Deborah and Janet are considering contributing toward the creation of a building mural. Each can choose whether to contribute $200 to the building mural or to keep that $200 for a new sult. Since a building mural is a public good, both Deborah and Janet will benefit from any contributions made by the other person. Specifically, every dollar that either one of them contributes will bring each of them $0.80 of benefit. For example, if both Deborah and Janet choose to contribute, then a total of $400 would be contributed to the building mural. So, Deborah and Janet would each receive $320 of benefit from the building mural, and their combined benefit would be $640. This is shown in the upper left cell of the first table. Since a new sult is a private good, if Deborah chooses to spend $200 on a new suit, Deborah would get $200 of benefit from the new suit and Janet wouldn't recelve any benefit from Deborah's cholce. If Deborah still spends $200 on a new suit and Janet chooses to contribute $200 to the building mural, Deborah would still recelve the $160 of benefit from Janet's generosity. In other words, If Deborah decides to keep the $200 for a new suit and Janet decides to contribute the $200 to the public project, then Deborah would receive a total benefit of $200 + $160 = $360, Janet would receive a total benefit of $160, and their combined benefit would be $520. This is shown in the lower left cell of the first table.

Two individuals A and B have utility functions defined over two goods, a private good 'x') and a public good, 'F. The utility function of an agent 'i' is defined by ui = 2 log xi + log F where F =FA + FB. Each agent has 200 units of private goods x, as his endowment and 1 unit of private good can be transformed into 1 public good F. Answer the following (a) Find the Nash equilibrium values of FA and FB? (b) What is the Pareto optimal level of F? (c) In what condition the Pareto optimal level of F will not depend on the number of private goods? (d) What would be the consumption of x by each agent if they contribute equally towards the public good (F)? (e) Would it change if an agent had a larger endowment of x to begin with?

Kyoko and Rina are considering contributing toward the creation of a public park. Each can choose whether to contribute $300 to the public park or to keep that $300 for a weekend getaway. Since a public park is a public good, both Kyoko and Rina will benefit from any contributions made by the other person. Specifically, every dollar that either one of them contributes will bring each of them $0.90 of benefit. For example, if both Kyoko and Rina choose to contribute, then a total of $600 would be contributed to the public park. So, Kyoko and Rina would each receive $540 of benefit from the public park, and their combined benefit would be $1,080. This is shown in the upper left cell of the first table. Since a weekend getaway is a private good, if Kyoko chooses to spend $300 on a weekend getaway, Kyoko would get $300 of benefit from the weekend getaway and Rina wouldn't receive any benefit from Kyoko's choice. If Kyoko still spends $300 on a weekend getaway and Rina chooses to contribute…

Please answer everything in the photos.