2. (60 points) Consider the model of monetary policy and time inconsistency, There is a central bank with discretion with the objective function UP = X(31 - yn) - 571 (1) and the public have the following Expectations Augmented Phillips Curve for Output given by (2) (a) (10 points) Substitute the right hand side of Equation 2 in for y, in Equation 3. (b) (10 points) Differentiate the result from part a with respect to 7, and set the deriva- tive equal to zero