A carbon tax in a Hotelling model

It is rare that anyone wishes to broach this general topic, on either side of the debate.  This is from a new working paper by Geoffrey Heal and Wolfam Schlenker:

We highlight important dynamic aspects of a global carbon tax, which will reallocate consumption through time: some of the initial reduction in consumption will be offset through higher consumption later on. Only reserves with high enough extraction cost will be priced out of the market. Using data from a large proprietary database of field-level oil data, we show that carbon prices even as high as 200 dollars per ton of CO2 will only reduce cumulative emissions from oil by 4% as the supply curve is very steep for high oil prices and few reserves drop out. The supply curve flattens out for lower price, and the effect of an increased carbon tax becomes larger. For example, a carbon price of 600 dollars would reduce cumulative emissions by 60%. On the flip side, a global cap and trade system that limits global extraction by a modest amount like 4% expropriates a large fraction of scarcity rents and would imply a high permit price of $200. The tax incidence varies over time: initially, about 75% of the carbon price will be passed on to consumers, but this share declines through time and even becomes negative as oil prices will drop in future years relative to a case of no carbon tax. The net present value of producer and consumer surplus decrease by roughly equal amounts, which are almost entirely offset by increased tax revenues.

Here is an earlier MR post on the same topic, and it gives more of the theoretical intuition.


I am so glad America does not have any real problems we should be grappling with instead. Thank God we gave China all those awful CO2-producing, high-paying jobs-creating industrial plants. Now they (and the good jobs they create) are China's problem. We are so smart.

Yeah! Another Pigovian tax!

China has drastically cut air pollution in a very short time, some say by as much as 50% in some places. How did China do it? "The measures were notable for being outright bans on polluting activities, rather than incentives to clean up production, such as prices or taxes". https://www.economist.com/the-economist-explains/2018/01/25/how-china-cut-its-air-pollution

China has far outpaced the U.S. in investments in productive capital. How did China do it? The same way.

It's not a fair fight. The Trump administration's response is to demand that China adopt the U.S. system whereby markets rather than the government set policy. China's response is that it is a sovereign nation that will itself determine its internal affairs.

Reducing local air pollution and reducing global carbon emissions are two completely different problems. One key difference is that: a country can enforce an outright ban of some locally polluting activity only on its own territory (leaving the possibility of war and conquest). But a country can enforce a carbon tax on it's imports from anywhere in the world: this would just look like a tariff, calculated not on the value of the product but on the quantity of fossil carbon emitted to produce it.

Imagine if the US and UE imposed a 600$/ton carbon tax on all their import from China (as well as from each other, and on their own product, for the sake of equity). That would certainly be efficient in reducing China's emissions of carbon very quickly. More so than the presidents of the US and the EU commission declaring, "We outright ban all emission of Carbon in China, and let they remember we have bigger nuclear buttons than they do".

The response could be to ban imports from countries with a high level of carbon emissions/pollution. The effect would be immediate and would give the targeted country a great incentive to change their practices; indeed, an incentive to change their practices before a ban is imposed. I am greatly amused by the members of Trump's team who simultaneously argue that China's form of state capitalism is likely to collapse any day now and that China's version of state capitalism gives China an unfair advantage and therefore China must adopt the American version of market capitalism. Endless arguments about a carbon tax are just a way to avoid doing anything about carbon emissions/pollution; American firms shifted production to carbon and pollution emitting China for a reason, higher profits. But wouldn't the authority to impose bans on imports from polluting countries be used for political purposes? As if Trump isn't using (highly selective) tariffs for political purposes. No, I don't wish to adopt China's state capitalism, but the market capitalism I prefer may not be up to the task in these times.

Why would global carbon tax or global cap-and-trade be any more feasible than global nuclear disarmament or global oil-cartel pricing (OPEC) or global corporate taxation rates or global financial transactions taxes? There will always be defectors.

"If everyone would just [do X], then that would solve everything." But everyone will not just.

