Suppose people's expectations of inflation are subject to random shocks. That is, instead of being merely adaptive, the expectation in period t of inflation in period t + 1 is E_tt+1 = _t + _t , where _t is a random shock. The shock is normally zero, but it deviates from zero when some event beyond past inflation causes expected inflation to change. Similarly, E_t1t = t1 + _t-1.

(a) Derive both the dynamic aggregate demand (DAD) equation and the dynamic aggregate supply (DAS) equation in this slightly more general model. [10 points]

(b) Suppose that the economy experiences an inflation scare. That is, in period t, for some reason people come to believe that inflation in period t + 1 is going to be higher, so _t is greater than zero (for this period only). What happens to the DAD and DAS curves in period t? What happens to output, inflation, and nominal and real interest rates in that period? [15 points]

c) What happens to the DAD and DAS curves in period t + 1? What happens to output, inflation, and nominal and real interest rates in that period? [10 points]

(d) What happens to the economy in subsequent periods? [10 points]

(e) In what sense are inflation scares self-fulfilling? [5 points]