= 2. An economy has two types of firms that contribute GHG emissions to the atmosphere: coal power plants emitting 10 MtC/year (MtC/year 1,000,000 tons of carbon per year) per facility and cement factories emitting each 1 MtC/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. (a) Calculate the overall baseline emissions of the economy. If annual emissions should be reduced to 940 MtC/year, how many MtC have to be abated? The government decides to implement a cap-and-trade system. It sets an economy- wide cap at 940 MtC/year and auctions off allowances. Abatement costs for each firm in the coal sector are C₁(a) = 5a² for abating a MtC/year. Abatement costs for each firm in the cement industry are C2(a) = 6a+ 7.5a². All costs are measured in million AUD. Assume that there is full competition on the allowance market. (b) At what price do allowances trade? How many MtC of allowances do firms in each of the two sectors purchase? (c) Assume that the abatement costs in the coal industry are C₁(a) =2a rather than the above costs. How many MtC of allowances does the coal sector purchase? How many MtC of allowances does the cement sector purchase? (d) Say that instead of implementing a cap-and-trade system the government opted for a carbon tax. What tax ($ AUD per tC) should the government set to reduce annual emissions to 940 MtC/year?