The authors modify the Dynamic Aggregate Demand-Dynamic Aggregate Supply model in Mankiw's widely used intermediate macroeconomics textbook to discuss monetary policy when the natural real interest rate is falling over time. Their results highlight a new role for the central bank's inflation target as a tool of macroeconomic stabilization. They show that even when the zero lower bound is "not" binding, a prudent central bank must match every decrease in the natural real interest rate with an equal increase in the target rate of inflation in order to stabilize the risk of the economy falling into a deflationary spiral, which is an acute case of simultaneously falling output and inflation in which the economy's self-correcting forces are inactive.