Fed could change its inflation target temporarily to offset the effect of an aggregate demand shock (a-bar). In this problem, you can calculate by how much. Suppose that the economy starts in the steady state in 2021 with pi-bar = 2%, b-bar = 1/2, m-bar = 1/2, and v-bar= 1/2. An AD shock equal to a-bar = 2% occurs in 2021.

a. Using the simple monetary policy rule, show by how much inflation and short-run output change in 2021 if the Fed keeps its target inflation equal to 2%. Calculate inflation and short-run output for 2022 and 2023.

b. Use an AD/AS diagram to show how a decrease in the inflation target can keep inflation and short-run output from starting to rise in 2021. Explain your diagram and what it reveals about monetary policy.
c. Calculate how much the Fed needs to lower its inflation target pi-bar below 2% to keep inflation and short-run output from rising.
d. Suppose the Fed adopts a Taylor rule. Show how adding a term nY (n-bar Y-bar) to the simple monetary policy rule changes the shift in the AD curve following an aggregate demand shock a-bar n the AD equation. Using the parameter values for this question, calculate the value of n-bar for the Fed that keeps inflation and short-run output from rising.