Last year, the currency-deposit ratio was 0.2 and the reserve-deposit ratio was 0.2. Over the past year, the public changed its currency-deposit ratio, to which the Fed responded by reducing the reserve-deposit ratio to 0.15, to keep the money supply from changing and keeping the same monetary base. Calculate the new currency-deposit ratio. Show your work.
What will be an ideal response?
Because neither the money supply nor the monetary base have changed, the money multiplier must remain unchanged. The old money multiplier is (0.2 + 1)/(0.2 + 0.2) = 3. Letting c stand for the new currency-deposit ratio, the new money multiplier equals (c + 1)/(c + 0.15). Since this must equal the old money multiplier, we have:
3 = (c + 1)/(c + 0.15), so 3(c + 0.15) = c + 1, so 3c + 0.45 = c + 1, so 2c = 0.55, so c = 0.275.
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