Public Good Provision under VCG: Suppose there are two individuals i = 1, 2. Suppose that each individual has valuation v1 = v2 = v and that this is commonly known among the two individuals. Assume that the government who is designing the mechanism does not know each individual's valuation. The utility of each individual is i is ui(t1, t2) = vi log G ti , where G is the amount of public good provided and ti is the transfer contributed by each individual. (a) Calculate the level of public good provision in an pareto efficient allocation. (b) Consider a mechanism under which each individual chooses how much ti to contribute. Determine the Nash equilibrium under this mechanism. Is it efficient? (c) Determine the payment each individual makes and the amount of public good provided under a Vickrey-Clarke-Groves mechanism. (d) Calculate the initial transfer t under which the Vickrey-Clarke-Groves would collect transfers t1 t2 equal to the amount of public good spending. (e) Would it be possible for the government to set this t in order to ensure budget balancedness