Economics

Cobb-Douglas quality model and caching break-even analysis.

Q = X^α × Y^β × (b + Z)^γ

Bergemann, Bonatti, Smolin (2025) — The Economics of Large Language Models

Token Inputs

Input Tokens (X): 50K

Output Tokens (Y): 10K

Cache Tokens (Z): 5K

Parameters

α: 0.30

β: 0.35

γ: 0.20

Quality Score

10.36

Input contribution3.23

Output contribution2.24

Cache contribution1.43

Diminishing Returns

Cost by Model (50K in / 10K out)

Provider Capabilities