Coal Combustion: A System Asset Pricing Model

Each dollar of coal revenue destroys $6.95 in system welfare

Coal combustion imposes 6.9 trillion in annual welfare costs while generating 990 billion in excess private revenue, yielding a system beta of 8.64. No voluntary market mechanism can reduce this ratio below 3.0.

• β_W = 8.64: welfare cost per dollar of excess revenue
• ΠSA = −$6,085B/yr: net contribution to human welfare is deeply negative
• Carbon Intensity Floor Theorem: β_W ≥ 3.0 under current institutions

Standard metrics miss coal's full welfare cost

Climate scientists, epidemiologists, and energy economists each measure one channel in isolation. No single discipline assembles the six channels into a compound welfare-cost ratio.

• Climate damages: 2.85T/yr from 15 Gt CO₂ at 190/tonne SCC
• Air pollution mortality: 3.76T/yr from 1 million deaths at 3.76M VSL
• Governance failure: $117B/yr from regulatory capture and liability externalization

Air pollution mortality dominates at 55% of total welfare cost

Channel 2 alone accounts for $3.76 trillion annually. Climate damages add 42%. The remaining four channels—methane, extraction harms, mercury, and governance failure—contribute 3% combined.

• Channel 1 (climate): β_W = 2.88, weight 0.42
• Channel 2 (mortality): β_W = 3.80, weight 0.55
• Channel 6 (governance): β_W = 0.12, weight 0.02

β_W exceeds 3.0 under every plausible parameterization

A 100,000-draw Monte Carlo simulation integrating all six channels with lognormal distributions and ρ=0.3 correlation yields a 90% confidence interval of [5.7, 8.5].

• Median β_W = 8.64 from stored replication artifact
• Even halving SCC and zeroing governance channel leaves β_W > 5
• Reproducible via Python pipeline: github.com/epostnieks/sapm-mc-coal

C + O₂ → CO₂ creates a hard welfare-cost floor

The stoichiometric oxidation of carbon releases 3.67 kg CO₂ per kg carbon burned. This mass-balance constraint cannot be eliminated by cleaner combustion or efficiency gains, setting a minimum externality per unit of energy.

• No other major fuel has a comparable carbon-to-energy ratio
• Floor breaks the smooth marginal abatement cost assumption
• Only cement (CaCO₃ calcination) shares this chemistry-constrained impossibility

Regulatory capture locks in the welfare destruction

Documented coal-sector political influence—ACCCE's 126.4M in 'clean coal' advertising, Peabody's bankruptcy-mediated liability externalization (2.4B in self-bonded reclamation), and Indian Railways cross-subsidy—amplifies the chemistry floor.

• Governance channel adds 0.12 to headline β_W
• EU ETS windfall profits of €5B demonstrate capture of pricing mechanisms
• Senator Manchin's $492K/yr from Enersystems shows institutional capture

Carbon Intensity Floor Theorem: β_W ≥ 3.0 under voluntary mechanisms

When combustion chemistry, regulatory capture, and welfare-independence of bilateral transactions hold simultaneously, no voluntary market mechanism can reduce β_W below 3.0. The calibrated current-institution β_W is 8.64.

• Tier 1 deductive proof: falsifiable by violating an axiom
• Falsification: demonstrate a jurisdiction where voluntary mechanisms alone reduced β_W below 1.0
• Tenth impossibility/intractability result in the SAPM program

UK Carbon Price Floor proves sovereign rule change works

The UK Carbon Price Floor eliminated coal from the British grid within a decade by setting a carbon price above £18/tCO₂. This required sovereign intervention—mandatory plant retirement and carbon pricing at the social cost of carbon—not voluntary pledges.

• Carbon prices above £18/tCO₂ drove coal phase-out
• Sovereign intervention breached the chemistry floor
• Contrast with Indonesia's Cirebon-1 cancellation: transition rhetoric vs. financial reality

Coal phase-out requires sovereign rule change, not market incentives

The Carbon Intensity Floor Theorem implies that voluntary pledges (PPCA, JETP) and carbon markets (EU ETS) cannot reduce β_W below 3.0. Only mandatory plant retirement, carbon pricing at SCC ($190/tonne), and prohibition of new mine development can breach the floor.

• Break-even institutional efficiency μ* = 0.144: need to recapture 14.4 cents per dollar of externality
• Current recapture through carbon pricing achieves only 3–5 cents
• Highest-return intervention: fuel-switching mandate + carbon price > $190/tonne

Coal ranks among the highest welfare destruction in SAPM domains

With β_W = 8.64, coal sits between monoculture agriculture (8.6) and tobacco (6.5) on the welfare-destruction axis. Only PFAS (35.2) and cement (chemistry-constrained) are worse.

• Bitcoin: β_W = 5.0; AMR: 2.1; nuclear power: 0.7
• Common metric lets regulators compare resource allocation across domains
• Coal is classified as a 'Carbon Intensity Hollow Win'—private gains, systemic losses

Coal combustion is a compound system failure requiring sovereign action

The paper's integrated measurement, chemistry-floor identification, governance-channel quantification, and cross-domain positioning lead to one verdict: coal phase-out demands sovereign rule change, not voluntary pledges or market incentives.

• β_W = 8.64: highest absolute welfare destruction of any calibrated SAPM domain
• ΠSA = −$6,085B/yr: net contribution to human welfare is negative under every defensible parameterization
• Policy portfolio: mandatory retirement, carbon pricing at SCC, no new mines