Consider the AE/PC model with time lags. Suppose the economy starts in 2019 with output at potential and constant inflation. In 2020, an adverse supply shock occurs, shifting the Phillips curve up.
a. Show the paths of output and inflation over time if the central bank keeps the real interest rate constant.
b. Can the central bank prevent inflation from rising temporarily as a result of the supply shock? Can it prevent inflation from rising permanently? Explain.
c. Suppose policymakers want to return inflation to its 2019 level as quickly as possible and then keep inflation constant. What path should policymakers choose for the real interest rate? What are the resulting paths of output and inflation?