EconomicsCobb-Douglas quality model and caching break-even analysis.Quality ModelCaching ROIQ = Xα × Yβ × (b + Z)γBergemann, Bonatti, Smolin (2025) — The Economics of Large Language ModelsToken InputsInput Tokens (X): 50KOutput Tokens (Y): 10KCache Tokens (Z): 5KParametersα: 0.30β: 0.35γ: 0.20Quality Score10.36Input contribution3.23Output contribution2.24Cache contribution1.43Diminishing ReturnsCost by Model (50K in / 10K out)Provider Capabilities