That's a good question. Global cap-and-trade seems indeed no more feasible than global nuclear disarmament. But as I said in my answer to Rayward above, a carbon tax seems more feasible even without the agreement of big carbon emitter like China.

Politically, the idea on a $600/ton carbon tax on China's import into the US would be liked be the Democrats and all who (claim to) care about carbon emissions, but it also would be loved by Trump. There could be a be-partisan agreement on this tin the US. (In the UE the idea would be even more popular, but yet more difficult to pass because UE is much less democratic than the US).

Too bad we don't do bipartisan agreements in the US anymore.

"Politically, the idea on a $600/ton carbon tax.. " is completely insane. No one that actually understands the numbers would seriously entertain such an idea.

$600 per ton = $0.30 per pound

So a rick of wood (2 tons, half carbon), which currently costs $100-200 would go to $700-800 per rick.

A kWh of natural gas contains roughly .3 pounds of Carbon. The current consumer market rate for natural gas is roughly $0.10 per kWh. This would double it to $0.20 per kWh.

A $600/ton carbon tax would send the US economy into a severe recession immediately. The results would be similar to the oil shock of the mid 1970's.

Oops, I thought they were talking about a $600 per ton Carbon tax, but if they actually mean $600 per ton of CO2, then multiply all the costs by 44/12 = 3.67.

This article does not take into account costs of renewables and carbon capture. A carbon price of 200 dollars means that renewables are much, much cheaper than oil. In fact, current solar costs imply that the equivalent energy of a barrel of oil used by a car engine can be produced through solar power to power an electric car for about 12 dollars a barrel. That means that, when electric cars are as cheap as gasoline cars, then oil's equilibrium price is 12 dollars a barrel, since a barrel of oil emits about 250 kg of Co2 then it would pay 50 dollars in taxes, which means the equilibrium price of oil is about -38 dollars. Clearly, the equilibrium level of oil production will be zero.

Let me see if I remember 5th grade arithmetic? A 42 gallon barrel of oil emits 250 kg of CO-TWO: The average barrel of domestic crude oil weighs 302.82 pounds, 7.21 lbs. * 42 gallons. And, 250 KG of CO-TWO emitted by that barrel weighs 2.24 * 250 = 560 lbs. of CO-TWO! So, 302.82 lbs. of crude oil makes 560 lbs. of CO-TWO. Unbelievable, Einstein.

Economics 101. If solar electricity generation were that much less expensive than coal, gas, oil electricity generation, why does the government need to heavily subsidize sunbeams? Because it isn't.

carbon + oxygen = carbon dioxide + water

methane combustion
ch4 + 2o2 = co2 + 2h2o

1 lb of methane (75% carbon, 25% hydrogen weight) will produce 1.5 lb or so of co2.

the carbon input to co2 output will vary with the molecule composition, but 1:1 carbon:co2 is not what you'd expect from most combustion processes

"why does the government need to heavily subsidize sunbeams? "

They used to, but at least the Federal government doesn't heavily subsidize them anymore. 2016 Federal subsidies for solar and wind were $2.8 billion for the year. The bulk of that subsidy is expiring in 2021.

Keep in mind that in 2016 the US produced about 264 billion kWh in electricity from solar and wind. That comes to about $0.01per kWh.

The cost of solar and wind has dropped dramatically in the last 10 years. Solar and wind with some kind of backup (natural gas, battery, pumped hydro, normal hydro, etc) will be the cheapest source of power going forward.


The world effectively solved the AGW carbon problem sometime in the last decade, but nobody actually pays attention to the data. Everyone is too busy pushing their agenda to realize the fight is over. Unless there's some massive disruption, fossil fuels outside of the transportation industry will be too expensive to operate on a continuous basis in 20 years.

On the scale of US power consumption, existing and likely pumped storage capacity is effectively zero.

Hydro power could be held offline to backup solar/wind, but it currently only meets about 6% of US power needs.

