Shadow Price of Carbon — Definition and GHG Accounting Context
Every project that emits carbon faces two very different carbon numbers. One is the price actually charged today — an emissions trading allowance, a carbon tax, sometimes nothing at all. The other is the price those emissions ought to carry if the decision is to line up with a climate target — a figure that rarely appears on any invoice, yet quietly decides which projects are worth building. Governments and companies need a defensible value for that second number to appraise policies and long-lived investments whose emissions stretch decades ahead.
The shadow price of carbon is that second number — the cost of a tonne of CO₂e you calculate and apply in the model, not the one you pay.
The shadow price of carbon is a notional price per tonne of CO₂e used to value emissions in appraisal — the marginal cost of abating the last tonne needed to meet a climate target. It steers decisions but is paid to no one, and is distinct from the damage-based social cost of carbon.
Definition — the Price You Calculate, Not the One You Pay
The shadow price of carbon (SPC) is a monetary value placed on one tonne of carbon dioxide equivalent (CO₂e) and applied inside appraisal, cost-benefit analysis, and optimisation models — a value that is used in the arithmetic of a decision but paid to no one. It lets an analyst weigh the emissions consequences of a choice in the same units as its financial costs and benefits, so a project’s carbon shows up in the numbers even where no real carbon price yet applies. The value is chosen to be consistent with a policy objective — usually the marginal cost of the abatement needed to meet an emissions target.
The term has a precise root in economics. A shadow price is the value of relaxing a constraint by one unit — formally, the Lagrange multiplier on that constraint in a constrained optimisation. Apply it to a carbon cap: the shadow price of carbon is the extra cost a system incurs to cut its emissions by one more tonne while still meeting the cap. At the least-cost solution that equals the marginal abatement cost of the final measure deployed to hit the target — which is why a shadow price is often read straight off a marginal abatement cost curve at the target level of reduction.
In plain terms, it is the price carbon would have to carry for a rational actor to make the choices that meet the climate goal. It is a calculated, notional price used to steer decisions — a companion to, but not the same thing as, the real carbon prices set by markets and taxes.
A shadow price of carbon is a decision value, not a payment and not an inventory figure. Applying it changes which options look best in an appraisal; it moves no cash, settles no liability, and does not alter the tonnes an organisation reports under the GHG Protocol. Its only effect on emissions is indirect — through the better decisions it drives.
Shadow Price vs Social Cost of Carbon
The single most common confusion is between the shadow price of carbon and the social cost of carbon (SCC). They answer different questions and are built from different evidence — a distinction set out in the UK’s founding guidance on the subject and still load-bearing today.
| Shadow price of carbon | Social cost of carbon | |
|---|---|---|
| Question it answers | What must a tonne cost for us to meet the target? | What damage does one extra tonne cause? |
| Basis | Marginal abatement cost — target-consistent | Marginal climate damage — impact-based |
| Where it comes from | Optimisation / MAC curve against an emissions cap | Integrated assessment models (DICE, FUND, PAGE) |
| Moves with | The stringency of the target | Damage estimates, discount rate, climate sensitivity |
| Example anchor | UK non-traded value ≈ £241/tCO₂ (2020) | US EPA 2023 estimate ≈ $190/tCO₂ (2020 $) |
In a perfect, first-best world the two would coincide — a target set exactly where marginal damage equals marginal abatement cost. In practice they diverge: the shadow price follows a politically chosen target (such as net zero), while the social cost of carbon follows the modelled damages, and the two can differ by a large multiple. The UK deliberately moved from a partly damage-based number to a purely target-consistent one — see the history below. (A dedicated social-cost-of-carbon term and a side-by-side comparison are natural next pages.)
Where the Number Comes From
Because the shadow price is the marginal abatement cost at the target, it is derived, not assumed. Rank every available abatement measure from cheapest to most expensive per tonne — the marginal abatement cost curve. Read across until cumulative abatement reaches the target. The cost of that last, marginal measure is the shadow price of carbon for that target: measures cheaper than it are already worth doing, and measures above it are not yet needed.
Two consequences follow. First, a tighter target pushes you further up the curve, so the shadow price rises — which is why appraisal values are quoted as a rising trajectory to a target year, never a single flat figure. Second, the shadow price is only as sound as the abatement data and the target behind it. Build the curve and locate the marginal cost in the Marginal Abatement Cost Calculator, with the full approach in the marginal abatement cost methodology.
Units, Basis, and How It’s Quoted
A shadow price of carbon is quoted in currency per tonne of CO₂e — £/tCO₂e, $/tCO₂e, or €/tCO₂e. The tonne is a CO₂-equivalent tonne: each greenhouse gas is first converted to CO₂e by its global warming potential, so methane counts as 29.8 and nitrous oxide as 273 tonnes of CO₂ over 100 years before any price is applied. A quoted shadow price is close to meaningless without three further pieces of context.
| Dimension | Why it matters |
|---|---|
| Currency & price year | A price is stated in real terms of a base year; a £/tCO₂e and a $/tCO₂e figure are not comparable and must not be converted with a spot FX rate as if identical. |
| Flat vs trajectory | Target-consistent prices rise over time as abatement gets harder; a single number needs its target year and growth path to mean anything. |
| Traded vs non-traded | Where a market price already exists (an ETS), appraisal may use that “traded” value; sectors outside it use a “non-traded” value derived purely from the target. |
| Central / high / low | Values are published as a sensitivity range around a central estimate, not a single point. |
A shadow price with no currency, no price year, and no trajectory is just a number. Quote all three. And never compare or convert shadow prices across currencies with a spot rate — a £250 and a $250 value express different levels of ambition, not the same one.
