3. Dynamic AD-AS Model Suppose that the economy is governed by the following equations Yt = Y t (rt ) + t (1) rt = it Ett+1 (2) t = Et1t + (Yt Y t) + vt (3) Ett+1 = t (4) it = t + + (t ? t ) + Y (Yt Y t) (5) 1. Derive the long-run equilibrium for the dynamic AD-AS model. Assume there are no shocks to demand or supply and that inflation has stabilized. Use the above equations to derive the value, and show the steps and logic in your work. 2. Now suppose that monetary-policy has the following rule it = t + 0 + (t ? t ) + Y (Yt Y t) (6) where 0 is not equal to , and it is the wrong natural rate of interest. The rest of the model is the same. Solve for the long-run equilibrium under this solutions. Explain your intuition behind the solution 3. Suppose that the central bank does not satisfy the Taylor Principle (i.e. the nominal interest rate rises less than one for one with inflation). Use a graph to analyze the impact of a supple shock. Does this analysis contradict the Taylor Principle as a guideline for Monetary Policy