Minnesota Has Two Oil Refineries That Emit Methane Gas

Essay

Minnesota has two oil refineries that emit methane gas. The Bend refinery emits 300 units of methane, and the Park refinery emits 900 units. Government regulators would like to reduce total methane emissions from 1,200 to 900 units. Bend's total abatement and marginal abatement costs are TC_B = 400Q_B + 4Q_B² and MAC_B = 400 + 8Q_B, where Q is units of methane. Park's total abatement cost and marginal abatement costs are TC_P = 40Q_P + 2Q_P² and MAC_P = 40 + 4Q_P.
a. Suppose that government regulators require each refinery to remove 150 units of methane. What is the total cost of removing these 300 units (TC_B + TC_P)?
b. Now suppose that the government regulators evenly split 900 methane pollution permits between the two refineries. What is the total cost of removing 300 units of methane, using a tradable permit system?