The money multiplier calculator shows you how a change in the money supply relates to a given change in the monetary base of the central bank. In the following, you can learn what is a money multiplier and get familiar with the money multiplier formula. You can also study the relationship between the money multiplier and other monetary variables connected to the money supply.
What is a money multiplier
In macroeconomics, more specifically, in monetary economics, a money multiplier signifies the ratio of the money supply to the monetary base. If you found this definition confusing, the following section may give you some help to grasp the mechanism behind this relation.
The history of money and banking is a broad subject that we do not intend to cover here, however introducing the chief advancements in the progress of modern banking might be a practical starting point to understand the money creation and the money multiplier:
- The advent of deposits and loans
The harbingers of professional banking were medieval goldsmiths who built secure vaults to keep their valuable commodities safe. As wealthy people were also interested in protecting their gold, they began to assign goldsmiths to look after their money. After some time, goldsmiths realized that the volume of deposited gold largely surpasses the amount being withdrawn at any time. As a result, they decided to begin lending money, and making a profit off of it, even though it didn't belong to them. In this fashion, goldsmiths became the first rudimentary bankers that paved the way to the evolution of modern banking.
- The appearance of bank notes - the fiat money
As the banking profession developed and trade networks grew, people faced the growing problem of the inconvenience and vulnerability arising from transporting the gold required for conducting business. It motivated banks to issue private bank notes that empowered the holder of the record - independently from the person who first brought the gold into the bank - to receive the gold from the bank by presenting the document; that is, creating the foundation of today's fiat money.
- The emergence of central banks
As a result of the uncontrolled proliferation of different bank notes in circulation, it became extremely burdensome to follow the credibility of the thousands of various types of bills issued by hundreds of banks. After a while, to stabilize the perplexing structure, central banks emerged.
- Fractional reserve banking
Later, the scope of central banks expanded from the mere authorization of the commercial banks to more complex tasks regarding economic policy issues. One of the most revolutionary development was the introduction of the fractional reserve system. In such a system, banks are obliged to keep a fraction of the funds on deposit. For example, if a bank receives a 1,000 dollar deposit, it needs to retain 100 dollars and the rest can be lent out. By controlling the level of reserved deposit in this manner, central banks became able to regulate the creation of money, and thus the level of money supply by a multiplier effect.
But how do banks create money? And how does the multiplier effect work? Probably the best way to understand it is to illustrate it through a simple example:
Let's imagine that Jack decides to open his money box, where he saved 1,000 dollars. He recognizes that it would be safer and more convenient to keep this money in a bank, so he decides to deposit the 1,000 dollars at Magic Bank. How will this action affect the money supply?
The below table summarizes the course of Jack's thousand dollars and how it effects different aspects.
|Currency in circulation||Bank deposit||Money supply|
|First stage: Jack keeps the money in his money box||$1,000||0||$1,000|
|Second stage: Jack deposits $1,000 in Magic Bank||0||$1,000||$1,000|
|Third stage: The Magic bank lends out $900 to Mary who spends it on a laptop||$900||$1,000||$1,900|
|Fourth stage: The computer shop deposits $900 in Corner Bank which lends out $810 to another borrower||$810||$1,900||$2,710|
When Jack places his savings in the Magic Bank, the money supply remains the same; however, this action allows the bank to lend out according to the current reserve requirement set by the central bank, that is, the Federal Reserve in the United States. If the reserve requirement is 10 percent (which is applied on most of the deposits accounts in the U.S.), Magic Bank is obliged to keep the 10 percent of Jack's thousand dollars as a reservable deposit, that is, 100 dollars, and the rest it can lend out.
Magic Bank quickly finds a borrower for the 900 dollars, in the form of Mary, who decide to finance her laptop purchase by the cash acquired from the bank. At this moment, the money supply grows by the amount of money lent out as the money in circulation rises, and the deposit remains the same.
After the purchase, the computer shop deposits the money at another bank that again lends out the money by fulfilling the 10 percent reserve ratio. The process can continue until all the loanable part of the deposit is lent out. The money expansion that accompanies this procedure refers to the money-multiplier process.
The money multiplier formula
Following the previous example, you may wonder what the total expansion of the money supply initiated by Jack's deposited thousand dollars is.
One obvious way is summing up the incremental increases; however, it would take some time.
Money Supply = $900 + $810 + $729 + ...
The first increase is 900 dollars as the bank need to keep 100 dollars to fulfill the 10 percent reserve requirement of the central bank.
If we would like to write down the equation by including the reserve ratio (RR), we get the following formula.
