2. (15 points) Barro-Gordon Model Suppose that the government in a Xantia cares about unemployment and inflation. They would like to see as little of both as possible. The Phillips Curve in Xantia is represented by equation (1) below: U=U" -0.28(1 - 1) (1) where U is the unemployment rate, U" (the natural rate of unemployment) equals 0.05, 7 is the inflation rate, and " represents the level of inflation expected by agents in the economy. The government's preference for inflation and unemployment are represented by the following Loss function: min L = U +4x (2) a. (2 points) Describe the intuition behind the Loss function. b. (3 points) Minimize the loss function with respect to inflation and hence, solve for the discretionary solution (i.e. find the level of inflation that the government should target whilst following discretionary policy). C. (2 points) Assuming rational expectations, what is the expected level of inflation in the economy? Calculate the value of the loss function, _" , at the discretionary solution. Consider an alternative optimal policy strategy, where the government announces a target level of zero inflation. d. (3 points) Calculate the value of the loss function for this alternative policy, I' . e. (3 points) Using a figure, or otherwise, show why this optimal policy rule will not work. f. (2 points) Considering your answer to part (e), suggest two possible solutions that might resolve the issue