Chapter 13: Problem 474

When does the lowering of the reserve requirements have the same effect as open market purchases on the money supply?

Short Answer

Expert verified

Lowering reserve requirements and open market purchases have the same effect on the money supply when the increase in the Money Multiplier due to the decrease in reserve requirements is equal to the increase in the Money Multiplier due to the higher amount of excess reserves as a result of open market purchases, while keeping the reserve ratio the same. In other words, when reserve requirements decrease (lower R) and excess reserves increase due to open market purchases, both actions lead to the same increase in the Money Multiplier and thus the same effect on the money supply.

Step by step solution

Understand Reserve Requirements and Open Market Purchases

Reserve Requirements: The minimum amount of money that banks must hold in reserves, either as cash or in their accounts at the central bank, expressed as a percentage of the total deposits. Open Market Purchases: When a central bank buys government securities in the open market, increasing the monetary base and expanding the money supply. The connection between these two concepts lies in the money multiplier. When the reserve ratio decreases or the central bank purchases government securities, financial institutions have more reserves to lend, increasing the money supply.

Derive the Money Multiplier formula

The Money Multiplier (MM) formula is used to calculate the potential expansion of the money supply based on the reserve ratio (R) and the amount of excess reserves (ER) in the banking system. The basic formula for Money Multiplier is: MM = \( \frac{1}{R} \)

Understand the impact of reserve requirements on the Money Multiplier

When the reserve requirement ratio decreases, the Money Multiplier increases. This happens because there is a lower amount of money that banks are required to hold in reserves, giving them more money to lend, which can increase the money supply. In other words, if R decreases, MM increases.

Understand the impact of open market purchases on the Money Multiplier

When a central bank conducts open market purchases, it buys government securities and introduces new reserves into the banking system. As a result, banks have more reserves that they can use to make loans and create new money. In essence, when Open Market Purchases increase the excess reserves, the effect on the Money Multiplier depends on the reserve requirements established. If reserve requirements stay constant, the Money Multiplier remains constant as well.

Determine the conditions for both actions to have the same effect on the money supply

For lowering reserve requirements and open market purchases to have the same effect on the money supply, they must lead to the same increase in the Money Multiplier. Based on our analysis, we can conclude that: 1. Reserve requirements must decrease (lower R). 2. Excess reserves must increase due to open market purchases, but the reserve ratio must remain constant. These two actions will have the same effect on the money supply when the increase in the Money Multiplier due to the decrease in reserve requirements is equal to the increase in the Money Multiplier due to the higher amount of excess reserves as a result of open market purchases, while keeping the reserve ratio the same.