This paper provides a new explanation of why inflation is sluggish in response to aggregate demand shocks and why aggregate output changes as result of such shocks. We argue that these phenomena are related to lags between inputs and outputs in the production process, "production lags" for short. The broad intuition is that production activities in a modern economy are interconnected through complex input-output relations, with production lags within individual firms, and that it takes considerable time for cost and price changes to penetrate the entire input-output system. Our analysis provides a rationale for a prolonged inverse relation between inflation and unemployment. The paper suggests that the interaction of inflation persistence and unemployment persistence may offer a possible explanation of high and prolonged European unemployment.