How much do AI agents cost to run, and how do I keep the bill under control?

Token prices for equivalent quality fall roughly 10x a year, yet agent bills keep rising because agents burn 50 to 500 times the tokens of a chat: every step re-sends the whole history. A simple task can cost a fraction of a cent while a long agent session runs several dollars. The levers that matter: prompt caching (up to 90% off repeated context), routing easy steps to cheap models, trimming history, and measuring cost per completed task rather than per token.