3. Consumption Smoothing [10 points) Consider the case of a home country where under normal conditions the level of GDP is Q=1000 and consumption C=1000 and 1=G=0. Initially, these conditions are expected to last forever. The world interest rate is r*=0.05=5%. Assume it is now time 0, and that external wealth at the end of all previous period was zero. a. At time 0, under this scenario [1]: What is the present value of output? PV(Q) = What is the present value of consumption? PV(C) = b. Now suppose conditions have changed, and the country has learned of a negative output shock at time t=0. This shock is expected to last one year, and will lead to an output drop of 210 units. That is, GDP at time 0 falls to Qo = 790, then returns to 1000. At time 0, under this scenario [1]: What is the present value of output? PV(Q) = What is the present value of consumption? PV(C) = Assume forward-looking agents desire smooth consumption over time. Compute the new planned levels of consumption at t = 0 and 1 under this scenario. [1] Co = C1 = Compute the trade balance, NFIA, current account, and wealth at t = 0 and 1 under this scenario. [1] TB = NFIA, = CA) = Wo = TB1 = NFIA1 = CA1 = W1 = 3. Consumption Smoothing [10 points) Consider the case of a home country where under normal conditions the level of GDP is Q=1000 and consumption C=1000 and 1=G=0. Initially, these conditions are expected to last forever. The world interest rate is r*=0.05=5%. Assume it is now time 0, and that external wealth at the end of all previous period was zero. a. At time 0, under this scenario [1]: What is the present value of output? PV(Q) = What is the present value of consumption? PV(C) = b. Now suppose conditions have changed, and the country has learned of a negative output shock at time t=0. This shock is expected to last one year, and will lead to an output drop of 210 units. That is, GDP at time 0 falls to Qo = 790, then returns to 1000. At time 0, under this scenario [1]: What is the present value of output? PV(Q) = What is the present value of consumption? PV(C) = Assume forward-looking agents desire smooth consumption over time. Compute the new planned levels of consumption at t = 0 and 1 under this scenario. [1] Co = C1 = Compute the trade balance, NFIA, current account, and wealth at t = 0 and 1 under this scenario. [1] TB = NFIA, = CA) = Wo = TB1 = NFIA1 = CA1 = W1 =