I propose a theory for the simultaneous rise in wages and complexity observed in industries such as finance, pharmaceuticals, or law. I study a moral hazard problem where a principal delegates a complex task to boundedly rational agents of varying skill - some experts, others novices. While higher complexity increases agents' cognitive costs, it also leads to higher agency rents, as principals must compensate them for their effort. This incentivizes agents to push for the highest complexity they can manage within their cognitive constraints. Because of heterogeneous cognitive constraints, aggregate equilibrium complexity can be moderated. However, as the share of experts in the economy rises, aggregate equilibrium complexity goes well beyond the preferred level of the principals, with low net returns and high agency rents. I develop a novel measure of occupation and industry complexity using NLP and ML to bring the model to the data. US evidence between 2002 and 2022 at the occupation and industry levels supports the model's implications.