Question

First Bank has cash reserves of \(\$ 200,000\), loans of \(\$ 800,000\), and deposits of \(\$ 1,000,000\). a. Prepare a balance sheet for the bank. b. If the bank maintains a reserve requirement of 15 percent, what is the largest loan it can make? c. What is the maximum amount by which the money supply can be increased as a result of First Bank's new loan? d. If the reserve requirement is reduced to 12 percent, how much larger of a loan can the bank make? How much more can the money supply be increased?

Short answer

Answer: The maximum amount by which the money supply can be increased when First Bank makes a new loan with a 15% reserve requirement is \$333,500.

Step-by-step solution

a. Prepare a balance sheet for the bank

To create a balance sheet for First Bank, we need to list the assets on one side, and liabilities and owner's equity on the other side. For this bank, the assets consist of cash reserves and loans, while liabilities are the deposits. | Assets | | Liabilities & Owner's Equity | | |-----------------|-------------|------------------------------|-------------| | Cash Reserves | \(\$ 200,000\)| Deposits | \(\$ 1,000,000\)| | Loans | \(\$ 800,000\)| Total Liabilities & Equity | \(\$ 1,000,000\)| | Total Assets | \(\$ 1,000,000\)|

b. Determine the largest loan the bank can make with a 15% reserve requirement

First, we have to find the required reserves: Required Reserves = Deposits * Reserve Requirement Required Reserves = \(\$ 1,000,000 * 0.15\) = \(\$ 150,000\) Next, we need to find the excess reserves the bank has: Excess Reserves = Cash Reserves - Required Reserves Excess Reserves = \(\$ 200,000 - \$ 150,000\) = \(\$ 50,000\) The largest loan the bank can make is equal to its excess reserves. Therefore, the bank can make a loan of up to \(\$ 50,000\).

c. Calculate the maximum amount the money supply can be increased due to the new loan

To find the maximum amount by which the money supply can be increased, we will use the Money Multiplier formula: Money Multiplier = \(\frac{1}{Reserve Requirement}\) Money Multiplier = \(\frac{1}{0.15}\) = \(6.67\) Now, we multiply the Money Multiplier with the Excess Reserves: Maximum increase in money supply = Money Multiplier * Excess Reserves Maximum increase in money supply = \(6.67 * \$ 50,000\) = \(\$ 333,500\) As a result of First Bank's new loan, the money supply can be increased by up to \(\$ 333,500\).

d. New loan and money supply increase with 12% reserve requirement

First, let's find the new required reserves with the 12% reserve requirement: Required Reserves = Deposits * Reserve Requirement Required Reserves = \(\$ 1,000,000 * 0.12\) = \(\$ 120,000\) New excess reserves = Cash Reserves - New Required Reserves New excess reserves = \(\$ 200,000 - \$ 120,000\) = \(\$ 80,000\) The new Money Multiplier with a 12% reserve requirement is given by: Money Multiplier = \(\frac{1}{0.12}\) = \(8.33\) Now, we multiply the Money Multiplier with the new Excess Reserves: New maximum increase in money supply = Money Multiplier * New Excess Reserves New maximum increase in money supply = \(8.33 * \$ 80,000\) = \(\$ 666,640\) First, let's calculate how much larger can the bank now make a loan: Larger loan = New Excess Reserves - Previous Excess Reserves Larger loan = \(\$ 80,000 - \$ 50,000\) = \(\$ 30,000\) Next, let's calculate how much more the money supply can be increased: Increased money supply = New maximum increase in money supply - Previous maximum increase in money supply Increased money supply = \(\$ 666,640 - \$ 333,500\) = \(\$ 333,140\) With a 12% reserve requirement, First Bank can make a \(\$ 30,000\) larger loan, and the money supply can be increased by \(\$ 333,140\) more.

Key concepts

Reserve Requirement

The reserve requirement is a crucial tool in a central bank's monetary policy framework. It dictates the minimum amount of reserves a bank must hold against its deposit liabilities. Simply put, it is a percentage of total deposits that banks must keep as cash in their vaults or pad with the central bank.

The primary purpose of reserve requirements is to ensure that banks have enough funds to meet depositor demands, keeping the banking system stable. Here’s how it works:

• If a bank has total deposits of $1,000,000 and the reserve requirement is 15%, the bank must hold $150,000 in reserves.
• These reserves are not available for loans or other investments.
• A higher reserve requirement means less money available to be loaned out, tightening the money supply.

This mechanism helps control inflation and affects the economy's overall liquidity. Lower reserve requirements increase the amount of funds available for banks to lend out, potentially stimulating economic activity.

Excess Reserves

Excess reserves represent any reserves held by a bank above the required minimum. These are the funds that banks can use to extend loans to customers.

Understanding excess reserves is essential, as they indicate the lending capacity of a bank:

• If a bank has $200,000 in cash reserves and a $150,000 reserve requirement, it has $50,000 in excess reserves.
• This $50,000 can be lent out as new loans, increasing economic activity.
• Excess reserves fluctuate with changes in the reserve requirement, impacting the bank’s ability to extend new loans.

For banks, excess reserves act as a buffer or cushion, providing flexibility in lending. They can also reflect the bank's anticipation of financial needs or future opportunities to loan more if reserve requirements are adjusted or the economic environment changes.

Money Supply Increase

An increase in the money supply can occur when banks lend out excess reserves, creating more money in the economy. The process is magnified through the banking system via the money multiplier effect.

The money multiplier represents how much the money supply can increase with each dollar of reserves:

• The formula for the money multiplier is \( \frac{1}{\text{Reserve Requirement}} \).
• With a 15% reserve requirement, the money multiplier is about 6.67.
• Excess reserves of \(50,000, once loaned out, can enhance the money supply by about \)333,500 (i.e., $50,000 x 6.67).

By reducing reserve requirements, central banks can further increase the money supply. For example, a new reserve requirement of 12% gives a money multiplier of 8.33, potentially boosting the money supply significantly more. These changes impact economic activity by affecting consumer spending and business investments.