1. Suppose there is an economy with one household who carm only about consumption of a nal good {clocks} and leisure. The household has h = lll. The household's preferences over consumption of clocks and leisure is given by the following utility function: NEE} = 25' + 5001MB}. There is a single rm which makes clocks. The rm uses household labour and a xed amount of capital equal to K = 16 to produce clocks. The production function for producing clocks is given by Y = z {hwy5 (In-5. Here a randomly uctuates between 3L = 12 and 23 = 15. You will need to use the quadratic formula for this question. {1.11.} [35 points) Complete the rst two columns of Table 1 for the two values that a can take. Use your answers to determine the qualitative predictions of this economy regarding the cyclical properties [procyclicaL oountercyclical, or acyclicalj of consumption, real wages, labour hours, average labour pro ductivity, and prots when there are technology shocks. Provide economic intuition to explain each of these cyclical properties. {1.13.} [2|] points} Suppose that for several periods, the economy was experiencing z = 15 and then 2 fell to z = 12 and remained at that level for several periods. During the periods when 2 = 12., the government follows an OUTPUT stabilization policy in which it forces the household to work a specied number of hours {which you need to calculate] so that output is at the same level as it is when 2 = 15. Complete Column 3 of Table 1 for a period in which 2 = 12 and the government follows its output stabilisation policy. Compare the values in Column 1 with the values in Column 3 and provide economic intuition for the direction of the dierenoes for each variable [that is, compare the values in an economy without government to the values in an economy in which government follows an output stabilization policy]. Also, use calculations to show that the household is NOT consuming at the point where their indifference curve is tangent to their overall constraint. Table 1: Aggregate Variables Without Government With Government Variable 555= 5*:555 5555555555 15555 5555 55 {1.C.) {15 points) [.'Fra'lar a single schematic PPF and Household ConsumptionLeisure diagram to depict output, lahour input, and household utility for the following three scenarios: 1. z = :3 = 15 E. z = 2:; = 12 and the government DOES NUT follow its stabilization policy. 3. z = 22;, = 12 and the government DUES follow.r its stabilisation policy. {1.11) {5 points} Suppose the government in this eoouomjr can dictate how man}.r hours the household must work and chooses a level of those hours that maximizes the welfare of the household? taking into account the technolog},r for producing clocks and the total amount of time that the household has. How many hours will the govermueut dictate that the household must work when .2 = 2L = 12