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 l=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 Q9 = 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] Compute the trade balance, N FIA, current account, and wealth at t = 0 and 1 under this scenario. [1] TBo = N Fle = CAD = We = T31 = NFIA1 = CA1 = W1 = C. Suppose period 0 ends as above. Now it is time 1, and suppose conditions have changed again, and the country learns of an identical negative output shock at time t=1. This shock is expected to last one year, and will lead to another output drop of 210 units. That is, GDP at time 1 falls to Q1 = 790, instead of 1000. Compute the new planned levels of consumption at t = 0, 1, 2 under this scenario buildmgomiathasalneadnhappenedin t=0. [1] Compute the trade balance, N FIA, current account, and wealth at t = 0, 1, 2 under this scenario building on what has already happened in t=0. [1] TBo= NFIAo= CAD= W0: TB1= NFIA1= CA1= W1: TBz= NFIA2= CA2= W2: Now return to that initial situation at t=0. Now suppose agents had learned at time t=0 that output was going to be at the level of 790 in both years 1 and 2, instead of 1000. At time 0, under this scenario: What is the present value of output? [1] PV[Q) = What is the present value of consumption? [1] PV{C) = How would planned levels of consumption differ here from the previous case where agents only learned in each year about the output drop in that year? [2]