# IPCC SR1.5 Carbon Tax Math

Guest seriousness by David Middleton

Over the past few days, I’ve posted a couple of articles by Michael Bastasch of the Daily Caller on the IPCC’s demands for a \$240/gal tax on gasoline and \$122 trillion to fight the Global War on Weather. Many commentators questioned the math behind the \$240/gal gasoline tax. So, I thought I would put together a post showing the math.

This is from page 2-79 of chapter 2 of SR 1.5:

Based on data available for this special report, the price of carbon varies substantially across models and scenarios, and their value increase with mitigation efforts (see Figure 2.26) (high confidence). For instance, undiscounted values under a Higher-2˚C pathway range from 10–200 USD2010 tCO2-eq–1 in 2030, 45–960 USD2010 tCO2-eq–1 in 2050, 120–1000 USD2010 tCO2-eq–1 in 2070 and 160–2125 USD2010 tCO2-eq–1 in 2100. On the contrary, estimates for a Below-1.5˚C pathway range from 135–5500 USD2010 tCO2-eq–1 in 2030, 245– 13000 USD2010 tCO2-eq–1 in 2050, 420–17500 USD2010 tCO2-eq–1 in 2070 and 690–27000 USD2010 tCO2-eq–1 in 2100.

SR15 Chapter 2 Page 2-79

The IPCC presented fairly broad cost ranges for the 1.5˚C and 2˚C pathways… So broad, they are almost meaningless. However, whenever a government agency says a program will cost between \$690 and \$27,000 per unit, it’s a good bet that it will cost at least \$27,000. The IPCC being an intergovernmental agency cannot be expected to be better at economics than a single government agency. Mr. Bastasch and I both focused on the high-end estimates, So, here is a table of the full ranges for both pathways:

 Un-discounted 2010 US Dollars Carbon Tax per Metric Ton of CO2 2˚C Pathway Low 2˚C Pathway High 1.5˚C Pathway Low 1.5˚C Pathway High 2030 \$10 \$200 \$135 \$5,500 2050 \$45 \$960 \$245 \$13,000 2070 \$120 \$1,000 \$420 \$17,500 2100 \$160 \$2,125 \$690 \$27,000

## Is this really a tax?

Some commentators have said that this isn’t a “tax.” It’s just the price of carbon emissions as estimated by the IPCC. Whether or not it takes the form of a direct tax, it’s a cost that the IPCC says needs to be extracted from the private sector in order to fund the Global War on Weather.

## Putting the IPCC price of carbon into context

Since it’s difficult to relate \$/ton of CO2, let’s look at it relative to common fuels used for transportation and electricity generation.

## Gasoline

The folks at Resources for the Future were kind (or naive) enough to put together a handy carbon tax calculator to demonstrate the effects on various fuels. While it only goes up to \$50/ton, it’s a good starting point for the math.

While numbers can vary depending on grades of gasoline, on average, the combustion of 1 gallon of gasoline yields 8.89 kg of CO2. How does a gallon of gasoline, which weighs less than 3 kg yield nearly 9 kg of CO2?

Molecular weight:

• O = 16
• C = 12

Chemical equation for combustion of octane:

• 2[C8H18] + 25[O2] → 16[CO2] + 18[H2O]

The C comes from gasoline, the O2 comes from the air.

Now, let’s translate a carbon tax into a gasoline tax:

 Carbon Tax per Gallon of Gasoline (8.89 kg/gal) 2˚C Pathway Low 2˚C Pathway High 1.5˚C Pathway Low 1.5˚C Pathway High 2030 \$0.09 \$1.78 \$1.20 \$48.90 2050 \$0.40 \$8.53 \$2.18 \$115.57 2070 \$1.07 \$8.89 \$3.73 \$155.58 2100 \$1.42 \$18.89 \$6.13 \$240.03

This morning, I paid \$2.70/gal at a Houston Texaco station. This price already includes \$0.184/gal in Federal and \$0.20/gal in Texas State taxes. That’s already a 17% tax at current prices.

This is how the IPCC carbon tax looks as a % of \$2.70/gal.

 Carbon Tax per Gallon of Gasoline % of \$2.70/gal 2˚C Pathway Low 2˚C Pathway High 1.5˚C Pathway Low 1.5˚C Pathway High 2030 3% 66% 44% 1811% 2050 15% 316% 81% 4280% 2070 40% 329% 138% 5762% 2100 53% 700% 227% 8890%

It’s fairly obvious that the carbon pricing for the 1.5˚C pathway and the high-end of the 2˚C pathway are ridiculous non-starters as it relates to gasoline prices.

However, when it comes to electricity generation, it’s even worse.

## Natural Gas

First, some US natural gas nomenclature:

SCF – Standard Cubic Foot is one cubic foot of gas at standard temperature and pressure (60 degrees F and sea level). Since both temperature and air pressure affect the energy content of a cubic foot of natural gas, the SCF is a way of standardizing. One SCF = 1020 BTUs.

Nat-G

While the Btu content of natural gas is variable, one thousand cubic feet (Mcf) is generally equivalent to one million Btu (mmBtu).

 scf Standard cubic foot 1 scf mcf Thousand cubic feet 1,000 scf Bcf Billion feet, 1 million mcf 1,000,000,000 scf Tcf Trillion cubic feet, 1 thousand Bcf 1,000,000,000,000 scf

In terms of British thermal units (Btu):

 scf Standard cubic foot 1,020 Btu mcf Million Btu, mmBtu 1,000,000 Btu Bcf Trillion Btu 1,000,000,000,000 Btu Tcf Quadrillion Btu, 1 Quad 1,000,000,000,000,000 Btu

Natural gas is the number one fuel for electricity generation in the US (31.7%), having edged out coal a few years ago. It’s also used for heating and cooking in many US homes. This is what the IPCC carbon tax would look like in \$/Mcf of natural gas.

