Question

Give the formula for the simple deposit multiplier. If the required reserve ratio is 20 percent, what is the maximum increase in checking account deposits that will result from an increase in bank reserves of \(\$ 20,000 ?\) Is this maximum increase likely to occur? Briefly explain.

Short answer

The formula for the simple deposit multiplier is the inverse of the reserve requirement ratio. With a required reserve ratio of 20 percent and an increase in bank reserves of $20,000, the maximum increase in checking account deposits that could occur is $100,000. However, this is unlikely to occur in the real world due to banks holding excess reserves and not all borrowed money being re-deposited.

Step-by-step solution

Derive the Formula for Simple Deposit Multiplier

Simple deposit multiplier is the inverse of the reserve requirement ratio. It is used to estimate the maximum amount that bank deposits can increase based on a new cash deposit. It is given as: \[ D = \frac{1}{RRR} \]where:\(D\) = deposit multiplier\(RRR\) = Reserve requirement ratio.

Application of Formula

Given the reserve requirement ratio is 20 percent or 0.2, the simple deposit multiplier (\(D\)) is calculated as:\[ D = \frac{1}{0.2} = 5 \]If there is an increase in bank reserves of $20,000, the maximum increase in checking account deposits can be calculated by multiplying this increase in reserves by the deposit multiplier:\[ Increase = D \times Increase\ in\ Reserves \]\[ Increase = 5 \times 20,000 = $100,000 \]

Logical Explanation

In an ideal situation, where all deposited money is lent out again and re-deposited, the process repeats itself and in theory, the maximum increase should occur. However, in reality, banks might hold excess reserves and not all individuals re-deposit the money they borrow. Therefore, the maximum increase is less likely to occur.

Key concepts

Reserve Requirement Ratio

The reserve requirement ratio (RRR) is a critical concept in banking that determines the minimum percentage of customer deposits that financial institutions must hold as reserves. This ratio is set by central banks and ensures that banks have a buffer of reserves to meet withdrawal demands. When a bank receives deposits, they are required to keep a part of it as reserves, instead of lending it out. This portion is dictated by the reserve requirement ratio. For example, with a 20% reserve requirement ratio, for every $100 deposited, a bank must keep $20 in reserve. The functionality of the reserve requirement ratio ensures stability within the banking system:

• Protects against bank runs by ensuring liquidity.
• Limits the amount banks can lend out, controlling money supply.

Understanding how this ratio impacts lending and overall economic activity is essential for comprehending bank operations and the broader macroeconomic policy.

Bank Reserves

Bank reserves are the actual cash available in the bank's vault or at the central bank, fulfilling the reserve requirement. Reserves can be seen as the bank's safety net, ensuring they can meet withdrawal demands without needing to liquidate assets or borrow funds. Types of reserves include:

• Required Reserves: This is the minimum amount mandated by the reserve requirement ratio. It is crucial to maintain these to avoid penalties or operational issues.
• Excess Reserves: Any reserves held beyond the required amount. Although holding excess reserves is a cautious approach, it can also mean missed opportunities for lending.

An increase in bank reserves, like the example of $20,000, can enable more lending if reserves are moved beyond the required minimums, thus facilitating economic growth. Understanding bank reserves helps explain why banks might not lend every dollar they receive, and how reserves are integral to economic stability.

Checking Account Deposits

Checking account deposits are the funds that customers keep in their daily-use accounts. These accounts are generally free from restrictions, allowing withdrawals through checks, debit cards, or electronic transfers. Checking accounts are central to everyday financial transactions and are a primary component of M1 money supply, the most liquid form of money. When we talk about the simple deposit multiplier, the focus is on how new deposits can ripple through the banking system, expanding overall deposits. In the exercise, the deposit multiplier is seen at work: With a deposit multiplier of 5 and an initial reserve increase of $20,000, the potential maximum increase in checking account deposits could be $100,000. Deposits in these accounts are foundational to bank operations because:

• They provide banks with funds that can be lent out to others, generating interest income.
• Checking accounts bear little to no interest, making them a cost-effective source of funds.

Understanding how deposits circulate and amplify in an economy sheds light on connections between individual banking actions and broader financial systems.