2. (20 points) Consider a society composed of three people, each with an inverse demand for a public good, z: P(z) = 10-z P2(z) = 10-z P3(2)=5-z Suppose that the total cost of producing z is c(z) = 15z and so, the marginal cost of producing a unit of z is $15. == a. Find (and draw a diagram of) the total demand for z. b. Find the socially optimal level of z. c. Now suppose that this society determines the level of z by majority vote. If the cost of producing z is split evenly among the members of this society, which quantity of z would each vote for? (Assume that people vote truthfully in the sense that they vote for their preferred quantity of the good.) d. Given majority voting and your answer for part (c), how much of the public good will this society produce? How does it compare to the socially optimal level? e. What does this suggest about the use of political means to correct instances of market failure?