 Carbon Tax per Thousand Standard Cubic Feet of Natural Gas (53.12 kg/1,000 scf) 2˚C Pathway Low 2˚C Pathway High 1.5˚C Pathway Low 1.5˚C Pathway High 2030 \$0.53 \$10.62 \$7.17 \$292.16 2050 \$2.39 \$51.00 \$13.01 \$690.56 2070 \$6.37 \$53.12 \$22.31 \$929.60 2100 \$8.50 \$112.88 \$36.65 \$1,434.24

The average residential price for natural gas in the US in 2017 was \$10.91/Mcf (about 3X the wellhead price). This is what the IPCC carbon tax looks like as a % of \$10.91/Mcf:

 Carbon Tax per 1,000 scf of Natural Gas % of \$10.91/1,000 scf 2˚C Pathway Low 2˚C Pathway High 1.5˚C Pathway Low 1.5˚C Pathway High 2030 5% 97% 66% 2678% 2050 22% 467% 119% 6330% 2070 58% 487% 204% 8521% 2100 78% 1035% 336% 13146%

## Coal

Coal is the second most prevalent fuel for electricity generation in the US (30.1%). Coal comes in a lot of “flavors”: Anthracite, bituminous, sub-bituminous and lignite… and sometimes coke. For simplicity and due to its dominance in US coal production, I limited my analysis to Powder River Basin sub-bituminous coal. The low-end of the IPCC carbon tax for a 2˚C pathway would immediately more than double the price of Powder River Basin coal:

 Carbon Tax per Short Ton of Powder River Basin Sub-Bituminous Coal (1,686 kg/short ton) 2˚C Pathway Low 2˚C Pathway High 1.5˚C Pathway Low 1.5˚C Pathway High 2030 \$16.86 \$337.20 \$227.61 \$9,273.00 2050 \$75.87 \$1,618.56 \$413.07 \$21,918.00 2070 \$202.32 \$1,686.00 \$708.12 \$29,505.00 2100 \$269.76 \$3,582.75 \$1,163.34 \$45,522.00

The average price for Powder River Basin coal in September 2017 was \$12.10/short ton. This is how the IPCC carbon tax looks as a percentage of that price:

 Carbon Tax per Short Ton of Powder River Basin Sub-Bituminous Coal % of \$12.10/short ton 2˚C Pathway Low 2˚C Pathway High 1.5˚C Pathway Low 1.5˚C Pathway High 2030 139% 2787% 1881% 76636% 2050 627% 13377% 3414% 181140% 2070 1672% 13934% 5852% 243843% 2100 2229% 29610% 9614% 376215%

While claims of the “death of coal” have all proven premature, the IPCC carbon pricing scheme would almost immediately kill the world’s second most prevalent energy source:

## Oh… But the carbon tax will be rebated!

At least that’s the claim of some nominally Republican snake oil salesmen.

## THE FOUR PILLARS OF OUR CARBON DIVIDENDS PLAN

### I. A GRADUALLY INCREASING CARBON FEE

The first pillar of a carbon dividends plan is a gradually rising fee on carbon dioxide emissions, to be implemented at the refinery or the first point where fossil fuels enter the economy, meaning the mine, well or port. Economists are nearly unanimous in their belief that a carbon fee is the most efficient and effective way to reduce carbon emissions. A sensible carbon fee should begin at \$40 a ton and increase steadily over time, sending a powerful signal to businesses and consumers, while generating revenue to reward Americans for decreasing their carbon footprint.

### II. CARBON DIVIDENDS FOR ALL AMERICANS

All the proceeds from this carbon fee would be returned to the American people on an equal and monthly basis via dividend checks, direct deposits or contributions to their individual retirement accounts. In the example above of a \$40/ton carbon fee, a family of four would receive nearly \$2,000 in carbon dividend payments in the first year. This amount would grow over time as the carbon fee rate increases, creating a positive feedback loop: the more the climate is protected, the greater the individual dividend payments to all Americans. The Social Security Administration should administer this program, with eligibility for dividends based on a valid social security number.

Border adjustments for the carbon content of both imports and exports would protect American competitiveness and punish free-riding by other nations, encouraging them to adopt carbon pricing of their own. Exports to countries without comparable carbon pricing systems would receive rebates for carbon fees paid, while imports from such countries would face fees on the carbon content of their products. Proceeds from such fees would benefit the American people in the form of larger carbon dividends or could be used for transitional assistance for industries or regions hurt by the carbon fee. Other trade remedies could also be used to encourage our trading partners to adopt comparable carbon pricing.

### IV. REGULATORY SIMPLIFICATION

The final pillar is the elimination of regulations that are no longer necessary upon the enactment of a rising carbon fee whose longevity is secured by the popularity of dividends. Many, though not all, of the Obama-era carbon dioxide regulations could be safely phased out, including an outright repeal of the Clean Power Plan. Robust carbon fees would also make possible liability rationalization for emitters. To build and sustain a bipartisan consensus for a regulatory rollback of this magnitude, however, the initial carbon fee rate should be set to significantly exceed the emissions reductions of all Obama-era climate regulations, and the carbon fee should increase from year to year.

Does anyone really believe that any of this sort of revenue would be evenly rebated to each and every American?

Firstly, Mordor on the Potomac would spend this faster than they could collect it.

Secondly, how in the Hell would they pay for the \$122 trillion Global War on Weather, if they rebated the carbon tax to the taxpayers (and non-taxpayers)?

Thirdly, I apologize for the general lack of sarcasm in this post.

## Carbon vs Carbon Dioxide

CO2 is part of the carbon cycle.  The combustion of hydrocarbons combines carbon from fossil fuels and oxygen from the air to make CO2.  Carbon cycle is correct.  Carbon emissions can consist of CO2, CH4 and other carbon compounds.  Carbon emissions isn’t wrong, but carbon compound emissions would be better..  The tax is on CO2 equivalent emissions… carbon tax isn’t wrong, but carbon compound emissions tax would be better.

https://debunkhouse.files.wordpress.com/2018/10/carbon-tax.xlsx

## 59 thoughts on “IPCC SR1.5 Carbon Tax Math”

1. Sara says:

I’ve already calculated my monthly charge for gas for heating and cooking in the winter for one month (January) at a freakingly astonishing amount of \$17,333.48.

There is no way on God’s green Earth that a \$2,000 rebate per year would cover even a dime of that charge.

It is LONG past time that the IPCC was dismantled and sent packing. They are the biggest frauds on the planet.. Period.

• Sam Pyeatte says:

It is impossible to take anyone who advocates a \$240 per gal tax seriously. It is a sign of acute mental illness.

2. Retired_Engineer_Jim says:

Minor quibble – in the aerospace industry, the standard atmospheric conditions are 59 degrees F (15 degrees C) and 1 atmosphere of pressure (29.92 inches of mercury). [I apologize to the majority of you who use the metric or System Internationale systems of measurement – I’ve used the conventional system measures for way to many years to even know what 1 atmosphere is the proper systems.] These are the values in the ICAO Standard Atmosphere tables. It is interesting to see that the natural gas industry uses 60 F and 1 atmosphere (“sea level”).

