Solve the following problem: The Phillips curve of an economy is defined by the following relationship: The = The + 0,08 + 0,1m - 0,5ut In which m is the mark-up of prices over wages. Initially the value of the mark-up is 20%, but after an oil price shock, it rises to 40% (period t+1). (a). Find the Phillips curve and the natural rate of unemployment before the oil shock. How does the natural rate of unemployment change after the shock? (b). If expected inflation is given by my = On 1 with 0 = 1 ,where initially actual inflation was 2% and rose to 4% in period t, then what was the unemployment rate in the period? (c). How does your answer in (b) change after the oil shock? What happens to inflation in periods t+1, t+2 and t+3, if the authority wanted to keep unemployment at the level found in period t? (d). How do your answers in (a) and (b) change if expected inflation is given by THE = 0,5Tit-1? (e) What happens if 20% of workers have their inflation expectations indexed to past inflation? (f) Analyze the inflation adjustment if in period t+3, the authority would like to return to the initial inflation of 2%. Okun's law is given by: Ut - Ut-1 = 0,2(gyt - 3%) Note: gyt is the real GDP growth rate in period t