Social Cost of Carbon
What is Social Cost of Carbon?
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.
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.
Social Cost of Carbon: a worked example
Take a stripped down illustration: suppose one extra ton of carbon dioxide causes a single $10 loss thirty years from now and nothing else. At a 3 percent discount rate the present value is $10 ÷ 1.03^30 = $10 ÷ 2.43, about $4.12. Raise the discount rate to 5 percent and the same damage is worth $10 ÷ 1.05^30 = $10 ÷ 4.32, about $2.31. Nothing about the physical damage changed, yet the estimate fell by nearly half, which is why arguments over the social cost of carbon are so often arguments about the discount rate.
The mistake students make with social cost of carbon
Many students read the social cost of carbon as a cost the polluting firm already pays, or as an observed market price. It is neither. It is an estimate of damage borne by other people, which is exactly why it never appears in the firm's own cost curve and why output sits above the efficient level without policy. Setting a per ton tax equal to it is what pulls that external cost into the firm's marginal cost.
Social Cost of Carbon questions
How is the social cost of carbon calculated?
It is calculated by projecting the climate effects of one extra ton of carbon dioxide, converting those effects into dollar damages with a damage function, and discounting the damages back to present value. The chain runs from emissions to concentrations to temperature to economic losses. Every step carries large uncertainty, so published estimates cover a wide range.
Why does the discount rate matter so much for the social cost of carbon?
The discount rate matters because most climate damage arrives decades or centuries after the ton is emitted, and discounting shrinks distant dollars quickly. A small change in the rate compounds over a long horizon and can move the estimate by a factor of two or more. That is why the choice of rate is treated as an ethical judgment about future generations, not just a technical input.
Is the social cost of carbon the same as a carbon tax?
No, the social cost of carbon is a damage estimate while a carbon tax is an actual policy price. The two match only if lawmakers deliberately set the tax equal to estimated marginal damage, which is the textbook prescription for a corrective tax. Real carbon taxes are usually settled by political bargaining instead.
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