Part II. Pigou versus Pareto. Pigouvian taxes correct market failures, and in the presence of a Pigouvian tax set to the correct level, the market outcome is Pareto efficient. But, moving from the status quo (no corrective tax) to this point is not a Pareto improvement, but it is a Kaldor Hicks improvement. This problem illustrates this in an example with numbers. - The market for cobalt has Total Benefit = 100Q 2Q2 and Total Cost = 3Q2. Production of cobalt causes a negative externality equal to 20Q, so that each unit of cobalt production has a negative externality equal to 20. 4. If there is no corrective tax, what is the consumer and producer surplus? (2 points, no explanation required) 2 5. Now assume that the Pigouvian tax of $20 per unit is implemented. What is the new consumer and producer surplus? (Remember that the price paid by consumers is now different from the price received by the producers, with the difference equal to the tax.) (2 points, no explanation required) 6. We have seen that Pigouvian tax leads to losses in consumer and producer surpluses, but it also reduces total externality, which improves the welfare of consumers, producers, and external agents. Suppose that producers get 25% of the benefits of the reduction in externality, consumers get 50% of the benefits, and the remaining 25% goes to households that are not part of the cobalt market. Therefore, in evaluating consumers' and producers' welfare, we need to consider both the loss in consumer and producer surpluses and the welfare improvement from reduced externality. In this case, how much of the government revenue must be given to consumers in order to make them no worse off under the policy (e.g., to get consumer and producer welfare back to the original level of consumer and producer surpluses)? How much of the government revenue must be given to producers in order to make them no worse off under the policy? (4 points, show your work.)