Suppose the money multiplier in the United States is 3. Suppose further that if the Fed increases the discount rate by 1 percentage point, banks initially change their reserves by 400. To reduce the money supply by 4,200 the Fed should:

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The money multiplier formula is $ \Delta M = m \times \Delta R $, where $ \Delta M $ is the change in the money supply, $ m $ is the money multiplier, and $ \Delta R $ is the change in reserves. To reduce the money supply by 4,200 with a multiplier of 3, the change in reserves needed is $ \Delta R = \frac{\Delta M}{m} = \frac{4200}{3} = 1400 $. Since a 1 percentage point increase in the discount rate initially changes reserves by 400, to achieve a change of 1400 in reserves, the discount rate needs to be raised by $ \frac{1400}{400} = 3.5 $ percentage points.

Suppose the Money Multiplier in the United States Is 3