The Shadow Price of Intelligence: Quality Degradation in LLM Inference as a Supply Chain Problem
Abstract
Large language model providers are compute constrained, and a common response to congestion is to degrade service. A degraded answer fails with some probability, and a failed answer either returns as a retry or departs as churn, destroying LTV on an unaccounted ledger. We model inference allocation as a newsvendor whose stockout cost is churned lifetime value, a geometric retry multiplier in which the recycled product is dissatisfaction, and a two-regime transient fluid queue whose arrival rate is made endogenous by retries. Statically, there is a regime in which a cheaper model saves energy per initiated task while consuming strictly more capacity per initiated task, so the discount inverts when capacity binds. Dynamically, a reactive throttle fired during a surge can cross an ignition threshold beyond which it manufactures more traffic than it sheds, and a release rule set below the degraded equilibrium converts a transient surge into a permanent degraded regime. With heterogeneous customers, throttling is a transportation problem in retry-inflated load whose optimal policy rations intelligence by critical ratio, and whose dual, the shadow price of intelligence, prices a marginal query by class and by hour. Under congestion, throttling is not a cost lever but a demand lever.
Related
- The price of a weak shadow variable: inference under nonignorable missingness as relevance vanishes
- Regarding the inference of causality in observational non-controlled studies. Comment on “Assessment of sexual function and its association with quality of life and disease severity in patients with atopic dermatitis”
- Mathematical inverse problem for the world data inference of the parton distribution functions of the proton
- Causal Inference with Generative Artificial Intelligence: Application to Texts as Treatments
- Post-Inference Model Chaining: A Problem Statement and a Model-based Bootstrap for Training End-to-End Digital Twins
BibTeX
@misc{sanabria2026shadow,
title = {{The Shadow Price of Intelligence: Quality Degradation in LLM Inference as a Supply Chain Problem}},
author = {Elioth Sanabria},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.23986},
eprint = {2608.23986},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.23986},
}
RIS
TY - UNPB
TI - The Shadow Price of Intelligence: Quality Degradation in LLM Inference as a Supply Chain Problem
AU - Elioth Sanabria
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2608.23986
UR - https://arxiv.org/abs/2608.23986
AB - Large language model providers are compute constrained, and a common response to congestion is to degrade service. A degraded answer fails with some probability, and a failed answer either returns as a retry or departs as churn, destroying LTV on an unaccounted ledger. We model inference allocation as a newsvendor whose stockout cost is churned lifetime value, a geometric retry multiplier in which the recycled product is dissatisfaction, and a two-regime transient fluid queue whose arrival rate is made endogenous by retries. Statically, there is a regime in which a cheaper model saves energy per initiated task while consuming strictly more capacity per initiated task, so the discount inverts when capacity binds. Dynamically, a reactive throttle fired during a surge can cross an ignition threshold beyond which it manufactures more traffic than it sheds, and a release rule set below the degraded equilibrium converts a transient surge into a permanent degraded regime. With heterogeneous customers, throttling is a transportation problem in retry-inflated load whose optimal policy rations intelligence by critical ratio, and whose dual, the shadow price of intelligence, prices a marginal query by class and by hour. Under congestion, throttling is not a cost lever but a demand lever.
ER -