If the required reserve ratio decreases, the money multiplier will:

Question

BlackTom AI · Accepted Answer

The money multiplier in the simple deposit model is the reciprocal of the required reserve ratio: m = 1 / rr. This core relationship means the multiplier is inversely related to the reserve ratio.

Step-by-step reasoning:
1. Start with the basic formula: m = 1 / rr. The required reserve ratio (rr) is a positive fraction (for example 0.10 for 10%).
2. If rr decreases, the denominator of 1/rr becomes smaller. A smaller positive denominator yields a larger quotient, so m increases.
3. Numerical example (simple model): if rr = 0.10 then m = 1 / 0.10 = 10. If rr falls to 0.05 then m = 1 / 0.05 = 20. The multiplier rises from 10 to 20.
4. More general formula (including currency and excess reserves): m = (1 + c) / (rr + e + c), where c is currency/deposit ratio and e is excess-reserve/deposit ratio. Holding c and e constant, reducing rr lowers the denominator and so increases m. Example: c = 0.2, e = 0: with rr = 0.10, m = 1.2 / 0.30 = 4. With rr = 0.05, m = 1.2 / 0.25 = 4.8 — again m rises.

Why the correct answer is correct:
Because the multiplier equals (roughly) 1 divided by the required reserve ratio, a decrease in rr reduces the divisor and therefore raises the multiplier. Banks are able to lend a larger fraction of deposits, creating more money through successive rounds of lending.

Why other options are incorrect:
a. “become negative” — rr is positive, so 1/rr cannot be negative. b. “fall” — that would contradict the inverse relationship; lowering rr increases m, not decreases it. d. “stay the same” — changing rr changes the multiplier unless offset by other parameter changes.

Conclusion: The money multiplier will rise, so answer c. rise is correct.

If the required reserve ratio decreases, the money multiplier will:单项选择题

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