1. Suppose there is an economy with one household who cares only about consumption of a nal 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: n(C',) = 20 + 5001n(). 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: ZUVD)'5 (Io-5. Here 2 randomly uctuates between 2;, = 12 and 23 = 15. You will need to use the quadratic formula for this question. (1.A.) (35 points) Complete the rst two columns of Table 1 for the two values that 2: 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 prots 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 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 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 stabilization policy). Also, use calculations to show that the household is NOT consuming at the point where their indierence curve is tangent to their overall constraint. Table 1: Aggregate Variables Without Government With Government 2 = zL = 12 Z = ZH = 15 Z = zL = 12 Variable Column 1 Column 2 Column 3 Y* C* N LP* = Y*/N* Household Utility 2655.52