An Uncertainty-ShockInduced Liquidity Trap Consider a two-period sticky-price economy populated by identical households with preferences dened over consumption in period 1, 01 and consumption in period 2, 02, and described by the utility function In 01 + 5E1 lnCa, where 01 denotes consumption in period 1, C2 denotes consumption in period 2, )3 = 1/1.1 is a preference parameter, and E1 denotes the expectations operator conditional on information in period 1. In period 1, potential output, 171, is 10 kilos of apples, and in period 2, potential output, 172, is also 10 kilos of apples. Assume that nominal prices are xed, in particular P1 = P2 = 1, and that the central bank sets the nominal interest rate, 1', so as to bring about full employment at all times, that is, so that in each period all apples are sold and consumed, subject to the constraint i 2 0. 1. State the household's budget constraint in period 1 and period 2. 2. Find the equilibrium level of consumption in period 1, 01, the nominal interest rate, 2', and savings, 31. (Your answer should be 3 numbers.) Assume now that potential output in period 1 continues to be 10 apples, but that due climate change the apple harvest in period 2 might be either very plentiful or really poor. Specically, assume that with probability 1 / 3 climate-change induced increases in apple pests will lead to a 40 percent reduction of the harvest in period 2. At the same time, with probability 2 / 3, rainfall and sunshine conditions will be so favorable that in period 2 the apple harvest increases by 20 percent. 3. Find the expected value of potential output in period 2, E1172. 4. Suppose the monetary authority fails to respond to this increase in uncertainty and keeps the nominal interest rate unchanged. Find consumption in period 1. 5. Suppose now that the monetary authority does respond to the increase in uncertainty and adjusts the nominal interest rate to stimulate demand in period 1. Find the optimal monetary policy response, that is, nd i, and the associated value of consumption in period 1