3. N= {1,2} is a two-person company. Each individual i has an endowment Wi that he must devote to the purchase of a private good and a public good according to the respective quantities xi and gi. The price of the private good is p1= 2 and that of the public good is p2 = 1. Each individual i has a utility function ui(G,xi)=3G^1/3xi^2/3 where G=g1+g2 is the quantity of the public good. (a) Demonstrate the condition for the efficient provision of the public good assuming that the two agents receive equal weight from the social planner. (b) Describe the set of allocations that are Pareto efficient. (c) What must be the difference in endowment between the two agents for agent 2 to contribute zero at equilibrium?