Consider a continuous-time version of the Mankiw–Reis model. Opportunities to review pricing policies follow a Poisson process with arrival rate α > 0. Thus the probability that a price path set at time t is still being followed at time t+i is e−αi . The other assumptions of the model are the same as before. (a) Show that the expression analogous to (7.81) is a(i) (b) Consider the experiment of a permanent fall in the growth rate of aggregate demand discussed in Section 7.7. That is, until t = 0, all firms expect m(t) = gt (where g > 0); thereafter, they expect m(t) = 0. (i) Find the expression analogous to (7.83). (ii) Find an expression for inflation, p˙(t), for t ≥ 0. Is inflation ever negative during the transition to the new steady state? (iii) Suppose φ= 1. When does output reach its lowest level? When does inflation reach its lowest level?
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