Money Multiplier Formula: The term “money multiplier” belongs to the aspect of credit formulation due to the partial reserve banking arrangement under which a bank is expected to operate a certain amount of the deposits in its reserves in line to be ready to meet any potential withdrawal demand. So, it means that a bank has to hold a portion of all the deposits as reserves, while it can increase the residual as loans to create more money in the economy.
The mandatory reserve maintained by the bank divided by the total deposits received by the bank is known as the required reserve ratio. The formula for money multiplier is simple and it can be derived by dividing one by the required reserve ratio. Mathematically, it is represented as, Money Multiplier = 1 / Required Reserve Ratio.
Multiplier Effect & Formula
The multiplier effect refers to the proportional amount of increase, or decrease, in final income that results from an injection, or withdrawal, of spending.
Key Points
- The multiplier effect refers to the proportional amount of increase, or decrease, in final income that results from an injection, or withdrawal, of spending.
- The most basic multiplier used in assessing the multiplier effect is calculated as a change in income/change in spending and is used by companies to evaluate investment efficiency.
- The money supply multiplier is also another variety of a standard multiplier, using a money multiplier to investigate effects on the money supply.
Understand the Multiplier Effect With An Example
Usually, economists are normally the most interested in how capital infusions surely affect income. Most economists believe that capital infusions of any kind, whether it be at the governmental or corporate level, will have a broad snowball effect on various features of economic activity.
As its name implies, the multiplier impact provides a numerical value or estimate of a magnified required increase in income per dollar of investment. In general, the multiplier used in gauging the multiplier effect is calculated as follows:
Multiplier = Change in Income ÷ Change in Spending
The multiplier effect can be observed in several different types of situations and used by a variety of different analysts when examining and estimating expectations for new capital investments.
For example, consider a company that makes a $100,000 investment of capital to expand its manufacturing facilities in order to produce more and sell more. After a year of production with the new equipment working at maximum capacity, the company’s income rises by $200,000. This indicates that the multiplier effect was 2 ($200,000/$100,000). Simply put, every $1 of investment produced an extra $2 of income.
Many economists think that new investments can go far away just the effects of a company’s income. Thus, depending on the type of investment, it may have widespread effects on the economy at large.
A key tenet of Keynesian economic theory is the notion that economic activity can be easily influenced by investments causing more income for companies, more income for workers, more supply, and ultimately greater aggregate demand. Therefore, on a macro level, different types of economic multipliers can be used to help measure the impact that changes in investment have on the economy.
- When looking at the economy at large, the multiplier would be the difference in real GDP divided by the change in investments. Investments can hold government spending, private investments, taxes, interest rates, and more.
- When considering the effects of $100,000 by the manufacturing company on the economy overall, the multiplier would be much less. For example, if GDP grew by $1 million, the multiplier effect of this investment would be 10 cents per dollar.
Some economists also like to factor in measures for savings and expenditure. This requires a somewhat different type of multiplier. When looking at savings and expenditure, economists might measure how much of the added economic income consumers are saving versus spending. If users save 20% of new income and spend 80% of net income then their marginal propensity to consume (MPC) is 0.8. Using an MPC multiplier, the equation would be:
MPC Multiplier = 1 ÷ (1-MPC) = 1 ÷ (1-0.8) = 5
Therefore in this example, every new production dollar creates extra spending of $5.
Money Multiplier Effect & Formula
Economists and bankers often look at a multiplier effect from the perspective of banking and money supply. This multiplier is called the money supply multiplier or just the money multiplier. The money multiplier involves the reserve requirement set by the board of governors of the Federal Reserve System and it varies based on the total amount of liabilities held by a particular depository institution.
The most current Federal Reserve reserve requirements prior to the COVID-19 pandemic mandated that institutions with more than $127.5 million have reserves of 10%. This improved as the FED returned to the COVID-19 pandemic by eliminating these elements to free up liquidity.1
In general, there are multiple levels of the money supply over the entire U.S. economy. The most familiar ones to the general public are:
- The first level, named M1, refers to all of the physical currency inflow within an economy.
- The next level, called M2, adds the stability of short-term deposit accounts for a summation.
When a customer makes a deposit into a short-term deposit account, the banking institution can lend one minus the reserve requirement to someone else. While the primary depositor maintains ownership of their initial deposit, the funds created through lending are made based on those funds. If a second borrower subsequently deposits funds received from the lending institution, this raises the value of money supply even though no extra physical currency actually endures to support the new amount.
