Total Cost of Agency: Exact Attribution of Memory Injection Cost in Multi-Agent LLM Workflows

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arXiv:2609.23790v1 Announce Type: new Abstract: Every node in a multi-agent large language model (LLM) workflow retrieves context from memory and injects it into its prompt, where those injected tokens are billed as input tokens at the same per-token price as the system prompt and the user query. Production observability tools report total token cost but do not separate the tokens a node generates from the tokens it is handed, so this component of the bill is invisible to the teams paying it. We introduce the Total Cost of Agency (TCA), a decomposition of multi-agent workflow cost into base prompt, inference, memory injection, miss penalty and context-accumulation components, and an exact attribution method: a two-pass, non-billable token count that measures injected tokens directly rather than estimating them from word-count proxies. On a 200-task enterprise benchmark executed against real model APIs, memory injection accounts for 13.6 percent of the variable cost a compile-time optimizer can act on, about 12 percent of the full billed cost, and its share rises from a structural zero at workflow depth one to 27.6 percent at depth six. Injected tokens grow linearly with depth over the measured range (R^2 = 0.9974, depths two through six); a quadratic fit yields a negative leading coefficient, so the data do not exhibit convex growth at these depths. We show the component is controllable at fixed model tier: reducing the retrieval window capacity from 32 to 2 entries lowers injected tokens by 28.7 percent with an accuracy change within seed-level variation. We report in full that our graph-rewriting transforms are approximately cost-neutral in isolation, that two of the five decomposition terms are zero by construction in this harness, and that total workflow cost is dom