11.22. (Cagan, 1956.) Suppose that instead of adjusting their real money holdings gradually toward the desired level, individuals adjust their expectation of inflation gradually toward actual inflation. Thus equations (11.70) and (11.71)

are replaced by m(t) = Cexp(−bπe(t)) and π˙e(t) = β[π(t)−πe(t)], 0 < β < 1/b.

(a) Follow steps analogous to the derivation of (11.75) to find an expression for π˙e(t) as a function of π (t).

(b) Sketch the resulting phase diagram for the case of G > S MAX. What are the dynamics of πe and m?

(c) Sketch the phase diagram for the case of G < S MAX.