Three agents Amy, Brian and Cathy are to decide whether or not to buy a discrete public good that costs R102 to provide. The valuation that each agent has for the public good are: Agent Valuation Amy R0 Brian R55 Cathy R40 a. Is the provision of the public good socially efficient? Explain your answer. [3 marks] b. Suppose the agents put the matter to a vote with the following rule: if the majority votes in favour of provision, then each agent pays an equal share of the cost. Will voting result in the socially efficient decision? Explain. [3 marks] c. Suppose that a social planner adopts a Clarke tax, so each agent is asked to submit a net valuation for the good. If the reports sum to more than R0, the good is provided. Pivotal agents are required to pay the sum of others' reports. If all agents are truthful, which agent(s), are pivotal? Explain your answer.