3. (12%)The Phillips curve describing an economy takes the form: u = u' - a(1 - n'),a> where u is the unemployment rate, u" is the natural rate of unemployment, and i and ne the actual and expected rates of inflation, respectively. The social lost function is given by: L(u, n) = u + Bn?,B > 0. The central bank chooses the rate of inflation to make the loss small as possible. Private agents resist being fooled and maximize -(n - n)2. (1) What are the optimal it and i if the central bank can make a commitment? (4%) (2) What are the optimal 7 and m if the central bank could not make a commitment? (4%) (3) Compute the social loss under (1), which is the rule, and under (2), which is discretion Compare the losses and which one has the larger loss? (4%)