 # How to Calculate the Money Multiplier

| Updated Oct 8, 2017

In a fractional reserve banking system, most of the money supply is generated by commercial banks. This is possible because the banks only have to hold a fraction of all deposits as reserves. That means, they can use the rest to make loans and thereby create new money. The maximum amount of new money that can be created through fractional reserve banking can be estimated with the so-called money multiplier. Therefore, we will look at how exactly this works and how to calculate the money multiplier below.

## Money Creation in Fractional Reserve Banking

As we already know, in fractional reserve banking, commercial banks are only required to hold a certain percentage of all deposits as reserves. This percentage is called the reserve ratio. The remaining deposits can be used to give out loans and thereby increase money supply. However, the creation of money does not stop there. The newly created money can be deposited it in another bank, which in turn can loan a fraction of that money to other customers and so on. In theory, this process can be repeated forever.

Now, this may sound a bit confusing. So let’s look at a simple example. Let’s say you deposit USD 1000 in a bank called First Bank. By law, First Bank is required to hold 10% (i.e. USD 100) of your deposit in reserve. So the bank can use the remaining USD 900 to give out a loan, which it does. Now, let’s assume the borrower uses that money to buy a high-end TV from his neighbor. The neighbor then deposits the USD 900 he received for his old TV in another bank called Second Bank. Again, Second Bank is required to hold 10% (i.e. USD 90) of the deposit in reserve. Therefore, Second Bank can make USD 810 in loans. This money can then be deposited by someone in Third Bank, which holds USD 81 in reserve and can give out another loan of USD 729. This process can be repeated indefinitely.

Every time one of those banks makes a new loan, new money is created. At the same time however, the loans become smaller and smaller, because each bank has to hold 10% of the deposits in reserve. Because of this, even though the process can be repeated over and over again, the amount of new money that can be created is limited. In the example above if we add up all the loans (i.e. 900 + 810 + 729 + …), we find that eventually, a total of USD 10,000 can be created. Of course, it is not feasible to add up all these numbers, so we need an easier way to calculate the total amount of new money. And this is where we need the money multiplier.

## How to Calculate the Money Multiplier

The money multiplier is defined as the amount of money the banking system generates with each dollar of reserves. Obviously, this depends on the reserve ratio. The more money banks have to hold in reserve, the less they can use to make loans. Thus, the money multiplier can can be calculated as the inverse value of the reserve ratio. That is, if the reserve ratio is R, the money multiplier is 1/R

To understand why this makes sense, let’s look at our example again. We assumed that First Bank holds USD 1000 in deposits. Since the reserve ratio R (i.e. the ratio of reserves to deposits) is 10%, it has to hold USD 100 in reserves. If we turn this idea around, we can also say that with USD 100 in reserves, the bank can only hold a maximum of USD 1000 in deposits. And this is exactly what the money multiplier does; it gives us the ratio of deposits to reserves (i.e. 1/R).

That means, if the reserve ratio in our example is 10% (i.e. 0.1), the money multiplier is 10 (i.e. 1/0.1). Thus, an initial deposit of USD 1000 will end up creating a total of USD 10’000 in new money (see above).

## In a Nutshell

In a fractional reserve banking system, most of the money supply is generated by commercial banks. This is possible because the banks only have to hold a fraction of all deposits in reserve (i.e. the reserve ratio R). We can calculate the maximum amount of new money that can be created through fractional reserve banking with the money multiplier. The money multiplier is defined as the amount of money the banking system generates with each dollar of reserves. It can can be calculated as the inverse value of the reserve ratio (i.e. 1/R).