Question 2 A small community is considering building a public park, which would be accessible to all residents without excluding anyone from its use. There are two individuals in the community, Robban and Berra, each of whom derives utility from the amount of the public good G provided, as well as their private consumption of a numeraire good X (that is, the price of X is set to one).The cost of providing the public good is shared between Robban and Berra, and its total cost is given by C(G)= G, where G represents the amount of the public good provided (think of this as square meters of park. Each individual has the following utility function: Robban: Up(Xp,G) = XpG Berra: Up(Xp,G) = XG where Xr and Xz represent the private consumption of Robban and Berra, respectively, and G represents the quantity of the public good. Each individual has an endowment of 100 units of the numeraire good. a) b) c) d) Explain why the public park in this scenario fits the definition of a public good. (5 points) Determine the socially optimal (efficient) level of the public good, G*. (7 points) Assume now that Robban and Berra each decide how much to voluntarily contribute to the provision of the public good. Derive the equilibrium level of G when each individual acts independently, maximizing their own utility given the contribution of the other (hint: think of this as deriving a best response). (7 points) Compare the level of the public good G under the voluntary contribution equilibrium to the socially optimal level. Explain in terms of economic theory any differences you find, if any. (6 points)