Question

If the central bank sells \(\$ 500\) in bonds to a bank that has issued \(\$ 10,000\) in loans and is exactly meeting the reserve requirement of \(10 \%,\) what will happen to the amount of loans and to the money supply in general?

Short answer

After the central bank sells \(500 in bonds to the bank, the amount of loans that the bank can issue decreases by \)5,000, and the money supply in general also decreases by $5,000.

Step-by-step solution

Calculate Initial Reserves

To find the initial reserves, we first consider the reserve requirement. The reserve requirement is 10% and the bank issued $10,000 in loans, which means it must hold 10% of this amount as reserves. Calculate the initial reserves using the formula: Initial Reserves = Loans * Reserve Requirement Initial Reserves = \(10,000 * 0.1\) Initial Reserves = $1,000

Calculate New Reserves

The bank purchases \(500 in bonds from the central bank. This takes away \)500 from its reserves. Calculate the new reserves by subtracting the bond purchase from the initial reserves: New Reserves = Initial Reserves - Bond Purchase New Reserves = \(1,000 - 500\) New Reserves = $500

Calculate New Amount of Loans

Now we know the new reserves, and we know the bank must still maintain a 10% reserve requirement. To find the new amount of loans, we can use the formula: New Loans = New Reserves / Reserve Requirement New Loans = \(500 / 0.1\) New Loans = $5,000

Calculate Change in Loans and Money Supply

To find the change in loans, subtract the new amount of loans from the initial amount of loans: Change in Loans = New Loans - Initial Loans Change in Loans = \(5,000 - 10,000\) Change in Loans = -$5,000 Since loans contribute to the money supply, the money supply will also decrease by $5,000. In conclusion, after the central bank sells \(500 in bonds to the bank, the amount of loans that the bank can issue decreases by \)5,000, and the money supply in general also decreases by $5,000.

Key concepts

Reserve Requirement

The reserve requirement is a critical tool used by central banks to influence the banking system and, ultimately, the economy. It refers to the minimum fraction of customer deposits and notes that each commercial bank must hold as reserves, rather than lend out. This requirement is typically established by a country's central bank, which in this case is assumed to be set at 10%.

To put it simply, if a bank holds customer deposits of $10,000, it is required by the central bank to keep 10% of these deposits in reserve. This means the bank must hold $1,000, which cannot be loaned out. The remaining $9,000 can be used to issue loans or for investment purposes. Reserve requirements are fundamental in mitigating risk and ensuring that the bank has enough liquidity to meet depositors' demands.

• Ensures banks have a buffer of funds available during high demand or withdrawal periods.
• Acts as a safeguard against bank runs.
• Influences how much money banks can loan out.

The reserve requirement affects the capacity of banks to create new money through lending. A higher reserve requirement means banks can lend less, while a lower requirement allows them to lend more.

Money Supply

The money supply is the total amount of monetary assets available in an economy at a specific time. It includes all the money that households and businesses own in the form of cash and deposits in the bank. The money supply can be affected by several factors, particularly the actions of the central bank.

When a bank's ability to issue loans is reduced, as seen in the example where a central bank issued bonds led to a decrease in available reserves, the money supply declines. Essentially, when banks have less to lend, there's less new money entering the economy.

• Loans increase the money in circulation; hence, fewer loans mean a reduced money supply.
• Changes in money supply can affect inflation, interest rates, and overall economic growth.
• A decrease in money supply can slow down the economy by reducing consumer spending and business investments.

By selling bonds and reducing reserves, the central bank can mitigate inflation and stabilize the economy by controlling the money supply. This exercise showed an example of how the central bank's actions can impact the money supply negatively.

Central Bank

A central bank is a pivotal financial institution that carries out a country's monetary policy, aiming to maintain financial stability and guide the economy. It has the unique ability to control the money supply and the functioning of banks within the economy. In the provided example, the central bank took action by selling bonds, which impacted the bank's reserves and consequently, its lending capacity.

Central banks use a range of tools to manage economic activity, with the reserve requirement being one among them. By increasing or decreasing the reserve requirement, a central bank can influence how much money banks can lend, impacting the overall money supply.

• Central banks help stabilize the national currency and economy.
• They manage inflation and employment levels through monetary policy instruments.
• They use open market operations like buying or selling government bonds to control short-term interest rates and the money supply.

The bond sale in the example led to lower reserves for the bank, forcing it to reduce its lending, demonstrating the central bank's powerful role in managing and influencing the economy. This action is an example of monetary policy in play, aimed at creating desired economic outcomes by adjusting banking operations and the overall money supply.