Why does paying more make your LLM reply faster?

Why does Claude respond faster when you pay more? And why does a longer conversation cost disproportionately more than a short one? For the longest time I simply accepted these as "it's just how it works". Like most engineers, I burn through Claude and GPT tokens all day and assumed "longer prompts cost more" was just a billing convention. As it turns out, memory is one of the factors that influence LLM pricing. Now memory in AI systems lives in a lot of places. vector stores for RAG, Redis f...