In the country of Examnia, the monetary base is B = $1000, and the currency-deposit ratio is 0.2. The money supply is M = $3000. Calculate the reserve-deposit ratio
Question
In the country of Examnia, the monetary base is B = 3000. Calculate the reserve-deposit ratio
Solution
To calculate the reserve-deposit ratio, we first need to understand the concept of the money multiplier. The money multiplier (m) is the amount of money that banks generate with each dollar of reserves. The formula for the money multiplier is:
m = 1 + c / r + c
where c is the currency-deposit ratio and r is the reserve-deposit ratio.
We know that the money supply (M) is equal to the monetary base (B) times the money multiplier (m). So we can rearrange the formula to solve for the reserve-deposit ratio (r):
r = c / (m - 1 - c)
We know that M = 1000, and c = 0.2. So we can calculate m as M / B = 1000 = 3.
Now we can substitute these values into the formula to find r:
r = 0.2 / (3 - 1 - 0.2) = 0.2 / 1.8 ≈ 0.111
So, the reserve-deposit ratio in the country of Examnia is approximately 0.111, or 11.1%.
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