• David Middleton says:

In the metric version (SI), a standard cubic meter (scm) of natural gas is also at 59 °F (15 °C). The US oil industry avoids the metric system like the plague.

We drill to depths measured in feet, measure pressures in PSI, and temperatures in Fahrenheit. Velocities are in ft/sec… Although we use meters when describing cable lengths of seismic surveys.

• MarkW says:

“Although we use meters when describing cable lengths of seismic surveys.”

Camel’s nose

3. Fraud requires deception, which describes the IPCC, whose deceptive pseudo science supports the UNFCCC.
The UNFCCC is very transparent about its repressive, globalist agenda, so fraud doesn’t apply to them, but extortion certainly does.

4. Thomas Homer says:

The intrinsic power of our current fossil fuel distribution infrastructure is that it distributes this resource down to the individual. With this level of accessibility, each person can access and decide how to leverage the power that fossil fuel provides. The power is owned by the individual. Once this fossil fuel distribution infrastructure is dismantled, control of power will be centralized.

Knowing also that CO2 feeds life, is integral to the Carbon Cycle, and that no one has yet been able to measure the purported ‘Greenhouse Gas’ property in Earth’s atmosphere, what then is the real incentive to make fossil fuels inaccessible?

• John Endicott says:

what then is the real incentive to make fossil fuels inaccessible?

I think you answered your own question when you said “Once this fossil fuel distribution infrastructure is dismantled, control of power will be centralized”. It’s all about power and control.

• Thomas,

The ‘Greenhouse Gas’ property you speak of is readily identified, both theoretically and by measurement. The complete NET effect of GHG’s and clouds is to boost each W/m^2 of solar forcing into 1.61 W/m^2 of emissions at the surface, such that the effective emissivity of a gray body model of the planet whose temperature is that of the surface and whose emissions are what we observe at TOA is 1/1.61 = 0.62.

At 288K, the surface emits 390 W/m^2. A temperature increase to 288.3K increases the emissions by 1.61 W/m^2 , thus the theoretical ECS is about 0.3K per W/m^2. This can be cross checked by calculating directly as 1/(4*.62*o*T^3) = 0.3 K per W/m^2.

The data is equally clear as seen in this scatter plot that I have shown many times.

The X axis is the planet’s emissions and the Y axis is the surface temperature. The green line is the prediction based on modeling the planet as a gray body with an emissivity of 0.62. Each of the 10’s of thousands of tiny red dots represents one month of data for each 2.5 degree slice of latitude across 3 decades of weather satellite data. The larger dots are the averages for each slice over all samples which undeniable matches the prediction. Even monthly averages are quite close to the predicted LTE response.

The IPCC’s self serving consensus can’t acknowledge that the relationship between the surface temperature and planet emissions follows that of a gray body with an emissivity of 0.62 because the resulting sensitivity limits are far too small to support the continued existence of the IPCC/UNFCCC. This denial has spread to many skeptics who also can’t wrap their heads around the relative simplicity of the macroscopic behavior of the planet, largely because of all the excess complexity that has been introduced by the IPCC whose sole purpose is to obfuscate this reality.

But the ECS gets even smaller …

If we plot solar input vs. surface temperature, the measured sensitivity (the slope of the relationship at the average temperature), is that of a black body at the surface temperature which is only about 0.18 K per W/m^2. In this next plot, the magenta line is the prediction of the surface temperature vs. solar forcing based on the equation,

Psun + Pfb = oT^4

where Psun is the post albedo solar input, Pfb is the 141 W/m^2 fed back to the surface from the atmosphere and T is the surface temperature, the slope of which, dT/dPsun is the sensitivity of an ideal BB at T. Once again, the average of the data verifies this prediction.

For reference, Pfb is calculated as half of the 74% of surface emissions absorbed by the atmosphere as this quantifies the energy absorbed by the atmosphere and returned to the surface and to be sure, has a dependence on CO2 concentrations.

The fact that we can derive and measure the relationships between solar forcing and the surface temperature and between the surface temperature and planet emissions and that these calculations and measurements bound the ECS to values well below what’s claimed by the IPCC is unconditional proof that they could not be more wrong about the ECS they require to support their continued existence.

• Thomas Homer says:

co2isnotevil – Thank you for an informative reply.

I appreciate your analysis, however I remain skeptical. If what you say is true: “The ‘Greenhouse Gas’ property you speak of is readily identified, both theoretically and by measurement”, then why aren’t we measuring it? I would expect to see charts for these measurements by location and circumstance. Similar to what we gather for humidity, barometric pressure, etc. But there are no charts. We can’t compare how this property manifests itself by elevation. Denver has less atmosphere than Miami, that should impact the measurements. We can’t see immediate effects of any localized increase in CO2 due to forest fires.

We should be able to derive how the Greenhouse Gas property of CO2 manifests itself on Mars, and then confirm this derivation by direct measurement. Alas, we have neither.

• Thomas,

The measurements confirming the theory are shown in the scatter plots. This measured data even comes from GISS! It’s not that we haven’t measured it, but that the true nature of its measurement is being denied.

The combination of the radiant GHG effect and the return of surface emissions absorbed by clouds is what increases the surface emissions from 1 W/m^2 per W/m^2 of forcing as it would be without an atmosphere to 1.6 W/m^2 per W/m^2 of forcing as it is for the Earth with its current atmosphere, moreover; this is far from the 4.3 W/m^2 of incremental surface emissions per W/m^2 of forcing the IPCC claims is the nominal sensitivity.

The reason the gray body model is denied is because the resulting ECS is undeniably less than the lower limit required by the IPCC. Since they are the arbiter of what is and what is not climate science by what they publish in their reports, and they need a much higher ECS in order to justify their existence and support for the UNFCCC, the IPCC will never acknowledge this truth as it would foretell their demise and the #1 goal of a bureaucracy is self preservation.

As for Mars, we don’t have sufficient data to measure the relatively small GHG effect from its very thin CO2 atmosphere, moreover; the Mars average reported temperatures seem to be equally weighted temperature averages, rather than the equivalent temperature of geometric and temporally averaged emissions, which is how it would need to be expressed given the wide range of surface temperatures at any one place on the surface.

The only reason we have sufficient data to verify the theory in the case of Earth is because we have decades of continuous measurements by weather satellites and those satellite sensors directly measure emitted and reflected Watts of power.

