If the world’s roughly 430 nuclear power plants melted down all at once and vented fully into the atmosphere, that would be bad. Really bad. In the jargon of the International Monetary Fund, it’d be a huge externality – a social cost of using nuclear plants not fully reflected in the rates charged by the utilities or governments that operate those facilities.

In this catastrophic example, let's assess the cost at, say, infinity – given the damage to human health and property involved. Under the logic of a recent and extensive IMF study on world energy subsidies, the cost of that potential damage should be included in electricity rates.

What is the true cost of using hydrocarbons for energy?

Of course infinity is too much to pay to watch television or run your air conditioner. And the risk of a simultaneous catastrophic meltdown of nuclear plants around the world is very small, so the cost would have to be multiplied by that very small probability.

It is hard to multiply by infinity. But presumably infinity times even a very small number yields a substantial amount.

Yet according to footnote 19 in Appendix I of the IMF’s study, the potential externality costs of nuclear power were not factored into its report. It was just too much for the 30 researchers involved to get a grip on.

“It is extremely difficult to quantify the risks from radioactive waste and meltdowns,” the footnote reads.

The “nuclear exclusion” is just one of a number of issues that might be raised with the study, the thrust of which is that governments are underwriting the use of fossil fuel to the tune of $1.9 trillion a year, and ought to stop because it makes no sense to underwrite the use of products that are making the climate warmer.

Some of that $1.9 trillion is straight ahead subsidy – governments in the Middle East trying, in the words of IMF First Deputy Managing Director David Lipton, “to placate restive populations” with cheap gas and electricity. It gets really hot in Saudi Arabia, and with a couple of million imported workers outnumbering your own people, you want to ensure them a few creature comforts. Egypt without air conditioning? Mubarak’s fall would be tame by comparison.

But most of the $1.9 trillion doesn’t exist as an actual “subsidy” in the way non-economists would use the word. It exists only in a sort of negative sense -- as the “lack-of-a-tax-the-IMF-thinks-should-exist.” That is, the fund feels that fossil fuel use “costs” about $1.4 trillion a year in environmental damage and climate change risk that is not reflected in the price paid for gasoline at the pump or forked over to PEPCO every month.

Voila, a new tax.

Yet like any study of this sort, the numbers rest on some assumptions and some shortcuts that are open to question.

Excluding nukes, for example, raises one set of issues. Given that nuclear plants are a substitute for the thing you are measuring (the cost of carbon emissions) wouldn’t it be important to weigh the potential externalities of one against the potential externalities of the other?

According to the Energy Information Administration, the average nuclear plant produces 12.2 billion kilowatt hours a year. Multiplying that by the Environmental Protection Agency’s carbon equivalence tables means the typical reactor prevents the emission of something like 8.6 million tons of carbon dioxide a year.

In the IMF’s study, carbon emissions are “priced” at $25 a ton – which makes the carbon not emitted from each nuke worth about $215 million a year.

Seems that governments could dump $100 million a year per plant into new reactors, eliminate all of the carbon involved with electricity generation, and have $115 million left over.

Footnoting away the role of nuclear power begs the question — and no doubt the several tens of thousands of people still displaced by the Fukushima disaster in Japan would like  to know where the IMF comes down on the issue.

And where does that $25 a ton figure for carbon emissions come from? The IMF study acknowledges that researchers have been all over the map on how to set a cost for the damage done by carbon pollution – with estimates of anywhere from $12 to $85 a ton.

In a paper that is meant partly as a conversation starter – to press governments to think about the economic distortions subsidies can cause – you have to pick a number. The IMF took its cue from the U.S. government’s Interagency Working Group on the Social Cost of Carbon.

That study tried to develop guidelines for federal agencies to do cost-benefit analyses of regulations that reduced energy use and carbon emissions. It looked, for example, at the effect carbon emissions have on “net agricultural productivity, human health, property damages from increased flood risk, and the value of ecosystem services due to climate change.”

But it did not produce a single number – rather a range of numbers based on several models and sets of financial assumptions, from a low of $4.70 a ton to a high of $136.20. The IMF study does not explain how it picked $25 out of the working group’s analysis.

Climate change activists noted also that the IMF did not account for the production, drilling and exploration tax breaks that the fossil fuel industry enjoys - and which would have likely pushed the subsidy total higher.

And then there’s insurance. According to the IMF, the U.S. needs to impose a $1.40 per gallon “corrective tax” on gasoline to cover “externalities associated with motor vehicle use.” Along with pollution, that includes road accidents.

It isn’t clear from the report, and I am not sure about the rest of you, but I think I just covered my share in the last check to Travelers.