The money supply multiplier effect can be seen in a country’s banking arrangement. An increase in bank lending should translate to an increase in a country’s money supply. The size of the multiplier depends on the percentage of deposits that banks are expected to hold as reserves. When the reserve requirement decreases the money supply reserve multiplier increases and vice versa.
Most economists view the money multiplier in terms of reserve dollars and that is what the money multiplier formula is based on. Theoretically, this leads to a money (supply) reserve multiplier formula of:
Money Supply Reserve Multiplier = 1 ÷ Reserve Requirement Ratio
For example, when looking at banks with the highest required reserve requirement ratio, which was 10% prior to COVID-19, their money supply reserve multiplier would be 10 (1/.10).1 This means every one dollar of reserves should have $10 in money supply deposits.
If the reserve requirement is 10%, then the money supply reserve multiplier is 10 and the money supply should be 10 times reserves. When a reserve requirement is 10%, this also means that a bank can lend 90% of its deposits.
Formula
Money Multiplier = 1/Required Reserve Ratio
The expected reserve ratio is the fraction of deposits that a bank is expected to hold in hand. It can lend out an amount equals to excess reserves which equal (1 − required reserves).
Higher the required reserve ratio, lesser the excess reserves, lesser the banks can give as loans, and lower the money multiplier. Lower the required reserve ratio, higher the excess reserves, more the banks can lend, and higher is the money multiplier.
In the above relationship, it is believed that there is no currency drainage, i.e. the borrowers keep 100% of the amount received in banks.
Currency drainage
In actuality, borrowers do keep a fraction of loans taken in cash. This reduces the money multiplier. When there is some currency drainage, the money multiplier is determined as per the following formula:
Money multiplier when there is currency drainage= 1 + drainage ratio/required reserve ratio + drainage ratio
Examples
Example 1: Ishkebar is an alien country that has recognized little financial innovation. Its central bank expects commercial banks to keep 100% of their deposits as reserves. Calculate money multiplier for the economy.
Money multiplier = 1/required reserve ratio = 1/100% = 1
The country has a money multiplier of 1. No money creation is possible because, in response to an increase in bank collaterals of say 100 million Ishkebar dollars (I$), the money supply will increase by 1 × I$100 million = I$100 million.
Example 2: North Sarawak is operated by a dictator who recognizes no economics and is not willing to listen to any advice. He assumes he can always print money whenever a depositor wants to withdraw so he does not think having any needed reserve ratio for the sole bank of the country is necessary. What could be the consequences?
Zero required reserve ratio means infinite money multiplier and infinite money creation. Infinite money creation means no scarcity of money which means money would no longer be money since it would no longer be a store of value.
Example 3: Palmolive has a needed reserve ratio of 30% and currency drainage of 15%. Calculate the money multiplier and compare it with Parazuela, a country where drainage is zero and the required reserve ratio is 30%.
Money multiplier in Palmolive = (1 + 15%) ÷ (30% + 15%) = 2.56
Money multiplier in Parazuela = 1/30% = 3.33
Parazuel has a higher money multiplier which makes sense because it has zero drainage. Zero drainage means all of the excess reserves loaned out in round 1 form part of total reserves in round 2.
Money Multiplier in the Real World
In an easy theory of the money multiplier, it is assumed that if the bank lends $90 – all of this will return. However, in the real world, there are many causes why the actual money multiplier is significantly less than the theoretically possible money multiplier.
- Import spending. If consumers buy imports the money leaves the economy.
- Taxes. A percentage of income will be taken in taxes.
- Savings. Not all money is spent and circulated, a significant percentage will be saved.
- Currency Drain Ratio. This is the % of banknotes that particular consumers keep in cash, rather than depositing in banks. If consumers put all their cash in banks, there would be a bigger money multiplier. But, if people keep funds in cash then the banks cannot lend more.
- Bad loans. A bank may lend out $90 but the company goes bankrupt and so this is never dropped bank into the banking system.
- Safety reserve ratio. This is the % of deposits a bank may like to keep above the legal reserve ratio. i.e. the required reserve ratio maybe 5%, but banks may like to keep 5.2%.
- It might not be possible to lend more money out. Just because banks could lend 95% of their deposits doesn’t mean they can, even if they wanted to. In a recession, people may not want to borrow, but they prefer to save.
- Banks may not want to lend Also, at various times, the banks may not want to lend, e.g. during a recession, they feel firms and individuals more likely to default. Therefore, the banks end up with a higher reserve ratio.
Therefore, due to these factors, the reserve ratio and money multiplier are theoretical.