• Thomas Homer says:

co2isnotevil – Thank you for another informative reply, and again, I appreciate your thoughtful analysis.

• Frank says:

Thomas wrote: “no one has yet been able to measure the purported ‘Greenhouse Gas’ property in Earth’s atmosphere.”

The Greenhouse Gas property of CO2 is measured by the infrared spectrum of CO2. The data from the infrared spectrum is used in “radiative transfer calculations”, which is quantum mechanics (an well validated theory having nothing to do with climate change) applied determining the rate at which energy escapes from the surface of our planet to space. Such calculations can be done online at:

http://climatemodels.uchicago.edu/modtran/

To make things simple, I suggest you first make all of the Greenhouse Gases 0 and choose the US Standard Atmosphere – an average for the whole planet (without clouds). Notice that the Surface Temperature has been set to 288.2K (you can adjust it) and that 380.3 W/m2 of thermal infrared would be expected to be escaping to space with no GHG’s in the atmosphere. (The emissivity of the surface isn’t quite 100%, so the result isn’t 390 W/m2.)

Now add just 1 ppm of CO2 to the atmosphere. Emission to space calculated for 70 km (above all essentially all of the atmosphere) drops to 374.3 W/m2. That CO2 both absorbs and emits thermal infrared, but absorption doesn’t depend on temperature and emission does. Since the CO2 molecules that absorb upward radiation near 666 cm-1 are generally
colder than the surface or CO2 molecules lower in the atmosphere emitting radiation near 666 cm-1, the net effect of both absorption and emission caused by 1 ppm of CO2 is a modest reduction in outward radiative cooling to space. If we start at a steady state temperature (with no CO2) where incoming and outgoing fluxes are equal and add 1 ppm, the slowdown in radiative cooling to space will cause the planet to warm until a incoming and outgoing radiation are again in balance.

Unfortunately, this program doesn’t show you that CO2 has a much smaller effect on incoming SWR.

You can then add more CO2 and then other GHGs to obtain an atmosphere like our own. In the calculation, you are specifying the surface temperature and the concentration of GHGs in the atmosphere. When you choose the “Locality”, you are also choosing the average temperature change with altitude normally found above that location. For the US Standard Atmosphere, the temperature drops uniformly from 288.2 to 216.8 K over the first 11 km (the troposphere), remains constant for the next 9 km (the tropopause), and rises in the stratosphere. This calculation doesn’t try to predict how much warming will occur, it simply addresses what the radiative flux reaching space will be for the conditions you have specified. (It isn’t an AOGCM.) The US Standard Atmosphere scenario doesn’t have any clouds, so it predicts that the current atmosphere will emit about 269 W/m2 with 300 ppm of CO2 and 266 W/m2 with 600 ppm of CO2. If you choose different “Localities”, these number change.

The predictions of radiative transfer calculations have been verified by spacecraft observing the IR spectrum of radiation reaching space, by airplanes, and by observing the downward infrared radiation reaching the surface. So the predictions of quantum mechanics and infrared spectra of GHGs have been confirmed in the real atmosphere.

The Earth emits like a blackbody at 288 K between about 750 and 950 cm-1, where no GHGs absorb. It emits like a blackbody at 220 K from 600-700 cm-1 (where CO2 absorbs) because photons at that wavelength emitted by the surface and lower atmosphere have all been absorbed and been replaced by photons emitted from CO2 at the tropopause, where it is much colder and therefore emission is weaker. The reduction seen on this web page is calculated, but the same thing is observed from space. This is the essence of the “greenhouse effect”. There is no doubt that it has been observed and measured.

If you slow down the rate at which our planet radiatively cools to space but maintain constant solar input, our planet must warm. That is a prediction of the law of conservation of energy. It doesn’t tell us how much it must warm – that is a vastly more complicated problem.

CO2isnotevil has been promoting his misleading graph for years. Traditionally, we put the independent variable – surface temperature – on the x-axis and the dependent variable – power out (which is certainly controlled by temperature) – on the y-axis. Most of the surface is between 273 and 303 degK. Everything else comes from mostly from the poles, a tiny fraction of our planet. If you look carefully at the relevant region of the graph, the power out caused by these surface temperatures is not a very linear function of surface temperature. This is because about 90% of the photons that escape to space are not emitted by the surface, they are emitted by GHGs (and cloud tops, which cover more than half the sky) at various altitudes (and therefore temperatures) in the atmosphere. To predict climate change, we need to know how much additional power will be emitted when the whole planet warms a few degC, not how much more radiation is currently emitted when we MOVE to a new location that is a few degC warmer.

Due to the lower heat capacity of the NH (more land and less ocean) our planet’s mean surface temperature rises 3.5 K during summer in the NH. (When you calculate temperature ANOMALIES, this seasonal warming is eliminated.) From space, CERES has observed an average increase in OLR every summer of nearly 8 W/m2 or 2.2 W/m2/K. This is a much more reliable value than CO2isnotevil provides by “producing warming” by moving to a warmer location and asking how much OLR leaves the planet from that warmer location.

5. F. Ross says:

Time to defund and dissolve the IPCC; it’s useless anyway in the real world.

6. Willis Eschenbach says:

David, thanks much for your note of sanity. When you put up your last post, the numbers were so outrageous I thought for sure that you must have made some arithmetic error.

Since I rarely believe numbers until I’ve run them myself, I did the math and was astounded to find out that you are correct—they are advocating a gasoline tax of US\$240 per gallon!!!

My best to you,

w.

• David Middleton says:

Thanks Willis. A math compliment from you is like a batting compliment from Babe Ruth… 🙂

The craziest thing about the IPCC numbers is the range… The spread makes the numbers useless for any sort of economic planning. You would think they might have published a statistical distribution of their model runs. Then you would at least have a P50 number.

• It doesn't add up... says:

I think they are really advocating riots and revolution. Whether theirs would be the necks strung from lamp posts only history would tell in due course. Would the use of diesel in army tanks also be taxed? Who would armies side with anyway?

Of course, revolution and a life of grinding poverty is what they aspire to on our behalf anyway. But history has a habit of confounding the over-ambitious.

Those deprived of power and gas in the aftermath of Michael tolerate the situation because they know that efforts are being made to restore normality. Take away that hope, and the National Guard would be very busy.

• Curious George says:

Now that’s the real damage function.

