9.17. (Cagan, 1956.) Suppose that instead of adjusting their real money holdings gradually toward the desired level, individuals adjust their expectation of in- flation gradually toward actual inflation. Thus equations (9.39) and (9.40) are replaced by m(t) = Ce-b) and (t) = B[(t)(t)], 0 < <1/b.

(a) Follow steps analogous to the derivation of (9.45) to find an expression for (t) as a function of (t).

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

(c) Sketch the phase diagram for the case of G