Economic mechanics at work in this question?

From Book 6 exam 2 AM session, question 38. The answer is: In the aggregate supply-aggregate demand model, an unannounced decrease in the growth rate of the money supply will decrease output and prices in the short run, but in the long run inflation will decrease more and output will return to the full-employment level as short-run aggregate supply increases in response to the decrease in inflation. Can someone explain the mechanics here? I’m having hard time wrapping my head around why output (supply) decreases in the short run AND prices decrease. If money supply growth is less than expected, inflation is less than expected, so real wage rates are higher than expected, which would move the short run supply curve to the left as suppliers reduce labor costs, but I don’t see how this *decreases* price if the short run demand curve remains constant. Help?

A decrease in oney supply will decrease AD, so AD shifts left, which means less Q and less P (supply hasn’t changed). As a result, interest rates rise and inflation decreases (because of the reduced demand)…eventually producers raise their output (since their cost is now lower due to the decreasing inflation). When that happens prices decrease even more, and output rises to full employment again. Looks straightforward.