• Curious George says:

I am beginning to understand why Enron … pardon, Exxon … lobbies for carbon tax.

• David Middleton says:

If you start with the assumption that the US government will, at some point, regulate CO2 emissions, it’s the least bad option from an oil industry perspective.

The huge tax on coal might even make CCS for enhanced oil recovery much more economically viable.

• John Endicott says:

If you start with that assumption and then actively campaign for it, it becomes a self-fulfilling prophecy.

7. StephenP says:

It is all a ridiculous idea.
The costs of administering it and auditing the way the money is spent will be phenominal.
Who will decide what it will be spent on? I can just see some of the less scrupulous powers that be rubbing their hands with glee at the prospect of all that free money, which will go down the black hole that so much foreign aid has gone.
Still, to look on the bright side there will be plenty of work for bureaucrats and accountants!

• oeman50 says:

Refund all of the money? Call me skeptical.

8. Farmer Ch E retired says:

You can stop reading at “For instance, undiscounted values . . .”
Is this evaluation actually based on “undiscounted” values?!?
I want to borrow some of this money at 0% interest. Apparently it’s out there if they are going to publish “undiscounted” cost of carbon. /s
Lets see how well the math works at 5% which is recommended or 10% which is the S&P 500 returns for many, many decades.

• David Middleton says:

We use 10% in oil & gas reserve valuation (PV10).

7% is generally the standard for regulatory analysis. A 7% discount rate zeroes out any “benefits” of a carbon tax.

• Farmer Ch E retired says:

Thanks – For several years, I performed environmental reserve and cash flow calculations for one of our clients, a national gas pipeline company. We used several discount rates at the client’s request and I recall using 5% at one time. I’ve seen the gov report but forgot 7% was in the guidance.

• David Middleton says:

7% is the guidance. They only used 3% in calculating the Social Cost of Carbon.

• Farmer Ch E retired says:

It’s their way to hide the fact that there not a Social Cost of Carbon; however, there is a true Social Benefit of Carbon.

9. markl says:

When will people understand that AGW is nothing more than a way to fund the “One World Government” espoused by the UN? What is obvious is if they succeed in killing off fossil fuels what will then become their funding source?

10. NeedleFactory says:

I’m curious about the “Do not cite, quote or distribute” on your second illustration.
Has the document been released yet?

• I open a cage with a bird in it. Do not track, monitor, or capture my bird. I have not released it yet.

11. Thanks, David M, for the attempt at in-depth explanation.

The phrase, “price of carbon”, still seems very obscure to me. When I think of a price, I think of a good or service that somebody is willing to pay to acquire at that price.

What is the good or service involving carbon that someone would be willing to pay to acquire?

Okay, I see, in the IPCC report that I am NOT supposed to cite, quote, or distribute [what a joke]:

“The price of carbon assessed here is fundamentally different from the concepts of optimal carbon price in a cost-benefit analysis, or the social cost of carbon (see Cross-Chapter Box 5 in this Chapter and Section 3.5.2). Under a cost-effective analysis (CEA) modelling framework, prices for carbon (mitigation costs) reflect the stringency of mitigation requirements at the margin (i.e., cost of mitigating one extra unit of emission).”

Such stilted language !

I assume this means that prices of carbon reflect how much it would cost civilization to keep CO2 emissions at a level that computer models predict cause a particular global-average-temperature increase.

Costs to keep CO2 at a level models say cause a 2 C rise would be greater than costs to keep CO2 at a level models say cause a 1.5 C rise. These costs are what IPCC calls “prices of carbon”, right ?

These costs, however, have to be paid by someone in order to acquire the service of reducing CO2 to the desired computer-modeled level of increase.

Okay, who, then pays for this service ? Does the IPCC just assume that all humanity wishes to pay for this service? — that all humanity agrees that the computer models causally relating CO2 and global average temperature are valid ? — that fossil fuel companies will pay for this service ? — and if they do, then they pass these costs along to consumers ? — and we consumers agree that the computer models are valid enough to drive fossil fuel companies to want to pay for this service, to pass along the costs to consumers ?

That’s quite an assumption — namely that all humanity has the same faith in both IPCC climate models and IPCC economic models that model what the climate models say.

So, we have an overly presumptive economic model that models highly questionable climate model output into global economic policy.

The phrase, “price of carbon”, then seems purposefully obscure. It REALLY means “cost of keeping human- produced CO2” at a specified level, … right ? And who pays this cost to buy this service of keeping human-produced CO2 at the specified IPCC level ? ANSWER: Consumers of CO2-producing products and services.
What’s a major CO2-producing product that we consumers use? ANSWER: Gas. So, I guess the question becomes how do the costs that fossil fuel companies incur to control CO2 levels get paid for? ANSWER: Increase the price of fossil-fuel products to cover those costs that fossil-fuel companies incur to provide this CO2-controlling service.

Do I want to buy this service? ANSWER: Not only NO, but HELL NO. Having some international government organization trying to dictate what I should or should not have to pay for, based on models that I find unfit, is nothing short of attempted dictatorship.

On this issue, where is MY vote heard ? If I am a member of a global society, then where is the global voting process that allows MY voice on this to be registered ? ANSWER: Nowhere. A platform to register agreement on this does not exist. Voting rights of the global society are NOT recognized. Again, dictatorship.

12. Earthling2 says:

“Whether or not it takes the form of a direct tax, it’s a cost that the IPCC says needs to be extracted from the private sector in order to fund the Global War on Weather.”

Where the carbon tax is being directly collected in North American jurisdictions, I am not aware of any of it being used to fund the global war on weather. It all goes into general revenue and is spent to bribe the citizenry and get reelected. Some give rebates to poor people, but I doubt this covers the increased costs of everything that goes through the economic value chain related with fossil fuels. Which most everything is, even if it is renewable energy, because fossil fuels were used to build that infrastructure to begin with.

Is there any jurisdiction on earth that actually uses the carbon tax proceeds to actually try and do anything related to ‘climate mitigation’? Or does Cap and Trade actually try and do anything, whether it works or not? I can’t seem to find answers or see any results from this, even token attempts. Or do they claim that the tax incentives they give for electric cars and renewables is directly paid out of the carbon tax where it is collected?

13. I went to David M’s spreadsheet to get the steps I was looking for:

* 1 gallon of gas produces about 8.89 kg of CO2

* 1,000 kg = 1 metric ton

* Carbon cost of \$27,000 per metric ton of CO2 = \$27,000 / 1,000 kg CO2 = \$27 per kg CO2

* (\$27/kg CO2) x (8.89 kg CO2)/(gallon of gas) = \$240.03/(gallon of gas)

If I can do this simple math, then so should climate alarmists.

