Final answer:
The money supply is calculated by multiplying the monetary base by the adjusted money multiplier. With a reserve-deposit ratio and currency-deposit ratio of 0.1, the money multiplier is 5.5, resulting in a money supply of $275 billion.
Step-by-step explanation:
To calculate the money supply given the monetary base (b), the reserve-deposit ratio (rr), and the currency-deposit ratio (cr), we first need to determine the money multiplier. The formula for the money multiplier is 1 divided by the reserve ratio. The reserve ratio, in this case, being the reserve-deposit ratio (rr) as it denotes the fraction of deposits a bank holds in reserve. Given that the reserve-deposit ratio (rr) is 0.1, the money multiplier is 1/0.1, which equals 10.
Next, to account for the effect of the currency-deposit ratio (cr) on the multiplier, we adjust the formula to include cr. The adjusted money multiplier is calculated as:
(1 + cr) / (rr + cr)
Substituting the given values of rr = 0.1 and cr = 0.1, we get:
(1 + 0.1) / (0.1 + 0.1) = 1.1 / 0.2 = 5.5
We then multiply the monetary base (b) by the adjusted money multiplier to determine the money supply. Since the monetary base (b) is $50 billion:
The money supply = Monetary base (b) × Adjusted money multiplier = $50 billion × 5.5 = $275 billion.