Consider two abatement technologies that have costs C^{1}(a_{1}) = a_{1}^{2(on the top of a)} and C^{2}(a_{2}) = 3a_{2}^{2(on the top of a)}. The marginal benefit of abatement is equal to 48 −12A, where A = a1 + a2 (A is total abatement).

(a)Calculate the socially optimal amount of abatement for each technology and in total. Also calculate the total cost at this optimal allocation.

(b) Now suppose that instead of this optimal allocation, the amount abated by each technology is equal and they add up to the same A you found above (A = 24 just in case you missed part (a)). Calculate the total cost.

(c) Draw a graph that shows the marginal abatement costs of each technology on the same graph. Show the total costs under the optimal allocation by shading the relevant areas.

(d) Draw a second graph that shows the marginal abatement costs of each technology on the same graph, but this time show the total costs under the equal abatement allocation by shading the relevant area.