We introduced the Diamond model as a case where the Pigouvian prescription needs to be amended. This problem walks you through a closely related problem. In class, we motivated the model thinking about heterogeneous consumers, but here I ask you to think about two different firms. Two local mines, named Asscher and Oval, extract identical diamonds. Suppose that the mines are small operations and are therefore price takers in the global diamond market, where the price per unit is currently $30. The Asscher mine is located in a low population part of Napa County where the mine creates an externality by using up fresh water supplies. The private cost of Asscher extraction is equal to TCA = 0.527, while the total social damages from water use are equal to TEDA = QA. The Oval mine is located in Richmond, and the mine leaches chemicals into the Bay that cause significant problems. The private cost of Oval extraction is TCo = 40%, and the total social damages from the chemical leakage is TEDo = 200. 12. Suppose that the Bay Area Social Planner could impose a per unit tax on Asscher, and a separate tax on Oval. What would be the tax on each? Call these the first-best mine-specific tax rates, labeled #'B. (1 point) Answer for +5: Answer for 15: 13. Now, suppose instead that the Bay Area Social Planner must choose one tax rate that will apply to both mines. According to the Diamond model, will the second-best tax be closer to the first-best mine-specific tax rate for Asscher, or the one for Oval? Briefly explain why. (1 point; the explanation will not be graded, but you should try to explain this for yourself.) O Closer to Asscher (*# ) O Closer to Oval (15B) 14. What is the second-best tax rate on diamond extraction, assuming the tax rate must be the same for both mines? (2 points) 15. Extension question: When the government must impose a uniform tax rate for both firms, the tax rate will be "wrong," which creates inefficiency. The second-best tax rate minimizes the deadweight loss summed across the two firms (equivalently, it maximizes the efficiency gains from taxation). Derive an expression for the deadweight loss in Asscher and the dead- weight loss from Oval as a function of the tax rate, labeled "5. (You should then be able to confirm that the answer you gave above minimizes the sum.) (2 points)