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?

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 | \(\$ 1,000,000\)|

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 \(\$ 50,000\).

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 \(\$ 333,500\).

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.