Exercise 1 (A Negative Supply Shock). Consider a two-period sticky-price economy populated by identical households with preferences defined over consumption in period 1, C1 and consumption in period 2, C2, and described by the utility function where C1 denotes consumption in period 1, C2 denotes consumption in period 2, and 3 = 1/1.1 is the subjective discount factor. In both periods, potential output is equal to Y. Let Pi and P2 denote the price levels in periods 1 and 2, respectively. Assume P1 = P2 = 1 and that the economy is always in full employment in period 2 (the long run). 1. Calculate the nominal interest rate that guarantees full employment and no excess aggregate demand. 2. Now assume that in period 1 the economy suffers a negative supply shock. Specifically, assume that potential output falls from Y to HY. That is, after the negative supply shock we have "Y. Supply in period 2 is unchanged. Assuming the nominal rate is unchanged from the level you found in the previous question, find the level of aggregate demand in period 1 and the level of excess demand (or supply) in period 1. 3. How should the central bank respond to the negative supply shock in period 1? Specifically, find the value of the nominal interest rate such that aggregate demand in period 1 is equal to aggregate supply in period 1. Provide intuition for your finding