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The geometry of demand collapse: n-ball volume, dimensional recurrence, and the Slutsky decomposition of hotel revenue metrics
Journal article   Peer reviewed

The geometry of demand collapse: n-ball volume, dimensional recurrence, and the Slutsky decomposition of hotel revenue metrics

Xuan Tran, Rachel Austin and Kendall Morman
Journal of revenue and pricing management, Vol.25, pp.463-477
10/2026
DOI: https://doi.org/10.1057/s41272-026-00618-0
Web of Science ID: WOS:001839560400001

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Abstract

n-Ball volume Slutsky decomposition Hotel revenue management ADR RevPAR occupancy Curse of dimensionality High-dimensional optimization Spiky spheres Total Revenue Management Business, Management and Commerce Hotel or Restaurant Management
This paper applies the n-dimensional unit ball recurrence to hotel revenue management, demonstrating that the seventh revenue dimension first destroys feasible optimization volume (threshold n = 2 pi approximate to 6.28). The "revenue ball" is the hotel's feasible strategy space; distributing 12 monthly multipliers 2 pi/k across the calendar year predicts United States average daily rate (ADR), occupancy rate, and revenue per available room (RevPAR) within 2-3% of STR/CoStar data (2023-2025). Three geometric consequences are derived and confirmed: ADR bimodality, OCC shell concentration near 50%, and RevPAR distance collapse producing the 2025 budget miss of 11.9-13.2%.

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