margie deposits \$1,000,000 into the banking system, total reserves go up by \$1,000,000. That means banks will separate \$100,000 and call it required reserves, because ten percent times \$1,000,000 equals \$100,000. The remainder of these reserves is considered excess reserves, which is 90% times \$1,000,000, or \$900,000. This is the amount the bank is allowed to loan out and generate a profit on by charging interest. So far, out of Margie’s \$1,000,000 deposit, the bank is able to loan out \$900,000 of it.

When Dylan, a pizza shop owner, shows up at the bank asking to borrow additional money to build a second pizza shop in town, he happens to borrow \$900,000. When he receives his check, he promptly places it in a checking account at the Second Bank of Ceelo, and the fractional reserve cycle starts all over again. That \$900,000 is now a deposit, and that bank is required to set aside ten percent of this amount – or \$90,000 – and call it required reserves. The remaining \$810,000 out of the \$900,000 can be loaned out to someone else. In this case, it’s Lanny, who needs to build a toy factory for exactly \$810,000 (what a coincidence).

So far, here are the transactions we’ve talked about: \$1,000,000 times ten percent turned into \$100,000 required reserves, which left excess reserves of \$900,000. That \$900,000 was loaned out, so then ten percent of that (or \$90,000) was set aside as required reserves, which means that excess reserves were \$810,000. Then that now becomes a deposit of \$810,000. Then ten percent of that, which is \$81,000, has to be set aside as required reserves, which leaves, of course, \$729,000 of excess reserves. Etc.

This can be a very tedious process, calculating both types of reserves for every deposit and watching it filter through the economy so you can discover how much the money supply went up. Thankfully, though, we’ve got you covered.

## The Money Multiplier

The money multiplier is the relationship between the reserves in a banking system and the money supply. The money multiplier tells you the maximum amount the money supply could increase based on an increase in reserves within the banking system. The formula for the money multiplier is simply 1/r, where r = the reserve ratio.

A little too easy, right? It’s the reciprocal of the reserve ratio. When r is the reserve ratio for all banks in an economy, then each dollar of reserves creates 1/r dollars of money in the money supply. That means the smaller the reserve ratio is, the larger the increase it brings to the money supply, because more of the customers’ deposits get loaned out by the bank. For example,

• When the reserve ratio is 0.25, that means the money multiplier is 4.
• When the reserve ratio is 0.2, that means the money multiplier is 5.
• When the reserve ratio is 0.1, that means the money multiplier is 10.

Of course, this works in reverse as well. The larger the reserve ratio, the smaller the multiplier is, and therefore the smaller the increase in the money supply.

## Calculating Changes in the Money Supply

So how do we calculate changes in the money supply? To calculate the maximum increase in the money supply generated by an increase in reserves, you simply multiply excess reserves by the money multiplier, like this:

Maximum change in the money supply = excess reserves x the money multiplier

When Margie deposited \$1,000,000 into her bank, the reserve ratio was ten percent. This initial increase in the reserves of the banking system led to an increase in the money supply of \$1,000,000 X 10 = \$10,000,000.

## The Multiplier Is a Tool of the Central Bank

Why is the money multiplier so important? Because it’s used by the central bank as part of monetary policy to control the money supply and therefore influence economic growth. They tend to do this when the economy is at an extreme. For example, when the economy is in recession, the central bank often increases the money supply in order to cushion the blow. On the other hand, when the economy is overheating with inflation, they often reduce the size of the money supply in order to help the economy slow down and tame that inflation problem. Because of the multiplier effect, the central bank can use small changes in the reserves of the banking system to affect much larger changes in the money supply of the economy.

## Lesson Summary

Alright, it’s time to review. Banks make money by charging interest on loans. This gives them an incentive to loan out as much of their deposits as possible under the law.

There are two types of reserves in the banking system. Required reserves represent the fraction of a customer’s deposits that a bank is required to withhold on reserve in their vault or on deposit with the central bank. Required reserves are an amount of money; however, we can express it in percentage terms by using the reserve ratio. Reserve requirements are set by the Federal Reserve, and this is the centerpiece of what we call the fractional reserve banking system. Excess reserves represents the fraction of a customer’s deposits a bank is able to loan out to borrowers so they can earn a profit. Banks make a profit by loaning out excess reserves. In the process, they play an important role in the economy by increasing the money supply through their lending.

The total reserves in the banking system are the sum of required reserves plus excess reserves. For any change in bank reserves, the money supply will ultimately change by a multiple of that amount. This is what economists call the multiplier effect.

The money multiplier is the relationship between the reserves in a banking system and the money supply. The money multiplier tells you the maximum amount the money supply could increase based on an increase in reserves within the banking system. The formula for the money multiplier is simply 1/r, where r = the reserve ratio.

To calculate the maximum increase in the money supply generated by an increase in reserves, simply multiply the change in reserves by the money multiplier, like this: Maximum change in the money supply = change in reserves x the money multiplier.

## Learning Outcomes

After watching this lesson, you should be able to identify excess reserves and required reserves in the banking system and use the money multiplier formula to calculate reserve ratios and maximum money supply increases.