In country RBC, only labor is used in production, The production function is Y = zN where z is labor productivity.

In country RBC, only labor is used in production. The production function is Y = 2N, where z is labor productivity. In country RBC, economic booms and recessions are due to cyclical movements of zs. For simplicity suppose that 2 takes two values: either 2 = 195 or z = 205. The chance that z = 205 is 0.7 turd 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 utility tic-,1) = ,5 + 20? 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 lump-sum 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 = 8.2634 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 lump-sum tax (tax cut financed with debt). The representative household's budget constraint becomes the following. c=w(l+s)(ll)T. Show that s = 6.5375% and T = 4.5412 during recession will achieve the goal of stable output as well. 4. (4 points) Let (cl'Jb) denote the equilibrium consumption and leisure (luring booms and (r:", F) is those during recessions. The welfare of the representative households is given by the following: welfare = 0.7- \"(ch Z\") + 0.3 - u(c'",l") 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 find