Economics of Prompting AI

How should a principal communicate with an AI system whose internal response function is unknown? We develop a model of robust delegation in which a principal assigns tasks to a large language model (LLM) by choosing how to frame each task, focusing on the importance of the task. The AI follows a trained policy that maps the principal's framing signal to computational effort, but the principal does not know this mapping precisely. We show that the optimal framing rule is proportional: the principal should inflate importance by a constant factor relative to the task's true importance, and this inflation property is a strategic complement with AI capability. A real-world relevant experiment with GPT-4o-mini on 324 math problems confirms the model's predictions: proportional framing achieves the highest accuracy among alternative strategies tested, and the accuracy gains from importance inflation are larger for more capable models.