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There are two factories in a small town. Both of them emit carbon dioxide into the air. Their current monthly emissions, as well as their total costs for reducing emissions in 20-ton increments, are listed in the tables below. Factory 1 120 $50 $150 Current emissions (tons/month) Total cost of reducing emissions by 20 tons/month Total cost of reducing emissions by 40 tons/month Total cost of reducing emissions by 60 tons/month Total cost of reducing emissions by 80 tons/month Total cost of reducing emissions by 100 tons/month $270 $410 $570 Factory 2 160 $20 $60 Current emissions (tons/month) Total cost of reducing emissions by 20 tons/month Total cost of reducing emissions by 40 tons/month Total cost of reducing emissions by 60 tons/month Total cost of reducing emissions by 80 tons/month Total cost of reducing emissions by 100 tons/month $110 $200 $300
See Hint Assume that the existing technology does not allow for reductions in emissions beyond 100 tons/month. That is, the most each factory can reduce its emissions is 100 tons/month. Also assume that if a factory owner is indifferent between reducing pollution or paying taxes, the factory owner will choose to reduce pollution. With those assumptions in mind, suppose the government has a goal of reducing total monthly emissions by 160 tons. To achieve this goal, the government has decided to impose a tax on pollution. That is, for every 20-ton emission, a factory will have to pay some amount of money. To achieve (but not exceed) the desired reduction in emissions, the tax will have to be set equal to or above $ but below $ per 20 tons/month.