Senators Boxer and Sanders claim that their Climate Protection Act of 2013 bill would raise revenues of $1.2 trillion over five years. The bill starts a carbon tax at $20 per ton of CO2, and increases by 5.6% each year for ten years, where it settles at $32.65 per ton. That's not a very high tax, translating to about 30 cents per gallon of gasoline, assuming the current blend of ethanol. But where do the revenue numbers come from? Senators Sanders and Boxer, the co-sponsors, say that is a CBO estimate.
I could find no such CBO study, so I decided to try and re-create the numbers. The carbon tax does not adjust for inflation, so we have to discount future revenue collections from the carbon tax. I assumed a constant discount rate of two percent. One also has to assume a carbon elasticity -- the percentage change of GHG emissions to the percent change of the price of carbon. We don't know that, but there is a lot of research on energy elasticities, and the long-term response is usually somewhere just south of 1. I assume 0.8. It is adventuresome to assume that it will stay constant over a long period of time and range of prices, but I see no principled way to adjust for many uncertainties.
What is the cost of energy? In order to calculate the price effect of a carbon tax, we have to know the baseline energy cost on top of which the carbon tax sits. I average two approximately equal contributors to GHG emissions: electricity and motor vehicle emissions. The average cost of a kilowatt-hour of electricity in the United States is currently 11.53 cents. The average CO2 emissions for a kilowatt-hour of electricity in the United States in 2007 is 1.363 lbs. So for one ton of CO2 emissions, 1467 kilowatt-hours of electricty are produced, which cost an average of $169.
What about motor vehicle emissions? The average price of gasoline in the United States for 2012 was $3.62 per gallon. The average emissions per gallon of gasoline was 8,887 grams of CO2, and 10,180 grams of CO2 for diesel, in 2011. The ratio of diesel to gasoline consumption is fairly stable, and in July 2011 approximately 110,000 gallons of diesel were supplied and approximately 250,000 gallons of gasoline were supplied, so about thirty percent of all motor vehicle fuel is diesel. So in calculating a weighted average of emissions, it seems reasonable to say that the weighted average of vehicular emissions is
0.30 x 10,180 + 0.7 x 8,887 = 9275 grams, or 0.010224 short tons per gallon
So the average cost of emissions from motor vehicles was about $3.62/0.010224 = $355.
Let's just assume that the average cost of emitting in the United States the average of the cost of emissions for electricity ($169 per ton) and the cost of emissions for motor vehicles ($355 per ton). In 2010, electricity accounted for 34% of all GHG emissions, and transportation 27%, so that's not far off. These are in effect the base cost of emissions, against which a percentage change in price will be measured. In other words, the carbon tax is only a number that sits on top of these baseline costs.
I assumed emissions from 2011 numbers, estimated by EPA, of just CO2 and CH4. That was 5604.9 Tg of CO2 and 582.1 Tg of CO2-eq of methane. The total in 2011 was about 6820 Mt CO2-eq.
Now, just to make this back-of-the-envelope calculation, I assumed that about half of all emissions come from electricity and half come from motor vehicle emissions. I calculated the revenues collected from emissions from both elements, assuming that emissions will respond to the carbon tax. Because the baseline cost of gasoline is higher, a carbon tax creates a smaller incremental price increase in the cost of gas, and would therefore figure less prominently in gasoline users' consumption decisions. In short, we should expect less of a response to a carbon tax in vehicular emissions than we do for electricity emissions.
Under these assumptions, carbon tax revenues would be about $127 billion in the first year, and with a discount rate of two percent, would rise to $199 billion in year ten. The discounted flow of revenues would indeed be about $1.243 trillion.
What about emissions? This is the disappointing part. Assuming a constant carbon elasticity of 0.8, total emissions will only fall from 6820 Mt to about 6101 Mt, a 10.5% decrease. That's not very much.