Cap and Trade vs Social Cost of Carbon
Cap and Trade and Social Cost of Carbon are two Environmental Economics concepts in AP Economics that students often mix up. Cap and trade is a system that limits total pollution and lets firms buy and sell permits to emit within that cap. The social cost of carbon is an estimate of the total dollar damage caused by emitting one more ton of carbon dioxide, expressed in present value. Here is how they compare side by side.
The government sets a cap and issues tradable permits; firms that cut emissions cheaply can sell permits to those that can't. It puts a market price on pollution and achieves a target at the lowest total cost, addressing a negative externality.
Analysts build the number in steps: a climate model projects how one extra ton changes atmospheric carbon and temperature, a damage function converts those physical changes into dollar losses from things like lower crop yields, flooding and heat, and a discount rate collapses damages spread over future decades into a single present value. The result is a marginal external cost, so the textbook corrective tax on carbon is a per ton tax equal to it. Estimates vary widely, because the discount rate, the damage function and the treatment of low probability catastrophes are all contested, and a lower discount rate raises the number sharply. Do not confuse it with the price of a carbon permit, which comes from a market under a cap rather than from damage estimates.
Cap and Trade vs Social Cost of Carbon: A Market Mechanism Versus a Damage Estimate
| Cap and Trade | Social Cost of Carbon | |
|---|---|---|
| What it is | A system that creates and prices a scarce right | A number produced by a damage model |
| Where its figure comes from | Permit supply meeting firms' abatement costs | Projected future damages converted to present value |
| Which curve it belongs to | The cost of cutting emissions | The damage from emitting them |
| What moves it | A tighter cap, cheaper technology, weaker output demand | A different discount rate or damage projection |
| How it can be wrong | The cap can be set too loose or too tight | The estimate can be too high or too low |
| Efficiency test | Right when the permit price it produces equals this number | Serves as the benchmark the cap gets judged against |
| Needs the other to exist | No, caps get negotiated on political grounds too | No, the estimate stands with no policy at all |
The permit price says what cutting costs; the social cost of carbon says what emitting costs
One is an outcome of a policy design and the other is the target that design should aim at, so efficiency means making the two meet. Suppose a hypothetical economy would emit 100 tons unregulated, the cost of removing one more ton after A tons have been removed is 2A, and analysts put the social cost of carbon at 50 per ton, treating marginal damage as constant across this range. Efficiency requires the last ton avoided to cost what it saves in damage, so set 2A equal to 50 and abate 25 tons. The cap is therefore 75 tons, and the permit price it produces is exactly 50. That match is the entire test. Now suppose the cap gets negotiated at 90 tons instead. Firms abate only 10 tons and the permit price settles at 2 times 10, or 20. Every ton between the efficient 75 and the permitted 90 causes 50 of damage while costing between 20 and 50 to remove, so the avoidable harm piles up. Summed, that loss is a triangle with a base of 15 tons and a height of 30, which comes to 225. A permit price sitting below the social cost of carbon is the tell that a cap is too generous, and /glossary/marginal-social-cost is the curve it should have been checked against.
The discount rate moves the social cost of carbon further than any permit market moves the permit price
Most of the damage from a ton emitted now arrives decades later, so the estimate is dominated by the rate used to bring future harm back to the present. Take a stylized case where one extra ton causes 200 of damage 30 years out and nothing before then. Discount at 5 percent and the present value is 200 divided by 1.05 raised to the power of 30, or roughly 46. Discount at 3 percent and it is 200 divided by 1.03 to the power of 30, or roughly 82. Two percentage points nearly doubled the number without changing a single fact about the atmosphere. Feed each back into the economy above, where removing the next ton after A tons costs 2A. A social cost of 46 justifies 23 tons of abatement and a cap of 77 tons. A social cost of 82 justifies 41 tons and a cap of 59 tons. The permit market would deliver whichever price the chosen cap implies, and that is the sentence worth carrying into an exam answer: trading is a mechanism for hitting a target at least cost, and it has nothing whatsoever to say about whether the target was set correctly. The discounting step itself is drilled at /calculate/present-value.
Frequently asked questions
How should a regulator use the social cost of carbon to set a cap?
Set the cap so that the permit price it produces equals the social cost of carbon. Working backwards, find the abatement level whose marginal cost matches the damage estimate, then issue permits equal to unregulated emissions minus that abatement. In the worked case above, a damage estimate of 50 against a marginal abatement cost of 2A gives 25 tons of abatement and therefore a cap of 75 tons.
Why do social cost of carbon estimates differ so widely?
Two modeling choices drive most of the spread. The first is the discount rate, since damages arriving decades ahead shrink or swell dramatically with the rate chosen, as the comparison above shows. The second is the damage function, meaning how much harm a given amount of warming is assumed to cause. Both are assumptions rather than measurements, which is why careful analysts using the same physics can publish estimates that differ by a large multiple.
Does cap and trade guarantee the efficient level of emissions?
No, cap and trade guarantees only that whichever cap gets chosen is met at the lowest total abatement cost. Efficiency is a separate question that turns on where the cap was set. A cap loose enough to leave the permit price below marginal damage permits too much emitting, and a cap tight enough to drive the price above marginal damage forces cuts that cost more than the harm they prevent.
Live Externalities graph. Drag the curves, or open the full version.
Related comparisons
Get AP Econ exam tips in your inbox
Occasional emails with study tips, new interactive graphs, and exam-season reminders. Free, no spam.
No spam. Unsubscribe anytime. Read our privacy policy.
Keep track of what you have studied
A free EconLearn account adds progress tracking, your quiz history, and achievements. Studying here is free either way, and there is nothing to pay for as a student.
Create a free accountAlready have one? Sign in
Last updated