When Do AI Gains Become Broadly Shareable? A Policy Threshold for AI-Driven Automation

AI-driven automation generates broad-based social benefit only if technical gains become visible, durable, and publicly claimable. We develop a policy-facing stress test by extending a standard task-automation growth model with an AI capability parameter that raises productivity on automatable tasks while holding the set of tasks fixed. The exercise is intentionally limited: it is not a forecast of AI timelines or a full welfare analysis, but a way to identify which institutions determine whether AI rents can support broad transfers. Calibrated to U.S. quantities, the model shows that capability alone is not decisive. Public capture, deployment costs, automation scope, and market structure jointly determine when AI gains become shareable. The main policy lesson is that moving from low to moderate public capture (33\%) can substitute for substantial AI capability growth, while pushing capture further to full nationalization yields smaller gains, especially if deployment or safety costs are high. Competition policy also has distributional consequences: opening concentrated AI markets may improve fairness and resilience, but can reduce the rent pool unless alternative public-claim institutions are built. Cross-nationally, tax-heavy systems lower the needed AI capability threshold through stronger effective revenue collection, while Singaporean and Abu Dhabi-style public-asset models show that governments can also capture AI gains through ownership and investment returns rather than taxes alone. Our framework therefore identifies which levers governments can act on now to make future AI gains easier to measure, claim, and distribute broadly.