$$T_{\mathrm{turn}} = T_{\mathrm{system}} + T_{\mathrm{tools}} + \sum_{i=1}^{n} T_{\mathrm{result},i} + T_{\mathrm{exchange}}$$

Equation 1 · AI Infrastructure

The Economics, Energy, and Physical Limits of Tool Protocols and the Model Context Protocol

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

A useful way to see the shape of the tax is to write out what actually occupies a turn’s context budget: $T_{\mathrm{turn}} = T_{\mathrm{system}} + T_{\mathrm{tools}} + \sum_{i=1}^{n} T_{\mathrm{result},i} + T_{\mathrm{exchange}}$. $T_{\mathrm{system}}$ is the operator’s own instructions, $T_{\mathrm{tools}}$ is the serialised cost of every tool schema currently declared, $T_{\mathrm{exchange}}$ is the live user message and the model’s own reply, and the summation term is every prior tool result the session has decided to keep. The point of writing it this way is that $T_{\mathrm{tools}}$ is paid in full on the very first turn, before a single tool has been called and before it is known whether any tool will be needed at all. A deployment that registers thirty MCP servers, each exposing a handful of…

Meanings in this article

• $T_{\mathrm{exchange}}$: the live user message and the model’s own reply, and the summation term is every prior tool result the session has decided to keep.

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