Tiered Super-Moore's Law: Price Evolution, Production Frontiers, and Market Competition in Large Language Model Inference Services

This paper provides the first systematic economic analysis of token pricing in the large language model (LLM) inference market. Assembling a novel dataset integrating OpenRouter API data (318 models), Epoch AI records (3,237 models), and 62 cross-validated milestone observations spanning 2020-2026, we document an approximately 600-fold decline in token prices and propose the "Tiered Super-Moore" hypothesis. Economy-tier models exhibit a price half-life of 1.10 years and mid-tier models 1.55 years -- both significantly faster than Moore's Law's two-year benchmark -- while flagship models display near-zero exponential fit (R^2 = 0.031) due to a reasoning premium averaging 31.5 times non-reasoning prices. A Chow structural break test identifies May 2024 as the critical market inflection point (F = 5.74, p = 0.005), marking a transition from technology-driven to competition-driven price acceleration. Cost decomposition reveals that total factor productivity residuals account for approximately 103.7% of cost reduction, with GPU hardware contributing only -0.9%, confirming that software and architectural innovation -- not hardware advances -- drive the decline. Data Envelopment Analysis shows a Malmquist Productivity Index peaking at 4.11 during 2024Q1-Q4, with technological frontier shift (TC = 4.13) as the dominant driver. Training cost-inference pricing elasticity is 0.432, and the 63-fold training cost gap between U.S. and Chinese firms is statistically attributable to architectural innovation ($/FLOP difference insignificant, p = 0.228) rather than factor price differentials. Market concentration declined sharply, with HHI falling from 4,558 to 2,086 over three years. These findings establish token economics as a distinct subfield of digital goods pricing and carry implications for competition policy, AI accessibility, and international technology governance.