$$C_{\mathrm{LC}}(Q) = Q \cdot p_{\mathrm{in}} \cdot E$$

Equation 8 · AI Agents & Systems

The Hidden Infrastructure Bill Behind Every RAG Answer

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

where S is index size in gigabytes, r(S) is Pinecone’s documented read units per query as a function of that size, Q is monthly query volume, and $p_{\mathrm{store}}$ , $p_{\mathrm{ru}}$ , and $p_{\mathrm{rerank}}$ are the published per-unit rates given earlier. Set against it, the cost of skipping retrieval and instead inlining a fixed block of extra context on every single call is $C_{\mathrm{LC}}(Q) = Q \cdot p_{\mathrm{in}} \cdot E$. where E is the number of extra context tokens each call would need to carry in place of what retrieval would otherwise have selected, and $p_{\mathrm{in}}$ is the applicable — possibly long-context-tiered — input price.

Meanings in this article

• $Q$: monthly query volume, and $p_{\mathrm{store}}$ , $p_{\mathrm{ru}}$.
• $p_{\mathrm{in}}$: the applicable — possibly long-context-tiered — input price.
• $E$: the number of extra context tokens each call would need to carry in place of what retrieval would otherwise have selected.

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