Econ303 Homework MB 1 In country RBC 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 RBC has a. preference represented by the following: u(c,) = w:- + 20v? 1. (8 points} Compute the competitive equilibriums in country BBC in booms and in recessions. 2. (4 points) The government in country RBC wants to use the government spending to reduce business cycle uctuations. The government can collect a lump-sum 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. 3. (4 points) The above stabilization policy leads to a waste of resources, hence may not be favored by households. Instead the government stabilizes production through wage subsidies nanced by a. lump-sum tax, which is equivalent to a. tax cut nanced with debt. The representatiw household's budget constraint becomes the following: c=m(1+s)(1i)T. Show that s = 6.5375% and T = 4.5412 during recessions will achieve the goal of stable output as well. 4. (4 points) Let (ob, 1") denote the equilibrium consumption and leisure during booms and (6313") those during recessions. The welfare of the representative household is given by the following: welfare = 0.7 - ufchb) + 0.3- u(c'",l") Compute the welfare in country BBC without stabilization scal policy, that with increased government spending during recessions, and that with wage subsidy during recessions. What do you nd