I have written several times that if the gubmnt is concerned about the burning of carbon-based fuels, then it should "tax the snot" out of them [see here, here, and here]. More formally, and along these same lines, Greg Mankiw has unofficially formed what he terms "The Pigou Club", which includes economists like me who recommend taxing things that generate negative externalities.
Alex Tabarrok recently challenged the Pigouvian approach, arguing that taxes will not reduce pollution much, at least not in the short run if the supply curves are highly inelastic. If so, then taxing the product will reduce the demand, sliding it down along a (nearly) vertical supply curve, and the total amount of the activity, in real terms, will not change much, if at all. Here is a graph that illustrates his position:

As you can see, I'm no wizard with drawing programmes, but the idea is clear. The tax on consumers shifts the demand curve downward from D to D', leading to a drop in the equilibrium price. In the very short run (some people refer to these very-short-run supply curves as "market-period" or "instantaneous" supply curves), when the demand drops, it is very difficult and costly to reduce the quantity supplied in response to a drop in the price. In the oil industry, for example, it is costly to stop and shut down or even cut back the refining process overnight. In that sense, and in similar situations, Alex's point is worthy of consideration.
In the longer run, however, as firms have the opportunity to adjust their capacity, their output, and their techniques and procedures, then the quantity supplied will indeed respond to the drop in price. And when that happens, people will engage in less of the offending activity. This makes sense. Long-run marginal cost curves tend to be flatter than short-run marginal cost curves for most firms; and long-run supply curves tend to be much flatter than short-run supply curves for competitive industries.
Notes:
- The point of this posting is to show that Pigouvian taxes can be [not necessarily will be] effective in reducing negative externalities.
- Pigouvian taxes are more likely to be effective in the long run than in the short run.
- Nobody really has any good or reliable idea as to how big the taxes should be.