Revised 12/31/2018.

Continuing the previous discussion, I am attempting to make a more accurate assessment of a Pigovian tax on CO₂ emission than my previous estimate, which was based on a number pulled from a Wikipedia article. It turns out that “social cost of carbon” is a known term for the externalized cost of CO₂ emissions, and can be easily searched for. People have been working on getting good estimates of the number. The most plausible reference I’ve found is Valuing Climate Damages: Updating Estimation of the Social Cost of Carbon Dioxide by the (United States) National Academies (of Sciences, Engineering, and Medicine).[1][2]

That study discusses all of the uncertainties involved in calculating the social cost. It turns out that one of the factors with the most influential uncertainty is the discount rate — the amount we mark down costs that will be incurred in the future. This is really important because the damage from CO₂ emitted today continues for many years. If you skip over all the discussion of uncertainties and go directly to the summary on page number 30 (page 49 of the PDF), the cost ranges from $10 to $212 per (metric) ton of CO₂. It looks like $100 can be taken as a reasonably conservative figure and $200 as a seriously conservative figure. So let us do our analysis using a carbon tax of $200/ton of CO₂.

And here is where I made my mistake in the previous version: 1 ton of CO₂ contains 0.27 tons of carbon, so a tax of $200/ton of CO₂ is $740/ton of carbon. Since all of the following calculations are done in tons of carbon, the cost numbers are 3.7 times higher than my incorrect version.

From this we can calculate what the carbon tax would be on specific types of energy: A ton of coal produces about 8100 kWh, so the tax on coal-generated electricity would be 9.1 cents/kWh. A gallon of gasoline weighs about 6 pounds, and most of that is carbon, so the tax on it would be $2/gallon. The conventional retail unit of natural gas is the “CCF”, which weighs 0.0026 ton (mostly carbon), so the tax on it would be $1.95/CCF.

Looking at my utility bills reveals some interesting patterns. My electric bill for November is $62.79 for 250 kWh, so it would increase by $22.75, which is a 40% increase. But within that $62.79, only $28.49 is for “supplier charges”, i.e., the rest is to pay for the distribution system that carries the electricity to my house. The price of the electricity itself is 11.4 cents/kWh, and the carbon tax would be an additional 80% on that. That could be significant for industrial users. (Although much of the electricity consumed in New England is hydro power and so would be tax-free.)

My gas bill for November is $52.00 for 29 CCF. The bill converts the 29 CCF into 30 therms, and a therm is effectively 1 CCF of natural gas of standardized composition. So the carbon tax would be $58.5, an additional 112%. But again, the supply cost of my natural gas is only $16, 53.5 cents/therm, so for large-scale consumption, the price increase would be 365%.

So what we see is that a Pigovian tax on CO2 is a substantial incremental cost for home consumption, but a seriously large increase for industrial users.

It’s not immediately clear what fraction of CO₂ emissions would be eliminated by a carbon tax of this magnitude. Unexpectedly, that is one of the benefits of the carbon tax approach — it eliminates emissions where the damage caused exceeds the benefits of the emitting activity, and continues emissions where the demage caused is less than the benefits of the emitting activity, and it’s not clear beforehand which activities fall in wich category. But in 2013, the Congressional Budget Office estimated that a carbon tax of a mere $20/ton CO₂, increasing 5.6% per year afterword, would lower carbon emissions by about 8 percent. It seems likely that a tax of $200 a ton will cut emissions a lot more than that, though it’s unlikely to reduce it by 80 percent.

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