Suppose in the NKRE model that from time 0 until time T -1, the natural rate of interest is r₁*, where r₁* < -π*, and from time T on the natural rate of interest is r₂* > 0. Also, suppose that the central bank can achieve its inflation target from period T onward and that the central bank sets the nominal interest rate to zero from time 0 until time T - 1.

a. What will happen to inflation and output from period 0 until period T - 1. Explain with the aid of a diagram.

b. What can the central bank do about the problem that arises in part (a) Discuss.