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In order to find the correct answer for this, it is necessary to know the equation for a change in the money supply in this situation. That equation is:
Actual money supply change = initial change in excess reserves x money multiplier.
Now, we need to find two things. First, we need to find out how much excess reserves have changed. Second, we must find the money multiplier.
The central bank has increased total reserves by $50,000. If your professor is being precise, this is not the same thing as the increase in excess reserves. That is because 7% of that $50,000 must be kept as required reserves. That means that $3500 ($50,000*.07) must be kept in required reserves and $46,500 is the initial change in excess reserves.
Now, we need to know the money multiplier. The formula for finding that is:
Money multiplier = 1 / required reserve ratio.
In this case:
Multiplier = 1/.07 = 14.3
Now that we have that, we can find the actual change in money supply. The initial change in excess reserves was $46,500 and the multiplier is 14.3
$46,500*14.3 = $664,950
So, when the central bank takes this action, the money supply increases by $664,950.
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