SinoXivThe Geometry of Demand Collapse: N-Ball Volume, the Recurrence Vₙ = (2π/n)·Vₙ₋₂, and the Slutsky Decomposition of Hotel Revenue Metrics
Abstract
This paper applies the n-dimensional unit ball recurrence Vₙ = (2π/n)·Vₙ₋₂ to hotel revenue management, demonstrating that the seventh revenue dimension first destroys feasible optimization volume (threshold n = 2π ≈ 6.28). We introduce the “revenue ball” as the hotel’s feasible strategy space and embed the Hicksian–Marshallian Slutsky decomposition within it: the substitution effect represents surface motion at constant RevPAR; the income effect measures radial expansion. Distributing the 12 monthly multipliers 2π/k across the calendar year predicts US ADR, occupancy, and RevPAR within 2–3% of STR/CoStar data (2023–2025), explaining observed ADR bimodality, occupancy shell concentration, and RevPAR forecasting collapse. JEL Classification: D11, D21, L83, C61, C65
Keywords
Citation Information
@article{xuantran2026,
title={The Geometry of Demand Collapse: N-Ball Volume, the Recurrence Vₙ = (2π/n)·Vₙ₋₂, and the Slutsky Decomposition of Hotel Revenue Metrics},
author={Xuan Tran and Rachel Austin and Kendall Morman},
journal={Journal of Revenue and Pricing Management},
year={2026},
doi={https://doi.org/10.21203/rs.3.rs-9349641/v1}
}
