The money multiplier is smaller when:

Question

BlackTom AI · Accepted Answer

The money multiplier is given by m = (1 + c) / (r + e + c), where c = currency/deposit ratio, r = required reserve ratio, and e = excess reserve/deposit ratio.

1) Relevant knowledge points and concepts
- Money multiplier measures how much the money supply expands for a given base money injection.
- It depends on public currency holdings (c), required reserves (r), and excess reserves (e). A larger denominator lowers m; a larger numerator raises m.
- Velocity (the rate at which money circulates) affects nominal spending (MV = PY) but does not directly change the banking-sector money multiplier.

2) Step-by-step reasoning
- If the required reserve ratio r increases, the denominator (r + e + c) increases while the numerator (1 + c) stays the same ⇒ m falls.
- If banks hold fewer excess reserves (e decreases), denominator falls ⇒ m rises.
- If currency holdings by the public decrease (c decreases), numerator and denominator both fall; in typical parameter ranges this increases m (see calculation).
- Velocity changes do not enter the multiplier formula.

3) Calculations with intermediate steps (numerical example)
- Start: r = 0.10, e = 0.02, c = 0.20.
  m = (1 + 0.20) / (0.10 + 0.02 + 0.20) = 1.20 / 0.32 = 3.75.
- Increase r to 0.15 (other values unchanged):
  m = 1.20 / (0.15 + 0.02 + 0.20) = 1.20 / 0.37 ≈ 3.243.
  The multiplier falls from 3.75 to ≈3.243, confirming it becomes smaller.

4) Why the correct answer is correct
- Raising the required reserve ratio forces banks to hold more reserves per deposit, reducing the fraction available for lending. That directly reduces the money creation process and so lowers the multiplier.

5) Why the other options are incorrect
- a) Fewer excess reserves (e decreases) reduces the denominator and increases m, so the multiplier would be larger, not smaller.
- b) Lower currency holdings (c decreases) typically raise m because the banking system holds a larger share of money as deposits that can be loaned; the example above shows m increases.
- c) Velocity increases affect spending but not the banking reserve/deposit relationships that determine the multiplier; velocity does not reduce the money multiplier.

6) Conclusion
These points confirm that increasing the required reserve ratio makes the money multiplier smaller. Final answer: d. Required reserve ratio increases.

The money multiplier is smaller when:单项选择题

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