6. Let N = {1,2} be a society of two individuals. Each individual i has an endowment w; to be spent on a private good and a continuous public good in the amounts of X, and 9;, respectively. The price of the private good is p, = 2 and that of the public good is P2 = 1. Each individual i has a utility function u; (G, x;) = In(10) + -In(G) + =In (x;), where G = 91 + 92 is the amount of the public good provided. (a) Demonstrate the condition for the efficient provision of the public good assuming that both agents are identically weighted. (7) (b) Describe the set of Pareto efficient allocations. (5) (c) How big does the wealth difference between the two agents have to be for agent 2 to contribute zero in equilibrium? (9)