AE6102 ADVANCED MACROECONOMIC THEORY
PROBLEM SET 2 IS-MPR-PC
Instructions: You are required to work on Problem Set 2 for submission on NTULearn by 15 December 2024, 1159pm. Group 3 is to present Question 1, Group 4 Question 2 and Group 5 Question 3.
1. The IS curve is given by:
yt = yt(*) — α(it — πt — r *) + εt(y)
Monetary policy rule (MPR) is:
it = r * + π * + βπ (πt — π *)
And the Phillips curve (PC) is:
πt = πt(e) + Y(yt — yt(*)) + εt(π)
All variables and parameters are as described in the lectures. Assume that βπ > 1.
(a) Derive the IS-MPR curve by substituting the monetary policy rule into the IS curve. Show the full derivation and explain the role of βπ in determining the slope and intercept of this curve.
(b) Assume a positive aggregate demand shock. Solve for the new equilibrium levels of output and inflation algebraically. Provide graphical illustrations.
(c) If inflation expectations rise following the aggregate demand shock, analyze how this amplifies the impact on inflation and output. Discuss the central bank’s response under different values of βπ .
2. Using the IS-MPR-PC model, examine the effects of a rise in public inflation expectations when the central bank adjusts interest rates according to a Taylor rule with an additional response to the output gap such that:
it = r * + π * + βπ (πt — π *)+βy (yt — yt(*))
(a) Derive the IS-MPR curve with the Taylor rule, showing how βy modifies the relationship between inflation and output.
(b) Solve for inflation and output when inflation expectations rise. Discuss how the central bank's response coefficients βπ and βy interact to influence the outcomes.
(c) Evaluate the conditions under which the central bank can stabilize both inflation and output effectively. Discuss trade-offs that arise when βπ and βy are too low or too high.
3. Analyze the implications of adaptive inflation expectations in the IS-MPR-PC model, incorporating supply shocks.
(a) Derive the dynamic path of inflation and output over four periods (t, t + 1, t + 2, t + 3) following a temporary positive supply shock and an aggregate demand shock.
(b) Discuss the conditions under which the economy exhibits counter-cyclical inflation-output loops. Analyze how these dynamics depend on βπ , α , and Y . Provide both graphical and algebraic explanations.
(c) Compare the outcomes under adaptive expectations to a scenario where inflation expectations are anchored at π * . Discuss policy implications for central bank communication strategies and inflation targeting framework.