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 $50. 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 MCA QA, while the social damages from water use are equal to MEDA = 1. 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 MCo = 4Qo and the social damages from the chemical leakage is MED. = 2. 20. 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. (2 points) 21. Now, suppose instead that the Bay Area Social Planner must choose one tax rate that will apply to both mines. According to the model of Peter Diamond that we discussed in class, will the second-best tax be closer to the first-best mine-specific tax rate for Asscher, or the one for Oval? Explain why in one or two sentences.* (2 points) 22. What is the second-best tax rate on diamond extraction, assuming the tax rate must be the same for both mines? (2 points) (Hint: One way to solve this is to maximize social welfare, which is tax revenue plus firm profits minus the externality. You can also apply the Diamond formula directly.) 23. Draw and upload two graphs that depicts the deadweight loss that results from imposing a uniform tax on the two mines. (Include one graph for each mine. You can draw them side by side and upload as one image.) Your graph should include the marginal benefit, marginal cost, marginal social cost, the second-best uniform tax, the quantity the firm will choose given that tax, and the socially optimal quantity. (4 points) 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 $50. 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 MCA QA, while the social damages from water use are equal to MEDA = 1. 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 MCo = 4Qo and the social damages from the chemical leakage is MED. = 2. 20. 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. (2 points) 21. Now, suppose instead that the Bay Area Social Planner must choose one tax rate that will apply to both mines. According to the model of Peter Diamond that we discussed in class, will the second-best tax be closer to the first-best mine-specific tax rate for Asscher, or the one for Oval? Explain why in one or two sentences.* (2 points) 22. What is the second-best tax rate on diamond extraction, assuming the tax rate must be the same for both mines? (2 points) (Hint: One way to solve this is to maximize social welfare, which is tax revenue plus firm profits minus the externality. You can also apply the Diamond formula directly.) 23. Draw and upload two graphs that depicts the deadweight loss that results from imposing a uniform tax on the two mines. (Include one graph for each mine. You can draw them side by side and upload as one image.) Your graph should include the marginal benefit, marginal cost, marginal social cost, the second-best uniform tax, the quantity the firm will choose given that tax, and the socially optimal quantity. (4 points)
