Dynamic AS-AD Model [10 points]

Consider a dynamic AS-AD model. The dynamic aggregate supply curve is given by

_t = _t-1 +0.5(_t100)+_t

And the dynamic aggregate demand curve is given by

_t=1000.5(_t2),

where _t denotes output level and _t denotes inflation rate in percentage terms. _t captures a supply shock.

(a) [2 points] Calculate the long-run equilibrium values for output and inflation.

Suppose the economy is in the long-run equilibrium you computed in part (a). Suppose that at time =0 there is an adverse supply shock ₀=5 that lasts for two periods before reverting to zero. That is, ₀=₁=5 and _t=0 for all subsequent 2.

(b) [3 points] Compute the values of output and inflation in period =0 upon impact. What does this imply for the nominal and real interest rates in period =0? Explain how the actual inflation rate you find compares to the inflation rate that would have prevailed if there was no monetary policy reaction to inflation.

(c) [3 points] Compute the values of output and inflation in period =1. Explain how expected inflation in period =1 compares to expected inflation in period =0. What role does expected inflation play in determining output and inflation in period =1?

(d) [2 points] Explain qualitatively the subsequent time paths of output and inflation after the adverse supply shock ends (for 2). Does inflation return to its long run equilibrium value in period t = 2? Why or why not?