Need help clarifying if I did pard d correctly. And I also need help with parts e to k. Photos from notebook is my work for a to d and top 2 photos are the questions.

my answers for parts a-d are there, I need help with e through k. i forgot to add my answer to a but just added the photo. not sure what else to add

ResEe 313. PS 5 Chapters 10-11.3 vi 1. The Lamberts family have three children: Macy, Theodore, and Jane. Each of them has different attitude towards money. In particular, Macy's utility function is U(x)-60.5x and Theodore's utility function is U(x)=Sx". Unfortunately, we don't know Jane, the youngest kid's utility function yet. a) Given their utility functions, what are Macy and Theodore's u-values if they can get each of the following monetary payoffs for sure (fill your answers in the table? Dollar Value (5) Macy's u-value Theodore's w-value 0 10 20 30 40 SO 60 70 80 90 100 b) Draw the utility curves for Macy and Theodore you can either draw 2 curves separately or on the same graph). Label them carefully c) Now both are facing the following uncertain deal (Deal A). Find Macy's and Theodore's expected u-values of Deal A. Deal A $100 0.25 a 0.75 50 d) What are Macy's and Theodore's u-values of the certain equivalents of Deal A? e) What are their certain equivalents (CE) for Deal A? 1 Compare the values of CE you found in the previous question. Explain why there is such difference in their CEs for the same deal. 8) Jane is also interested in the deal. Even though we don't know her utility function, we are lucky to have her w-value for each dollar amount as shown in the following table, Dollar Value (52 0 10 20 Jane's value 0.00 2.53 7.16 BE a EPIC Jui 205ummer%202020%20Classes/UMass%20Amherst%20Classes%20Fall%202020%20(Coron Favorites D Book Chapters D Immigration Law P... Favorites Home USEmbassy.... DCEAC + A' Read aloud Draw 13.15 20.24 30 40 50 60 70 30 90 100 37.18 46.85 57.24 6831 80.00 As we don't know her utility function, we don't know exactly Jane's certain equivalent for the deal like we do in the cases of Macy and Theodore. But what can we say about the range of her certain equivalent (choose one of the option below)? Explain why you need to find her expected value for Deal A first and the deduce the range for her from the above the i Between 10 and 530 ii. Between $30 and $50 iii. Between $50 and 5100 iv. Over $100 h) Three of them is now facing another deal (Deal B) Deals DollarValue $50 $20 02 S10 Find the range of certain equivalent for Macy, Theodore, and Jane for the new deal. i) Among the two deals (A and B). what is the best deal for Macy, Theodore and Jane, respectively ) Suppose their parents decide to give them 523 with the condition that they have to give up any deal they chose above (let's call it Deal C) Who among them should walkway with 5237 k) Dewa decision tree which characterizes the decision situations Macy was facing (see Figure 10.15 p. 208 in the textbook for reference) Instructions Boxes represent decision alternatives (ie, Deal A Deal , d DealC) Ovalecles represent each state of nature for each deal Record probabilities, payoffs, and value for each branch of the tree Record w-value and certain equivalents for each deal (note that CE for Deal C is $23). BE a EPIC 5 Luc 10/01/12 Res-Econ 313 : Problem Set #s(chapters 10-11.3) 1) a.) Macy's utility function : u(x) = 6 +0.5x Theodore's utility function: u(x) = 5x - Macy's utility curve 41 30 2 Macy's Utility - VE 10 bollar Value (1) Theordore's Curve The ordere's U-value 13 50 15 3 25 12 to 5 Dollar Value (6) Macys utility function: Ux) = 6 + 0.5% Theo's stillty function: "(x)= x 2 0.25 chance of 100 0.79 chaned of to EW) 0.25 (Ukm) + 0.15((0) for Macy: F(u) = 0,25 (6 + 0.5 (100)) +0.75 18 +0.5 (6) =09(56) +0.25 = 14 +45 is Macy's expected utility for Thuadors: E (u) = 0.28 (56100%) +0.75 (story = 0,25 (so) is that's expected utility d.) contain Equivalent for Macy: 18.5 = 6 + osta 12.5 = Oska Theodore: 125= Syll us-values of certain, equiventants X: 6,25 Favorites Book Chapters Immigration Law P... Favorites Home |USEmbassy... D + 2 TA' Read aloud | DR ResEc 313 . PS 5 Chapters 10-11.3 vi 1. The Lamberts family have three children: Macy, Theodore, and Jane. Each of them has different attitude towards money. In particular, Macy's utility function is U(x)-6+0.5x and Theodore's utility function is U(x)-5x2 Unfortunately, we don't know Jane, the youngest kid's utility function yet. a) Given their utility functions, what are Macy and Theodore's u-values if they can get each of the following monetary payoffs for sure (fill your answers in the table)? Dollar Value (S Macy's u-value Theodore's -value 0 6 0 10 11 15.31 20 16 22 37 30 21 27.38 40 26 31.62 50 31 35.35 60 36 38.72 70 41 41.03 80 46 44.72 90 51 