Use the dynamic AD–AS model to solve for inflation as a function of only lagged inflation and the supply and demand shocks. (Assume target inflation is a constant.)
a. According to the equation you have derived, does inflation return to its target after a shock? Explain.
b. Suppose the central bank does not respond to changes in output but only to changes in inflation, so that θY = 0. How, if at all, would this fact change your answer to part (a)?
c. Suppose the central bank does not respond to changes in inflation but only to changes in output, so that θπ = 0. How, if at all, would this fact change your answer to part (a)?
d. Suppose the central bank does not follow the Taylor principle but instead raises the nominal interest rate only 0.8 percentage point for each percentage-point increase in inflation. In this case, what is θπ? How does a shock to demand or supply influence the path of inflation?