Edge nodes are capacity-constrained by design, yet many edge workloads can trade result quality for resource efficiency at runtime. Existing edge pricing mechanisms largely treat requests as fixed-configuration submissions and rarely exploit per-request quality flexibility under overload. We present PRICE, an incentive mechanism that couples a utilization-dependent price signal to per-request quality selection. As utilization increases, rising acceptance prices make resource-intensive variants less likely to be selected, shifting accepted requests toward lighter execution and allowing the node to serve significantly more requests while operating near capacity. Evaluation on real hardware under sustained overload shows that PRICE outperforms both fixed-allocation and dynamic-pricing baselines in accepted throughput and CPU utilization. The results are robust across pricing function families, task-duration distributions, and client populations. Result-quality flexibility is a powerful but underused control dimension for overload management at the edge, and pricing is an effective mechanism to exploit it.

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