• David Middleton says:

They flunked math… if they were even required to take any.

14. Steve O says:

Why would emissions need to be penalized at \$27,000 per ton if CO2 can be extracted at a cost of say, \$100 per ton?

• David Middleton says:

We certainly could do CCS for a lot less than \$27k/ton.

15. LarryB says:

HOW TO REDUCE FOSSIL CARBON EMISSIONS

First, forget the financial proposals included in the newly released IPCC Study Report, SR 1.5.

On Tuesday 10/9/18 Exxon Mobil, which has long faced criticism on climate change, committed \$1,000,000 to Americans for Carbon Dividends, a new group co-chaired by former Sens Trent Lott, a conservative Republican and John Breaux, a conservative Democrat, that supports a “gradually rising carbon FEE.”

https://www.afcd.org/

Their proposal is known as the Baker-Shultz Carbon Dividends Plan, which has been endorsed by more than 15 of America’s largest corporations. The effectiveness of this proposal in reducing fossil carbon emissions has been confirmed by many economic analyses, including a June 2018 report by the non-partisan Resources for the Future (RFF).

A carbon FEE that is collected by the US TREASURY DEPARTMENT on each pound of fossil carbon purchased by all consumers and REFUNDED IN EQUAL AMOUNTS to everyone who files an annual Federal tax return, including all their dependents, will result in a NET FINANCIAL GAIN for everyone in the bottom 70% income bracket. For those in the top 30% income bracket, the fees paid to purchase fossil carbon use will exceed the refund they receive on their tax return.

Everyone pays the same fee per pound of fossil carbon they use, but those in the lower 70% income bracket will get back a LARGER ANNUAL REFUND THAN THEY PAID IN CARBON FEES. Yes, the end result is financial redistribution from those who consume more fossil carbon to those who consume less, but can you propose a more effective way to reduce fossil carbon emissions?

• David Middleton says:

See this paragraph in the post… “Oh… But the carbon tax will be rebated!”

16. MIKE MCHENRY says:

I’m trying understand why this proposal was made. It is obvious it’s going no where. Political suicide for any politician who endorses it.

17. kramer says:

1) Has anybody noticed that this climate change cult movement is backed by quite a few rich people and families?

2) And has anybody noticed that if we end up with a carbon ‘tax’, that the bulk of the tax revenue going into government coffers will come from the middle class?

3) And has anybody noticed that if 2) happens, then that gets the rich off the hook of having their wealth taxed at higher rates?

4) Could wealth preservation for the really rich be one of the leftist ‘benefits’ of catastrophic climate change chaos solutions?

I believe the answer to 4) is yes.

18. Dan314 says:

I think all the numbers are interesting but boil down to one question: Do you think the government will spend the large transfer of wealth from its citizens more efficiently and effectively than the citizens themselves? If you do, please pass on the specific list and amounts of hallucinogens you are consuming daily so that the rest of us can partake.

19. Chorche says:

The co2 market is quite strange. We know how to buy the ton of co2, just paying the market price.
But where are the co2 factories to make the market run?
It’s just taxes
Taxes set by entities or of any market!
It’s political control
Will I get the co2 price for tea plantation? No!
Will I get for chemical absorb from air? No!
It’s just control and taxation

Will third world countries live much better and compete in unequal conditions? Yes!

In the other hand the drawback’s of co2 (if existing) will not be valuated against the benefits of fossil fuels? Not fair

20. Willem69 says:

I’m confused as how this is supposed to work.
Isn’t the objective to cut ‘carbon’ emissions to 0 by 2050? So why a carbon tax/cost/price beyond 2050 when there are no more emissions??

Furthermore, in any sane world the ‘cost of carbon’ would be based on one of two things, or a combination of both.
1)the added cost for the green alternative over the cheaper fossil fuel version. Or 2) the cost for ‘cleaning up’ the atmosphere (removal from the atmosphere and storing the CO2).
Why then do the costs escalate so dramatically with time? Generally costs go down as a technology matures and is scalled up??

As for the ‘American plan’ what is the effect on emissions if you first take my money and then give it back to me??? Again wasn’t the idea that emission go down?

But then again, I could be missing something??

Have a good one,
W

• David Middleton says:

The costs go up beacause the hypothetical damage goes up.

As discussed in the 2010 SC-CO2 TSD, estimates of the social cost of these greenhouse gases increase over time because future emissions are expected to produce larger incremental damages as physical and economic systems become more stressed in response to greater climatic change, and because GDP is growing over time and many damage categories are modeled as proportional to gross GDP.

https://19january2017snapshot.epa.gov/climatechange/social-cost-carbon_.html

21. Sigh,
It is “interesting” when ignorant little kids play at being “the big guy”
….no matter what their calendar age.

The “Strategic Goal” is to have grand-kids around to replace you.
If a person’s ancestors didn’t do this in the past 300,000 years, they aren’t here.

Dropping \$120,000,000,000 out of the “first world” is silly and a waste of time.
The Chinese “premier for life (dictator)” is playing these guys as fools.
That is enough cash to get to the Moon, Mars, and even Alpha Centauri
…and the fools wish to use it to “keep this one marble ok”.
=> fools, get your grand kids and great grand kids off this marble!

But I can only conclude they are exactly right: that is “all they know”.
Maybe they should protect their grand-kids rather than consigning them to be second-rate.

22. john says:

“Extracted from the private sector”. Ok, that won’t effect me as I’m a private citizen! Bureaucrat nonsense!
I run a business. If my costs go up a dollar I have only one place to source that dollar. My customers will have to pay it. All additional costs ( and taxes are certainly a cost) come from the public. And costs will go up for government, too. So they will have to raise taxes for that as well.

• John Endicott says:

john, don’t you know OPM is a bottomless well. At least that’s what the bureaucrat’s believe, and if anything the last few week should have taught you is that you don’t need evidence as long as you have belief (if you are a leftist/globalist/socialist).

23. Alasdair says:

Next phase in the calculation: What will be the cost of a kilogram of potatoes? These only arrive in your kitchen by use of fossil fuels. Bump up their cost and you bump up the price of spuds. Extrapolate that and indeed there is a problem.

