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 m_t, E_{tmt +1}, p_t, and Et p_t+1?

 

(b) Use the fact that synchronization implies that p_t and p_t+1 are both equal to xt to solve for xt in terms of m_t and E_{tmt +1}.

 

(c) What are y_t and y_t+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.