For my final exam question, I asked students to compare the pros and cons of cap and trade and Pigouvian taxes for reducing the negative externality from pollution. Many students gave useful answers, but many also made two big mistakes.
The first was to claim that an advantage was their propensity to reduce consumption (an excellent example of rewriting the question as the answer :).
The other was simultaneously frustrating and enlightening to me. Many students claimed that Pigouvian taxes created a deadweight loss, i.e., the tax would reduce surplus-generating activity.* That statement is true, in general, of fiscal taxes designed to generate revenue (e.g., income, property or expenditure taxes) that the government would spend elsewhere,** but it's NOT true of Pigouvian taxes that are designed to reduce behavior that generates harm that is not reflected in the price of the good being taxed, e.g., taxes on cigarettes to pay for additional health costs or taxes on fuels to reduce and/or ameliorate the costs of pollution.***
The trouble that my students encountered -- and many teachers of economics fail to clarify -- is that fiscal taxes distort prices to generate revenue while Pigouvian taxes correct prices to affect behavior. (We explore the tension between these two goals in this paper on groundwater taxes.)
Bottom Line: We use the same word ("tax") to refer to two different policy instruments. Fiscal taxes generate revenue with some reduction in efficiency; Pigouvian taxes generate revenue as they improve efficiency. (That's why they are called win-win, but don't tell that to the people creating the pollution!)
* Miscalibrated taxes of all types create deadweight losses from being set at the wrong level, but those losses are not present in theory.
** Deadweight losses will be lowest when behavior changes by the smallest amount, i.e., it's best to tax the most inelastic behavior.
*** For more on why politicians prefer command and control over Pigouvian taxes, read this paper [pdf] by Buchanan and Tullock. Buchanan just died; he and Tullock are responsible for much of Public Choice theory, i.e., the idea that politicians and bureaucrats may serve themselves, not the public interest. Here's my review of their brilliant book on constitutions and laws.