Hello, could you please help with these two questions? Will give thumbs up.

Question 9 Private agents form rational expectations of inflation, but policymakers move after and may deliver surprise inflation. Unexpected inflation may come with two benefits. The first is to lower unemploy- ment according to a Phillips curve: U = UN - a(1 - Te) where as usual u" denotes the natural rate of unemployment, i is inflation, is expected inflation, and o > 0 is a slope parameter. The second is that it lowers the real value of the public debt that the government must pay for. Consider a simple linear relation capturing this: b = b- 6 - 7(1 - Je) so that debt can fall from its initial level b because of unexpected inflation with sensitivity parameter 7 > 0, or because of sovereign default o. Society's loss function is: *(u - UN + k) 2 0b2 2 2 + 36 Society dislikes: inflation; unemployment above a desired rate that is k > 0 below the natural rate; debt above zero; sovereign defaults as they endanger financial stability. The parameters 1, 0, and B are all positive. (a) What is the level of inflation that the central bank wishes to choose? How does it depend on b and what is the economic intuition? (b) Assuming rational expectations, solve for the equilibrium level of inflation, unemployment and debt