Hello! I solved this problem by comparing SRAS and AD to be equal using the given natural unemployment level of 0.05, I became stuck calculating the final LR infation level because there's no related formula. Should be using the index to find it?

Thank you!

Consider an expectations-augmented Phillips curve of the kind TT= u+ + LL. The natural rate of unemployment is u = 0.05. Government preferences are represented by the following loss function: 1 = 12 + 12. a. Determine the long-run equilibrium rate of inflation (and expected inflation) b. Suppose that the government announces that the future rate of inflation will be 5%. Assume that this announcement is believed. Determine the actual (desired) rate of inflation that the government would deliver once the announcement of a 5% inflation rate is believed. c. Was it rational to believe the announcement of the government to begin with? What is the only credible announcement about the rate on inflation and unemployment combination in this model