I was teaching my class Friday on the economics of externalities. I’m using the 5th edition of Greg Mankiw’s Principles of Economics. Why the 5th edition? To save my students over $100 a pop. Textbooks rarely get much better after a few editions.

In his treatment of negative externalities, Greg makes a large, and unstated, assumption. He gives an example of aluminum production in which the production process causes pollution. Then he shows the supply curve of aluminum along with the social cost curve of aluminum (which includes private costs and external costs.) He shows that the equilibrium when the externality is not internalized is at a quantity of aluminum that is too high.

But then he jumps to the conclusion that the optimal outcome can be reached by taxing aluminum. That doesn’t follow. I’m not making the argument that many libertarians make–that the government can’t know the right tax, that it matters where the tax revenues go, etc. I’m sticking within Greg’s framework that the optimal outcome can be reached with a tax.

But here’s the relevant question: what should be taxed? Greg claims that the tax should be on aluminum. For that to make sense, there would have to be fixed proportions between aluminum production and pollution production. (There would also have to be a constant cost of each unit of pollution to the sufferers from pollution, but put that aside. There’s a problem even if that latter assumption is true.)

But what do we know about most production processes? We know that there are various ways to produce. There are probably more-polluting and less-polluting ways to produce aluminum. The problem is that if the government simply taxes per ton of aluminum, it does nothing to give an incentive to the company to use a less-polluting production process.

Remember that the problem is not aluminum per se; the problem is the pollution that comes from the process. So if there is to be a tax, it should be on the pollution, not on aluminum production.

I learned a basic principle early in my economics education. I learned it in a graduate international trade course at UCLA in which we went through Jagadish Bhagwati’s proofs that restrictions on trade are almost never first-best solutions to the problems that people want those restrictions to address. The principle is that if your goal is efficiency, the solution should be carefully tailored to aim directly at the problem. Again, the problem is not aluminum production: the problem is pollution.

And it turns out that this error matters for Greg’s exposition of his case for taxing gasoline. More on that anon.