please do only Part C,D and E in 25 minutes please urgently... I'll give you up thumb definitely

Free-Response #2: Alina would like a community garden in Venthria. The total cost of converting x acres of land into a community garden is 12x. Individuals' demand for garden space is private, meaning it cannot be directly observed by others. (a) (3 points) Alina pours her heart and soul into designing a sensible plan for the garden. Her valuation for x acres of garden is v^(x) = 20x - 8x2. If she cannot get anyone's help in paying for the garden and decides to build and pay for it herself, what value of x is optimal for her? (b) (3 points) Alina shares her ideas with the other two citizens of Venthria, Bruno and Cynthia, each of whom has a valuation of v(x) = 6x - x2. What is the socially optimal number of acres of garden? (c) (3 points) Citizen Alina decides the garden should be exactly 1 acre and proposes to Bruno and Cynthia her plan for building the Venthria Community Garden. However, because she did all the planning for the garden, her proposal requires that the $12 cost be split evenly just between Bruno and Cynthia, with Alina not having to pay any of the construction costs. What is the net valuation of each citizen for this proposal? If this proposal were put up to a majority vote, what would be the outcome of the majority vote? Explain. (d) (3 points) Instead of a majority vote, suppose that the citizens of Venthria use a VCG mechanism to determine the fate of the Venthria Community Garden proposal. Would they approve the proposal? Who, if anyone, would pay a tax, and how much? Explain. (e) (2 points) The citizens of Venthria can't actually agree on which process to use to make their decision on Alina's proposal, with some arguing for a vote-as in part (c)and some wanting to use the VCG-as in part (d). Suppose Alina tries to make the VCG more attractive by changing its rules so that all tax proceeds from the VCG are used to compensate people who are harmed by the group's decision. Briefly explain how this might affect how Bruno and Cynthia report their valuations? Free-Response #2: Alina would like a community garden in Venthria. The total cost of converting x acres of land into a community garden is 12x. Individuals' demand for garden space is private, meaning it cannot be directly observed by others. (a) (3 points) Alina pours her heart and soul into designing a sensible plan for the garden. Her valuation for x acres of garden is v^(x) = 20x - 8x2. If she cannot get anyone's help in paying for the garden and decides to build and pay for it herself, what value of x is optimal for her? (b) (3 points) Alina shares her ideas with the other two citizens of Venthria, Bruno and Cynthia, each of whom has a valuation of v(x) = 6x - x2. What is the socially optimal number of acres of garden? (c) (3 points) Citizen Alina decides the garden should be exactly 1 acre and proposes to Bruno and Cynthia her plan for building the Venthria Community Garden. However, because she did all the planning for the garden, her proposal requires that the $12 cost be split evenly just between Bruno and Cynthia, with Alina not having to pay any of the construction costs. What is the net valuation of each citizen for this proposal? If this proposal were put up to a majority vote, what would be the outcome of the majority vote? Explain. (d) (3 points) Instead of a majority vote, suppose that the citizens of Venthria use a VCG mechanism to determine the fate of the Venthria Community Garden proposal. Would they approve the proposal? Who, if anyone, would pay a tax, and how much? Explain. (e) (2 points) The citizens of Venthria can't actually agree on which process to use to make their decision on Alina's proposal, with some arguing for a vote-as in part (c)and some wanting to use the VCG-as in part (d). Suppose Alina tries to make the VCG more attractive by changing its rules so that all tax proceeds from the VCG are used to compensate people who are harmed by the group's decision. Briefly explain how this might affect how Bruno and Cynthia report their valuations