• simple-touriste says:

“Green” people love local food and short circuits of organic food. It means that instead of a chemical plant, the pesticides are made from specific plants growing in Africa or South America, (which are raised with pesticides made in chemical plant).

Organic food is much more expensive, and there are a lot of specific “incitations” and subsidies for organic (at least here in Europe). It’s probably because organic food depends a lot more an costly energy sources.

24. Sara says:

I have an even better idea for these geniuses at IPCC (and the UN). Move the UN to an island where there are no resources, somewhere in the general region of Antarctica where the cold winds blow all the time, and leave them there. If they last a week, I’ll be quite surprised, but they can take that week to change their minds.

I think they are either Space Aliens pretending to be human and see us as just another food source, or they know that it’s a scam and they think the rest of us are stupid enough to fall for it. And since it’s a scam, that means it’s fraud, and where I come from, fraud is a felony, so lock them up where they can’t get out and drop a box of food in once a month.

• simple-touriste says:

The claim that there is such thing as “renewable” anything and that you should PAY for it is a transparent scam. If it’s renewable, it’s free.

Renewable is codename for depending on natural flux, usually solar flux, more or less buffered. (Geothermal energy is another natural flux.) It means that the sun output is the charger of the natural battery you are using with “renewable”. You can tap on the battery knowing it’s filled in continuously by a natural flux.

But the natural flux is a DISTRACTION. The problem is the material need to collect the energy, the energy needed to built it, and manpower to keep it in good shape. The employees receive salary to pay for food, heating, energy… The employees who work there cannot work elsewhere and so their needs must be accounted in the impact of the system. That’s impact-with-employees-consumption-one-level, let’s say impact-L1. (You can iterate.)

There is always a natural flux in any industry at impact-L1: animals quadrupeds or bipeds need some food which is always based on vegetation (directly or indirectly), which mean solar flux.

So a coal plant at impact-L1 is “renewable” also. (Unless all employees eat food obtained only by light produced by fossil energy, I guess.)

25. Frank says:

David: Thank you so much for responding to my comments on other posts. Responding shows a lot of integrity on your part.

I’d like to draw your attention to Box 5 (page 2-77):

“Two approaches have been commonly used to assess alternative emissions pathways: cost-effectiveness analysis (CEA) and cost-benefit analysis (CBA). CEA aims at identifying emissions pathways minimising the total mitigation costs of achieving a given warming or GHG limit (Clarke et al., 2014). CBA has the goal to identify the optimal emissions trajectory minimising the discounted flows of abatement expenditures and monetised climate change damages (Boardman, 2006; Stern, 2007). A third concept, the Social Cost of Carbon (SCC) measures the total net damages of an extra metric ton of CO2 emissions due to the associated climate change (Nordhaus, 2014; Pizer et al., 2014; Rose et al., 2017a). Negative and positive impacts are monetised, discounted and the net value is expressed as an equivalent loss of consumption today. The SCC can be evaluated for any emissions pathway under policy consideration.”

In cost-benefit analysis, we are asking how much future damage (discounted back to current dollars) will be avoided by not emitting a ton of CO2 (or the equivalent). If we have a reasonably accurate estimate of that damage (WE DON’T), it would make sense to place a Pigou tax on those emissions. If we expect \$10 of damages from every ton of CO2 emitted, then it would arguably make sense to place a Pigou tax of \$10 a ton on CO2 emissions to ensure that the we are obtaining at least the cost of the fossil fuel + the cost of the Pigou tax from our use of that fossil fuel. If climate sensitivity were high and damages of \$100/ton were expected, then we want to obtain at least the cost of the fossil fuel + \$100/ton. Cost-benefit analysis and Pigou taxes are concepts all economists support, but they recognize that accurately calculating future indirect damages is often impractical and highly politicized. In theory, we place “sin taxes” on alcohol and tobacco to reduce demand and therefore the damage cause by these products, but we don’t calculate an optimum tax based on a calculation of the damage they cause.

If I understand correctly, cost effectiveness analysis (CEA) attempts to look at supply and demand curves and predict how much the demand will drop if we artificially raise the price through taxation. If we demand that warming be limited to 1.5 or 2.0 degC NO MATTER HOW MUCH IT COSTS, then CEA tells us how much the PRICE of carbon dioxide emissions will need to rise to reduce emissions as much as these targets require. (Since we don’t know TCR and ECS accurately, we can’t accurately predict the relationship between future emissions and future temperature.) NO ONE IN THEIR RIGHT MIND IS GOING TO IMPOSE A TAX EQUAL TO THIS PRICE OF CARBON DIOXIDE EMISSIONS TO CAUSE THE REQUIRED REDUCTION IN EMISSION. Such a tax wouldn’t make any sense from a cost-benefit perspective! Government will simply MANDATE emissions reductions without imposing such massive taxes. These high carbon PRICES simply tell governments that a Pigou tax (cost-benefit analysis) will not achieve their PURELY POLITICAL OBJECTIVES of 1.5 or 2.0 degC.

When we choose to purchase a fossil fuel including a Pigou tax, we hope to maximize utility (the benefits from the fossil fuel – costs of obtaining the fossil fuel – the Pigou tax to take into account future damage). By maximizing utility, we let the “marketplace” decide how much fossil fuel we should burn and how much warming and damage will result. In theory, we come out ahead when we maximize utility.

IMO, it is important to distinguish between a CARBON PRICE and a CARBON [PIGOU] TAX. The former tell you how much value citizens could obtain from the fossil fuel the government is not going to allow to be burned to meet a political target of 1.5 or 2.0 degC. The latter tells us how much to tax emissions to achieve an optimum outcome.

IMO, since the government needs taxes to raise revenue for government operations, it would certainly make sense to raise some revenue by imposing a carbon tax (that will reduce future damage from warming) rather raise revenue by taxing capital gains (which reduces the incentive to invest and damages the economy). All economists recognize that some forms of taxation (income taxes) cause more harm to the economy than others (consumption taxes).

• David Middleton says:

Frank,

I agree that this doesn’t make sense and won’t be imposed anywhere other than California.

Even if they had a firm grasp on TCR & ECS and could calculate, down to the penny, the Pigou tax required to stay below the 1.5 °C, no government on Earth would effectively spend the money. Rather than effectively spending it on decarbonization, it would be p!\$\$ed away on pet projects, boondoggles, paid out to special interest groups and/or redistributed to the recipient class to buy votes.

