Question

Problem 2. (Optimal policy) Suppose the Phillips curve of an economy is given by Also suppose the objective of the policymaker is to minimize the loss function L given by In this question we are going to evaluate a variety of policy rules the policymaker can implement. (a) If the policymaker commits to the policy rule and is credible, then the agents' expectation of the inflation is equal to the level of inflation picked by the policymaker. In other words, In this case, what is the level of inflation the policymaker should target in order to minimize their loss function? What is the value of the loss function? b) Now suppose the policymaker implements a discretionary policy, that is, the level of inflation is chosen after the agents have formed their inflation expectations First, solve the policymaker's problem. Assume the policymaker take agent's expectation as given, Et-iTt-. Solve for the inflation the policy maker should target to minimize their loss function (c) The consequence of a discretionary policy is that agents will take the policy rule into account when forming their inflation expectations. Set in part (b) to be the optimal inflation you have solved from part (b). What is the value of the loss function from a discretionary policy? (d) Compare the values of loss function under commitment and no commitment. Should the central bank commit to an inflation target?

Answer 1

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