If banks reduce their excess reserves by $1m, what will happen to the money supply (assume a reserve requirement of 2%, c = 0 and e = 0)? Group of answer choices it will increase by $100m it will decrease by $100 m it will increase by $50m it will decrease by $5m
The correct answer and explanation is:
Correct Answer: It will increase by $50 million
Explanation:
To understand how a $1 million reduction in excess reserves affects the money supply, we use the concept of the money multiplier in the banking system.
Key Terms:
- Reserve Requirement (rr): This is the fraction of deposits that banks must keep as reserves. In this question, it’s 2% or 0.02.
- Excess Reserves: Money that banks hold beyond what is required. If banks reduce this by $1 million, they are lending it out, which increases the money supply.
- Currency-deposit ratio (c): This is 0, meaning all money is held in bank deposits.
- Excess reserve ratio (e): This is also 0, meaning banks do not hold any extra reserves beyond the required minimum.
- Money Multiplier (m): m=1rr+e+c=10.02+0+0=10.02=50m = \frac{1}{rr + e + c} = \frac{1}{0.02 + 0 + 0} = \frac{1}{0.02} = 50
Step-by-Step Calculation:
- Reduction in excess reserves = $1,000,000
- Money multiplier = 50
- Increase in money supply = 1,000,000 × 50 = $50,000,000
Conclusion:
If banks reduce their excess reserves by $1 million and lend it out, the banking system multiplies this base money through the process of deposits and loans. With a reserve requirement of 2% and no currency or excess reserves held back, the entire $1 million gets multiplied by 50, increasing the money supply by $50 million.
Thus, the correct answer is: “It will increase by $50 million.”