Question

Although the U.S. Federal Reserve doesn't use changes in reserve requirements to manage the money supply, the central bank of Albernia does. The commercial banks of Albernia have $\mathrm{\$}100$ million in reserves and $\mathrm{\$}1,000$ million in checkable deposits; the initial required reserve ratio is $10\mathrm{\%}$. The commercial banks follow a policy of holding no excess reserves. The public holds no currency, only checkable deposits in the banking system. a. How will the money supply change if the required reserve ratio falls to $5\mathrm{\%}$ ? b. How will the money supply change if the required reserve ratio rises to $25\mathrm{\%}$ ?

Short answer

Answer: When the required reserve ratio falls to 5%, the money supply will increase by $1,000 million. When it rises to 25%, the money supply will decrease by $600 million.

Step-by-step solution

Calculate initial money supply

First, let's calculate the initial money supply given the required reserve ratio of $10\mathrm{\%}$. The money multiplier formula is: `Money Multiplier = 1 / Required Reserve Ratio` So, the initial money multiplier is: `Initial Money Multiplier = 1 / 0.10 = 10` Now, we can calculate the initial money supply by multiplying the initial money multiplier by the total reserves: `Initial Money Supply = Initial Money Multiplier × Total Reserves = 10 × $100$million=$$1,000$ million.

Case a: Required reserve ratio falls to 5%

To calculate the new money supply when the required reserve ratio falls to $5\mathrm{\%}$, we need to first calculate the new money multiplier. `New Money Multiplier = 1 / 0.05 = 20` Now, we can calculate the new money supply: `New Money Supply = New Money Multiplier × Total Reserves = 20 × $100$million=$$2,000$ million. The change in the money supply is: `Change in Money Supply = New Money Supply - Initial Money Supply = $2,000$million-\mathrm{\$}1,000$ million = $\mathrm{\$}1,000$ million. So, if the required reserve ratio falls to $5\mathrm{\%}$, the money supply will increase by $\mathrm{\$}1,000$ million.

Case b: Required reserve ratio rises to 25%

Now, let's calculate the new money supply when the required reserve ratio rises to $25\mathrm{\%}$. The new money multiplier is: `New Money Multiplier = 1 / 0.25 = 4` Then, the new money supply is: `New Money Supply = New Money Multiplier × Total Reserves = 4 × $100$million=$$400$ million. Finally, the change in the money supply is: `Change in Money Supply = New Money Supply - Initial Money Supply = $400$million-\mathrm{\$}1,000$ million = $-\mathrm{\$}600$ million. In this case, if the required reserve ratio rises to $25\mathrm{\%}$, the money supply will decrease by $\mathrm{\$}600$ million.

Key concepts

Required Reserve Ratio

The required reserve ratio is a crucial tool used by central banks to control the amount of money that banks can lend out. It is defined as the percentage of deposits that commercial banks must hold as reserves, either in their vaults or at the central bank.
Just like in the example with the country of Albernia, when the required reserve ratio changes, it can significantly affect the money supply.

• If the reserve ratio decreases, banks are required to hold less money, allowing them to lend more, which increases the overall money supply in the economy.
• Conversely, if the reserve ratio increases, banks must hold more money in reserve and are able to lend less, which decreases the money supply.

Let's look at an example. With a reserve ratio of 10%, out of every $1,000 million in deposits, banks must keep $100 million on reserve. If the reserve ratio drops to 5%, banks can now keep only $50 million on reserve, freeing up $50 million for lending. This shift allows the money supply to grow, boosting economic activity. These adjustments directly impact the lending capacity of banks and, by extension, the broader economy.

Money Multiplier

The money multiplier is a fundamental concept in banking; it illustrates how much the money supply is expected to increase through the lending activities of banks. It is calculated as the inverse of the required reserve ratio.

• For example, if the reserve ratio is 10%, the money multiplier is computed as: $\text{Money Multiplier}=\frac{1}{0.10}=10$.
• This multiplier indicates that for every dollar held in reserves, the banks can create $10 in the economy through lending.

When the required reserve ratio changes, so does the money multiplier.

If the reserve ratio in Albernia is lowered to 5%, the money multiplier becomes 20, allowing the money supply to double. Conversely, a reserve ratio of 25% reduces the multiplier to 4, significantly decreasing the money supply. Therefore, the money multiplier effectively measures the degree to which the banking system amplifies the money supply, contingent on regulatory constraints such as the reserve requirement.

Central Banking

Central banks play a pivotal role in managing a nation's economy by controlling the money supply and interest rates. By setting the required reserve ratio, a central bank like Albernia's can influence the lending abilities of commercial banks, thereby affecting the money supply.

This control is part of a broader strategy known as monetary policy, which aims to achieve economic goals such as stable prices, low unemployment, and economic growth.

• A lower reserve ratio set by the central bank can stimulate economic growth by increasing the money supply and encouraging more lending and investment.
• On the other hand, a higher reserve ratio can help cool down an overheated economy by restricting the money supply, thus curbing inflation.

Though the U.S. Federal Reserve rarely uses reserve ratio adjustments to manage the money supply, preferring tools like open market operations and the discount rate, other central banks might find them effective in their unique economic landscapes. Central banks must carefully balance these tools to manage liquidity in the financial system effectively, maintaining economic stability and confidence.