Does Context Length Affect Inference Cost Linearly? We Measured Why It Doesn't

Long-context pricing is billed as linear, but serving cost is not. We measured Ministral 3 14B on a DigitalOcean H200 across 2K-256K tokens: KV cache pool capacity drives a 3.84x cost-per-token rise and a 256K crossover against the $0.20/1M serverless rate.