Battery capacity is less than pumped storage, and it is going to be a long time before capacity significant. You will note that most press releases state X MW capacity, but storage capacity is MW hours. Most of the current implementations are tiny, and quoted based on only 4 hours of power to boot.

So its natural gas. As a full system backup, that means build and maintain the plants to run the country on that windless night. Could be done technically, but you really have to include that in the cost of solar/wind.

Yes, I agree with what you wrote. However, if you just use market demand pricing it will effectively go a long way towards capacity issues. Hydro then can be released at night versus the day when the prices are higher.

Current natural gas plants can go from 24/7 mode to 2/4 hour ramp up mode. Granted, that's substantially less efficient, but an extra 2 cents per kWh would certainly make it economical.

None of this will happen overnight. But with solar and wind projects going online at the same cost as Natural Gas it's probably inevitable.


The projected LCOE for NG CC plants entering service in 2023 is $0.428 per kWh. The cost of wind and solar $0.428/$0.488.

When you factor in the risk inherent in natural gas prices, that essentially makes wind and solar the cheapest marginal supplier.

I think of wind and solar as a cheap way to avoid burning natural gas. If you had a mechanism to reduce your natural gas consumption by 30-40% and it cost about the same as producing the gas, but protected you from the volatility of fuel prices, it would be a highly valued function.

Now the one caveat, is that solar and wind are capital intensive and rely on low interest rates. If interest rates were to start climbing it would change the underlying economics.

"On the scale of US power consumption, existing and likely pumped storage capacity is effectively zero."

It's currently 2%. Not a lot, but it's actually larger than current solar power production.

The elasticity assumptions in these papers are always straight garbage

That and facts don't matter unless they advance the agenda.

"The elasticity assumptions in these papers are always straight garbage"

+1, the idea that someone could casually implement a $600/ton tax on carbon is idiotic. At the least such a move would trigger a massive recession. It would be similar to the oil shock of the 70's but on a much broader portion of energy costs.

Yes, I was going to comment that this line bothered me: "the supply curve is very steep for high oil prices".

That's believable for the short run, much less so for the long run.

If the price of oil were to rise tomorrow to $200 per barrel, the supply response in the short run would be very small.

But in the long-run (which might take only 5-10 years), not only would fracking take off again, but we'd probably see whatever the next technological step is, tertiary oil extraction techniques or whatever.

And similarly for downward supply responses if the price fell from $200 to $100. They say the response would be small; sure, in the short run. But not in the long run.

As a point of reference, 100 gallons of gasoline produces 0.98 tons of CO2 according to EPA. So a $200 per ton CO2 tax translates to a $2 per gallon gas tax. (Of course, most of your life's CO2 byproduct occurs elsewhere behind the scene.)

The UK has about $2.75/ US gallon tax on gasoline at the moment, equal to about $270/ton by my calcs. But Nordhaus estimates Social Cost of Carbon of only $35/tonne. So the UK is way ahead of what is needed, but people are still driving cars there. Which is going to infuriate the environmentalists. They don't actually want the problem solved, they want to change society to their model with the carbon tax. So the fact that a high carbon tax will cause a collapse of society is not a flaw for them, it is a desirable goal.

The CO2 tax would also apply to other sources of carbon emissions like natgas and coal, which the authors suggest would end up leaving plenty in the ground. So, although the effects on oil at "typical" tax levels might not be encouraging, the total effects overall might be. Still, good to be thinking about these dynamics.

That’s right, and this is the whole point of a carbon tax that it encourages reductions in the sectors where it is cheapest. Given that transport is only ~20% of emissions it is fine to only have 4% reduction as long as other sectors are reducing more

>It is rare that anyone wishes to broach this general topic

Well, that's because it's a deeply stupid topic.

"For example, a carbon price of 600 dollars would...."

Would be laughed at and never implemented outside of a few areas that didn't rely on much carbon to start with.

