1. Time inconsistencies (based on Barro-Gordon (1983), Rules, Discretion, and Reputation in a Model of Monetary Policy, Journal of Monetary Economics, 12:101-121) Assume that the preferences of the benevolent policy maker can be represented through the following loss function (i.e., the utility of the policy maker is higher the lower the loss)L=a2?2?b(???=e)where a and b are two positive constants,? is inflation, and ?e expected inflation.(a) Provide an interpretation for thefirst term of the loss function(b) Does the policy maker care about unemployment?(c) Assume that the policy maker announces an intention to achieve zero inflation, and that this is believed by the agents. Show that it is optimal for the policy maker to deviate from its initial announcement. Explain.d. Assume now that the private sector does not believe the announcement. What is the corresponding inflation rate in that case? Would society gain by imposing rules on the policy makers decisions?