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 it; is 114021,??2) : 'U lOgG 35}, where G is the amount of public good provided and t.- is the transfer contributed by each individual. (a) Calculate the level of public good provision in an pareto efcient allocation. (b) Consider a mechanism under which each individual chooses how much t;- to con- tribute. Determine the Nash equilibrium under this mechanism. Is it eicient'? (c) Determine the payment each individual makes and the amount of public good provided under a VickreyClarkeCroves mechanism. (d) Calculate the initial transfer if under which the VickreyClarkeGroves would col lect transfers 1 + 752 equal to the amount of public good spending. (e) Would it be possible for the government to set this if in order to ensure budget balancedness