please give the answer in 40 mins.

The New Keynesian Phillips curve we derived in class is given as: 7T: = 51Et7rt+1 'l' 551: + Ht: where 7r; is inflation, 37 is the output gap, and #t is a costpush shock unrelated to the level of the output gap. You can assume that the natural level of output is eicient, i.e. a zero output gap is desirable. 1. Discuss why price rigidities make zero ination the efcient outcome. Think about the distortions that non-zero ination introduces under Calvo price setting. 2. Explain what \"divine coincidence\" is in the absence of costpush shocks (m E 0). 3. Suppose that at > 0 for one period only. Should the central bank keep the current output gap at zero? Discuss the tradeoff monetary policy faces in this case