6. Assume that the aggregate supply in an economy is characterised by the following relationship (Phillips curve): nit - It-1 = -0.4ut + 0.015, where i denotes the inflation rate and u the unemployment rate. (a) Solve for the natural rate of unemployment. Show all steps in your calculations [10 points] ( b ) Assume the inflation rate in the previous year was one percent. The government is determined to use monetary policy to achieve a two-percent unemployment rate permanently. Find the value of the index j indicating the period in which the inflation rate It would reach two percent. Show all steps in your calculations [15 points] (c) How could the government achieve a permanent four-percent unemployment rate without letting inflation out of control in the economy? [15 points]