3. This question compares lump-sum taxes to proportional income taxes for financing government spending in our static model without capital with a single household. The household has h = 100 units of time and its preferences over consumption of the final good, leisure, and government spending are given by the following utility function: U(C, e) + XV (G) = 9In(5 + C) + 6In(1 + () + 1G0.6 where A is a constant to be specified below. Production of the final good uses labour only with technology Y = 5ND. There is a government who may be spending G = 150 financed by taxation of the household. The government may finance this by a lump-sum tax or by a proportional income tax of the household. If the government uses a proportional income tax, according to my calculations, the government can finance this level of spending by imposing a tax at rate t* = 0.5017 or by imposing a tax at rate t* = 0.9868;that is for either rate, t*'w*N* : G. For questions {3.A.)(3.C.)7 let the A in the utility function equal A = 2.0. (3.A.) (18 points) Complete Table 3. (3.B.) (12 points) Provide economic intuition for the direction of change in each of the variables of Table 3 in moving from Column 1 to Column 2 and separately, in moving from Column 1 to Column 3. (3.C.) (10 points) Using your results from Table 3, rank the four different scenarios for government behaviour in Table 3 from best to worse if the government's objective is to maximize household utility. Provide economic intuition for your ranking. Table 3: Lump-Sum and Proportional Income Taxation No Taxes Lump-Sum Taxes Proportional Taxes G20 0:150 G2150 G2150 T* = t* = 0 T* = 150 25* = 0.5017 t* = 0.9868 Row Variable Column 1 Column 2 Column 3 Column 4 1 N* 00.20 2 1\" 301.00 3 C* 301.00 4 U(C*,*) 73.76 5 U(C*, 13*) + AV(G) 73.76 (3.D.) (4 points) For this question. let A : 0.0. Using part of your results from Table 3, rank the four different methods of taxation (including zero taxation) from best to worse if the government's objective is to maximize household utility. Provide economic intuition for your ranking