The only potential benefits of a carbon tax would be to improve the economics of carbon capture & storage (CCS) and nuclear power. A carbon tax might actually kill wind & solar and save coal & nuclear.

• Frank says:

David wrote: “Even if they had a firm grasp on TCR & ECS and could calculate, down to the penny, the Pigou tax required to stay BELOW the 1.5 °C, no government on Earth would effectively spend the money.”

David still doesn’t understand the difference between a Pigou tax and a carbon price. A carbon price is the price needed to keep warming below 1.5 or 2.0 degC – whether or not this makes sense from a cost-benefit point of view. A Pigou tax (or the SCC) is the amount of tax that would minimize future damage (measured in today’s dollars) at the minimum cost to society. Users will continue to emit carbon when the use of fossil fuels is important enough to be worth paying a Pigou tax (+ the cost of the fossil fuel itself), but users will chose some other alternative when the use is only worth paying the cost of the fossil fuel itself. With a Pigou tax equal to say \$5/gallon, we might burn enough fossil fuel to allow temperature to rise 3 degC, because gasoline is worth \$8.50/gallon on most trips.

The US government rationed many items during WWII and might ration gasoline in the future. Everyone might get an equal allotment and the affluent might buy the rations of the non-affluent. In theory, those private transactions should take place at the “carbon price” predicted by the IPCC. With a Pigou tax, the amount of gas burned is not capped. The higher price caused by the Pigou tax reduces demand in an economically optimum fashion.

David wrote: “The only potential benefits of a carbon tax would be to improve the economics of carbon capture & storage (CCS) and nuclear power. A carbon tax might actually kill wind & solar and save coal & nuclear.”

If I remember correctly, CCS is projected to add about 100% to the cost of electricity generated by coal. If a Pigou tax on the burning of coal without CCS was 200% of the price of coal, CCS might be voluntarily adopted.

Electricity is a very perishable product: If it isn’t used immediately, it has almost no value because it can’t be stored cost effectively and long transmission lines are too expensive. The electricity used during periods of peak demand is far more expensive to produce because the capital cost of production is only paid back during a fraction of the time. Nuclear power, wind and solar have the highest capital costs and therefore compete with each other to provide baseload demand, but non-dispatchable wind and solar can never reliably meet baseload demand.

26. Frank says:

David: The most important factor in calculating a carbon tax or the social cost of carbon is determining the optimum discount rate to use. It has been proven mathematically that the optimum discount rate depends on the sum of the risk-free cost of capital and the future growth rate of the economy. Rich liberal who think their descendants will be worse off because we have irrepairably damaged the environment and depleted our resources expect little or perhaps negative economic growth and therefore apply a low discount rate to future damages, instinctively calculating a high SCC and Pigou carbon tax. If our descendants are already going to have a difficult time due to our excesses, it is immoral for us to add climate change to their problems.

India and the rest of the undeveloped world see that imitating China and burning lots of cheap coal can potentially produce decades of 5+% economic growth. They instinctively apply a high discount rate when calculating or thinking about the SCC, producing a negligible Pigou tax. They say: If our descendants are going to be far richer than we are if we burn cheap fossil fuels. Let’s burn them, and let our rich descendants deal with the resulting problems. However, if the West is willing to subsidize the cost of renewable energy so it is less expensive than coal, the developing world is happy to pledge at Paris minor reductions in emissions GROWTH contingent on subsidies (that will never be provided).

Republicans who believe in technological progress and future economic growth and non-affluent Americans may think like people in India: Let’s get richer and let our rich descendants deal with the environmental issues. Earlier poorer generations left environmental problems our affluent society could afford to deal with.

To some extent, the problem with calculating a SCC, a Pigou tax, or emissions reductions is that different groups perceive the world in different ways. Even in a very idealistic world, developing nations are never going to agree to preventing emissions growth at the cost of economic growth. The left, the right and the non-affluent have different expectations about economic growth. No one believes the West is going to significantly subsidize renewables in developing countries, but that is essential to meeting political goals.

• David Middleton says:

The proper discount rate is easy.

As a default position, OMB Circular A-94 states that a real discount rate of 7 percent should be used as a base-case for regulatory analysis. The 7 percent rate is an estimate of the average before-tax rate of return to private capital in the U.S. economy…

• Frank says:

David writes: “The proper discount rate is easy.”

This discount rate was arbitrarily chosen by the OMB. The Ramsey equation has been mathematically proven to provide economists with an optimum discount rate for problems such as discounting future damage from climate change. There is a Wikipedia article on this subject, but it is written for academic economists. Nordhaus has a very clear explanation in one of his early papers, but I can’t find it. The National Academy has recently written a book on recommending improvements in the process by which the Obama administration calculated the SCC. Chapter 6 (Discounting Module) of that book has a reasonably clear discussion and starts with the OMB discount rate you cite above:

Most of the discussion centers on the Ramsey equation:

r = δ +η*g

where r is the discount rate, δ is the time preference for money (how much more valuable a dollar today is than a dollar a year from now assuming no risk), g is the growth rate of the economy, and η is the elasticity of consumption change in the utility of an additional dollar of consumption as society gets richer. (Does some spending \$100,000/year get as much additional value from the last dollar he spends as someone spending \$50,000/year).

None of the liberal academics I have read seem to have the slightest idea that the citizens of India and the rest of the developing world expect their governments to attempt to emulate the Chinese and grow their economies 5-10%/year (using cheap fossil fuels, especially coal). Their expectations are not the same as those of elite Western academics who calculate the SCC.

Let’s set aside the mathematics of the Ramsey equation and reasoning more intuitively. When one is poor and expecting one’s grandchildren to become far richer than one is today, spending money today to make the lives of grandchildren or great grandchildren easier doesn’t make much sense. We didn’t expect our poorer grandparents and great-grandparents (in the Great Depression or during WWI or WWII) to properly dispose of toxic mining or chemical waste. Today, we can afford to pay to correct those mistakes. The Chinese have KNOWINGLY been permitting huge environmental problems to develop because they would rather spend money growing their economy than protecting the environment. In another couple of decades, their richer descendants will be able to afford clean up.

When you are a rich environmentalist who expects your grandchildren to be poorer because of environmental damage and non-sustainable practices, you feel a moral obligation to prevent carbon emissions from making their lives even more difficult.

The Ramsey equation for selecting an optimum discount rate contains the mathematics that bridges these different perspectives. It also tell me that the developing world is never going to accept significant limitations on the growth of their emissions until they have been rich.