microeconomics asap

Consider two consumers, a and b. The consumer is indexed by a superscript i = a, b. Both have the same preferences over a private good 2i and a public good x: 1 2 logzi + % log 3:. ui(zi,x) = For each 1' = a, b, let ei stand for the initial endowment of the private good. The marginal cost of the public good is 1. (a) Suppose the social planner wants consumer I) to reach utility level Eb. What is the optimal amount of the public good 95*? How much each consumer must contribute to the public good in order to achieve the optimal amount? (b) Let yi denote the contribution made by consumer i to the public good. Find the best response functions, f\" (yb,e\") and fb (31\