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Use the dynamic AD-AS model we have discussed in class to solve for inflation as a function of only lagged inflation and supply and demand shocks. Assume target inflation is constant.
1. According to the equation you have derived, does inflation return to its target after a shock? Explain. Hint: Look at the coefficient on lagged inflation.
2. 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)?
3. 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)?
4. Suppose the central bank does not follow the Taylor principle but in-stead 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?
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