# How high of a carbon fee would reduce global emissions by 50% in 15 years?

OVERVIEW OF THE EMF 32 STUDY ON U.S. CARBON TAX SCENARIOS https://www.worldscientific.com/doi/pdfplus/10.1142/S201000781840002X

About half of the EMF 32 models met a 50% reduction in carbon emissions within 25 years when they assumed the highest: $50 / +5% carbon fees. HR 763 will nearly match the 25th year value in its 15th year and has provisions to exceed this value by 27%. The one thing that I am most uncomfortable with is that although all of the model projections and pending carbon fee and dividend legislation believe that they can drop total CO2 demand below 10% of current levels, even an absurdly high price for gasoline will not drop quantity demanded below 30% of current levels. It seems to me that having a carbon fee of \$100 and increasing it by $100 every year for thirty years until the price of gas hits \$30 per gallon would provide the skin-in-the-game incentive for most everyone to switch to electric cars and provide the incentive for producing much lower carbon electricity. HR 763 could be adapted with the following idea so that it always charges exactly the right carbon fee.

# If legislators are very confident that their carbon fees will reduce the quantity demanded of carbon to the levels of their projections then they should have no problem agreeing to a Carbon Fee Fail-safe and Safeguard that only kicks in if their projections are wrong.

Carbon Fee Fail-safe and Safeguard
It would be great if we had a Carbon Fee FAIL_SAFE that raises the carbon fee based on the number of years we are behind schedule and a SAFE_GUARD that skips the fee increase every year that we are more than a year ahead of schedule:

Every year once a year:
if (Years_Behind Schedule > 1.0) -----Carbon Fee FAIL_SAFE
Carbon_Fee = Carbon_Fee + (Years_Behind Schedule * $15); else if (Years_Behind Schedule > 0.0) Carbon_Fee = Carbon_Fee +$15; ----- HR 763 Trigger

else if (Years_Behind Schedule > -1.0) // Carbon Fee SAFE_GUARD
Carbon_Fee = Carbon_Fee + $10; -----HR 763 Default Worst Case Scenario Carbon Fee Worst Case Scenario Carbon Fee It seems to me that the price elasticity of demand for gasoline might be a good worst case scenario proxy for the price elasticity of demand for carbon. The most reliable figure that I could get on this was -0.58. A price that is much above \$30 per gallon has little effect on quantity demanded. The $30 price only reduces quantity demanded down to 35% of original. It would seem that increasing the price of gasoline \$1.00 per year for thirty years would have everyone switching to electric cars at some point before \$30 per gallon. A \$10 price per carbon equates to a ten cents per gallon price of gasoline, thus a maximum increment of \$100 for the price of carbon over 30 years seems to be maximum carbon fee required. It would seem to me that people would find ways to drive very much less to save their carbon dividend to buy an electric car. Even as average demand for carbon drops thus reducing the average carbon consumed the dividend price goes up so that the dividend might increase fast enough for everyone to buy replacement hardware. We could add a surcharge to the border adjustments as an incentive for countries not having a carbon fee and dividend program to adopt such a program. Unless they adopt such a program they would see the relative demand for their goods drop. The carbon dividend cannot be taxed because it is supposed to do the best it can to have everyone with average carbon consumption break even throughout the duration of the program. If the price of gasoline goes up \$1.00 then any taxes taken out of the dividend prevent breaking even.

According to the most elastic price elasticity of demand estimates for gasoline of -0.58
PDE=((Q1-Q0)/(Q1+Q0))/((P1-P0)/(P1+P0))

-0.58=((50-100)/(50+100))/((P1-2.66)/(P1+2.66))
P0=\$2.66 P1=\$9.85
Q0=100
Q1=50 ----Reduction to 50%

-0.58=((34-100)/(34+100))/((32.62-2.66)/(32.62+2.66))
P0=\$2.66 P1=\$32.62
Q0=100
Q1=34.0 ----Reduction to 34.0%

Even though the price elasticity of demand for gasoline will probably change over time to become more elastic as the capital expenditure of switching to electric vehicles becomes increasingly more cost effective it seems reasonable to consider the -0.58 figure a good worst case scenario basis for carbon price ceilings.

Here is what the Point formula derives:
-0.58 = ((50-100)/100) / ((4.95-2.66)/2.66)
-0.58 = -0.5 / 0.86

# Historical records for (1998 to 2008) show that an inflation adjusted 300% increase in the price of gasoline corresponded to a 20% increase in miles driven.

It might also be possible that a PED figure of -0.58 is too optimistic. Here is the original midpoint (interval) formula using PED = -0.50:

-0.50=((50-100)/(50+100))/((P1-2.66)/(P1+2.66))
P1 = \$13.30 # This works out to a carbon fee that increases \$71 per year for fifteen years.

