The Shadow Price of Intelligence: Quality Degradation in LLM Inference as a Supply Chain Problem

Abstract:Large language model providers are compute constrained, and their universal response to congestion is to degrade service: route queries to smaller models, cut reasoning effort, truncate context. The industry's accounting says this saves money. We show the accounting is wrong, because it prices a query when the customer buys an answer. A degraded answer fails with some probability, and a failed answer either returns as a retry, inflating arrivals when the system is most loaded, or departs as churn, destroying lifetime value on a ledger no cost dashboard displays. We model inference allocation with three classical primitives: 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 queue whose arrival rate is made endogenous by retries. Statically, there is a nonempty, measurable regime in which a cheaper model saves energy per satisfied answer while consuming strictly more capacity per satisfied answer, so the discount inverts exactly 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, class by class, and whose dual, the shadow price of intelligence, prices a marginal query by class and by hour; closed-form trajectories make it computable in milliseconds. Stochastic analysis sharpens rather than erodes the thesis: the ignition boundary acquires a predicted width, and noise punishes the reactive policy that parks the system against it. Under congestion, throttling is not a cost lever but a demand lever.

40 pages, 12 figures. Numerical instances calibrated to public benchmark data for five LLM providers

Optimization and Control (math.OC); Artificial Intelligence (cs.AI); Performance (cs.PF)

arXiv:2608.23986 [math.OC]

(or arXiv:2608.23986v1 [math.OC] for this version)

https://doi.org/10.48550/arXiv.2608.23986 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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