Haute Lumière
Commerce · VII.02 · MMXXVI · daylight
ASSESSMENT · Chapter VII.02 — Climate as an Economic System
Three instruments: a ten-point quiz, eight reflection questions, five essay prompts. The quiz checks comprehension rather than recall. The reflections are private and first-person. The essays are arguable from more than one side.
THE QUIZ — ten points
Four on recall.
1. Name the five modules of an integrated assessment model, in order, and say which one produces the social cost of carbon.
Socioeconomics → emissions → carbon cycle → climate → damages, followed by discounting. None of them produces the social cost of carbon on its own. It is the difference between two complete runs of the loop, one with an extra tonne emitted today. One mark for the five modules in order, one for recognising the SCC as a difference between runs rather than an output of the damage module.
2. Write the DICE-2016R damage function, give its coefficient, and state the damages it implies at 3 °C and 6 °C.
D(T) = a2 · T²witha2 = 0.236 %of global income per °C², andΩ(T) = D / (1 + D). Damages are 2.1 percent of global income at 3 °C and 8.5 percent at 6 °C. The stronger answer notes the function is a smooth quadratic and therefore contains no threshold or tipping point — not because the world has none, but because the estimates it was fitted to had none.
3. Give the EPA's 2023 social cost of CO₂ for a tonne emitted in 2020, at each of its three near-term Ramsey discount rates, with the dollar year.
$120 at 2.5 percent, $190 at 2.0 percent, $340 at 1.5 percent, in 2020 dollars. A figure quoted without its rate and dollar year scores zero: the rate is most of the range and the dollar year decides the comparison.
4. State the coverage, price and revenue of global carbon pricing as of 1 April 2025, and what the figures do not include.
80 instruments covering 28 percent of global greenhouse gas emissions — about 15 of 52 gigatonnes — raising over $100 billion in 2024, at an emissions-weighted average of $19 a tonne across covered emissions and $5 across all emissions. They exclude indirect carbon pricing — fuel excise duties above all — which in many regions is the larger signal.
Four on application.
5. A colleague says: "Nordhaus says $31 and Stern says $200, so the number is whatever you want it to be." Answer him in three sentences.
Both figures are reproducible inside Nordhaus's own model. The $31.2 baseline and the $197.4 Stern-discounting run differ by 6.33× with the same damage function and the same climate module; the difference is the discount rate, which is a choice about how to weigh future people, not a disagreement about physics. The strongest answer adds that the model's own 2.5 °C-cap row gives $184.4 — 5.91× the baseline — so the gap is also reproducible by changing the question from marginal damage to the price of a constraint, without changing any parameter at all.
6. Your firm has a 1.5 °C-aligned target and an internal carbon price of $20. Diagnose the position.
The two do not multiply out. A target is a constraint, and the relevant price for a constraint is its shadow price — in DICE roughly 5.91× the marginal-damage figure. Meanwhile $20 is 10.5 percent of the EPA's central $190, and a quarter of firms with an internal price sit below that threshold. The good answer notes the diagnosis does not require settling the damage-function argument: the inconsistency is internal to the firm's own commitments.
7. An advocate cites Sweden, Britain and the EU ETS as proof that carbon pricing solves the problem. A critic cites the same schemes as proof it does nothing. Adjudicate with numbers.
Both are quoting half the evidence. The ex-post synthesis over 80 evaluations and 21 schemes finds reductions of 5 to 21 percent, or 4 to 15 percent bias-corrected, with immediate effects in 17 of 21 schemes — so the critic is wrong that nothing happens. Applying the bias-corrected midpoint of 9.5 percent to the 15 gigatonnes covered gives 1.43 gigatonnes a year, 2.74 percent of global emissions against a 1.5 °C requirement of about 22.36 gigatonnes — so the advocate is wrong that it is sufficient. The instrument works and is too small.
8. A supplier offers to sell you forest-conservation credits at $8 a tonne to discharge your scope 1 emissions. Give your answer and your reason.
Decline for discharge; consider for funding. The Commission's CDM study found 85 percent of projects had a low likelihood of additionality and only 2 percent a high one; West and colleagues found roughly 6 percent of credits from 18 forest projects represented real reductions, meaning 13.72 million tonnes of the 14.6 million already used to offset did not occur. The policy line is one sentence: offsets may fund abatement outside your boundary; they may not discharge a tonne inside it.
Two that cannot be answered without doing the arithmetic.
9. Your board is choosing between a 2.5 percent and a 1.5 percent near-term discount rate for appraisal. (a) By what factor does the EPA's social cost of CO₂ change? (b) What is the per-half-point multiplier? (c) A project abates 40,000 tonnes a year for twenty years; how much does the shadow value of that abatement change per year between the two rates? (d) What would a 0.25-point move do, using the elasticity?
