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Question 1 [50 points] Two firms have abatement cost functions given by C1(a1) = = a], C2(a2) = 3. and BAU emissions given by ed = ey = 1000 tons. The damage from emission e = e1 + ez is given by D(e ) = =e2. a) [10 points] Find the socially optimal emission levels of both firms. b)[10 points] Suppose the government uses a tradable permit system and issues 1000 permits, with each permit allowing one ton of emission. Thus, the total emission will be reduced by half, from 2000 to 1000 tons. Find the equilibrium permit price, and the final emission level of each of the two firms under this scheme. c)[20 points] Suppose the government imposes an emission tax at the rate of $400/ton. Further, suppose there is a new technology that will reduce the abatement cost of each firm by half, to C1(a, ) = = a;, C2 (a2) = 5 a2. Find each firm's gain from adopting the new technology. (Hint: first find each firm's emission levels before and after adopting the new technology.) D10