Pigovian Taxes are not efficient if the money gets wasted

In an argument on my LJ, I said that if a carbon tax did not go towards sequestering carbon, it was not efficient. In general, if you waste a Pigovian tax, the tax has not done its job. Someone replied:

It's been a while since my days in econ classes, but if I recall correctly, the real goal of internalizing the externality is to set the level of consumption properly, such that including externalities, people will only consume the good if they get more out of it than it costs. What the money gets spent on is certainly important, but it can be completely separated from the source of the money.

This is incorrect, and you can see why with a simple exercise in economic efficiency. (The question of whether economic efficiency is a good metric is outside the scope of this discussion).

The whole point of setting the level of consumption properly is so that people will only make economically efficient decisions, those which gain the world more than they cost. If activity X costs $10 in resources, and imposes $5 of negative externalities, then anytime someone who values X at V does X, the result for the world is a net of V - $10 (cost) - $5 (externality), or V - $15. If V is < $15, the world loses, and since the person is faced with a cost of $10, they will do X if V is between $10 and $15, even though the world loses.

Now suppose we follow the Pigovian approach, and we charge people $5 for doing V, and we give the money to me. Now the equation for the world's loss is still V - $10 (cost) - $5 (externality), or V - $15, because the transfer doesn't affect total wealth. Since the person is faced with a cost of $15, they will only do X if V > $15, which means they only do things that are a net gain. Perfect!

Now, consider how Pigovian taxes would be implemented by a completely wasteful government: Charge $5 for doing V, use the money to obtain 5$ worth of resources, and burn them. Now the equation for the world's loss is V - $10 (cost) - $5 (externality) - $5 (stuff burned), or V - 20$. Since the individual only faces $15 in costs, they will do X if V > $15. Yet when V is between $15 and $20, the world loses. The loss is smaller, since the bad range is higher, therefore less people will do it, but it's still a loss. You have "internalized the externality" only by creating another externality.

In practice, however, while the government doesn't use its money efficiently, some of the "waste" consists of transfers. If you pay farmers not to grow things, you only lose the value of what they would have done with their time, not the full amount you pay them. So it's not quite as bad as the "buy and burn" strategy, but neither is it as good as the "give the money to Patri" strategy.

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