Applying the System Asset Pricing Model to Frontier AI: Measuring the System Welfare Cost of the Capability-Safety Gap

Frontier AI destroys 7.51 of welfare for every 1 of private payoff

The paper calibrates the System Asset Pricing Model (SAPM) to frontier AI, finding a system beta of 17.96. Each dollar of frontier-model revenue is paired with $7.51 in welfare loss.

• Private payoff Π = $30.0B/yr (frontier-model race revenue)
• System welfare cost W = $225.4B/yr (six channels)
• System-adjusted payoff Π^SA = −$195.4B/yr — industry is welfare-negative

SAPM translates CAPM from market risk to social loss

The paper builds on the familiar CAPM structure: beta measures systematic risk. In SAPM, β_W = W/Π, where W is annual welfare cost and Π is annual private payoff.

• CAPM: E[R_i] = R_f + β_i(E[R_m] − R_f)
• SAPM: β_W = W/Π, Π^SA = Π − W
• Frontier AI calibration: β_W = 17.96, 90% CI [5.5, 10.4]

Six welfare channels sum to $225.4B per year

The paper decomposes welfare cost across six empirically grounded channels, each with data sources and dollar estimates.

• Fraud and cybercrime: $24.0B/yr
• Labor displacement: $104.4B/yr
• Capability-safety gap: $29.4B/yr
• Market concentration: $39.2B/yr
• Governance failure: $16.3B/yr
• Irreversible diffusion: $12.0B/yr

100,000 draws never produce a welfare-positive median

The Monte Carlo simulation uses lognormal/normal/triangular distributions across channels. P(β_W < 1) = 0.0000%.

• Median β_W = 17.96, 90% CI [5.5, 10.4]
• Welfare multiplier κ = 7.51 (= W/Π)
• System welfare ratio S_W = 0.117 — only 11.7 cents of each dollar remains

Three axioms make voluntary governance impossible before Q2–Q3 2027

The Alignment Ceiling Theorem (Postnieks 2026a, Theorem 20) proves that under Capability Competition, Deployment Necessity, and Irreversible Diffusion, no voluntary arrangement can reduce β_W below the critical threshold before the Oversight Crossover Point.

• Capability Competition: firms cannot slow scaling without losing market share
• Deployment Necessity: revenue requires deploying models with unverifiable safety
• Irreversible Diffusion: open-weight replication within 3–8 months

Human supervision becomes structurally unreliable by mid-2027

Using METR's empirical doubling law (task-completion horizon doubles every 4–7 months) and Engels et al.'s oversight degradation function (success rate < 52% at 400 Elo gap), the crossover point is estimated at Q2–Q3 2027.

• AI reasoning complexity exceeds human real-time supervisory capacity
• After crossover, scalable oversight success rates drop below 52%
• Current trajectory: capability doubles every 4–7 months

Break-even efficiency is 0.87; observed efficiency is 0.12

The paper computes the institutional correction efficiency μ required for welfare neutrality. μ* > 0.87, but observed voluntary commitments achieve only 53% compliance and 17% model weight security compliance, yielding μ̂ ≈ 0.12.

• Required efficiency μ* = 0.867 — must close 86.7% of welfare gap
• Observed efficiency μ̂ ≈ 0.12 — sevenfold gap
• 11 of 16 White House signatories score 0% on model weight security

Voluntary commitments fail: 53% average compliance, 0% on security

The paper prices governance failure as a welfare channel: $16.3B/yr from institutional underperformance. Only 2% of AI research addresses safety; capability scaling consumes >95% of compute investment.

• White House voluntary commitments: average compliance 53%
• Model weight security compliance: 17% average, 11 of 16 at 0%
• Open-weight replication lag: ~3 months (Epoch AI 2026)

Both canonical externality frameworks break on frontier AI

Pigouvian taxation requires a stable taxable unit and observable marginal social cost — capability is multi-dimensional and doubles every 4–7 months. Coasean bargaining requires reversibility — open-weight diffusion makes capability non-recallable.

• No regulator can price harm at capability pace
• Administrative recalibration lags the technology
• 8 billion affected parties cannot bargain; information asymmetry is severe

Frontier AI ranks 19 of 61 SAPM domains, in critical-urgency tier

The paper places frontier AI in the critical-urgency tier (β_W > 5.0). Cross-domain comparability lets policymakers rank AI against other systemic risks like PFAS contamination or antimicrobial resistance.

• System beta tier: Critical (β_W > 5.0)
• Impossibility status: Active (Theorem 20 triggered)
• Temporal urgency: Crossover estimated Q2–Q3 2027

The result shifts AI governance from voluntary to regulated

The paper's impossibility theorem implies that voluntary governance cannot close the welfare gap. Mandatory pre-deployment safety evaluation (EU AI Act model), compute governance, and international coordination are required to shift the game from a voluntary race to regulated development.

• Mandatory safety evaluations (EU AI Act model)
• Compute governance: export controls + threshold reporting
• International capability race pause mechanism
• Liability framework for frontier AI harms