Question

Suppose the banking system has vault cash of \(\$ 1,000\), deposits at the Fed of \(\$ 2,000\), and demand deposits of \(\$ 10,000\). a. If the reserve requirement is 20 percent, what is the maximum potential increase in the money supply, given the banks' reserve position? b. If the Fed now purchases \(\$ 100\) worth of government bonds from private bond dealers, what are the excess reserves of the banking system? (Assume that the bond dealers deposit the \(\$ 100\) in demand deposits.) How much can the banking system increase the money supply, given the new reserve position?

Short answer

Answer: After the Fed buys $100 worth of government bonds, the new maximum potential increase in the money supply is $5,400.

Step-by-step solution

Calculate the total reserves

The total reserves of the banking system can be calculated by adding the vault cash and the deposits at the Fed. Total Reserves = Vault Cash + Deposits at the Fed = \(\$ 1,000 + \$ 2,000 = \$ 3,000\)

Calculate the required reserves

The required reserves can be calculated by multiplying the demand deposits by the reserve requirement, which is 20% in this case. Required Reserves = Demand Deposits × Reserve Requirement = \(\$ 10,000 × 0.20 = \$ 2,000\)

Compute the excess reserves and the maximum potential increase in the money supply (a)

Since we now know the total and required reserves, we can calculate the excess reserves: Excess Reserves = Total Reserves - Required Reserves = \(\$ 3,000 - \$ 2,000 = \$ 1,000\) The maximum potential increase in the money supply can be calculated using the money multiplier (1/Reserve Requirement) formula: Money Multiplier = 1/Reserve Requirement = 1/0.20 = 5 Maximum potential increase in the money supply = Excess Reserves × Money Multiplier = \(\$ 1,000 × 5 = \$ 5,000\)

Calculate the total reserves after the bond purchase by the Fed (b)

Now, let's consider the Fed purchasing \(\$ 100\) worth of government bonds. The bond dealers deposit the \(\$ 100\) in demand deposits, increasing the total reserves: New Total Reserves = Original Total Reserves + Bond Purchase Amount = \(\$ 3,000 + \$ 100 = \$ 3,100\)

Calculate the new required reserves and the excess reserves (b)

The new required reserves can be computed by multiplying the new demand deposits (which is now increased by the bond purchase amount) by the reserve requirement: New Demand Deposits = \(\$ 10,000 + \$ 100 = \$ 10,100\) New Required Reserves = New Demand Deposits × Reserve Requirement = \(\$ 10,100 × 0.20 = \$ 2,020\) Now, let's find the new excess reserves: New Excess Reserves = New Total Reserves - New Required Reserves = \(\$ 3,100 - \$ 2,020 = \$ 1,080\)

Find the new maximum potential increase in the money supply (b)

Using the money multiplier (from step 3) and the new excess reserves, we can calculate the new potential increase in the money supply: New maximum potential increase in the money supply = New Excess Reserves × Money Multiplier = \(\$ 1,080 × 5 = \$ 5,400\) To summarize: a. The maximum potential increase in the money supply, given the banks' reserve position is \(\$ 5,000\). b. After the Fed buys \(\$ 100\) worth of government bonds, the excess reserves are \(\$ 1,080\), and the new maximum potential increase in the money supply is \(\$ 5,400\).