Consider the time inconsistency model without economic shocks. Assume that the social cost of inflation = so that the marginal social cost of inflation MC = . Assume that the (unemployment reduction) benefit of surprised inflation is 9 (- - 0.07) so that the marginal benefit of surprised inflation MB = 9(n-n-0.07). Also assume the Phillips curve is given by - = -3(u-u) where u 0.06 (6%) is the natural rate of unemployment. = - a. Suppose = 0. Show graphically (in the MC and MB graph) and algebraically that it is optimal for the monetary authority to implement some positive inflation policy. How does such "cheating" outcome compare to a "zero- inflation rule" outcome? Which one is more socially desirable? Explain. b. For any given expected inflation, use the marginal condition to derive the policy response function of the government? Graph the policy response function. Find the discretionary outcome that satisfies the marginal condition as well as the rational expectation condition = . Solve for it algebraically, as well as show it graphically in the graph of the policy response function. c. Compare the "zero-inflation rule" outcome and the "discretionary" outcome in (b), which one is better? Explain. d. Suppose before time to, the economy operates under discretion without any commitment device. After to, however, the Central Bank Independence and nominal anchor make the zero-inflation rule credible and as a result inflation outcome follows such rule. Draw the log P vs time graph from some time before to and some time after to. (You need to show your explanations and analysis to earn points in this question.)