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-fun polution emissions I Firm 1 total abatement cost = [10-301 where x is the amount of pollution Firm 2 total abatement cost - (20-23:)x where x is the amount of pollution 100 81 64 49 36 25 400 324 256 196 144 100 64