Consider the following macro model, where the variables are in logarithms: (1) m = p + y (2) p = pe + a(y-y*), a > 0 (3) m = m + w. Equation (1) is the demand function for money, (2) is the Phillips curve and (3) the monetary policy rule. y* is the potential output. w is a shock to monetary policy. Its mean is zero and the variance is finite. mis some constant. pe is the expected price level. Solve the rational expectations equilibrium of the model, i.e. solve the level of aggregate output (y) and price level (p) in that equilibrium. What is pe, when the economic agents have rational expectations?