Question 3 Assume a central bank with preferences that are described from the following loss function: L = (3': _ye)2 +(-t 1:132: where y, defines output at period t, y, defines medium-run equilibrium output (given; exogenous), It, is the inflation rate at period 1:, ET is the inflation target (given; exogenous), and B > 0 an exogenously given parameter that defines the degree of central bank's inflation aversion. The supply-side of the economy is described by the following PC relation: \"t = 5\"lite + \"(Yr _ ye): where 1:? defines expected inflation at period t and a: > 0 is an exogenously given parameter that shows the responsiveness of inflation to changes in the output gap. We further assume 1:? = (1 6)::7 + 911,4, where 0 0 is the interest sensitivity of aggregate demand and A a positive constant. Both a and A are exogenously given parameters. We assume that the real policy rate affects aggregate demand with a lag. (i) Explain the parameters a, a, and A. What can affect those parameters? Moreover, explain what determines the medium-run equilibrium level of output, ye, following equilibrium in the labour market. [10 marks] (ii) Derive the central bank's monetary rule (MR) in period 1, assuming that the central bank faces a given inflation rate at period 0; so, no. What does this rule show? [10 marks] (iii) Solve for the inflation rate (as deviation from the target rate of (W) (V) inflation) and output (as deviation from the equilibrium output) in period 1, and for the real policy rate in period 0 (as deviation from the medium-run equilibrium policy rate). Interpret your results. Does it matter if the inflation rate at period 0 is different from the target rate of inflation? What is the role of the degree of inflation persistence? [10 marks] Draw the necessary graphs (lS-PC-MR), assuming adaptive expectations, and briefly explain the adjustment of the economy to the inflation shock; i.e., when no > 1:7. [10 marks] Critically discuss the current state of the debate on the optimal inflation rate (i.e., inflation target). Should central banks adopt a higher (than a 2%) inflation target? [10 marks]