Who Gets the AI Dividend When Housing Supply Cannot Keep Up

Abstract

Artificial intelligence can raise productive capacity without improving the purchasing power of households that own little capital or housing. This paper develops an exchange-production model linking an AI-responsive output dividend, the income share received by renters, and housing supply. Closed-form results distinguish output growth, nominal income, housing access, and consumption-equivalent welfare. Under common Cobb-Douglas preferences, renters lose when the elasticity of their income-share decline exceeds one minus the housing expenditure share divided by one plus the housing supply elasticity. Consequently, nominal income can rise while welfare falls. An illustrative 50% output expansion raises renters’ nominal income by 4.1% but reduces their welfare by 9.6% under fixed housing supply. A dividend financed by 8.9% of net housing rents restores their initial welfare in that scenario. A constant-elasticity-of-substitution extension shows how limited consumption substitution strengthens the adverse price channel. Balanced transfers leave prices unchanged under common homothetic preferences; heterogeneous housing propensities generate partial price offsets, while recipients still benefit within the model. Analytical proofs and 7,644 deterministic parameter cases verify the results. These are conditional mechanisms and numerical illustrations, not estimates of AI’s observed effects. The contribution is a tractable welfare and compensation framework that connects technology distribution policy to housing capacity, with explicit fiscal limits and testable restrictions.