6.16. Consider an economy consisting of some firms with flexible prices and some with rigid prices. Let pf denote the price set by a representative flexible-price firm and pr the price set by a representative rigid-price firm. Flexible-price firms set their prices after m is known; rigid-price firms set their prices before m is known. Thus flexible-price firms set pf = p∗

i = (1 − φ)p + φm, and rigid-price firms set pr = E p∗

i = (1 − φ)E p + φEm, where E denotes the expectation of a variable as of when the rigid-price firms set their prices.

Assume that fraction q of firms have rigid prices, so that p = qpr+ (1−q)pf

.

(a) Find pf in terms of pr, m, and the parameters of the model (φ and q).

(b) Find pr in terms of Em and the parameters of the model.

(c) (i) Do anticipated changes in m (that is, changes that are expected as of when rigid-price firms set their prices) affect y? Why or why not?