1. Suppose there is an economy with one household who cares only about consumption of a final good (clocks) and leisure. The household has h = 100. The household's preferences over consumption of clocks and leisure is given by the following utility function: u(C, () = 20+ 500 In((). There is a single firm which makes clocks. The firm uses household labour and a fixed amount of capital equal to K = 16 to produce clocks. The production function for producing clocks is given by Y = = (ND ) .(K).5. Here z randomly fluctuates between zz = 12 and zH = 15. You will need to use the quadratic formula for this question. (1.A.) (35 points) Complete the first two columns of Table 1 for the two values that z can take. Use your answers to determine the qualitative predictions of this economy regarding the cyclical properties (procyclical, countercyclical, or acyclical) of consumption, real wages, labour hours, average labour pro- ductivity, and profits when there are technology shocks. Provide economic intuition to explain each of these cyclical properties. (1.B.) (20 points) Suppose that for several periods, the economy was experiencing z = 15 and then z fell to = = 12 and remained at that level for several periods. During the periods when z = 12, the government follows an OUTPUT stabilization policy in which it forces the household to work a specified number of hours (which you need to calculate) so that output is at the same level as it is when z = 15. Complete Column 3 of Table 1 for a period in which = = 12 and the government follows its output stabilization policy. Compare the values in Column 1 with the values in Column 3 and provide economic intuition for the direction of the differences 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 stabilizationpolicy]. Also, use calculations to show that the household is NUT consuming at the point where their indi'erence curve is tangent to their overall constraint. Table 1: Aggregate Variables Without Governnrent With Government (Lil) (15 points] Draw a single schematic PPF and Household ConsumptionLeisure diagram to depict output, labour input, and household utility for the following three scenarios: 1. z = 2;}; = 15 2. z = 2:; = 12 and the government DUES NUT follow its stabilisation policy. 3. z = 31, = 12 and the government DUES follow its stabilization policy. (1.1).) (5 points} Suppose the government in this economy can dictate how many hours the household must work and chooses a level of those hours that maximizes the welfare of the household, taking into account the technology for producing clocks and the total amount of time that the household has. How many hours will the government dictate that the household must work when 2 = 2L = 12