A mining company, Dwarves Co., mines for coal in the mountains of Middle-earth. But in this process, a small amount of wastewater infiltrates and contaminates the soil. For each ton of coal produced, 20 gallons of wastewater goes into the soil. The wastewater generates an external cost of $0.15 per gallon.

Let P be the price of coal (measured in dollars) and Q the quantity of coal (measured in tons).

The mining company's Marginal Private Cost (MPC): MPC = 2 + Q

Coal consumers' Marginal Private Benefit (MPB), which is the same as the Marginal Social Benefit (MSB): MPB = MSB = 12 Q

a. In the market equilibrium, how many tons of coal will the mining company produce?

b. What is the socially efficient level of coal production?

c. The government wants to achieve the socially efficient level of coal production by imposing a tax of $t per ton of coal. (The tax is levied on the coal instead of the wastewater, because it's much easier to measure the quantity of coal than to measure the amount of wastewater.) What should $t be? Explain.

d. Suppose now the government implements the tax on coal that you designed in (c). A scientist, Dr. Gandalf, invents a new technology that can turn wastewater into clean water. Gandalf charges $0.01 for each gallon of wastewater cleaned. For example, if Dwarves Co. chooses to have Gandalf clean 30 gallons of wastewater, it needs to pay Gandalf a total of $0.01 30 = $0.30. Given the tax and the new technology, how much wastewater will Dwarves Co. choose to clean?

e. With Gandalf's new technology described in (d), what is the socially efficient level of coal production now?