3) (20 points) Consider a 3 person 2 good economy where there is a private good x and a public good y. Agent 1 has a private endowment of 1 unit, agent 2 has a private endowment of 2 units and agent 3 has a private endowment of 3 units. Initially there is no public good in the economy but each unit of the public good can be produced using 1 unit of the private good. That is, the cost function is C(y) = y. Utility functions of the agents are as follows: U₁(x₁, y) = x₁y U₂ (x₂, y) = (x₂)²y U3(x3, y) = (x3)³ y Either prove or disprove that market failure occurs in this environment.
