3:1,, where s = job separation rate (the percentage of the employed who lose their jobs) and f = hob-nding rate (the percentage the unemployed who nd new jobs). a) Differentiate the ecmation for the natural rate of unemployment with respect to f. Then show how an increase in f affect that rate. Explain your answer. b) Differentiate the equation for the natural rate of unemployment with respect to 5. Then show how an increase in 3 affect that rate. Explain your answer. c) Show the net effect on the natural rate of unemployment of increases in f and 5. Explain your answer. l. (30 pts) Formula for the natural rate of unemployment: ten, = 2. (40%) In a certain economy the expectations-augmented Phillips curve is it = TIE 2(u - an] and an = 6% (0.06]. a) Graph the Phillips curve of this economy for an expected ination rate oft). 10. If the Fed chooses to keep the actual ination rate at 0. 10, what will be the unemployment rate? b) An aggregate demand shock (resulting from increased military spending) raises expected ination to CI. 12 (the natural rate of unemployment is unaffected). Graph the new Phillips curve and compare it to the curve you drew in part (a). What happens to the unemployment rate if the Fed holds actual ination at 0. 10'? What happens to the Phillips curve and the unemployment rate if the Fed announces that it will hold ination at {l 10 after the aggregate demand shock, and this announcement is fully believed by the public? c) Suppose that a supply shock {a drought) raises expected ination to D. 12 and raises the natural rate of unemployment to 0.08. Repeat part (b). 3. (30%) Consider a central bank that has an inflation target, I*. The Phillips curve is given by It - It-1 = -a(ut - un) a) If the central bank is able to keep the inflation rate equal to the target inflation rate every period, will there be dramatic fluctuations in unemployment? b) Is the central bank likely to be able to hit its inflation target every period? c) Suppose the natural rate of unemployment, un, changes frequently. How will these changes affect the central bank's ability to hit its inflation target? Explain