From the UK’s Shadow Price of Carbon to Target-Consistent Values
The phrase entered official use in the UK, and its evolution is the clearest illustration of what a shadow price of carbon is — and what it is not.
| Year | Approach | Central value | Basis |
|---|---|---|---|
| 2007 | DEFRA “Shadow Price of Carbon” | ≈ £25.50/tCO₂ (2007 prices), rising ~2%/yr | Partly damage-based, uplifted from the social cost of carbon |
| 2009 | “Carbon Valuation in UK Policy Appraisal” — replaced the SPC | Separate traded + non-traded carbon values | Target-consistent: marginal abatement cost of meeting UK targets |
| 2021 | Updated valuation of GHG emissions | Non-traded ≈ £241/tCO₂ for 2020 (2020 prices), +~223% | Single target-consistent series, aligned to net zero |
The 2007 Shadow Price of Carbon was built partly from damage estimates — closer to a social cost of carbon. In 2009 the UK replaced it with target-consistent “carbon values”, and the 2021 update raised the non-traded value sharply and tied it to the net-zero pathway. The name “shadow price of carbon” is now used generically for any such notional, target-consistent appraisal value, in the UK and well beyond it.
Worked Micro-Example
A government is appraising a sector with a legally binding emissions cap. Ranked cheapest-first, the abatement measures needed to reach the cap run out at a measure costing £250 per tonne. (Figures illustrative.)
Target: cut sector emissions to the cap.
Cheapest measures first: insulation £20/t, heat pumps £90/t, … up to the last measure needed at £250/t.
Shadow price of carbon at this target = £250/tCO₂e — the marginal cost of the final tonne required.
Every project in the appraisal is now charged £250 for each tonne it emits and credited £250 for each it avoids — no cash moves, but low-carbon options rise up the ranking.
The £250 was not chosen; it fell out of the target and the abatement costs. Raise the target and the marginal measure — and the shadow price — climb with it. To apply a shadow price like this across a real portfolio of business decisions, most organisations adopt it as an internal carbon price and size it in the Internal Carbon Price Calculator.
Shadow Prices, Internal Prices, Taxes, and the ETS
The shadow price of carbon sits at the centre of a family of carbon prices, and the differences are exactly what people get wrong:
- Internal carbon price. When a company adopts a shadow price to guide its own investment decisions, that is the shadow-price form of an internal carbon price — the same idea, applied inside one organisation rather than across an economy.
- ETS allowance price and carbon tax. An emissions trading scheme price and a carbon tax are real prices actually paid. A shadow price is notional — often set by reference to where those market prices should sit to meet the target, and used precisely where they don’t yet reach.
- Scenario carbon prices. Forward carbon-price paths such as the NGFS climate scenarios supply ready-made shadow prices for stress-testing and disclosure — including the internal-carbon-price disclosure required under CSRD / ESRS E1 (datapoint E1-8).
Common Confusions
- Confusing it with the social cost of carbon. The shadow price is abatement-cost and target-based; the SCC is damage-based. The two can differ by a large multiple.
- Treating it as a real price paid. No money changes hands; it is applied only in the model, never on an invoice.
- Thinking it lowers reported emissions. It changes decisions, not the inventory — the footprint falls later, through those decisions.
- Quoting it without basis. A shadow price needs its currency, price year, and trajectory; a bare number is not usable.
- Converting across currencies with a spot rate. A £250 and a $250 shadow price are not the same level of ambition.
- Assuming one correct value. It moves with the target and the abatement data; central / high / low ranges are the norm, not a single point.
Frequently Asked Questions
The shadow price of carbon is a notional monetary value per tonne of CO₂e used to value emissions in appraisal, cost-benefit analysis, and modelling — not a price paid to anyone. It represents the marginal cost of abating the last tonne needed to meet a climate target, which makes it target-consistent rather than damage-based. Governments use it to appraise policies and long-lived investments; companies apply it as an internal carbon price to guide capital decisions. No money changes hands, and applying it does not change reported emissions.
The shadow price of carbon is the marginal abatement cost of meeting a target — what a tonne must cost for a country or company to hit its climate goal. The social cost of carbon is the marginal damage an extra tonne causes, estimated from integrated assessment models. One is built from abatement costs and a target; the other from modelled damages, a discount rate, and climate sensitivity. In a first-best world they coincide; in practice they can differ several-fold — the UK’s target-consistent non-traded value was around £241/tCO₂ for 2020, while damage-based estimates such as the US EPA’s 2023 figure sat near $190/tCO₂.
It is derived from a marginal abatement cost curve and a target. Rank abatement measures from cheapest to most expensive per tonne, then read across until cumulative abatement meets the target; the cost of that last, marginal measure is the shadow price. Formally it is the Lagrange multiplier on the emissions constraint in a cost-minimisation — the extra cost of tightening the cap by one tonne. Because tighter targets push further up the curve, shadow prices are quoted as rising trajectories rather than flat figures.
No. A shadow price of carbon is notional — applied only inside appraisals and models. It is not an ETS allowance, a carbon tax, or an offset: no money is paid, no liability is settled, and no credit is retired. Real carbon prices are what you actually pay; the shadow price is what you calculate to make target-consistent decisions, often set by reference to those real prices. Adopting one does not change the emissions you report.
There is no single figure — it depends on the target, the currency, and the year. As anchors: the UK’s 2021 non-traded value was about £241 per tonne of CO₂ for 2020 (2020 prices), rising over time; the High-Level Commission on Carbon Prices put the Paris-consistent range at roughly $50–100 per tonne by 2030. Damage-based social-cost-of-carbon estimates, which answer a different question, range even more widely. Always quote a shadow price with its currency, price year, and whether it is flat or on a rising path.