Question

Suppose a bank acquires an additional \(\$ 1\) of deposits and no required reserve ratio exists. By how much could this one dollar deposit theoretically expand the money supply?

Short answer

Theoretically, if there is no required reserve ratio and banks can lend out the entire amount of the deposit, the money multiplier would become infinitely large. This means that the $1 deposit could, in theory, expand the money supply by an infinite amount. In reality, banks would not lend out the entire amount due to various factors, but the theoretical expansion would be much larger than with a required reserve ratio in place.

Step-by-step solution

Understand the concept of the money multiplier

The money multiplier is a measure of the amount of money that banks can generate for each dollar of reserves (the amount of money banks hold in their accounts). In a fractional reserve banking system, banks are required to keep a certain percentage of their deposits as reserves and lend out the rest. When a bank receives a deposit, they can lend out all or a part of it. The portion they are allowed to lend out is determined by the reserve ratio. If there is no reserve ratio, we need to assume that banks can lend out the entire amount of the deposit.

Determine the money multiplier formula

The money multiplier (M) can be determined through the following formula: \[M = \frac{1}{RR}\] Where: - M is the money multiplier - RR is the reserve ratio

Calculate the money multiplier with no reserve ratio

As there is no required reserve ratio, we can assume that banks can lend out the entire amount of the deposit. Thus, RR = 0. Using this value, we calculate the money multiplier: \[M = \frac{1}{0}\] However, dividing by zero is undefined in mathematics. Theoretically, if banks can lend out the entire amount of the deposit and there is no reserve requirement, the money multiplier would become infinitely large. This means that the $1 deposit could, in theory, expand the money supply by an infinite amount. In reality, banks would not lend out the entire amount of the deposit due to various factors such as risk management, liquidity needs, and regulatory restrictions. Therefore, the true money multiplier would not be infinite, but the theoretical expansion of the money supply would be much larger than with a required reserve ratio in place.

Key concepts

Fractional Reserve Banking

Fractional reserve banking is a system where banks are required to keep only a fraction of their deposits as reserves. The remaining portion can be used for lending or other investments. This system effectively allows banks to create money by making loans, as borrowers and depositors both have claims to the same money. Banks profit by lending the deposited money out at a higher interest rate than the interest they pay to depositors.

The core idea of fractional reserve banking is to expand the availability of credit while maintaining stability and liquidity. There are several key features of this system:

• Allows for increased financial activity and economic growth because the money supply is effectively multiplied.
• Ensures banks have enough reserves to meet withdrawal demands, providing a safety net against bank runs.
• Requires careful management of reserves to balance profit and risk.

Fractional reserve banking is crucial to understanding how modern economies function, especially regarding money supply and credit availability.

Reserve Ratio

The reserve ratio is the portion of depositor's balances banks must have on hand as cash. It acts as a regulation to ensure banks do not overextend themselves and remain liquid enough to meet any withdrawal demands from depositors. The reserve ratio is typically set by a country's central bank and can vary depending on economic conditions.

Here’s how the reserve ratio works:

• A lower reserve ratio means that banks can lend out more of their deposits, which increases the money supply.
• A higher reserve ratio requires banks to hold more money in reserve, reducing the amount they can lend out and slowing money supply growth.

Changes in the reserve ratio are a tool used by central banks to control the money supply in an economy. For example, during economic slowdowns, a central bank might lower the reserve ratio to boost lending and stimulate economic activity.

Bank Deposits

Bank deposits are the money that customers place in a bank, which can be in the form of a checking account, savings account, or certificates of deposit (CDs). Deposits are crucial because they provide banks with the funds they use to make loans. When you deposit money into your bank account, the bank doesn’t just store it in a vault. Instead, banks lend most of these funds to other customers, thus earning interest on the loans.

Here’s how bank deposits impact the banking system:

• Deposits increase the bank’s ability to provide loans and other financial services.
• Depositors typically earn interest, which incentivizes saving and contributes to financial growth.
• Deposits are considered a liability for banks since the bank must repay the depositor on demand or on a set future date.

Bank deposits represent a simple but effective means of money management and are a foundational concept within fractional reserve banking.

Money Supply Expansion

Money supply expansion refers to the increase in the total amount of money available within an economy. In a fractional reserve banking system, money supply expansion occurs primarily through the lending activities of banks. When banks lend out a portion of their deposits, those funds are deposited into another account, and the process repeats itself, increasing the overall money supply.

Here’s how the money supply expands:

• Initial deposits lead to multiple rounds of lending and re-depositing, which increases the money supply through the money multiplier effect.
• The size of the expansion is influenced by the reserve ratio, with lower ratios typically resulting in greater money supply growth.
• This expansion can stimulate economic activity by providing businesses and consumers with the funds necessary for investment and spending.

Understanding money supply expansion is vital for grasping how changes in banking regulations and economic policy impact inflation, interest rates, and overall economic health.