Will be very appreciated if following questions are solved in steps

Suppose that there are a large number, H, of identical households with utility function: U(th, (h, G) = alna +(1-a) Ine tylG y>0, 0 0. (3) h=1 h=1 Given that if asked to contribute voluntarily to the provision of the public good agents will free-ride, the government proposes to provide the good publicly, financing its production with an income tax at rate to. a. What is the optimum quantity of public good for the government to provide, given the constraint that they must finance with distorting taxation? b. Does this quantity satisfy the Samuelson condition? That is, is the outcome Pareto efficient