Monetary policy in an economy with sticky prices Suppose now that firms get the opportunity to change prices infrequently, so Equation (1) describes the equilibrium conditions of this economy. (a) Assume that monetary policy follows a simple interest rate rule it = p +277t + yt = = where the necessary and sufficient condition for uniqueness of equilibrium klr 1) + (1 B)y > 0) is assumed to hold. Notice that there are no monetary policy shocks in this exercise. Instead, assume that productivity follows the process at = Paat-1 + (with Pa E (0,1) and so being an iid shock with zero mean). Guess that the solution takes the form t VyaQt and Tt = UrqQt, where ya and Ura are coefficients to be determined. Impose the guessed solution in the equilibrium conditions of the model and find the coefficients Wya and Pra using the method of undetermined coefficients. (b) How does the output gap and inflation respond to a positive shock ay over time? In order to sign these effects use the constraint klr 1)+(1-B)dy > 0. Provide an economic intuition for your results. (c) Assume that Py = 0. Realizing that the output gap is defined as the deviation of output from its flexible price counterpart (Yt-47), compare the dynamic response of output and inflation to productivity shocks in the model with staggered price setting and the dynamics of output and inflation in a model with flexible prices (those derived in question 2). Provide the economic intuition behind your results. 7T Monetary policy in an economy with sticky prices Suppose now that firms get the opportunity to change prices infrequently, so Equation (1) describes the equilibrium conditions of this economy. (a) Assume that monetary policy follows a simple interest rate rule it = p +277t + yt = = where the necessary and sufficient condition for uniqueness of equilibrium klr 1) + (1 B)y > 0) is assumed to hold. Notice that there are no monetary policy shocks in this exercise. Instead, assume that productivity follows the process at = Paat-1 + (with Pa E (0,1) and so being an iid shock with zero mean). Guess that the solution takes the form t VyaQt and Tt = UrqQt, where ya and Ura are coefficients to be determined. Impose the guessed solution in the equilibrium conditions of the model and find the coefficients Wya and Pra using the method of undetermined coefficients. (b) How does the output gap and inflation respond to a positive shock ay over time? In order to sign these effects use the constraint klr 1)+(1-B)dy > 0. Provide an economic intuition for your results. (c) Assume that Py = 0. Realizing that the output gap is defined as the deviation of output from its flexible price counterpart (Yt-47), compare the dynamic response of output and inflation to productivity shocks in the model with staggered price setting and the dynamics of output and inflation in a model with flexible prices (those derived in question 2). Provide the economic intuition behind your results. 7T