Following are the marginal abatement costs of two sources. They currently emit 10 tons each.
a. What would the total abatement costs be for an equiproportional cutback to a total of 10 tons?
b. Suppose we print up 10 transferable discharge permits, each of which entitles the holder to 1 ton of emissions. We distribute them equally to the two sources. What will the final emissions be for each of the two sources, and the total abatement costs after all adjustments have been made? 

c. Show that if the permits are originally distributed in a different way (say all to one source and none to the other), the final results will be the same in terms of total and individual emissions, but the distribution of the gains from trade will be different between the two sources.

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Emissions (tons) 10 9 8 7 6 5 4 3 210 Marginal Abatement Costs Source A Source B 0 0 4 8 2 4 6 8 10 12 14 18 28 48 14 20 30 42 56 76 100 180