Compute cost in automated essay scoring (AES) is usually treated as a technical efficiency issue rather than a measurement design concern. Yet deployment decisions require more than reporting latency, model size, or inference expense. In high-stakes settings, total burden includes validation, monitoring, adjudication, compliance, and governance; in instructional settings, pricing, licensing, and integration may dominate cost. This paper reframes AES as a cost-constrained measurement system and introduces the Cost-Aware Measurement Design (CAMD) Framework, a four-layer structure consisting of metering, allocation, unit economics, and decision, for translating computational and workflow resource records into decision-relevant cost constructs. Direct cost is specified as monetary outlay plus attributable labor and time, and two criteria, design attribution and auditability, determine what the cost boundary excludes. Burdens that satisfy neither criterion, such as institutional capability and governance posture, are represented as constraints on which designs are admissible rather than priced. The paper defines cost per defensible score (CPDS) and argues that AES systems should be compared by quality-cost sufficiency: minimizing cost among defensible scoring designs that satisfy measurement requirements. Scoring volume conditions all four layers, so cost per defensible score is treated as a function of scale rather than as a single transferable number. CAMD provides a portable basis for representing, comparing, and evaluating cost across AES studies and deployment contexts.

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