Consider a simple public good economy with two people and two goods: one public (x) and one private (y). Assume that one unit of public good can be produced with two units of private good. Person 1's utility function is U1(X,yı) = 2x1/2 + y₁ and Person 2's utility function is u₂(x,y²) = x¹/² + y₂. Consider the private good provision mechanism where Person 1 makes a contribution for the public good first, then Person 2 follows. a. Find the optimal output of the public good by using Samuelson condition. b. Show that in the private good provision mechanism Person 2 rides free. c. Is the private good provision mechanism efficient? Explain.
