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<p>This paper applies the n-dimensional unit ball recurrence <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\( {\text{V}}_{{\text{n}}} = (2{\uppi }/{\text{n}}) \cdot {\text{V}}_{{{\text{n}}^{{ - 2}} }} \)</EquationSource> </InlineEquation> to hotel revenue management, demonstrating that the seventh revenue dimension first destroys feasible optimization volume (threshold n = 2π ≈ 6.28). The “revenue ball” is the hotel’s feasible strategy space; distributing 12 monthly multipliers 2π/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%.</p>

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

  • 期刊论文

  • 发表日期：

    2026年8月4日

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  • Xuan Tran,
  • Rachel Austin,
  • Kendall Morman

摘要

This paper applies the n-dimensional unit ball recurrence \( {\text{V}}_{{\text{n}}} = (2{\uppi }/{\text{n}}) \cdot {\text{V}}_{{{\text{n}}^{{ - 2}} }} \) to hotel revenue management, demonstrating that the seventh revenue dimension first destroys feasible optimization volume (threshold n = 2π ≈ 6.28). The “revenue ball” is the hotel’s feasible strategy space; distributing 12 monthly multipliers 2π/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%.