Assume that banks do not hold excess reserves. The banking system has $20 million in reserves and has a reserve requirement of 20 percent. The public holds $10 million in currency. Then the public decides to withdraw $5 million in currency from the banking system. If the Bank of Canada wants to keep the money supply stable by changing the reserve requirement, then what will the new reserve requirement be?
A)20 percent
B)18.2 percent
C)15.8 percent
D)15 percent

Question

Quizplus · Accepted Answer

Initially, the banking system has $20 million in reserves and a reserve requirement of 20 percent. This means that the total deposits in the banking system are $100 million ($20 million / 0.20).

When the public withdraws $5 million in currency, the reserves in the banking system decrease to $15 million. This means that the total deposits in the banking system are now $75 million ($15 million / 0.20).

To keep the money supply stable, the Bank of Canada needs to increase the reserves in the banking system back to $20 million. This can be done by reducing the reserve requirement.

Let x be the new reserve requirement. Then we have:

$10 million + $75 million * x = $20 million

Solving for x, we get:

x = 15.8 percent

Therefore, the new reserve requirement is 15.8 percent. Choice C is the correct answer.

Assume That Banks Do Not Hold Excess Reserves