In country BBC only labor is used in production. The production function is Y = 2N, where z is the labor productivity. In country RBC economic booms and recessions are due to cyclical movements of labor productivity. For simplicity suppose that 2 takes two values: either 2 = 195 or z = 205. The chance that z = 205 is 0.7 and the chance that z = 195 is 0.3. Roughly country BBC is in economic boom 70% of time and recession 30% of the time. The representative household in country BBC has a preference represented by the following: u(c, l) = J5 + 20W (4 points) The government in country RBC wants to use the government spending to reduce business cycle uctuations. The government can collect a lumpsum tax to nance its spending. The objective of the government is to pick a spending level, 9, during recessions so that the output in recessions is the same as the output in booms. The Spending will be thrown in the ocean.(wasted) Show that g = 8.2634 during recessions will roughly achieve the goal