11.11. The importance of using rather than saving your ammunition in the presence of the zero lower bound. Suppose inflation is described by the accelerationist Phillips curve, ˙π(t) = λy(t),λ > 0, and that output is determined by a simple IS curve, y(t) = −b[i(t) − π(t)], b > 0, Initially, the central bank is setting the nominal interest rate at a strictly positive level: i(0) > 0. Assume

−b[i(0) − π(0)] < 0 < bπ(0).

(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.