The Shadow Price of Reasoning: Economic Perspective on Optimal Budget Allocation for LLMs

Computer Science > Artificial Intelligence [Submitted on 2 Jun 2026] The Shadow Price of Reasoning: Economic Perspective on Optimal Budget Allocation for LLMs Xu Wan, Speed Zhu, Jianwei Cai, Guang Chen, XiMing Huang, Wiggin Zhou, Mingyang Sun Inference-time scaling has emerged as a critical avenue for enhancing Large Language Models' performance, yet real-world deployment is constrained by strict computational budgets. In this work, we formulate inference budget allocation as a global constrained optimization problem governed by economic principles. By modeling per-query reasoning utility with a shifted-surge function, we derive an optimal allocation policy based on a global shadow price that equilibrates marginal utility under resource scarcity. Based on this theory, we propose Constrained Latent-utility Equilibrium Allocation for Reasoning (CLEAR). It performs rational abandonment and reallocates resources from insolvent queries to solvable queries near their emergence thresholds. Extensive experiments on several reasoning tasks with different traffic streams demonstrate that CLEAR significantly improves the Pareto frontier of total token cost versus mean accuracy. In resource-scarce regimes, CLEAR achieves up to a 3x improvement in global accuracy compared to uniform allocation. Subjects: Artificial Intelligence (cs.AI) Cite as: arXiv:2606.03092 [cs.AI]   (or arXiv:2606.03092v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2606.03092 Focus to learn more Submission history From: Xu Wan [view email] [v1] Tue, 2 Jun 2026 03:26:55 UTC (4,933 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-06 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)