Final answer:
In scenario A, the Fed would use expansionary monetary policy to counteract a decrease in the velocity of money, while in scenario B, it would use contractionary monetary policy. The response is based on the Fed's primary goal in each scenario and how the shock affects the variables it cares about.
Step-by-step explanation:
In scenario A, where the Fed cares only about keeping the price level stable, its response to an exogenous decrease in the velocity of money would be to use expansionary monetary policy. It would increase the money supply to compensate for the decrease in velocity, which would help stimulate aggregate demand and prevent a decrease in the price level.
In scenario B, where the Fed cares only about keeping output and employment at their natural levels, its response to an exogenous decrease in the velocity of money would be to use contractionary monetary policy. It would decrease the money supply to counteract the decrease in velocity, which would help reduce aggregate demand and prevent an increase in output and employment beyond their natural levels.
In both scenarios, the Fed's response is determined by its primary goal and how the shock affects the variables it cares about.