Money supply = $900 + ($900 * (1 − RR)) + ($900 * (1 − RR) ^ 2) + ($900 * (1 − RR) ^ 3) + ...
In mathematics an infinite geometric series in this manner can be simplified to a straightforward formula:
Change in the money supply = Increase in loanable deposit / Reserve Ratio = $900 / 0.1 = $9,000
Thus, in our imaginary model with a ten percent reserve ratio, a 900 dollars increase in the loanable deposit will increase the money supply by 9,000 dollars, hence the money multiplier equal to 10.
Money multiplier = Change in money Supply / Increase in loanable deposit = $9,000 / $900 = 10
In a system where all of the money in circulation is deposited in bank accounts and none exists as physical currency, the money multiplier is equal to the value of bank reserves divided by the reserve ratio. In other words, if the reserve ratio is 10 percent, each dollar of reserve held by a bank triggers
$1 / RR = $1 / 0.1 = $10 of checkable bank deposits.
In the real world, however, the level of the money multiplier is lower than in our hypothetical example. The reason is that many people decide to keep their money as cash instead of in deposits; thus, part of the money is leaking out during the multiplier effect. It means that the Federal Reserve controls the sum of the bank reserves and the currency in circulation, called the monetary base, but it doesn't control the allocation between them. Practically, the main difference between a dollar in a bank reserve and a dollar as part of the money supply (either in the circulation or on bank's checkable deposit) is that a dollar that is part of the reserve is not available for spending, but a dollar in someone's pocket or in his or her bank account can be spent. Therefore the money supply is the total value of money available for spending in an economy at a specific time.
The below graph illustrates the relationship between the monetary base and money supply. As you can see, the money supply consists of a large part of the checkable deposit and also the currency in circulation that is part of the bank reserves as well.
Source: Economics Krugman, P. and Wells, R. (2015). Economics (Forth Edition). Worth Publishers
We hope that you already recognized that a one-dollar increase in the monetary base causes the money supply to increase by more than one dollar. The money multiplier is equivalent to the level of this change; thus, it is the ratio of the money supply to the monetary base. Accordingly, the actual money multiplier formula that reflects the real economic system is the following:
Money multiplier = Money supply / Monetary Base
How to use this money multiplier calculator
There are several variables you can take into consideration with our platform. Most of them you have already met previously, but for the matter of clarity, we outlined them below.
Checkable Deposit: Bank accounts from which the owner can withdraw funds on demand, with no notice.
Reserve Ratio (RR): The ratio of bank reserves to bank deposits. The Federal Reserve sets the minimum reserve ratio in the U.S.
Bank Reserves (Reservable Deposit): Currency in its vaults plus the deposits held in the account by the Federal Reserve.
Currency in Circulation: the total value of the physical form of money (coins and paper currency) that has been issued.
Monetary Base: The sum of the currency in circulation and the bank reserves.
Money Supply: The total value of monetary assets available in an economy at a specific time in the form of physical currency and checkable deposits.
Money Multiplier: The ratio of the money supply to the monetary base.
The money multiplier formulas that are applied in our money multiplier calculator are the following:
Monetary Base = Currency in Circulation + Bank Reserves
Bank Reserves = Reserve Ratio * Checkable Deposit
Money Multiplier = Monetary Base / Money Supply
Relevance in macroeconomics
Money supply, being strongly connected to lending activity, is one of primary concerns in monetary economics. As it was mentioned, central banks can attempt to affect the level of the money supply through reserve requirements; however, under the current practice, the Federal Reserve doesn't alter the reserve ratio (the last significant change in reserve requirements was 1992). Yet there is another policy tool that is aimed at adjusting the money supply, namely, open-market operations. In the frame of this concept, the Federal Reserve buys or sells U.S. Treasury bills (aka short-term government bonds) through a transaction with commercial banks. For example, the immediate effect of the purchasing of Treasury Bills by the FED would be a change in the bank reserves, as the bank use reserves in the transaction, extend the banks lending activity. Thus, the FED doesn't control the money supply directly; it controls only the monetary base and currency in circulation. Still, by controlling the monetary base, the Fed can influence the money supply and hence the money multiplier, although this also depends on the willingness of bankers/borrowers to lend/borrow money.
In turn, changes in the money supply, especially in the long run, determine the overall level of prices. In the short term, the situation where governments print money to finance their debt often leads to hyperinflation.
To conclude, the way that central banks conduct monetary policy, and the level of money multiplier, can affect the state of the economy and economic growth.
- Economics Krugman, P. and Wells, R. (2015). Economics (Fourth Edition). Worth Publishers