Oh Treasury, Why Hast Thou Forsaken Us?

Reading the Law Commission report on the review of alcohol taxation and regulation that Eric linked to yesterday, I noticed this sentence in the Treasury advice to the Commission:

Within existing constraints then, the best proxy for a progressive Pigouvian tax is an alcohol excise that equates to the net costs of the consumption of alcohol for society as a whole.

The constraints they refer to are the fact that the external costs of alcohol are typically higher for large users than for low users, so that ideally large users should pay a larger tax per drink than low users. Let’s leave aside the fact that a Pigouvian tax should be set to equal the marginal social cost not to equate tax revenue with the total social cost. My problem with this statement is that if one is constrained to apply the same tax to high-social cost and low-social cost users, the optimal policy needs to ask about the relative responsiveness of demand to price of the two groups. Let’s imagine that high-social-cost users have relatively inelastic demand and low-social-cost users have more elastic demand. Then a Pigouvian tax will have little effect in reducing the harmful consumption of the former group and a large effect in reducing the non-harmful consumption of the latter group. The optimal Pigouvian tax in this world would be much lower than one that equaled net social marginal costs. Indeed, in the extreme case where the high-social-cost users had demand that was completely unresponsive to price, the optimal Pigouvian tax would be zero!