Question 1: [30] Consider the following equations: AD from IS curve: Y, Y-ar-p)+m, +e, where Y, is the output level at time t, Y is output, r, is the real interest rate at time t, p is the natural level of money supply shock and ɛ, is a demand shock with zero expected the natural level of interest rates, m, is a value. Fisher equation: i, =r, +π +1 Phillips curve: T, =π-ß(u, -u)+v, where л, denotes the inflation rate at time t, ," denotes expected inflation, u, is the unemployment rate, u is the natural level of unemployment and v, is a supply shock. Okun's law: Y-Y=-(u, -u) Taylor Rule: i,=, +(л,-)+o, (Y-Y) I where i, is the nominal interest rate at time t, is the inflation target (constant over time) of the central bank, Øy and Q, are positive monetary policy parameters that govern how much bank's interest rate target responds to changes in output and inflation respectively. Adaptive expectations: " =₁-1 (a) [10 marks] Derive the DAD and the DAS and find the equilibrium levels of output and inflation assuming p=0. (b) [10 marks] Suppose that at time t-1 the economy is at the long run equilibrium, inflation is zero and '=0. At time there is a negative demand shock that lasts for only two periods. Using a graph to illustrate your answer, explain the effect of such a shock on the equilibrium of the DAD-DAS model. How can monetary policy be used to offset the effects of such a negative shock? (c) [5 marks] Explain briefly what the effects of the shock in b) would have been under rational expectations. (d) [5 marks] According to empirical evidence, nominal interest rates are procyclical. They rise when the economy booms and they fall during recessions. Is this empirical evidence consistent with DAD-DAS models? Explain and use graphs to illustrate your answer.