(a)
340 / 120 =2.83×. (b) The two half-point steps are190/120 =1.58× and340/190 =1.79×; their geometric mean is 1.68×. (c) At $120:40,000 × 120 = $4.80 milliona year. At $340:40,000 × 340 = $13.60 milliona year. The difference is $8.80 million a year, or $176 million over twenty years undiscounted. (d)ln(340/120) / 0.01 = 104.1per unit of rate, so 1.04 percent per basis point. Compounded over 25 basis points that is 1.30× — a 30 percent move. Full marks require the elasticity to be applied multiplicatively: read linearly it gives 1.26×, which is wrong, and wrong low.
10. A firm emits 250,000 tCO₂e in scope 1; 60 percent falls under a scheme priced at $70.4; EBITDA is $120 million. Compute (a) the cash carbon cost, (b) the cost at a $190 shadow price, (c) the unpriced exposure, (d) both as a share of EBITDA, and (e) say which number belongs in a board paper and why.
(a)
250,000 × 0.60 × 70.4 =$10.56 million. (b)250,000 × 190 =$47.50 million. (c)47.50 − 10.56 =$36.94 million a year. (d) 8.8 percent and 30.8 percent of EBITDA. (e) Both, together. The 8.8 percent is why the exposure is currently a procurement line; the 30.8 percent is why it is a board item. The strongest answer observes that the gap between the two percentages is itself the finding — it measures how much of the firm's carbon position is invisible to its own management reporting.
REFLECTION — eight questions, for one person and a pen
These are private. Nobody marks them and nobody sees them.
- What number have you been carrying for a tonne of carbon, and where did you get it? Did you ever check its discount rate, its dollar year or whether it was a tonne of carbon or a tonne of carbon dioxide?
- When you learned that most of the spread in the social cost of carbon comes from a parameter that is chosen rather than measured, what was your first reaction — relief, suspicion, or something else? What does that reaction tell you about what you wanted the number to be?
- Think of a decision you have made whose consequences fall mostly on people who are not yet in the room. What rate did you implicitly use, and would you write it down and sign it?
- Where in your own work is there a quantity that is measured in a physical unit and has no price attached? Who would have to agree for it to get one?
- You have read that a quadratic damage function contains no tipping points because the studies it was fitted to had none. Where else in your work does a model's shape rule out a behaviour you privately believe is possible?
- When you last used a conservative estimate, did you say out loud which way it was conservative? What changed for the people hearing it when you did — or would have, if you had?
- Which is harder for you to hold: that carbon pricing demonstrably reduces emissions, or that it demonstrably delivers about one part in fifteen of what is required? Sit with the one that is harder.
- If you were to adopt one price and one decision rule this quarter and nothing else, what would you choose — and what is actually stopping you from proposing it on Monday?
ESSAY PROMPTS — five
Each is arguable from more than one side. Each requires at least one source the chapter cites and at least one it does not.
1. "The social cost of carbon is a number about ethics wearing the costume of a number about science." Assess.
Use the chapter's computed sensitivities — 6.52× across 2.5 points of discount rate inside DICE, against 3× to 5× for the entire damage literature — and Chapter III.05 on which Ramsey terms are empirical. Then go outside: read Broome's Climate Matters (2012) or Parfit's Reasons and Persons (1984) on the ethics of discounting future persons, and argue whether a costume is a disguise or simply a common currency. The strongest essays will notice that "ethical" is not a synonym for "arbitrary".
2. Damage functions above 3 °C are weakly grounded. Does that argue for using a lower number, a higher number, or a different kind of number entirely?
Begin with Nordhaus's own uncertainty treatment — the coefficient's standard deviation of 0.118 against a mean of 0.236, and a Monte Carlo standard deviation of $31.5 against a mean of $31.2 — and the EPA's statement that omitted damages are implicitly valued at zero. Then bring in a source the chapter does not use: Weitzman's dismal-theorem argument (2009) or Pindyck's critique of the models as policy tools (2013). Argue for one of: a lower point estimate, a higher one, a bound, or a constraint-based price.
3. "Free allocation is not a loophole." Defend or attack, using the firm-level evidence.
Colmer and colleagues (2024) find 14 to 16 percent abatement with no output or employment effect under output-based allocation; the revenue arithmetic shows only $6.67 of the posted $19 average price is actually collected — 35.1 percent. Add a source outside the chapter on leakage or on the EU's Carbon Border Adjustment Mechanism. Is preserving the marginal signal while rebating the average cost good design or a subsidy with good manners?
4. Carbon pricing delivers about one part in 15.7 of the 2030 requirement. Is the right response a higher price, wider coverage, or a different instrument?
Work all three arithmetically before arguing: what price, what coverage, or what non-price instrument would close the 1.43 against 22.36 gigatonne gap? Use the World Bank's coverage data and at least one source on standards, mandates or public investment that the chapter does not cite. Note that the honest answer may be "none of the three alone".
5. "An offset that is not additional is an emission with a receipt." Does that sentence rule out crediting entirely, or only its use for discharge?
Use the CDM study's 85 percent / 2 percent split and West and colleagues' 6 percent. Then find a source the chapter does not cite on Article 6 of the Paris Agreement, on corresponding adjustments, or on the newer integrity initiatives, and argue whether the failure is in the concept of additionality or in its verification. A strong essay will say what evidence would change its mind.