Consider the time-inconsistency model of monetary policy. Suppose aggregate supply has the simple form: y = y" + (x - It ) + & where y is aggregate output, y" is flexible-price output, and it is inflation expectation. The aggregate supply shock & is i.i.d. with mean E[&] = 0 and variance var(E) = o . The central bank has a loss function that is different to the social loss function. In particular, the central bank, subject to an aggregate supply constraint, sets inflation it in order to minimize: LCB = =(y - ky" )2 + za'(1- 1*)2 where it* is the central bank's inflation target, a' > 0 reflects the central bank's preference for stabilizing inflation and k > 1. The social loss function is: [society = (y - ky")2 + ha(n-n*)2 where a > 0 reflects society's relative preference for stabilizing output around target inflation. (a) What are the equilibrium levels of output, y, and inflation, 7, if the central bank has discretion, i.e., chooses policy taking expectations as given? I (b) Explain whether a central bank with the largest possible dislike for inflation would lead to minimum social loss in the presence of disturbances to aggregate supply. Now consider the IS curve of the form: y = y" + a - fr + w where r is the real interest rate a > 0, and B > 0. The aggregate demand shock w is i.i.d. with mean E[w] = 0 and variance var(@) = ow. (c) Using the expression derived for y, solve for the equilibrium real interest rate in terms of &, w and the parameters of the model. (d) | How does the central bank adjust the real interest rate in response to an aggregate demand shock? Explain whether this response constitutes a stabilization policy