An economy has two types of firms that contribute GHG emissions to the atmosphere: coal power plants emit 10 Mt CO2/year per firm and cement factories emit 1 MtCO2/year per firm (where 1 MtCO2/year = 1,000,000 tons of carbon dioxide per year). There are 100 coal power plants and 300 cement factories. The two types of firms are different, but within each sector firms are the same. Total abatement costs for each coal power plant are C1(a1) = 5(a1)^2 , where a1 is abatement for a coal power plant, measured in Mt CO2/year. Total abatement costs for each firm in the cement industry are C2(a2) = 6a2 + 7.5(a2)^2 .

1. Calculate the overall baseline emissions of the economy. If annual emissions should be reduced to 940 Mt CO2/year, how many Mt CO2 have to be abated? The government decides to implement a cap-and-trade system. It sets an economy-wide cap at 940 MtC02/year and auctions off permits. Assume that there is perfect competition on the permit market.

2. At what price do permits trade? How many MtCO2 of permits do firms in each of the two sectors purchase?

3. Assume that the total abatement costs in the coal industry are C1(a1) = 2a1 rather than the above costs. How many MtCO2 of permits does the coal sector purchase? How many MtCO2 of permits does the cement sector purchase?