Econ303 Homework ll 1 In country RBC, only labor is used in production. The production function is Y = 2N, where z is labor productivity. In country REC, economic booms and recessions are due to cyclical movements of 2s. For simplicity suppose that 2 takes two values: either 2' = 95 or z = 105. The chance that z = 105 is 0.8 and the chance that 2: = 95 is 0.2. Roughly, country BBC is in economic boom 80% of time and recession 20% of the time. The representative household in country BBC has utility u(c,l) = \\/5+14\\/l 1. (8 points) Compute the competitive equilibriums in country RBC in booms and in recessions. 2. (4 points) Government in country RBC wants to use government spending to reduce business cycle uctuations. Government can collect lumpsum tax to nance its spend ing, The objective of government is to pick a spending level 9 during recessions so that output in recessions is the same as output in booms. The spending 9 will be thrown in the ocean.(wasted) Show that g = 8.3355 during recession will roughly achieve the goal. 3. (4 points) The above stabilization policy leads to a waste of resources, hence may not be favorable to households. Instead, government stabilizes production through wage subsidies nanced by a lumpsum tax. The representative household's budget constraint becomes the following. c=w(1+s)(lil) 7T. Show that s = 13.78% and T = 5.0474 during recession will achieve the goal of stable output as well, 4. (4 points) Let (Cb, lb) denote the equilibrium consumption and leisure during booms and (CT, Z7") is those during recessions. The welfare of the representative households is given by the following: welfare 2 0.8 - u(cb, lb) + 0.2 - u((:r, Zr) Compute the welfare in country RBC without stabilization scal policy, that with increased government spending in recessions, and that with wage subsidy in recessions. What do you nd