Suppose the Federal Reserve's short-run response to any change in the economy is to change the money supply to maintain the existing real interest rate

What would happen to money supply if there were a reduction in government purchases? Given the Fed's policy, what would happen in the very short run (before general equilibrium is restored) to output and the real interest rate? What must happen to the LM curve and the price level to restore general equilibrium?

The decrease in G shifts the IS curve down and to the left. The Fed's policy decreases the money supply and shifts the LM curve up and to the left, so the real interest rate doesn't change. But output declines in the very short run. To restore general equilibrium, the price level must decline to shift the LM curve down and to the right. If the Fed wanted to keep the price level from changing so much, its correct policy would have been to increase the money supply, not decrease it.