• This is an interesting topic, but what is your question? – heh Oct 10 at 20:22
• @heh How high of a carbon fee would reduce global emissions by 50% in 15 years? – polcott Oct 10 at 22:01
• You should explain how your wall of text fits in with the question (in your title). It seems like you've done some of your own research, then simply copy-pasted a bunch of it here. The text should more clearly explain what you're looking for (and what you're not looking for), and why what you've already found is not satisfactory. – Kenny LJ Oct 11 at 2:08
• @KennyLJ Sure that sounds quite reasonable. – polcott Oct 11 at 3:02
• That's not really the relevant question. The question is what the value we put on the marginal cost of carbon. That's what the tax should be. – Acccumulation Oct 17 at 22:19

## No one knows

No one knows how high a carbon fee would be required to reduce annual global emissions by 50% in 15 years: that would require a global restructuring that takes us outside the bounds of any currently-understood elasticities. Our known elasticities are only valid for a certain range of prices - one can't simply just extrapolate them indefinitely and expect them to stay constant. (which is why your own calculations are wrong)

Furthermore, there's little indication that there's any scope to introduce such a global carbon fee, with intransigent regressive politicians running each of the six most polluting countries currently - China, USA, India, Russia, Japan and Brazil (as well as other significant polluters such as Saudi Arabia and Iran).

There are system models that attempt to predict infrastructure investment. However, running them with a 15-year horizon usually means taking them outside the boundaries that they were designed for - it's too short - so there would be a lot of uncertainty over their results. Those models are likely to say that the carbon price would have to be huge.

## Some sample numbers

A carbon fee of USD 500/tCO2e would add (very roughly) USD 250 per MWh of CCGT-generated (natural gas) electricity, and that should be enough to drive pretty much all electricity grids to very low carbon content (<50gCO2/kWh), in a 15-year timespan.

Currently, in the UK, petrol/gas is around USD 1.60 per litre (USD 6 per US gallon), and consumption is still high, with sales of electric vehicles still very low (just 1.3% of new car sales in Jan-Sep 2019); nevertheless, the UK is getting close to the tipping point where total cost of ownership is now cheaper for electric vehicles, for some drivers. So at double the current UK fuel cost, i.e. if it rose to USD 12 per US gallon, we should expect that a near-complete switch to electric cars over 15 years would be highly likely. At ~9kg CO2e / gallon, and an estimated USA current gas price of USD 3 per gallon, that implies that a carbon fee of USD 1000 / tCO2e could be sufficient to get most drivers to switch to electric vehicles over a 15 year period.

## Beyond a carbon fee

Any feasible carbon fee (even in tandem with a dividend) on its own isn't sufficient. There needs to be the incentives there to replace existing infrastructure that has sunk capital costs. That is, the climate emergency requires the proscription of carbon-intensive infrastructure.

So, by all means, let's have a global carbon fee. But we also need to be much more straightforward with enforced regulation, because we know that can be very effective when done well. Here's the sort of thing that countries should be doing: no more fossil-fuelled cars for sale after 2025, or in use after 2035; no burning of coal for heat or electricity after 2035; no more than 10% of electricity to come from natural gas after 2035. And then the right policies, incentives and structures need to be put in place to enable the market to deliver new zero-carbon infrastructure to replace the existing polluters.

It will also require policies to ensure that society continues to the function through the duration of this massive industrial restructuring

## Negative emissions

There are several factors which increase the uncertainty of the level of an effective carbon price. There are several negative-emissions options, some of which have fairly well understood costs, others do not, but all of which are quite hard to assess how quickly they can be scaled up - the only way to get a reliable idea of those costs, is to actually do it. There is mass afforestation, and there's direct air capture and sequestration.

## Start high, then reduce

Note that contrary to what's sometimes suggested, it would be more effective to set a high carbon fee initially, and the reduce it over time (rather than start low and then increase). That's because there's a lot of sunk costs out there, a lot of existing infrastructure, and a lot of low-carbon technology that's still in development, with costs that will come down over time.

• It looks like we agree on the gist of things. My key reason for this post is to test the degree that legislation such as HR 763 might otherwise lock us in to a program that has carbon fees that are just too low. I propose the "Carbon Fee Fail-safe and Safeguard" because it could save us if their projections are wrong and might be politically implementable. If people are so sure that their projections are right then they should have no objection to a backup plan that only kicks in if they are wrong. – polcott Oct 11 at 5:43
• Can the price elasticity of demand for gasoline be used as a reasonable worst case scenario proxy for the price elasticity of carbon? Is -0.58 a reasonable PED for gasoline? – polcott Oct 11 at 17:02
• Elasticity isn't a constant. Have a re-read of the second paragraph in the section "Some sample numbers", and think about the implied interval elasticies. – EnergyNumbers Oct 12 at 11:35
• Yes I know that you must be right. If we did assume that it was a constant then there is no hope of reducing US total emissions to their targets. If we assume that PED is constant (as a hypothetical worst case scenario) we see that a total carbon fee over $3000 will not help. It does seem intuitively clear that the HR 763 maximum increase of the price of gasoline of \$4.30 per gallon is not nearly enough whereas a maximum of \\$30 per gallon should be plenty. – polcott Oct 12 at 14:45
• Yes your sample numbers seem quite plausible and about double the HR 763 maximums. I am hoping that the "Carbon Fee Fail-safe and Safeguard" gets implemented, that way we don't have to guess. Fees would be automatically adjusted to exactly the right amount and these adjustments only kick in if the projections are wrong. – polcott Oct 12 at 14:55