47.43 100 56 50 b) Draw the utility curves for Macy and Theodore (you can either draw 2 curves separately or on the same graph). Label them carefully. a 8 E EPIC ResEe 313. PS 5 Chapters 10-11.3 vi 1. The Lamberts family have three children: Macy, Theodore, and Jane. Each of them has different attitude towards money. In particular, Macy's utility function is U(x)-60.5x and Theodore's utility function is U(x)=Sx". Unfortunately, we don't know Jane, the youngest kid's utility function yet. a) Given their utility functions, what are Macy and Theodore's u-values if they can get each of the following monetary payoffs for sure (fill your answers in the table? Dollar Value (5) Macy's u-value Theodore's w-value 0 10 20 30 40 SO 60 70 80 90 100 b) Draw the utility curves for Macy and Theodore you can either draw 2 curves separately or on the same graph). Label them carefully c) Now both are facing the following uncertain deal (Deal A). Find Macy's and Theodore's expected u-values of Deal A. Deal A $100 0.25 a 0.75 50 d) What are Macy's and Theodore's u-values of the certain equivalents of Deal A? e) What are their certain equivalents (CE) for Deal A? 1 Compare the values of CE you found in the previous question. Explain why there is such difference in their CEs for the same deal. 8) Jane is also interested in the deal. Even though we don't know her utility function, we are lucky to have her w-value for each dollar amount as shown in the following table, Dollar Value (52 0 10 20 Jane's value 0.00 2.53 7.16 BE a EPIC Jui 205ummer%202020%20Classes/UMass%20Amherst%20Classes%20Fall%202020%20(Coron Favorites D Book Chapters D Immigration Law P... Favorites Home USEmbassy.... DCEAC + A' Read aloud Draw 13.15 20.24 30 40 50 60 70 30 90 100 37.18 46.85 57.24 6831 80.00 As we don't know her utility function, we don't know exactly Jane's certain equivalent for the deal like we do in the cases of Macy and Theodore. But what can we say about the range of her certain equivalent (choose one of the option below)? Explain why you need to find her expected value for Deal A first and the deduce the range for her from the above the i Between 10 and 530 ii. Between $30 and $50 iii. Between $50 and 5100 iv. Over $100 h) Three of them is now facing another deal (Deal B) Deals DollarValue $50 $20 02 S10 Find the range of certain equivalent for Macy, Theodore, and Jane for the new deal. i) Among the two deals (A and B). what is the best deal for Macy, Theodore and Jane, respectively ) Suppose their parents decide to give them 523 with the condition that they have to give up any deal they chose above (let's call it Deal C) Who among them should walkway with 5237 k) Dewa decision tree which characterizes the decision situations Macy was facing (see Figure 10.15 p. 208 in the textbook for reference) Instructions Boxes represent decision alternatives (ie, Deal A Deal , d DealC) Ovalecles represent each state of nature for each deal Record probabilities, payoffs, and value for each branch of the tree Record w-value and certain equivalents for each deal (note that CE for Deal C is $23). BE a EPIC 5 Luc 10/01/12 Res-Econ 313 : Problem Set #s(chapters 10-11.3) 1) a.) Macy's utility function : u(x) = 6 +0.5x Theodore's utility function: u(x) = 5x - Macy's utility curve 41 30 2 Macy's Utility - VE 10 bollar Value (1) Theordore's Curve The ordere's U-value 13 50 15 3 25 12 to 5 Dollar Value (6) Macys utility function: Ux) = 6 + 0.5% Theo's stillty function: "(x)= x 2 0.25 chance of 100 0.79 chaned of to EW) 0.25 (Ukm) + 0.15((0) for Macy: F(u) = 0,25 (6 + 0.5 (100)) +0.75 18 +0.5 (6) =09(56) +0.25 = 14 +45 is Macy's expected utility for Thuadors: E (u) = 0.28 (56100%) +0.75 (story = 0,25 (so) is that's expected utility d.) contain Equivalent for Macy: 18.5 = 6 + osta 12.5 = Oska Theodore: 125= Syll us-values of certain, equiventants X: 6,25 Favorites Book Chapters Immigration Law P... Favorites Home |USEmbassy... D + 2 TA' Read aloud | DR ResEc 313 . PS 5 Chapters 10-11.3 vi 1. The Lamberts family have three children: Macy, Theodore, and Jane. Each of them has different attitude towards money. In particular, Macy's utility function is U(x)-6+0.5x and Theodore's utility function is U(x)-5x2 Unfortunately, we don't know Jane, the youngest kid's utility function yet. a) Given their utility functions, what are Macy and Theodore's u-values if they can get each of the following monetary payoffs for sure (fill your answers in the table)? Dollar Value (S Macy's u-value Theodore's -value 0 6 0 10 11 15.31 20 16 22 37 30 21 27.38 40 26 31.62 50 31 35.35 60 36 38.72 70 41 41.03 80 46 44.72 90 51 47.43 100 56 50 b) Draw the utility curves for Macy and Theodore (you can either draw 2 curves separately or on the same graph). Label them carefully. a 8 E EPIC