3 Equation model (Carlin and Soskice, 2005)

. Assume that the IS curve of an economy is given by the following equation 9': = 100 4Tt_l, The economy is currently in the full-employment (long-run) equilibrium where yt = y,3 = 80 and ination is at the target level: 7r: = 7r* = 2. The short-run Phillips curve is given by 1 71': =7Tt1 + E09: '93)- The Central Bank selects monetary policy to minimize the following loss function: Lt = (y: ye? + 6 (m ff, (a) What is the value of the stabilizing interest rate (T5) in this equilibrium? (b) Derive the monetary policy rule/ monetary response function in terms of the pa- rameter )3. (c) If the economy receives a temporary ination shock that shifts the short-run Phillips curve upward to 7r: = 4 + 3-1 + i (gt ye) (the shock only occurs one period), graphically show the new short-run Phillips curve and derive/ calculate y, r, and 7r for the following two periods if )3 = 2 and if ,6 = 5. ((1) Now assume instead that there is a permanent shock that hits the IS curve and it causes it to shift to y: = 120 4rt_1. Calculate the new level of output and the rate of ination directly after the IS shock (assuming n has not changed due to the time lag). Further, derive/ calculate y, r, and 11' for the following two periods if=2andif=5. (e) Graphically illustrate how the economy returns to a stable equilibrium