Question

Analyzing Data The Fed sets the required reserve ratio at 10 percent. What is the initial deposit if the money supply increases by \(\$ 40,000 ?\) Use the deposit multiplier formula to determine your answer and show your calculations.

Short answer

The initial deposit is \(\$4,000\).

Step-by-step solution

Understanding the Deposit Multiplier

The deposit multiplier (or money multiplier) is a formula used to determine the maximum amount of new money that can be created with a given increase in reserves. It is calculated as the reciprocal of the required reserve ratio. In this case, the required reserve ratio is 10%, which translates to 0.10 as a decimal.

Calculate the Deposit Multiplier

To find the deposit multiplier, take the reciprocal of the reserve ratio, which is \( \frac{1}{0.10} = 10 \). This means that each dollar of reserves can support \(10\) dollars of deposits in the banking system.

Determine the Initial Deposit

Given that the money supply increases by \( \\(40,000 \), we can use the deposit multiplier to find the initial deposit. Since the deposit multiplier is \(10\), set up the equation: \( \text{Increase in Money Supply} = \text{Deposit Multiplier} \times \text{Initial Deposit} \). \( \\)40,000 = 10 \times \text{Initial Deposit} \).

Solve for Initial Deposit

Rearrange the equation to solve for the initial deposit: \( \text{Initial Deposit} = \frac{\\(40,000}{10} = \\)4,000 \). Therefore, the initial deposit is \( \$4,000 \).

Key concepts

Understanding the Required Reserve Ratio

The required reserve ratio is a regulation set by central banks, such as the Federal Reserve in the United States. It dictates the minimum fraction of customer deposits that each bank must hold in reserve, rather than lend out. This is usually expressed as a percentage. For instance, if the required reserve ratio is set at 10%, it means banks must keep 10% of deposits as reserves. This policy helps ensure that banks have enough funds to meet withdrawals and other obligations.

• If a bank has $1 million in deposits, with a 10% reserve ratio, it must keep $100,000 in reserve.
• The remaining %90 can be used for loans and other investments.

The required reserve ratio is a vital tool that helps control the money supply in an economy. By adjusting the ratio, central banks can impact the ability of banks to create money through lending.

Exploring the Concept of Money Supply

The money supply represents the total amount of money available within an economy at a particular time. It includes various forms of money, such as cash, coins, and balances held in checking and savings accounts. The money supply is crucial for economic stability and is often monitored and regulated by central banks.

• Two main components of the money supply include M1 and M2. M1 includes liquid forms of money like cash and checkable deposits, while M2 includes M1 plus savings deposits and other near-money assets.
• An increase in the money supply often leads to higher economic activity, but too much can cause inflation.

Central banks control the money supply through tools such as setting reserve requirements, adjusting interest rates, and conducting open market operations. By managing the money supply, they influence economic growth and price stability.

The Role of the Banking System

The banking system is a network of financial institutions that facilitate economic transactions and manage money within an economy. It plays a crucial role in the functioning of a modern economy by providing services like savings and checking accounts, loans, and currency exchanges.

• Banks accept deposits and use these funds to make loans, thus creating new money in the form of credit.
• The process of lending out more money than is kept in reserve is known as fractional-reserve banking, and it is pivotal in expanding the money supply.

The banking system also acts as an intermediary between savers and borrowers. It helps allocate resources efficiently by directing funds from those who have surplus money to those who require capital, often at interest. Moreover, it offers a safe place for individuals to store their money, backed by governmental regulations and insurance. This framework not only supports personal finance but also catalyzes larger economic growth and development.