Question: Please note that this problem has four parts (a, b, c, and d). You may need to scroll the screen down, navigate left and right to see the whole problem. Clearly label your parts when answering. You are allowed a Minimum of 1 File, Maximum of 3 Files for this problem. Must use a pen to answer. Show all calculations/results to FOUR PLACES AFTER THE DECIMAL POINT (except when all succeeding digits are zeros). Must Show all calculations/steps. Failure to do so will result in a score of "O even final answer is correct. Suppose Victoria faces an investment decision in which she must think about cash flows in two different years. Regard these two cash flows as two different attributes, and let X represent the cash flow in Year 1, and the cash flow in Year 2. She has assessed her individual utility functions for X and Y, and has fitted exponential utility functions to them: Ux(x) = 1.675 - 2.214 e -X/25250 Uy(y) = 2.214 - 4.2945 e -y/23740 Ux($7044.44)= 0 Uy($15728.56)= | 0 Ux($9413.36)= 0.15 Uy($17394.04)= 0.15 Ux($13154.35)= 0.36 Uy($18573.03)= 0.25 Ux($14944.46)= 0.45 Uy($19185.24)= 0.30 Ux($15996.70)= 0.50 Uy($19813.65)= | 0.35 Ux($17094.70)= 0.55 Uy($21529.91)= 0.48 Ux($18242.62)= 0.60 Uy($22508.15)= 0.55 Ux($19445.23)= 0.65 Uy($23232.43)= 0.60 Ux($22037.25)= 0.75 Uy($23979.50)= 0.65 Ux($23440.39)= 0.80 Uy($25548.10)= 0.75 Ux($24926.11)= 0.85 Uy($26373.06)= 0.80 Ux($26504.75)=0.90 Uy($27227.73)= 0.85 Ux($28188.71)= 0.95 Uy($29035.30)= 0.95 Ux($29993.05)= 1.00 Uy($29993.46)= 1.00 Furthermore, she has decided that utility independence hold, and so these individual utility functions for each cash flow are appropriate regardless of the amount of the other cash flow. She also has made the following assessments; She would be indifferent between a sure outcome of $19445.23 for Year 1 and $21529.91 for Year 2 and a risky investment with 40% chance of outcome of $22037.25 for the Year 1 and $27227.73 for the Year 2, 20% chance of outcome of $13154.35 for the Year 1 and $18573.03 for the Year 2, and 40% chance of outcome of $17094.70 for the Year 1 and $19813.65 for the Year 2, She would be indifferent between a risky investment with 72% chance of outcome of $14944.46 for the Year 1 and $25548.10 for the Year 2, and a 28% chance at $18242.62 for Year 1 and $29035.30 for the Year 2 and a sure outcome of $7044.44 for Year 1 and $29993.46 for Year 2. (a) Use her assessments to find scaling constants Kx and Ky, where scaling constant related to cash flow in Year 1 is represented by Kx and scaling constant related to cash flow in Year 2 is represented by Ky (Must show all works/justification to get full marks) (b) Should she consider these two attributes to be substitutes or complements? Why or why not? (c) Specify her full two-attribute utility function for year1 and year2 cash flow. (d) Use the full two-attribute utility function for the given scenario to recommend the best alternative among alternatives J, K and M? in the following decision tree. Why? (Must show all works/justification to get full marks) Cash Flow ($) Year 1 Year 2 22037.25 19185.24 JA 0.48 Alternative "J" JB 28188.71 22508.15 KA 24926.11 23979.50 KB 9413.36 28478.45 Alternative "K" 0.66 KC 13934.35 26373.06 MA 0.22 23440.39 25548.10 Alternative "M" MB 20708.00 29035.30 MC 0.62 26504.75 18938.48 Question: Please note that this problem has four parts (a, b, c, and d). You may need to scroll the screen down, navigate left and right to see the whole problem. Clearly label your parts when answering. You are allowed a Minimum of 1 File, Maximum of 3 Files for this problem. Must use a pen to answer. Show all calculations/results to FOUR PLACES AFTER THE DECIMAL POINT (except when all succeeding digits are zeros). Must Show all calculations/steps. Failure to do so will result in a score of "O even final answer is correct. Suppose Victoria faces an investment decision in which she must think about cash flows in two different years. Regard these two cash flows as two different attributes, and let X represent the cash flow in Year 1, and the cash flow in Year 2. She has assessed her individual utility functions for X and Y, and has fitted exponential utility functions to them: Ux(x) = 1.675 - 2.214 e -X/25250 Uy(y) = 2.214 - 4.2945 e -y/23740 Ux($7044.44)= 0 Uy($15728.56)= | 0 Ux($9413.36)= 0.15 Uy($17394.04)= 0.15 Ux($13154.35)= 0.36 Uy($18573.03)= 0.25 Ux($14944.46)= 0.45 Uy($19185.24)= 0.30 Ux($15996.70)= 0.50 Uy($19813.65)= | 0.35 Ux($17094.70)= 0.55 Uy($21529.91)= 0.48 Ux($18242.62)= 0.60 Uy($22508.15)= 0.55 Ux($19445.23)= 0.65 Uy($23232.43)= 0.60 Ux($22037.25)= 0.75 Uy($23979.50)= 0.65 Ux($23440.39)= 0.80 Uy($25548.10)= 0.75 Ux($24926.11)= 0.85 Uy($26373.06)= 0.80 Ux($26504.75)=0.90 Uy($27227.73)= 0.85 Ux($28188.71)= 0.95 Uy($29035.30)= 0.95 Ux($29993.05)= 1.00 Uy($29993.46)= 1.00 Furthermore, she has decided that utility independence hold, and so these individual utility functions for each cash flow are appropriate regardless of the amount of the other cash flow. She also has made the following assessments; She would be indifferent between a sure outcome of $19445.23 for Year 1 and $21529.91 for Year 2 and a risky investment with 40% chance of outcome of $22037.25 for the Year 1 and $27227.73 for the Year 2, 20% chance of outcome of $13154.35 for the Year 1 and $18573.03 for the Year 2, and 40% chance of outcome of $17094.70 for the Year 1 and $19813.65 for the Year 2, She would be indifferent between a risky investment with 72% chance of outcome of $14944.46 for the Year 1 and $25548.10 for the Year 2, and a 28% chance at $18242.62 for Year 1 and $29035.30 for the Year 2 and a sure outcome of $7044.44 for Year 1 and $29993.46 for Year 2. (a) Use her assessments to find scaling constants Kx and Ky, where scaling constant related to cash flow in Year 1 is represented by Kx and scaling constant related to cash flow in Year 2 is represented by Ky (Must show all works/justification to get full marks) (b) Should she consider these two attributes to be substitutes or complements? Why or why not? (c) Specify her full two-attribute utility function for year1 and year2 cash flow. (d) Use the full two-attribute utility function for the given scenario to recommend the best alternative among alternatives J, K and M? in the following decision tree. Why? (Must show all works/justification to get full marks) Cash Flow ($) Year 1 Year 2 22037.25 19185.24 JA 0.48 Alternative "J" JB 28188.71 22508.15 KA 24926.11 23979.50 KB 9413.36 28478.45 Alternative "K" 0.66 KC 13934.35 26373.06 MA 0.22 23440.39 25548.10 Alternative "M" MB 20708.00 29035.30 MC 0.62 26504.75 18938.48