2 AS/AD model [50 points total] 2.1 Warm-up Consider the short-run model that we analyzed in class: t = at - b(Rt - R) Rt - R = m(m - 7) Question 2.1 /5 points/ Derive the AS/AD model by substituting the monetary policy rule into the IS curve. Question 2.2 /5 points/ What conditions have to hold for each of the shocks and variables (i.e., for all quantities with a time subscript) in a steady state equilibrium? Solve for the output gap and inflation in this steady state equilibrium. 2.2 The dynamics after a shock Consider an economy with all parameters , b, m strictly positive. In the following questions, you are asked to depict the transition dynamics into the AS/AD diagram. Devote the following page to this diagram so that you can plot with enough detail. Make sure that you accurately represent the shifts of the curves and the resulting equilibria. Question 2.3 /20 points total for questions 2.3 - 2.6) The economy is in steady state in period 0. Depict the aggregate demand and aggregate supply curve in period 0, denoted ADo and ASo, respectively. Label axes and the steady state level of inflation and output gap. Denote the equilibrium in the economy as Eo- Question 2.4 This economy experiences an adverse demand shock in period 1, for example because of a decline in foreign demand for U.S. goods. Describe how is this shock represented in the equations for aggregate demand and aggregate supply (one sentence]. Then depict this shock in the AS/AD diagram by appropriately shifting the AS and/or AD curves. Denote the new curves AD, and AS1, the equilibrium in period 1 as E1, and the equilibrium output gap Yi and equilibrium inflation m in period 1. Question 2.5 In period 2, the adverse shock to aggregate demand continues with the same magnitude. Depict the new curves AD2 and AS2, the equilibrium in period 2 denoted Ez, and the equilibrium output gap Y2 and equilibrium inflation 72. ource was downloaded by 100000872326282 from CourseHero.com on 05-05-2024 11:27:05 GMT -05:00 coursehero.com/file/145382472/spring-2021-finalpdf Question 2.6 In period 3, the adverse shock reverts back to zero and stays at zero thereafter. Depict the new curves AD3 and AS3, the equilibrium in period 2 denoted E3, and the equilibrium output gap Y3 and equilibrium inflation 73. Question 2.7 /10 points/ Plot the trajectories for output gap and inflation (each into a separate graph with time on the horizontal axis, large enough so that you can later plot additional lines), starting in period 0, until period 10. Data for periods 1, 2, 3 should be inferred from the AS/AD diagram that you just plotted. The remaining periods can be sketched based on your knowledge about the convergence of the economy to the steady state, assuming that the economy is not hit by any additional shocks. Denote these trajectories for output gap and inflation as Case A. 2.3 Law of motion for inflation When you solve the system of equations given by aggregate demand and aggregate supply, you obtain the law of motion for equation and the associated equation for the output gap: 7 - 1 = +7 1 + vom (74-1 - 7) + 1 + vom - (vat + et ) Y = bm 1 + vom - (71-1 - 7)+ 1 + vom - (at - bmet) Question 2.8 /10 points) Imagine that the monetary policy is absent (i.e., the central bank does not respond to inflation). Use the law of motion for inflation and the equation for output gap to depict the trajectory of inflation and output gap in periods 0 to 10 in this case, assuming the same sequence of demand shocks as in questions 2.3 - 2.6. In the same graphs you did for Case A from question 2.7 add the trajectories for inflation and the output gap. Denote the new case Case B. Make sure that you correctly depict the relative positions of the trajectories in Case A and Case B