An important question in economics is how to minimize the total cost of pollution reduction (called the abatement cost, which is considered a "cost to society"). Two companies, Firm 1 and Firm 2, each emit 10 units of pollution per year. The table below shows the total cost for each company to reduce its pollution to a given value x. Due to technology differences, is more expensive for Firm 2 to reduce pollution than for Firm 1. When x = 10, no abatement has occurred (it is "business as usual"); when x = 0, no pollution is emitted. The table also shows an algebraic formula for each abatement cost. (BTW, it is a common economic approximation that abatement cost goes up quadratically.) Below, we solve this for two firms, but the method is applicable to a situation with multiple firms. Per-firm pollution emissions 0 1 2 3 4 5 6 7 8 9 Firm 1 total abatement cost = (10-x)2 100 81 64 49 36 25 where x is the amount of pollution 16 9 Firm 2 total abatement cost = (20-2x)? 400 324 256 196 144 100 64 36 16 4 where x is the amount of pollution 10 4 0 0 a. Each Firm is currently emitting 10 units of pollution (total pollution = 20). Government regulators decide to reduce total pollution in half, to 10 units total. What would be the total abatement cost if they require that each Firm reduce pollution by the same amount, i.e., by 5 units? (This is an example of the "command and control" approach to regulation.) An important question in economics is how to minimize the total cost of pollution reduction (called the abatement cost, which is considered a "cost to society"). Two companies, Firm 1 and Firm 2, each emit 10 units of pollution per year. The table below shows the total cost for each company to reduce its pollution to a given value x. Due to technology differences, is more expensive for Firm 2 to reduce pollution than for Firm 1. When x = 10, no abatement has occurred (it is "business as usual"); when x = 0, no pollution is emitted. The table also shows an algebraic formula for each abatement cost. (BTW, it is a common economic approximation that abatement cost goes up quadratically.) Below, we solve this for two firms, but the method is applicable to a situation with multiple firms. Per-firm pollution emissions 0 1 2 3 4 5 6 7 8 9 Firm 1 total abatement cost = (10-x)2 100 81 64 49 36 25 where x is the amount of pollution 16 9 Firm 2 total abatement cost = (20-2x)? 400 324 256 196 144 100 64 36 16 4 where x is the amount of pollution 10 4 0 0 a. Each Firm is currently emitting 10 units of pollution (total pollution = 20). Government regulators decide to reduce total pollution in half, to 10 units total. What would be the total abatement cost if they require that each Firm reduce pollution by the same amount, i.e., by 5 units? (This is an example of the "command and control" approach to regulation.)
