A Pollution Charge

A small firm emits 50 pounds of soot a year. Cutting the first 10 pounds costs it $300, because the cheapest and easiest fixes come first. The next 10 cost $500, the next $900, then $1,500, then $2,500. That rising pattern is the usual one: each further cut is harder than the last.

Now tax the pollution. The firm compares each 10-pound block against the charge and cuts whenever cutting is cheaper than paying. At $1,000 a block it cuts the first three, at $300, $500 and $900, and stops: the fourth block would cost $1,500 to cut and only $1,000 to pay for. So the charge buys 30 pounds of abatement without anyone telling the firm how to do it. The slider sets the charge, and the side panel shows where the firm stops.