The importance of using rather than saving your ammunition in the presence of the zero lower bound. Suppose inflation is described by the accelerations 
and that output is determined by a simple IS curve
Initially, the central bank is setting the nominal interest rate at a strictly positive level: i(0) > 0. Assume
(a) Suppose the central bank keeps i constant at i (0). Sketch the behavior of inflation and output over time.
(b) Suppose the central bank keeps i constant at i (0) until some time when bπ(t) < 0, and then permanently reduces i to zero. Sketch the behavior of inflation and output over time.
(c) Suppose the central bank permanently reduces i to zero at t = 0. Sketch the behavior of inflation and output over time.
(d) Explain your results intuitively.
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