Does cost-benefit analysis always council against extremism? In a reply to Arnold, Mankiw seems to argue that it does:

I am not a scientist and am therefore agnostic about a lot of issues surrounding global warming. Suppose I assign a probability p that Al Gore is right. The optimal policy from my perspective is not to oppose a carbon tax unless p exceeds some threshold. Instead, the optimal tax is increasing as a function of p and is positive for any p>0. A person who thinks p is small would not want a big carbon tax but should endorse a modest one.

But what if there is a fixed cost of having a carbon tax in the first place? For example, the net expected benefits could be:

-$1,000,000 + $10,000,000*p

The $1,000,000 might be the overhead of the carbon tax collectors, or the costs of every tax-payer who has to fill out a carbon tax form, or what have you. Given this fixed cost, for p<.1, the net expected benefits of a carbon tax are negative. On efficiency grounds, Arnold would be correct to council inaction until p exceeds that threshold.

Every micro textbook tells us that when the price of a good gets so low that firms can't recoup their fixed costs, it makes sense to simply close up shop – or not open in the first place. The same goes for government programs.