Consider a mechanism design problem. Suppose there are two agents. The social planner is considering whether to provide a public good that costs

K = 6. Let the valuations of the two agents be 1 = 2 and 2 = 8.

(a) Is it socially optimal to provide the public good?

(b) Consider the original VCG mechanism with h1(1) = 0 and h2(2) = 0 . What are the monetary transfers by the planner to each of the two agents? What is the problem with this mechanism?

(c) Show that the pivotal VCG mechanism resolves the problem encountered in question {b)