Pigovian calculation with a government

The continued discussion on Karl's website leads me to draw a distinction between textbook pigovian taxes and the fact that government response is all too often ignored in these textbook frameworks. It seems to me that the revenue generated from the pigovian tax which was used to pay for the social cost of pollution etc could in and of itself be used to pay for (as a tax cut etc) a social benefit to the environment - a postive externality not as of yet taken into account, whatever that might be. Or, the revenue could just go directly to bettering the environment.... That investment would act to reduce the level in which the tax must be raised in the first place - thereby making it more politically feasible.

This brings up yet another problem in applying textbook pigovian taxation to the real world. Textbooks assume no changes over time and therefore assume a fixed social cost to an activity (Carbon useage), and therefore apply a fixed tax to it. Yet, depending on how revenues are used etc, the marginal social cost of environmental damage caused by marginal carbon useage can in fact be lowered over time. For example, with signifcant investment in technology aimed at reducing emissions from a unit of carbon, the social cost of buying a given unit of gas etc may fall significantly over time. Another way of looking at that is to say that the social benefit of certain investments reduce the NET social cost of gas consumption over time.

I of course still do not support gas taxes, because the downside to the above scenario, as I'm sure Greg Mankiw is aware, is that you would not have new revenues with which to compensate the 'losers' of the gas tax - which would be poor consumers relatively speaking.

In terms of how to use the increased revenue, You are damned if you do and damned if you don't with Pigovian taxation.