Part 1: (50 points) This question examines government spending financed by lump-sum taxes. There is a single representative household which has h=10 units of time which it can divide between working and leisure. The household's preferences over consumption of the final good, C, leisure, l, and government spending, G, are given by the following utility function: U(C,l)+V(G)=3ln(C+a)+2ln(l)+G0.2 where is a constant to be specified below. For this question assume that a=4. Production of the final good uses labour only with technology Y=zND, where z fluctuates randomly between a relatively low level of zL=15 and a relatively high level of zH=20. The government finances government spending by lump-sum taxes equal to T=G imposed on the household. In periods in which productivity is high, the government does not spend or tax, G=T=0. But in periods when productivity is low, the government spends and taxes whatever amount it takes to keep output at the same level as it is when productivity is high. That is, the government uses government spending and taxation to eliminate fluctuations in output. A) (15 points) Determine the equilibrium levels of household consumption, leisure, labour hours, output, government spending, the tax level, and the real wage for the two types of periods (that is, periods in which productivity is low and government spending is positive and periods in which productivity is high and government spending is zero). B) (10 points) Suppose that =1.0. Determine whether or not the government's policy of spending and taxing to maintain a constant level of output is a good one if the government's objective is to maximize household utility. You should justify your answer by calculating household utility when z is low and G=0 and calculating household utility when z is low and G equals the value you calculated in (1.A) and comparing the two utility levels. Provide economic intuition for your finding. Part 1: (50 points) This question examines government spending financed by lump-sum taxes. There is a single representative household which has h=10 units of time which it can divide between working and leisure. The household's preferences over consumption of the final good, C, leisure, l, and government spending, G, are given by the following utility function: U(C,l)+V(G)=3ln(C+a)+2ln(l)+G0.2 where is a constant to be specified below. For this question assume that a=4. Production of the final good uses labour only with technology Y=zND, where z fluctuates randomly between a relatively low level of zL=15 and a relatively high level of zH=20. The government finances government spending by lump-sum taxes equal to T=G imposed on the household. In periods in which productivity is high, the government does not spend or tax, G=T=0. But in periods when productivity is low, the government spends and taxes whatever amount it takes to keep output at the same level as it is when productivity is high. That is, the government uses government spending and taxation to eliminate fluctuations in output. A) (15 points) Determine the equilibrium levels of household consumption, leisure, labour hours, output, government spending, the tax level, and the real wage for the two types of periods (that is, periods in which productivity is low and government spending is positive and periods in which productivity is high and government spending is zero). B) (10 points) Suppose that =1.0. Determine whether or not the government's policy of spending and taxing to maintain a constant level of output is a good one if the government's objective is to maximize household utility. You should justify your answer by calculating household utility when z is low and G=0 and calculating household utility when z is low and G equals the value you calculated in (1.A) and comparing the two utility levels. Provide economic intuition for your finding