Synchronized price-setting. Consider the Taylor model. Suppose, however, that every other period all the firms set their prices for that period and the next. That is, in period t prices are set for t and t + 1; in t + 1, no prices are set; in t + 2, prices are set for t + 2 and t + 3; and so on. As in the Taylor model, prices are both predetermined and fixed, and firms set their prices according to (7.30). Finally, assume that m follows a random walk.

(a) What is the representative firm’s price in period t, xt, as a function of mt, Etmt+1, pt, and Et pt +1?

(b) Use the fact that synchronization implies that pt and pt +1 are both equal to xt to solve for xt in terms of mt and Etmt+1.

(c) What are yt and yt +1? Does the central result of the Taylor model that nominal disturbances continue to have real effects after all prices have been changed still hold? Explain intuitively.