LLM推論サービスの階層型スーパー・ムーアの法則：価格変動、生産フロンティア、市場競争

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.