Why are cached input tokens cheaper with AI services?

When you see AI model pricing pages, you usually see things broken down like this: ModelContext LengthMax CoT TokensMax Output TokensInput Price (Cache Hit)Input Price (Cache Miss)Output Pricedeepseek-chat64K-8K$0.07 / 1M tokens$0.27 / 1M tokens$1.10 / 1M tokensdeepseek-reasoner64K32K8K$0.