While conducting pilot research on the effects of air quality on plants and fungus in 2014, employees of a government agency detected alarmingly high levels of cancer causing pollutants in areas surrounding two metals manufacturers in a mid-sized east coast US city. Besides being carcinogenic, these air pollutants are known to damage plants, pets, and human health through several pathways when their local concentrations are high. To reduce the concentration to acceptable atmospheric concentrations, it is established that the combined emissions of factories would have to be no higher than 44 metric tons of pollutant each year. Currently, one firm emits 40 tons of pollutant each year, while the other emits 20 tons each year.

The attached worksheet details each firm's emission level and the total costs associated with reducing emissions.

Assume that local officials, in an attempt to be "equitable", choose to allocate cleanup responsibility equally between the two firms.

1. How many tons would each firm need to abate?
2. What would the total cost to society be of the desired level of abatement?

FirmA Total Cost 40 39 3 3B 37 38 36 83 35 151 250 34 33 385 32 561 31 784 1,059 30 29 2B 27 26 25 24 1,392 1,788 2,252 2,791 3,410 4,114 4,909 5,800 6,793 7,893 23 22 21 20 19 18 17 16 15 9,105 10,436 11,891 13,475 15,194 17,053 19,058 21,214 23,526 14 13 12 11 11 10 9 8 7 23,526 26,001 28,644 31,460 34,455 37,634 41,003 44,567 48,331 52,302 5 4 3 2 1 56,485 60,885 0 Firm B Total Cost Q 20 19 0 18 17 1.1 3 5.9 10 15.5 22.6 31.5 42.4 55.5 71 89.1 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 2 1 1 110 133.9 161 191.5 225.6 263.5 305.4 351.5 O 402