The net present value of producer and consumer surplus decrease by roughly equal amounts, which are almost entirely offset by increased tax revenues.


Sorry but the carbon taxes are used by government to buy carbon. Hence there is no gain, carbon gets taxed regardless of user.

We have probably ended up with a combination of market incentives and mandates because that's what works.

And so a more aggressive plan would be made up of more of both.

On the other side of any move made to limit carbon emissions from automobiles, how many fewer Americans will: 1) be able to maintain and operate a motor vehicle? 2) be able to afford transport by any ride-sharing enterprise?

How would carbon taxes affect the business models of 1] Uber or Lyft? 2] Amazon or FedEx? 3] commercial airlines?

When do modern fleets of wooden ships return to our planet's fouled oceans? ditto for lighter-than-air airships in our planet's compromised atmosphere?

As I read this post I kept asking myself "over what period of time?" Of course, if a global carbon tax was imposed today this would have little effect on the existing supply of carbon-based energy. This is because exploration and development costs are sunk costs. But the development of new supplies would be effected. Isn't this what we want? Isn't the whole point of the carbon tax to gradually reduce our carbon consumption? By doing so we won't strand any of our existing carbon-based assets but instead replace them as they come to the end of their economic lives. This way we would be minimizing the cost of the transition.

It is vitally important to know the time period over which we must de-carbonize the economy. Is it 50 years? Or is it 50 months? A carbon tax is well suited for the former, but probably not the latter.

Time to expand the strategic petroleum reserve?

Carbon tax? Outlaw gas pumps, and insist motor fuels be sold only in (reusable) 10 ml vials. Mandate a deposit of $1. per vial.

Might just make walking seem an attractive alternative again!

Not having access to the full paper, the abstract makes this paper appear to be written by academics who don't understand that energy of all types is fungible into all other types. With number > 200 $/ton of CO2 (not carbon), coal would be out of business and recovery of CO2 from the atmosphere would be economical, especially with sequestration that would elevate sinking landmasses like some cities. Remember 200$/ton of CO2 = $733 / ton of carbon and a ton of carbon will produce somewhere in the range of 3 Mwh of electricity or $244/MWH = 24¢/kwh just for the tax when solar contracts are in the range of 2 to 3¢/kwh and nuclear energy in the 3 to 4¢ range.

With batteries approaching the $100/kwh range it won't take a $200/ton let alone a $600/ton CO2 tax to put most hydrocarbons out of business.

Their analysis is probably assuming no competition, linear elasticities over wide ranges and lack alternatives. At these tax levels, using solar to make hydrogen from water then using the hydrogen with recovered CO2 from the atmosphere to produce jet fuel (a proven process in South Africa when we shut off their oil supply -- they just use coal to make the hydrogen instead of solar electricity) would be cheaper than paying the CO2 tax.

With a worldwide > $200/ton of CO2 carbon tax, the middle east would go bust and they would quit fighting over worthless oil and start worrying about producing enough food and producing enough water from the oceans would force them to cooperate with Israel who understands water and agriculture in the desert.

In other words, the paper is probably just science fiction written by someone who doesn't understand science and believes in magic.

Here in Australia we may be able to remove CO2 from the atmosphere and sequester it long term for as little as $50 US per tonne. This puts an upper limit on carbon prices.

LeChatelier's Principle predicts that you'll get some reduction in fossil fuel consumption, but definitely not enough to cause the cost of the tax to consumers ever to go negative.

I will mention that a carbon price is extremely effective for reducing greenhouse gas emissions from electricity generation and industry, but for vehicles regulation is likely to be the best option. Telling someone now that gasoline price will rise by a modest amount in the future due to a carbon price is not likely to have much impact on what kind of car they buy now, but fuel efficiency standards does. Fortunately, fuel efficiency standards apparently work now in the US. (Regrettably, we have none in Australia despite only producing oil equal to about 13% of our consumption.)

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