(a) Consider a mechanism design problem. Suppose there are three agents. The social

planner is considering whether to provide a public good that costs K = 15. Let the

valuations of the three agents be 1 = 7, 2 = 2 and 3 = 7. If the good is provided,

then the total cost will be divided equally between the three agents.

i. Should the public good be provided? (2)

ii. Suppose the planner designs the pivotal VCG mechanism to elicit truthful revelation

of valuation by the agents. What monetary transfers will be imposed on the three

agents under this mechanism?