consider the following industry in which two firms produce electricity: a coal firm and a natural gas firm. Both firms sell electricity at the same constant price: P = PMB = $50/MWh The social cost of carbon emissions (i.e. the marginal externality) is $20/ton of CO The coal firm produces 1.5 tons of CO/MWh. Its marginal production costs (i.e. private marginal costs) (in units of $/MWh) are: PMCC = 10 + qc, where qe is the quantity of electricity (in units of MWh) produced by the coal plant. The natural gas firm produces 0.5 tons of CO/MWh. Its marginal production costs (i.e. private marginal costs) (in units of $/MWh) are: PMC = 4 + qg, where q, is the quantity of electricity (in units of MWh) produced by the gas plant. 12) If the government wanted to incentivize the socially optimal production with a carbon cap-and-trade program, what would be the cap (in units of tons of CO)? Please show your work. (2 pts) 13) If the government established a cap-and-trade program with a cap of 25 tons of CO, what would be the permit price (in units of $/ton CO)? Please show your work. (1 pt)