In a specific economy, the central bank reports a monetary base of 8 million dollars. The currency-deposit ratio (cr) in this economy is 0.2. If the money supply in this economy is 24 million dollars, what is the reserve-deposit ratio?
Question
In a specific economy, the central bank reports a monetary base of 8 million dollars. The currency-deposit ratio (cr) in this economy is 0.2. If the money supply in this economy is 24 million dollars, what is the reserve-deposit ratio?
Solution
The money supply in an economy is determined by the monetary base, the currency-deposit ratio (cr), and the reserve-deposit ratio (rr). This relationship is expressed by the money multiplier formula:
Money Supply = Monetary Base * [(1+cr) / (cr+rr)]
We can rearrange this formula to solve for the reserve-deposit ratio (rr):
rr = [(1+cr) / (Money Supply / Monetary Base)] - cr
Substituting the given values into this formula:
rr = [(1+0.2) / (24 million / 8 million)] - 0.2 rr = [1.2 / 3] - 0.2 rr = 0.4 - 0.2 rr = 0.2
So, the reserve-deposit ratio in this economy is 0.2.
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