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2. (25 points) 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,y) = 2x1/2 + y and Person 2's utility function is u(x,y) = x/ + y. Consider the private good provision mechanism where Person 1 makes a contribution for the public good first, then Person 2 follows. a. (5 points) Find the optimal output of the public good by using Samuelson condition. b. (15 points) Show that in the private good provision mechanism Person 2 rides free. c. (5 points) Is the private good provision mechanism efficient? Explain. 2. (25 points) 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,y) = 2x1/2 + y and Person 2's utility function is u(x,y) = x/ + y. Consider the private good provision mechanism where Person 1 makes a contribution for the public good first, then Person 2 follows. a. (5 points) Find the optimal output of the public good by using Samuelson condition. b. (15 points) Show that in the private good provision mechanism Person 2 rides free. c. (5 points) Is the private good provision mechanism efficient? Explain